The Great Myths of Rheology Part II: Transient and Steady State

1 The Great Myths of Rheology: Part II Transient and Steady State Melt Deformation: the question of Melt Entanglement Stability by Jean-Pierre Ibar IPREM-Laboratoire de Physique et Chimie des Polymeres Universite de Pau et Pays de l’Adour, Pau. France INTRODUCTION. Transient and Steady State Behavior. The deformation of polymers melts has received considerable attention ever since macromolecules were identified by Staudinger [1] as being responsible for their behavior. The field of physics that concerns the deformation of liquids under stress is called rheology, and, in part I of this series [2], we presented the continuing challenges facing the rheology of polymers due to the complexity of the interaction between the macromolecules. One of the most difficult problems to solve is to predict the deformation of the melt during its “transient” conditions, i.e. before it reaches its steady state deformation. Most of our present understanding concerns the steady state when properties, such as viscosity or modulus, no longer depend on time and remain invariant. Understandably, transient states and steady states both result from the deformation of the macromolecules and to their interactions, but is it the same mechanism involved in both? Analytical solutions have been sought to express the fact that steady states derive from the transient states, at long time. In essence, when all transient relaxation has taken place, then the steady state solution is apparent and can be analytically described. Early models to qualitatively represent transient and steady state behavior were given by the Voigt or 2 Maxwell models [3], often sophistically combined to be more realistic [4], and consist of deformed sets of springs and dashpots put in parallel or in series, or a combination of the two. More recent non-linear models are described in textbooks; in particular, Table 4.4.2 of Macosko’s book [5] compares the successes and shortcomings of popular constitutive equations that describe transient and steady state flow behavior. The author concludes “No single nonlinear constitutive equation is best for all purposes, and thus one’s choice of an appropriate constitutive equation must be guided by the problem at hand, the accuracy by which one wishes to solve the problem, and the effort one is willing to expend to solve it”. For an intuitive, first approach to the problem solution, a simple Maxwell element remains an excellent tool: for instance, in the case of a step strain experiment, the sudden deformation results in the “instantaneous” deformation of the spring, without any motion of the dashpot, so a stress is created, which is proportional to the strain, followed by a slow release of the stress in the spring as the dashpot expands at a rate that produces strain. When the dashpot has released, by its motion, all the strain that was initially produced by the deformation of the spring, the stress has relaxed to zero. The differential equation of motion of a Maxwell’s element is straightforward and provides the solution for the time dependence of the stress, and of the individual strains in the spring and dashpot that add up to the imposed strain. In a step strain experiment, the strain rate is very high at start up, then is zero. The transient state is simply the description of the time dependence of the relaxation process, and the steady state value is zero. For polymers, the behavior is more complex than that described by mechanical equivalents, such as dashpots and springs; nevertheless, it is assumed that, as the melt is deformed “instantaneously”, its modulus is raised to that of the glassy state and relaxes through the various regions representing the transition region, the rubber elastic plateau region and the 3 terminal region. This relaxation takes place very fast above the glass transition temperature since the macromolecules, or parts of them, can rearrange their position at rates between 1 sec at Tg to 10 -5 sec 100 degrees above Tg, this time being dependent on molecular weight and temperature. Many of the sophisticated mathematical models of non-linear viscoelasticity described in Mascosko’s textbook [ 5] are modifications of the differential equation of the Maxwell type, to account for a different stress tensor build up and/or a modified stress tensor relaxation rate. However, the physics behind the mathematics of the modifications, in terms of macromolecular deformation, becomes far less intuitive, and non-conclusive. Step Strain Experiment in the non-linear region. Figure 1 gives an example of step strain response for a PC melt sheared 55 oC above its Tg (137 oC) at a strain of 30%. The molecular characteristics of this PC were already described in Part I [2], the PC being labeled as Grade 1. The instrument to perform such a “stress relaxation” experiment was a classical equipment of rheology, a Rheometrics RDA-700 in this instance, utilizing a parallel plate geometry with a 2mm thick sample, 2.5 cm in diameter. 4 Fig. 1a Fig. 1b Fig. 1c Fig. 1d Fig. 1 Stress relaxation ( G(t) vs time ) at constant temperature (T=192 oC) and constant strain % (Figs. 1a, 1b, 1c: 30%, Fig. 1d: 10%) for PC-1. 5 Fig. 1a shows the strain plotted against time at start up. The step strain is not instantaneous, as one might have imagined, there is even a small overshoot followed by an even smaller undershoot, but the strain stabilizes to the commanded strain, 30%, in less than 0.66 sec. The strain rate, derivative of the strain, reaches a maximum (Figure not shown) of 4.55 sec-1 at time 30.22 ms, i.e. for a strain of 8.83%. The corresponding torque response is shown in Fig. 1b, which indicates that the stress build-up did not go as far as reaching the glassy region, far from it. The Torque reaches its maximum at time 62.5 ms, and the stress at the maximum corresponds to a modulus equal to only ~4% of GoN, the plateau modulus for PC (1.5 MPa at 150 oC [6]). Most of the relaxation of the Torque takes place in the transient region and is very fast at this temperature of 192 oC. More than 95% of the build up Torque (at the maximum) has relaxed when the strain has stabilized to 30%, and only 5% is left to relax. Fig. 1c is a plot of G(t, 30%) vs Time, including the transient portion at the beginning (the insert graph zooms in on that zone). The shear modulus reaches an apparent steady value of 162 dyn/cm2 (16.2 Pa) which is stable for at least the 60 seconds of total recording. The relaxation at constant strain can best be fitted with two relaxation times, one 0.38 sec, the other 1.4 sec. (Note, in passing, that the apparent “plateau” observed for the modulus is also visible at other lower temperatures, at other strains (see next paragraph), but ceases to exist at temperatures above T= 200 oC.). In summary, at this low temperature, the transient relaxation is phased-in with the relaxation of the stress: it follows the establishment of the commanded strain, and the value of the relaxation time is in line with what is calculated from dynamic viscosity measurements. Fig. 1d shows G(t, 10%) for the same PC, at the same temperature, just a different step strain value. The transient characteristics are different: the maximum strain rate is 1.31 sec-1, it 6 occurs at 37.2 ms, when the strain is 3.16%; the Torque reaches its maximum at 74.45 ms, the Torque max is 1/3 of that obtained for 30% strain. The apparent steady shear modulus is also different: 503 dyn/cm2 (50.3 Pa), more than 3 times greater than that at 30%. The relaxation times in the constant strain region are 0.38 sec (same value as for 30%) and 1.28 sec. This example illustrates the kind of questions addressed in this paper: can different transient relaxation history induce different steady state values? Are strain and strain rate playing a similar or separate role in setting up transient mechanisms prior to the steady state melt? For instance, shear rate is known to shear-thin viscosity; comparing modulus under increasing strain is also known to reduce its value, not just in the example given in Figs 1c and d, but in general. The modulus in the non-linear visco-elastic region., G(t, g), can be separated [Ref. 5, p. 160 ] into a time dependent term (given by linear viscoelasticity) and a strain dependent term, defining the damping function, h(g) . In other words, shear strain also “shear-thins” the melt; the phenomenon is called “strain softening. Can we combine the shear-thinning effect of strain rate and strain softening in the non-linear regime to boost shear-thinning? This concept is at the origin of a treatment process of polymer melts described later in this introduction, but first let us study the effect of strain rate in high strain rate conditions. Step Strain Rate Experiments under non-linear conditions. In the more complex case of a constant strain rate imposed, for instance in a pure rotational viscometry experiment with the system being instantaneously deformed from a zero rate to a constant strain rate, the transient behavior corresponds to the build up of the stress at initiation followed by the time it takes for the stress to relax to a constant value, which, when divided by the strain rate, becomes the steady state viscosity. Figure 2 gives an example of a step strain-rate experiment for a metallocene LLDPE melt (the Mw characteristics of which are 7 given later), submitted to a viscosity measurement in a parallel plate viscometer at T= 190 oC with strain rate= 1 sec-1. Figure 2a displays viscosity vs time, and Fig. 2b displays normal force vs time, the normal force being measured perpendicular to the direction of the flow by a sensitive probe positioned on the melt. Fig. 2a Fig. 2b Fig. 2 8 Pure Viscometry test at constant strain rate 1 sec-1 for LLDPE at T=190oC. Fig. 2a: Viscosity vs time; Fig 2b: Normal Force vs time. One sees, in the case of polyethylene in Fig. 2, that it takes a considerable length of time for the viscosity to reach a steady state value, if it ever does, (since its magnitude appears to be very low, almost 0, at this temperature), and one might wonder if this time is accounted for by the traditional explanation of relaxation times provided by classical rheology, in particular by the value of its terminal time, to, calculated from the steady state viscosity at that temperature, or from the cross-over of G’ and G” (to = 1/wx). What could explain a transient time of over 30 minutes for a polyolefin without long branches? The cross-over frequency is 87 rad/s at that temperature (see later), which is 255 o above the Tg of PE, 153 oC above the melting temperature (37 oC) for this metallocene copolymer. There is no doubt that the melt should behave like a typical amorphous melt, subjected to the laws of rheology. M/Me is between 200 and 300 for this polymer (the uncertainty is due to the poor determination of Me , the molecular weight between entanglements for PE, and the fact that it is a copolymer), so the entanglement density is fairly high. Nevertheless, the transient relaxation time (~600 sec) seems to be 43,500 times bigger than the terminal time (0.0115 sec), determined from the cross-over in the steady state regime. Since processing times in extrusion and injection molding machines and the like are of the order of seconds, perhaps a couple of hundreds of seconds in extrusion, it appears that the high viscosity encountered in processing plastic melts is due to transient flow. Needless to say, a great practical advantage would result if one could understand the transient regime and reduce it to non-existent, for instance by decreasing its 9 relaxation time significantly; in the example of Fig. 2 say from 600 sec to 5 sec or so. According to S.Q. Wang [7] who has recently carefully analyzed, with the special technique of particle velocity tracking (PVT), the behavior of melts during and after transients: “an effective particle tracking velocimetric (PTV) method was developed to allow determination of the velocity profile across the gap in various shear apparatuses including cone-plate and linear sliding-plate set-ups for startup shear, large amplitude oscillatory shear (LAOS) and step strain experiments. Our PTV observations show an initial linear velocity variation across the gap and a nonlinear velocity profile beyond the stress overshoot [Phys. Rev. Lett. 2006,96,016001], growth of shear banding in LAOS [Phys. Rev. Lett. 2006, 97, 196001] and elastic breakup of several entangled solutions after step strain [Phys. Rev. Lett. 2006, 97, 187801]. These results present great challenges to both the prevailing theoretical description of entangled polymer flow that is based on tube models and the conventional rheometric protocols used to experimentally determine constitutive flow behavior.” Wang asserts that the inhomogeneous deformation is caused by “catastrophic disentanglement” occurring in the bulk of the polymer melt, not just at the surface. Wang [7-10] shows that the stress overshoot, widely observed in startup shear, has been wrongly explained by the accepted reptation models [8], since it assumes that the melt remains homogeneous across the stress maximum, a situation that his PTV measurements revealed to be false. A critical strain rate and strain are proposed by Wang [8-10] for the onset of the velocity profile breakup. The critical strain rate is the inverse of the “Rouse time” that Wang determines from the terminal time (obtained at the cross-over of G’ and G”) and (Me/M): tR = to (Me/M). In addition, strain must be equal to at least 5/4 to trigger macroscopic motions across the gap leading to inhomogeneous flow. For the polymer conditions of Fig. 2, the critical rate equals either 17,400 sec-1 or 26,100 sec-1, depending on the value chosen for Me (700 or 1000 for PE). In any case, the chosen strain rate of 1 sec-1 in Fig. 2 is much inferior to this critical value, so we do not expect inhomogeneous flow in our experiment. The reason why both viscosity and 10 normal force appear to relax to zero (viscosity is 378 Pa-s in Fig.2a after 1800 sec, but still decreasing) must be explained by a different mechanism. As time increases, the rheometer continuously rotates the melt, and strain increases. It takes 125 sec to reach 125 % strain, another critical level that Wang claims corresponds to disentanglement in the melt [7-10], but the strain rate is far too low to meet both disentanglement criteria of Wang. The curves of Figs 2a and b can be fitted with two exponential terms, with the same relaxation times of 55 sec and 591 sec for both curves (assuming a steady state value of zero when the fit is done). The fast relaxation process (the 55 sec one) might be associated with the relaxation of the elastic energy pumped into the cohesive network of bonds by the initiation of the step strain rate jump, the second term (the 591 sec one) might be considered as a steady state of the first term that has become unstable and decays exponentially, perhaps as related to the kinetics of disentanglement. If it is the case, in particular if Me has increased due to disentanglement, the melt at the end of the 1800 sec must have rheological characteristics very different from the initial melt, before the transient relaxation took place. Hence a frequency sweep of the unsheeare melt and of the “sheared melt” should display large differences in G’ (w) and G” (w) and in the value of the terminal time. We will study such results in this paper. Strain Induced Transients under Oscillatory Shear. Figures 3a and b concern a PS melt studied with a dynamic rheometer (AR 2000, TA Instruments) in the time-sweep mode. The temperature is 165 oC (65 o above the Tg of PS), the frequency is 20 Hz (125 rad/s), and the strain % varies from 5% to 23%, the strain being increased at the end of a time-sweep step to take the next successive value indicated in Fig. 3a. Fig. 3b provides the variation of G’ and G” for the last step, corresponding to 23% of strain. It is apparent in Fig. 3a that a time dependent (transient) behavior is triggered by the increase of 11 strain during time-sweep. For 5% and 10% strain, the viscosity is constant, but starting at 15.2% in Fig. 3a, viscosity starts to decay. The magnitude of the effect increases with strain, its kinetics does too. What transient relaxation does this time dependence of G’ and G” describe? Could it be caused by “edge melt fracture”[60,61]? This question is discussed in a section below. Could it be related to the same disentanglement process, described for LLDPE in Fig. 2, triggered by a combination of strain rate and strain as suggested by Wang? The value of wx at T=165 oC for this PS melt is 0.1 rad/s, Mw/Me = 19, so the Wang’s critical strain rate would be 1.9 sec-1 at this temperature. In a dynamic (sinusoidal strain) experiment, the maximum strain rate depends on both frequency and strain, it is equal to gw, where g is the strain, here 0.152 at the onset of viscosity transient behavior :(20 Hz * 6.28*0.152)= 19 sec-1. This value is 10 times greater than the Wang’s strain rate criteria. In Fig. 3, however, the strain is not 100%, but only 23% at maximum. This misses the strain criteria by Wang to produce inhomogeneous flow [7-10]. This paper addresses the following questions: is the transient decay observed in Figs. 3a and 3 of the same origin as what is observed in Fig. 2? Does it converge to a steady state? Is this steady state stable, and can it be destabilized trough a disentanglement process? Do we need different criteria to explain the transient states obtained in pure dynamic mode and in pure rotation mode? 12 Fig. 3a Fig. 3b Fig. 3 Time sweeps for PS-2 at 20 Hz T=165 oC. Fig 3a: effect of strain% on the dynamic Viscosity vs time; Fig. 3b: G' & G" vs time for 23% strain. Combining Rotation and Oscillation Shear Modes. The work of Osaki et al. The combination of pure shear and dynamic shear in a rheometer, to determine how the superposed constant strain rate affects the value of G’(w) and G”(w), is not new and has been well described in the work of Osaki et al. for PS/toluene concentrated solutions of different molecular weights to cover different regions of the relaxation spectrum [11]. These concentrated solutions behave like entangled melts that can be studied at or near room temperature. The authors use a Couette configuration with the outer cylinder submitted to independently-controlled superposed rotation and oscillation. The inner cylinder is concentrically suspended in the outer cylinder by a wire of known torsional stiffness. The gap 13 is constant and equal to 1mm. The oscillation is performed at small amplitude to remain in the linear range and avoid disrupting the melt. Osaki’s use of the oscillation is to reveal the state of the melt (via G’(w) and G”(w), converted into a spectrum of relaxation times) when it is deformed under constant strain rate steady state conditions . This objective is different from the use of oscillation to induce transient effects by strain increase (Fig. 3), and from the combination of rotation and oscillation in the non-linear range, as described in the next section, to produce non-linear transients susceptible to altering the entanglement network. Osaki et al’s objective was to prove that “the non-Newtonian effect in the steady shear viscosity may be explained as a result of a decrease in degree of entanglement with increasing rate of shear… Measurements of the complex modulus provide important information on the nature of segmental coupling”. In other words, these authors suggest that shear-thinning is due to disentanglement. Figure 4 is taken from Osaki’s paper [11], providing the G’ and G” for a PS solution at 15% concentration of PS in toluene at 30 oC. 14 Fig. 4 (from Osaki et al [11] The Mv of the PS in the concentrated solution is 2.51 106, and, at this concentration, Mc is 3 105, according to Osaki, so (M/Mc) is 8.33 , which corresponds to M/Me ~ 17. The superimposed strain rate varies from 0 (purely dynamic frequency sweep) to 5.13 sec-1. Fig. 4 demonstrates clearly the net reduction of G’(w) and G”(w) with the value of the superposed constant strain rate, giving the qualitative aspect that the melt behaves as if its molecular weight had been reduced, or, alternatively, since the molecular weight remained constant, as if its (M/Me) ratio had been decreased by the increase of Me, i.e. by disentanglement. Osaki concludes “In a sense, the effect of the rate of shear resembles the effect of molecular weight depression as exemplified by the sharp cut of the long time end of the relaxation spectrum” In other words, these authors conclude that the terminal time to is reduced by the shear rate: “The results are such that the relaxation spectrum H(Lnt) as a function of logarithmic relaxation time is markedly cut off at the long time end and is heightened in the plateau region of shorter time scales” [11]. By extrapolation, a very strong strain rate would narrow the relaxation spectrum box to a single relaxation time: moving the melt faster would simplify its viscoelastic response. Effect of combining rotation and oscillation in the non-linear regime: Shear-Refinement under Dynamic Conditions. It appears conceivable that strain rates from pure rotation and oscillation deformations add up, increasing the amount of shear-thinning available for pseudo-plastic melts. Furthermore, one can foresee, from the work presented in Figs 2 to 4, that the combination of pure and 15 oscillatory shear create both new transient and new steady states capable of altering the cohesion of the network of bonds that interact, and thus the entanglement density. Figures 5a and b reproduce the schematic of equipment capable of achieving the combination of rotation and oscillation that we have described previously [12-14]. This equipment is used to shear or pre-shear polymer melts under a combination of pure rotational shear (at given strain rate, governed by the RPM of the rotor) and dynamic shear (at given frequency and strain, controlled separately); details of the mode of operation can be found in references [12-16]. Several samples analyzed in this paper were produced by this method. It was claimed that experiments conducted by this set-up produced pellets that were totally unique in terms of viscoelastic properties, and challenging to the existing theories of melt deformation. A large section of this article is dedicated to presenting the controversial findings. In particular, disks ready for dynamic analysis were pressed from “treated” pellets, produced by the apparatus of Figs 5a and b, and analyzed in the linear viscoelastic region. The results, presented below, are not merely difficult to understand within the currently accepted framework of melt theory, but, in our opinion, impossible to understand within that context. Figure 5a describes the elements composing one “shear refinement station”, and Fig. 5b shows the set-up for two stations put head to tail, each station being operated with its own set of specific parameters (temperature, pressure, gap, RPM of rotor, frequency and strain of the oscillation). The single station of Fig. 5a is connected (220) to a melt feeder section (an extruder) , and its exit melt (270) can either go through a strand die (with a pelletizing unit attached), or it can be pumped into the second shear-refinement station for further treatment before its exit to the pelletizing unit or a capillary rheometer positioned at the end of the second station. 16 Fig. 5a Thermal Mechanical History is created by flowing through various PROCESS STATIONS, each combining pressure flow with crossshhea flow induced by ROTATION and OSCILLATION of the Couette’s inner cylinder. In each station, one can vary T, RPM, frequency, strain amplitude FEED Viscosity measurement or pelletizer Fig. 5b 17 Fig. 5 Apparatus described in Refs. 12-14 to submit a polymer melt to a combination of shear-flow and extensional flow. The shear-flow can be the superposition of a steady rotational component and a vibration component. Fig. 5a provides the details for one treatment station. Fig. 5b shows the combination of two treatment stations. See text. A single treatment station (Fig. 5a) is essentially a Couette apparatus, with the rotor (260) capable of oscillation on top of rotation. An extruder, connected at (220), feeds the melt into the gap cavity (250). A motor assembly (not shown) rotates and oscillates the central shaft (280) connected to the treatment zone (cone area). In order to make the gap variable at will between 0.1 and 3 mm (as well as for other reasons [15]), the rotor is shaped as a cone, and the stator (230) designed so that the internal surface remains parallel to the rotor’s surface, maintaining the gap constant. The melt temperature is measured by a probe touching the melt (210) and controlled despite of shear heating by the circulation of a cooling fluid through specifically designed channels (240). The extruder can be operated to just feed the “treatment zone” and stop, or it can be operated to extrude continuously, submitting the treated melt to an additional strain rate from the extrusion. The continuous extrusion of the melt produces a pressure flow shear component that adds on top of the drag flow due to the cross-lateral rotational and oscillatory shear. In Fig. 5b, items 11 and 22 are the treatment stations of Fig. 5a, items 1, 2, 3 are gear pumps, items 111, 222 and 333 are zones with no drag flow. Details are provided in ref. 15. Combined Flow rates from Pressure Flow and Rotational Flow. The rheology of combining pressure flow and drag flow to decrease viscosity of melts has been developed by Cogswell [17], although this author did not include the oscillatory 18 component which boosts the results [Ibar, Refs [12], [18]). The rheology is not as complex as it may first appear, and can be simulated in a rather simple manner [18], following the work of Cogswell, by applying the constitutive equations applicable to a Couette configuration with separate strain rates, respectively applicable to extrusion and rotational flow [19], and by calculating the total strain rate from the vectorial sum of the individual strain rates [17, 18]. For our purpose in this paper it is sufficient to say that the apparatus described in Figs. 5a and 5b allows the design of sophisticated strain rate histories that combine the effect of cross-lateral drag flow (in pure shear or shear superposed to an oscillation) with coaxial pressure flow. Figs. 6a and b give an example of such combined flow, replacing the cone in Fig. 5a by a cylindrical rotor, and not activating the oscillation, which simplifies the transcription of the process in terms of rheological parameters. Fig. 6a 19 Fig. 6b Fig.6 LLDPE at T=210 oC. Combination of pressure flow (from extrusion) and drag flow from the rotation of the inner shaft of a Couette attached to the end of the extruder. Fig. 6a shows the establishment of the torque at the start up of cross-rotation of the shaft (60 RPM). Fig. 6b shows the torque vs time for a change of speed of the cross-rotation from 60 to 90 RPM. In Fig. 6a, the set up of Fig. 5a is used as a viscometer to measure the torque transient created by the onset of a sudden rotation of a melt extruded through the gap at given throughput, controlled by the extruder’s RPM (Mo= 10 RPM, corresponding to 350 g/hour, i.e. 0.12 cc/s). The extrusion has reached steady state for 20 min at time t=0 in Fig. 6a, start up of the crossrotaation The polymer is the same as in Fig. 2, LLDPE. Temperature is 210 oC. Fig. 6a applies to a step jump of the cross-rotation RPM of the rotor (called M2 in the Figure) from 0 to 60, corresponding to a shear rate of 15.81 sec-1. The longitudinal shear rate calculated from the extruder pressure flow is 1.36 sec-1, already big enough to bring the melt in the non-Newtonian 20 deformation range. Fig. 6b shows a subsequent step jump of M2 from 60 RPM to 90 RPM, corresponding to a sudden change of the shear rate from 15.81 to 23.71 sec-1. One sees that the experiments of Figs. 6a and b describe the transient startup of a step strain rate experiment, as described in Figs. 2a and b. An important difference between Figs. 6a and b is clearly visible: there is no overshoot of the torque for the strain rate of 15.81 (Fig. 6a) and the transient consists of the torque rising rather slowly to a steady state value of 20 N-m. Contrasting with that, in Fig. 6b, a clear overshoot of 5.60 N-m is visible when the strain rate jumps to 23.71 sec-1, followed by a decaying transient that can be fitted with two exponential terms, like in Fig. 2a. The fitting equation, given in the graph’s inset (2 exponential decay terms A1 exp(-(t-xo)/t1), A2 exp(-(t-xo)/t2 and a constant, yo) shows that the transient relaxation times are a short one, t2=18 sec and a long one, t1=210 sec, a similar situation to that of Fig. 2a. (Note that xo indicates the time at which the rotor’s speed is increased). An important difference with Fig. 2a is the value of the steady state viscosity; it is finite in Fig. 6b and near zero in Fig. 2a. What makes the start up transient flow so different in Figs. 6a and b? Matsuoka ([20], p 193) explains that below a critical strain rate (=1/to), the melt behaves like a viscoelastic deformed body, which explains a gradual increase of the torque to its steady state value, as shown in Fig. 6a . When the strain rate exceeds the limit of viscoelasticity, the overshoot is due to viscoplasticity, according to Matsuoka, who suggests it is similar to melt yielding: ” The maximum stress level reached in stress overshoot is the yield stress in the true sense, since it reflects the mechanical strength of the structure, or in this case the limit at which the knots can reptate without tearing through the polymer melt. The steady state is reached when the relaxation time that is the characteristic of the new structure under the ongoing strain rate is equal to the reciprocal of the strain rate. If the rate of strain happens to be less than the 21 reciprocal of the original relaxation time, the polymer can reptate without destroying the original structure, and viscoelastic relaxation ensues. In plasticity, steady state stress is determined by the ongoing rate of strain, whereas in viscoelasticity it is determined by the natural relaxation time. The virtual elastic strain ( to d g/dt) in plastic flow is thus 1…Stress overshoot means that the yield stress exceeds the steady state stress, hence it occurs when the plastic yield strain is greater than 1”. This argument qualitatively concurs with that of Wang quoted earlier [7-10] who also concluded that the transient relaxation, in particular the presence of the stress overshoot, was due to two criteria , one of a critical strain rate, and one of reaching a plasticity strain (125 % for Wang). Both Wang and Matsuoka agree that viscoplasticity, i.e. deformation of the melt at high strain rates, corresponds to the disentanglement of the structure of knots, as Matsuoka defines the entanglement network. In other words, shear-thinning is due to disentanglement. The stress overshoot is the onset of disentanglement and is due to plastic yielding. There are, indeed, some important differences between Wang’s and Matsuoka’s strain rate criteria, but these details are not important in this introduction, and left for the discussion section of the paper. However, another possible interpretation of the results of Fig. 2a or of Figs. 6a and b must be examined, due to the particular experimental set up leading to Figs. 6a and b. The melt was already flowing in a steady state when it was submitted to the lateral step strain rate deformation. In Fig. 6a, the initial steady state (at t=0) was that obtained from the extrusion pushing the melt in the gap of the static Couette (static in the sense that it is not rotating). Macromolecules were deformed in flow layers sheared according to a parabolic velocity profile in the 3mm gap, corresponding to a maximum strain rate value of 1.36 sec-1, that, to simplify the language, aligned them in the axial direction. The step strain rate of Fig 6a created 22 a deformation in the cross direction, disrupting the steady state in the axial direction. It is conceivable that the transient response, which is the description of how the system re-organizes its molecular interactions before reaching a new steady state, is dependent on the orientation of the melt in its initial steady state, not just a question of rate, but a question of entropy as well. In Fig. 6b, however, the step strain rate was applied in the same cross flow direction after the steady state of Fig. 6a had been reached. The difference of transient behavior observed in Figs. 6a and b might be primarily due to that. When starting from an already steady radial flow (the radial stress rate is more than 10 times the axial strain rate), the increased strain rate is acting like a jolt on the melt, which reacts elastically, creating a response more in line with a relaxation of stress under constant strain, as described in Figs. 1c and 1d. An “instantaneous” elastic strain, calculated from the ratio of the strain rates, (90-60)/60 = 50% here, was imposed in 50 ms or so, resulting in the application of a sudden start up strain rate of ~10 sec-1 and of the 5.6 N-m torque overshoot observed in Fig. 6b. The startup step strain rate experiment also resulted in a sudden increase of pressure in the gap, due to the normal stress, and a rise of the local temperature unless heat is actually removed from the treatment zone preventing the temperature to rise. In the apparatus of Fig. 5a , this is realized by circulating a cooling fluid in the orifices (240) of the stator jacket (230) The sudden increase of the strain rate is dissipated by reorganization of the network of interactive bonds, resulting in a new state of orientation of the macromolecules which adapt to the new strain rate gradient in the gap. In this explanation, there is no need to disentangle the melt to obtain the overshoot, the transient response is naturally due to the re-orientation of the entanglement network (not a decrease of the knots density) which initiates with an increase of the strain energy, like in the Maxwell spring and dashpot model in the first section of this Introduction. Concepts that must be elucidated are 23 “the orientation of macromolecules or parts thereof that induces shear-thinning”, and what is “the entanglement network of interactive bonds ”. We will propose an interpretation of these concepts in this paper. We will also address the question of the stability of the entanglement network, and re-consider issues of disentanglement as formulated by Wang [7-10], Matsuoka [20] and by the present author [21-24]. The influence of the orientation of the melt on the value of the steady state viscosity and on the relaxation spectrum has been studied and is assumed to be well known [4,5,11]. For instance, Osaki’s paper discussed above can be considered such a study. Osaki concluded that disentanglement explained his results [11], but he might have confused disentanglement and shear-thinning (see the discussion). For most rheologists, however, shear-thinning as well as other non-linear viscoelastic effects, such as the stress overshoot, are not due to disentanglement [25, 26]. In Fig. 6a, the experimental conditions suggest that it is more likely the influence of the original orientation of the melt in the axial direction, produced by the extrusion strain rate, that influences the transient characteristics so that no overshoot was observed, rather than a critical shear strain rate which, according to Wang’s criteria or Matsuoka’s criteria,.would preserve an homogeneous melt or linear viscoelastic behavior, for which no overshoot is predicted. This is the same polymer as in Fig. 2, but the temperature was 210 oC instead of 190 oC. This shifts the value of wx from 87 to 119 for this LLDPE (the activation energy for the Newtonian viscosity is 7.77 Kcal/mole). The critical Wang’s shear rate for inhomogeneous flow would be increased by 36% due to the temperature increase. The initial steady state strain rate (from pressure flow) 24 was 1.36 sec-1, i.e. far below the critical strain rate for the onset of inhomogeneous flow proposed by Wang and, for the shear rate of 15.81 sec-1 produced by the rotation of the shaft in Fig. 6a, it was still below that critical strain rate criteria by several decades. In summary, we were operating under conditions of homogeneous laminar flow for which no disentanglement should be observed. In Fig. 2a we saw that the viscosity (and thus the torque) decreased towards a zero steady shear value (perhaps not zero exactly, but very small), which might be due to combined relaxation (orientation) and disentanglement of the melt, as we argued earlier. In Fig. 6a, the start-up melt had an initial torque value of 5.5 N-m, not zero (and incidentally it was the same value as the overshoot of Fig. 6b), which grows to 20 N-m Torque after 750 sec. Following Cogswell [17], the torque increase between the two steady states would simply be due to a shear rate increase from 1.36 sec-1 to 15.87 sec-1 (the combined vectorial shear rate ). In the pseudo-plastic region, torque scales like the strain rate to the power n, where n is the melt power coefficient, around 0.2 for PE. In order to be more accurate, since the power law coefficient often varies with temperature and strain rate, which is the case for this LLDPE at 210 oC, a frequency sweep was done at that temperature to determine the effect of strain rate (or angular frequency w) on the torque at w = 1.36, 15.81 and 23.75 rad/s (the last value corresponding to the strain rate in Fig. 6b). For a jump between 1.36 and 15.81 sec-1, the expected steady state torque increase is 4.13 times. For a jump from 15.81 to 23.75, this ratio is 1.1645. This should be compared with (20/5.5)=3.63 and (20.77/20)=1.03 respectively, which are the ratios of the steady state torques taken from Fig. 6a and 6b. In other words, the torque predicted from the strain rate increase is too high by only a factor 1.135 in both figures. If there was disentanglement occurring in the steady states, it could only be due to this “extra 13% shear-thinning” observed. Perhaps this extra shear-thinning should be attributed to a kind of 25 strain softening, as suggested by the damping factor h(g) discussed previously (actually, the amount of strain on the system in steady state could be determined that way, by applying Wagner’s formula for h(g), for instance, h(g)=exp(-cg) [27] .For our present purpose, a 13% difference of viscosity is rather small, especially in view of the fact that the Cox-Merz’s law was applied, and it is logical to conclude that the steady state results of Figs. 6a and 6 are consistent with the classical shear-thinning views, and that no disentanglement took place. This conclusion is, of course, based on the assumption that shear-thinning itself has nothing to do with disentanglement, an essential topic of discussion in this paper. As far as the Matsuoka’s criteria for the presence of the overshoot is concerned, Fig. 6a passes the viscoelastic test since the strain rate was less than 1/to, and no overshoot occurred, but Fig. 6b fails the strain rate criteria, because the critical strain rate was still not reached, yet the overshoot is clearly visible. In summary, the melt fails all criteria for disentanglement by Wang or Matsuoka, its steady state response confirms predictions made by Cogswell [17] that the combined strain rates simply increases shear-thinning, yet it displayed a strong transient behavior with relaxation times that seem to implicate disentanglement, and it showed an overshoot at start up under strain rates where none should be observed. The situation is not clear. In the analysis above we saw that the magnitude of the combined strain rates from all sources determines the steady state viscosity, and nothing seems to indicate that there is an importance of the direction of flow, except in the vectorial calculation of the strain rate (the square root of the addition of the square of the strain rates). This might not be true for the transient response, as suggested in Fig. 6a by the very long time it took for the transient relaxation to vanish, as a change of the direction of flow took place from axial flow to almost entirely radial flow (the 26 melt advances helicoidally around the rotor shaft with an angle equal to 85o off the Couette axis of rotation). The effect of orientation of the melt on the transient kinetics seems an essential subject of investigation, as much important as the reverse effect, the influence of the transient kinetics on the new steady state of orientation, a subject discussed in the section on shear-refinement later on. In our approach, the transient and the steady state are both the result of the same deformation and re-organization of the network of molecular interactions; they are inseparable and must be studied as interdependent on one another. The formula successfully describing shear-thinning, the Cross or the Carreau equations, for instance [see discussion of that formula in Ref. [2]), apply to the steady state, and do not describe the transient behavior. Additionally, they do not directly relate to either the orientation of the melt or to whether a disentanglement mechanism, if any, can be triggered at a given critical strain rate. These are serious shortcomings, revealing the present lack of understanding of the deformation mechanisms of the “entanglement network”, at the molecular level, during transient and steady state response. Combined Oscillation and Rotation. We now consider experiments similar in nature to those described above, ones in which an oscillation is simultaneously added to the shear component produced by constant speed rotation. Figures 7a and b confirm the expectations that the added oscillation influences the transient and the steady states. The polymer melt was still the same LLDPE, operated at lower temperature, 130 oC, to enhance non-linear effects (wx is reduced ). In these figures, the melt was extruded in the treatment station at a higher temperature, the extruder was stopped to confine the melt in the gap, rotation was started and temperature was decreased to 130 oC. The 27 very high viscosity of the melt at T=130 oC was the reason why the RMP was started at a higher temperature; shearing the melt would not be possible otherwise, requiring too much torque. In Figs.7a and b, the current (proportional to the total torque) is plotted against time to detect changes occurring to the melt as it was submitted to either a simple cross-lateral shear produced by rotation of the Couette’s rotor, corresponding to the upper left portion of Fig. 7a, or the combination of the same rotational shear and added vibration (bottom right portion of Fig. 7a), or while “recovery” was done, such as shown in Fig. 7b, either by stopping the oscillation (at time = 0 in Fig. 7b) or by decreasing the rotational speed of the rotor (after Time = 1800 sec in Fig. 7b). Fig. 7a 28 Fig. 7b Fig. 7 Torque vs time for a melt confined in a gap with the inner surface rotating and oscillating (independently). In Fig. 7a the rotation is done without oscillation, then oscillation is added. In Fig. 7b, both rotation and oscillation are active at the start. Oscillation is first stopped, then the rotation RPM is reduced. Rotation alone (Fig. 7a) was capable of producing a steady state shear-thinned torque value that was within the limit of the capability of the motor turning the shaft. The initial amperage needed was 42 Amp. Rotation of 90 RPM (for a gap of 2mm) decreased the torque to 38 Amp. The superposition of an oscillation (7 Hz, 40% strain) is most spectacular. The current drops down elastically to 35 Amp, followed by a slow transient relaxing to a new, low, steady state of 31 Amp. The melt could be extruded at T=130 oC under those lower torque requirements. An increase of the oscillation frequency (the maximum available for the equipment producing the results of Fig. 7 is 30 Hz) reduced the torque further (not shown). An increase of the strain 29 amplitude (the maximum available was 80% at 7 Hz) had a drastic effect on the value of the steady state torque; this can be combined with the effect of frequency to decrease viscosity in the way described below. By increasing frequency and amplitude step by step, after letting the melt reach a new steady state at each step, we succeeded in reducing the torque to 8 Amp, which is 1 Amp above the value of the torque required to turn the shaft with no polymer melt filling the gap. In other words, by operating smoothly, increasing frequency and amplitude in steps of 15 min each, we were able to reduce the viscosity of this highly entangled LLDPE at T= 130 oC to almost nothing, a situation not very different from what was observed in Fig. 2 for the same polymer. Comparing the initial torque value, 35 Amp (42-7) to the final torque achievable (1 Amp), the viscosity appeared to be reduced 35 times, far exceeding the shearthinnnin ratio observed at the same Cox-Merz’s frequency/strain rate in a frequency sweep done at T=130 oC. To be sure that the melt was indeed of lower viscosity when the torque reading was very low, we took advantage of the lower viscosity to reduce the temperature down, step by step, and repeated the same scenario of increasing the oscillation and rotation speed of the rotor, increasing the rate of inflow of the cooling fluid to maintain the melt at the desired temperature despite the intense release of heat generated by the shear process. Incredibly, this repeated operation allowed to cool the melt down to 42 oC (just about the value of the solidification temperature by crystallization), while it continued to be sheared at fast rotation and oscillation. The experiment was successfully repeated several times. Application of the Carreau’s equation to the dynamic viscosity –angular frequency data generated at several temperatures (in a separate Rheometer, an ARES from Rheometrics) permits to extrapolate and calculate what the value of the viscosity would be at T= 42 oC, under the strain rate conditions used, assuming that rotational and vibrational shear rates are additive, as 30 mentioned before. The reduction of viscosity appears to be so extraordinarily large that our common sense in rheology raises the fundamental question: what is really happening to the melt? . Indeed, these experiments require answers and a careful analysis. Figure 7b describes the reverse process of Fig. 7a., starting from a steady state obtained under conditions of pure rotation and oscillation combined, the oscillation was interrupted, and one sees the quick elastic jump followed by a transient torque build up corresponding to a viscosity increase. Then, on the same figure, the rotation speed was lowered, which showed up as a spontaneous torque reduction followed by another transient where torque continued to build up towards a new steady state. All these transient responses are the translation of changes occurring within the network of interactions between the bonds belonging to the macromolecules, undoubtedly related to the entanglement network. But again, is disentanglement involved, starting at what value of the strain rate, under what other conditions of temperature and strain, and can the disentangled melt be frozen-in into pellets that, on reheating, will preserve the viscosity reduction benefits? The question of the stability of the disentangled melt appears to be crucial to study. Much of the second part of this article is dedicated to this question. Shear-Refinement: the Effect of Thermal-Mechanical History. “Shear-Refinement” is the observed influence on subsequent viscoelastic behavior (e.g. viscosity) of a pre-shearing treatment of a polymeric melt. Cogswell mentions the influence of thermo-mechanical history on viscosity in his book [17, p.53]: “Intense working, producing high shear, will usually lead to a reduction in viscosity and also a decrease in the elastic response”. 31 Note that the viscosity reduction discussed in this section is not due to a decrease of molecular weight, which is known to occur concomitantly, to a variable degree depending on the polymer and the experimental processing conditions. Most of the pioneering work was done 20 years ago by such authors as D. E. Hanson [28], M. Rokudai [29], B. Maxwell [30], JFF Agassant [31], H. P. Schreiber [32] (who wrote a review of the subject up to 1966), G. Ritzau [33,34], who provides details of a shear-refinement apparatus, J.R. Leblans and Bastiaansen [35], Van Prooyen et al [36], Munstedt [37], who studied the effect of thermal elongational history, and A. Ram and L. Izailov [38]. Hanson [28] showed that the Melt Flow Index of a branched PE could be modified by shear-refinement from 0.28 to 0.66 and that the MFI returned to the initial value 0.27 after solution and re-precipitation of the pre-sheared sample. Cogswell [17] comments as follows on the results obtained by Hanson and others [28-30]: “The change is seen to be reversible by solution treatment. Molecular weight characterization indicated that all these samples were identical… [Shearrefinnemen effects] “might at first appear to be the result of degrading the polymer, are frequently reversed by cooking the melt, though the time for which the melt may need to be cooked to achieve reversion may be much longer than the natural time of the material (viscosity/modulus at zero shear)”. J-F. Agassant et al. [31] show that the effects of shear-refinement are most obvious, and most commonly exploited, in the case of PVC which is known to have a morphology very sensitive to thermo-mechanical history. Recently interest is quickly re-emerging [39-53] as more data prove the value of the melt pre-treatment, and a large viscosity reduction ratio seems achievable for a variety of polymers, including linear polymers [31-53]. No clear explanation has been given to the origins of shear-refinement, except for the suggestion that disentanglement might be involved [31, 39-50]. 32 Bourrigaud [39], and Berger [40] have recently investigated the shear-refinement of long-chain branched (“LCB”) polyolefins in their thesis. Bourrigaud focused on several well characterized low density branched polyethylene grades and obtained proof of the influence of the strain amplitude of shear deformation on the degree of viscosity reduction during subsequent processing. Bourrigaud suggested that molecular topology is critical, and his results support the view that molecules with very long-chain branches are highly affected by shear refinement, whereas linear polyethylene seems to undergo much smaller changes (if any), under the experimental shear refinement conditions he used. Bourrigaud and co-workers [41] concluded that the degree of long chain branching or ramification qualifies or disqualifies, for the most part, the degree of viscosity reduction observed by shear refinement. In other words, controlled alteration by branching of the molecular weight distribution leads to the optimization of shear-refinement and of its benefits, according to these authors. Furthermore, Bourrigaud et al showed that refinement by elongation is more effective than refinement by shear for the same flow strength [39, 41]. Berger [40] and Berger et al. [42], worked with a long chain branched polypropylene under very high shear strain rates and found similar results. Additionally, Berger and coworkers [42] confirmed that the MFI of branched PP, collected as pellets, could be increased by shear-refinement, and that solvent dissolution would reverse the effect; after evaporation of the solvent, the MFI returning to its original value. These authors concluded that disentanglement was responsible for the decrease of viscosity and die swell [42]: The pre-treatment of the LCB-PP in the capillary rheometer at the highest shear stress applied causes a significant reduction of the tensile stress, which can be referred to the reduction of the mass-average molar mass. However, the significant decrease of the extrudate swell after the pre-treatment cannot be explained by the change of the molar mass, as the elastic behavior of polymer melts is known to be independent of the mass-average molar mass. Therefore, 33 the reduction of the extrudate swell is an indication of a change of the entanglement network during the pre-treatment. We published a series of papers during the last decade related to the use of vibrational methods during melt extrusion to induce shear-refinement by shear strain energy coupled with extensional flow[12-14, 18, 43-54]. The emphasis of this “dynamic shear strain refinement” process was on the improved processability of linear high molecular weight polymer melts, such as polycarbonate and Plexiglas (PMMA), i.e. polymers without branches. We showed [13, 14-16] that, to induce the shear refinement benefits, a combination of shear stress and superposed oscillation could raise the elasticity of the melt to a level identical or perhaps even superior to what branching could do. In other words, we proposed that, at least under dynamic conditions, both linear polymers and branched polymers could qualify for disentanglement by shear strain refinement. Furthermore, we drew attention to the requirement of rheological criteria to be fulfilled for shear refinement to occur [15,18, 46], and pointed out the importance of the shear strain amplitude of the oscillation to operate the melt in the non-linear viscoelastic range [43,45,48,49,51]. We suggested that “disentanglement” was only involved under certain conditions [47], and claimed that shear-thinning was a different mechanism of deformation, in many ways precursor to disentanglement, but not equivalent [14, 15, 18, 66]. Shear-refinement work has remained largely empirical. The viscosity reduction is temporary and rheological properties can be restored, which can occur in various ways not very well understood. Most of the comprehension necessary for its generalization and extrapolation to all macromolecules is still needed. For instance, for linear polymers, the relaxation times calculated from the standard models (reptation), seem to be much shorter than 34 those involved in shear refinement of the viscosity, sometimes by a factor 1000 or even 10 times that. The comprehension of shear-refinement in terms of transient kinetics is lacking in the literature, its positioning with respect to disentanglement confusing and debated. Properties of melts brought out of equilibrium are largely ignored. Yet, many plastic industries are directly concerned and will benefit from the fundamental understanding of what causes shear refinement viscosity drops, and how this can be applied to processing of polymer resins. The ability to process plastic melt at much lower temperature (50-80 oC below normal), because of reduced viscosity due to shear-refinement, opens up new boundaries not just in processing but also in blending, such as in nanoparticule dispersion, or for the processing of high temperature sensitive additives (wood flour, instable additives such as peroxides, etc.). Part I of this “Great Myths in Rheology” series, ref. [2], challenged the accepted views [25] that advances in rheology for the last 40 years have led to a better understanding of the influence of the chain configuration on its flow characteristics, such as viscosity. It was argued [2] that the de Gennes’ reptation model [55, 56] had reached its full maturity stage and showed signs of clear limitations, a view clearly shared by Wang [7-10]. More recently, modified versions by Marrucci et al [57], Wagner [58], and others, of the original reptation models by de Gennes [55], perfected by Doi and Edwards [25], have been claimed to provide a fairly good understanding of the flow behavior of entangled chains. Yet, many essential questions remain unanswered and/or are discarded by the present reptation school, such as the experiments by Wang [7-10], or how to explain the challenging results obtained by “shear-refinement” [28-42], or by shear induced, strain amplified, melt disentanglement under oscillation [43-54]. Bourrigaud [39] modified the McLeish and Larson’s pom-pom model [59] to account for the increase, due to branching, of the value of the tube renewal relaxation time and explained, at 35 least partially, some of the shear-refinement results, but linear, disentangled polymers present a real challenge to existing models of flow. Melt Fracture. Edge Fracture in Parallel Plate Experiments. In the deformation of a melt, studied either in a Couette or in a parallel plate (or cone and plate) apparatus, the motion imparted to the melt is driven by one surface in contact with the melt, the other surface remaining static. The question of the adhesion between the moving surface and the melt is essential to resolve. Another problem, regarding the formation of a “crack”, or indentation, at a critical shear rate on the free surface at the edge of the liquid, has been raised and analyzed by several authors [60-65]. According to this interpretation, large amplitude oscillatory shear studied with a parallel plate configuration is plagued with artifacts caused by the propagation of these edge cracks [60]. In an article published recently [61], Friedrich and coworkers follow up on their initial edge fracture work [60], and mention similar melt fracture instabilities investigated by McKinley et al. [62] , Oztekin et al. [63], Byars et al. [64], and Larson [65]. All these authors have assumed that the occurrence of sample instabilities during rheological experiments at high shear rates and/or large deformation strains was due to the formation and propagation of edge cracks-indentations. In essence, Friedrich et al. [60, 61] provide an edge fracture interpretation for results performed under similar conditions that were published by us in a series of communications starting in 1997 [43-51, 66, 67], apparently unknown to Friedrich [68], and interpreted very differently. In these publications we reported results conducted since 1995 on polycarbonate and LLDPE [1999] using a parallel plate rheometer under dynamic conditions, applying sufficient strain deformation to bring the melt into the non-linear range [15,44,45,47]. These are the same 36 experiments as shown in Figs. 3a and b for polystyrene. The observed decay of G’(t) and G”(t), and thus of viscosity, obtained under certain conditions of frequency and strain, which Friedrich et al. consider to be the signature of a surface fracture process, were described by us [12-18, 43-51,54, 66,67] as the orientation of the entanglement network, as defined in the Dual-Phase model [22-24], a situation very similar to what causes shear-thinning under strain softening conditions and/or shear-refinement, as described in the previous sections. We [43, 44] assigned the time dependence of the rheological parameters to the stability of the entanglement network, which can either elastically deform, to allow orientation of the dualphaase or plastically deform, creating a new entanglement network. To quote the 1999 paper [44 ]: “…the decrease of viscosity is not the result of a mechanism of slippage at the surface of the rheometer, nor a mechanical degradation of the chain macromolecules, but rather is due to the destruction of the EKNET network of interaction by a vibration induced dual mechanism of first stiffening (by shearthinnning and tearing (by a fatigue mechanism (induced) by the normal stresses) of the interpenetrating coils. All these concepts will be thoroughly developed in this article. We showed [47] that edge fracture can be avoided by slowly and step wisely increasing the strain amplitude, instead of jumping it to a large value, a procedure practiced by the edge fracture protagonists. By operating under the step-by-step-increase-of-strain conditions, and also by using smaller samples (12 mm in diameter vs 25 mm used by Friedrich et al. [60, 61 ], or thinner samples (less than 0.5 mm) and/or by using cups to confine the melt and serrated surfaces for the parallel plates, the artifacts caused by the non-linearity established too abruptly can be eliminated [47, 67]. This procedure and the validation of the assumptions that melt fracture is not involved in the results observed will be further discussed below. 37 Objectives of this Article. In conclusion, all the above results (Figs 1-7) seem to indicate that the stability of the network of entanglement should be a major subject of investigation; in particular, it would be practically very important to know whether entanglements can be manipulated (increased or decreased at will) to facilitate processing. This paper addresses the following issues: -How can we distinguish between a transient melt that is decaying towards its steady state from a disentangling melt? Under what conditions is the steady state a disentangled state, as suggested by Osaki et al. [11]? What is the difference, if any, between shear-thinning and disentanglement? Finally, the paper examines the following proposition: a polymer melt can be disentangled if, and only if, it goes through a specific process of “melt yielding”. How can a liquid yield, which is a phenomenon characteristic of solids (it is the transition between an elastic and a plastic state). What is melt yielding? It is mentioned by several authors: Ibar [21-24], Matsuoka [20 ], and Wang [8,9]. How does it affect the homogeneity of the melt [7-10], and the rheology results? Are the results in Figs. 2 and 3 due to or affected by a laminar structuration of the gap created by local yielding, or disentanglement? Is disentanglement confined to a thin layer that becomes a surface of lower viscosity (a lubricating layer), preventing the penetration of further disentanglement towards the other surface? Is there a critical gap for full penetration of disentanglement, and how can it be controlled? It is well known that the steady state viscosity varies with the strain rate, for high molecular weight polymers, as well as with molecular weight and temperature, and these experimental 38 facts were reviewed in part I of this series of papers [2]. It is expected that the transient behavior also varies with the same variables. An important issue addressed in this paper is to examine how the transient states and the steady states are related, whether they can simply be derived from one another or require specific separate treatments. In particular, the effect of strain and strain rate on the transient behavior is addressed, both in pure rotational viscometry, in dynamic experiments, and in experiments which involve the combination of oscillation and pure rotation. Can the combination of strain, strain rate and oscillation result in melt transients which relax to different steady states, and are those steady states stable? Is the melt capable of “yielding” in steady state or is it a property of the transient behavior? What are the macromolecules doing when deformed in steady state rotation? Is the concept of strain still valid when the melt has reached its steady state, under constant strain rate conditions? If strain is still a valid concept, what is the mechanism that makes strain grow to infinity in steady state? Is a steady state melt stretching and relaxing, orienting while stretching, orienting while relaxing, or both? Some would consider all these questions to be trivial, and the answers well understood by rheologists. Yet, as the next section will demonstrate, the question of a melt out of equilibrium is not a naïve question and bears to the fundamental issue of what entanglements are. If a melt can be brought out of equilibrium and stabilized in that state, at least for a long period of time, say for 1,000 to 10,000 times the value of its terminal time, what does it say about the nature of entanglements? What kind of topological change could make this happen, in terms of the reptation interpretation of entanglements? Additionally, if melts are capable of being 39 metastable, like glasses, new processing techniques can be used to either decrease or increase their viscosity and affect many physical properties. In the discussion section of the paper, we distinguish the mechanisms of deformation that lead to simple transient behavior, with a full return of the melt to its initial equilibrium after cessation of the cause that created the melt transient, from those specific mechanisms capable of producing a modification of the entanglement network, with interesting processing consequences. Can we produce by induced mechanical treatments, through a combination of stress, strain rate and strain history, melts which are maintained out of equilibrium and present new steady states characteristic of a lower viscosity melt, at the same temperature? Are these melts disentangled in the classic sense (Me is increased)? EXPERIMENTAL PROCEDURE, POLYMER CHARACTERIZATION, DEFINITION OF PARAMETERS, 1. Experimental Procedures In this section we describe several types of experiments that we classify and label by names that will be used throughout. 1A. The simple time sweep at given T, w and strain %. This is a classical test in rheology. The same tests were conducted by Friedrich et al. [60,61 ]. The only interest here is to explore the non-linear region, by choosing values of the rheological parameters 40 where G’ and G” are observed to become time dependent. A new sample is used for every single set of conditions chosen for the time sweep. Variables studied were: frequency, temperature, and time under oscillation. Strain was kept constant at 50%. 1B. The simple time sweep at given T, w and strain % immediately followed by a cooling ramp test performed in the linear range. An experiment of Type 1A is followed by another step, a cooling ramp test, at 1 oC/min, 1 Hz, 5% strain. As temperature cools down, the measurement of G’(T) and G”(T) is done until the torque exceeds its maximal permitted value, the apparatus automatically terminating the test. The second step, the cooling test, is always done under the same conditions, regardless of the parameters used during time sweep. In operating this way, the cooling curves obtained can be compared to reveal the changes, if any occurred, that resulted from the time sweep “treatment”. 2. The three step experiment of type FTF (Frequency-Time-Frequency) in a dynamic rheometer. Step 1 consists of a first frequency sweep (0.1 Hz to 40 Hz, at a given strain%, usually 5%) at a given temperature T (referred to as “1st Frequency Sweep” in some of the figures). Step 2 is a time sweep conducted for a given time, usually 20 min, chosen frequency and strain %. The temperature is either the same as for Step 1 (the type of the experiment is then called 2A) or different (Type 2B). Step 3 is a repeat of Step 1 done right at the end of the time sweep, also referred to as “2nd Frequency sweep” in some of the figures. Comparing the frequency sweeps at Steps 1 and 3 provide useful information regarding the changes occurring, if any, due to the time sweep “treatment”, as Step 2 is sometimes referred to in the figures. 41 3. The four step experiment of type FT1-FT2-FT1-FT2 in a dynamic rheometer. Step 1 consists of a first frequency sweep (0.1 Hz to 40 Hz, at a given strain%, usually 5%) at a given temperature T1. Step 2 , referred to as “annealing” in some of the figures, is a frequency sweep performed at a temperature T2 located 50 oC above T1.. The “annealing” time of Step 2 is the time it takes to run the frequency sweep, usually 5 min, including the equilibrium times. Step 3 is a repeat of Step 1 done after the sample is cooled back down to T1. Step 4 is a repeat of Step 2 after the sample is re-heated to T2. One can compare Step 1 and Step 3, Step 2 and Step 4. These tests can be considered an original melt frequency sweep and a rerun after annealing for 5 minutes at a higher temperature. 4. Pure viscometry. These tests are the most basic in rheology. They provide the value of viscosity and of the normal force for a given strain rate, at a constant temperature. Figs. 2a and b are typical examples. In a simple variant of this type of deformation, the same melt can be submitted to successive steps of various strain rates, or no strain rate (“annealing step”). The sequence creates a strain rate history. In order to compare the effect of various strain rate histories, the final step can be done at low Newtonian rate, revealing any change, if any, due to thermalmechaanica history. 5. Pure viscometry followed by a frequency sweep. This type of experiment is identical to Type 4, except that, at the end, a frequency sweep is performed in the linear viscoelastic range, to “reveal” the state of the melt. 42 6. Viscosity measurement under extrusion flow conditions. These experiments are illustrated in Figs. 6a and b. An apparatus was built with a Killion lab extruder attached to a house-made Couette, positioned perpendicular to the extruder’s axis. The rotor of the Couette was a cylindrical shaft. The dimensions are given in the section of the introduction above called “Combined Flow rates from Pressure Flow and Rotational Flow”. Both the extruder flow rate, determining the longitudinal shear rate and the residence time in the Couette section, and the cross-shear rate, calculated from the gap dimension, the rotor’s speed and the melt index, could be varied. 7. In-line viscosity measurement at the end of a “treatment processor”. For some experiments reported in this article an in-line capillary viscometer, that was also house-built, was used to reveal the state of the melt after its passage through a treatment station (see Figs. 5a and b). A small hole drilled on the side of the exit melt pipe directed a small portion of the melt through a miniature gear pump to a set of capillary tubes. Two capillary tubes, one short, one long, were positioned periodically in alignment with the flow, allowing pressure measurement to be made, from which viscosity was calculated. Viscosity was directly plotted as a function of time on a computer screen every minute or so (Fig. 8). 43 Fig 8 These 3 graphs, continuously updated, read the temperature (top), the pressure drop difference (between short and long capillary), and the viscosity (bottom) of the melt passing through a capillary viscometer after it has been “treated” (see Figs 5a and b). The operator “sees” the result of changing the rheological parameters in the treatment stations. Here the viscosity of the exiting melt has changed from 3,000 to 1,000 Pa-s. The melt is EVOH. The interest in such an in-line viscosity measurement was two fold: first, and most obviously, it provided a quick and continuous quantitative assessment of the rheological state of the melt, as we built new thermal-mechanical history to modify it. Second, the viscosity read-outs from the “just exited melt” could be compared with viscosity measurements performed on the 44 pellets, also extruded at the same time (Fig 5 b), which were melted subsequently in a Melt Flow Indexer.(Dynesco), as shown in Fig. 9. Fig. 9 This figure applies to a linear PC grade. One compares the MFI value found for pellets made out of a melt prepared by the treatment stations of Figs 5a and 5b with the value of viscosity measured by the in-line viscometer (shown in Fig. 8). Although the two temperatures are different (300oC for the MFI measurement, 275 oC for the in-line measurement), the correlation is validated: when the in-line viscosity drops, the melt has a higher MFI than the reference melt (11.3). In other words, the viscosity benefits obtained from the manipulation of the melt stability can be frozen into a state that will survive subsequent heating periods, about 20,000 times its terminal relaxation time value at 150 oC above its Tg. 2. Rheometers used. Several types of dynamic rheometers were used for Type 1, 2 and 3 experiments: RDAII from Rheometrics, ARES from Rheometrics (TA Instruments), CVO from Bohlin Instruments (Malvern), and AR 2000 from TA Instruments. Which instrument was used for which type of experiment will be specified in each section.. The viscometry experiments (Type 4 and 5) were conducted with the AR 2000 and the Bohlin. 45 3. Materials. Results given in this article concern experiments with different types of resins. 3.1 Polycarbonate: -PC-1: GE Lexan 141 (Mw=27,000 Mn=9,700 MFI= 9.7) -PC-2: Bayer Makrolon 3208 (Mw=32000, Mn=11000 , MFI= 4.3) -PC-3: Bayer Makrolon 2608 (Mw=26000, Mn=8800, MFI= 11.3 ) 3.2 Polystyrene: -PS-1: Total Petrochemicals PS 1450N (Mw=190,000, Mn=80,000 ),MFI= 6.5 M/Me=11 -PS-2: Total Petrochemicals PS 1070 (Mw=300,000, Mn= 120,000). MFI=1.5 M/Me=17 3.3 LLDPE -Dupont Dow Elastomers LLP Engage 8180 (Mw=173,000, Mn=(90,000 MFI=0.5 ). M/Me ~ 170 LLDPE is an octyl ethylene copolymer (metallocene technology) with a Tm of 38 oC, totally amorphous at T= 190-220 oC , the temperature range spanned in this paper (Figs 14-28) . . 4. Initial State and Sample Molding Procedure. 4.1 PC samples. All polymer resins studied came as pellets. PC pellets were systematically dried 4 hours at 120 oC before being processed in a Carver Press into 25mm diameter disks. The molding conditions were as follows: 10 ton platen force was applied onto 16 circular cavities of 2mm depth each, equally spaced in a 4*4 in plaque, each containing 1.57 g of dried pellets. Pre-heating time under no pressure :8 min; Heating time under pressure: 3 min; Cooling time 4 min; Number of disks prepared:16; Molding Temperature: 275oC. The disks were dried 17h under vacuum at 70oC prior to placing in the rheometer (the reason for this extra step and the low temperature of drying was that some samples were possibly heat sensitive (those which were “disentangled” prior to the viscosity measurements), and the drying at low temperature under vacuum was an extra caution to prevent any possible heat induced return to equilibrium state during drying too close to Tg). Test conditions were as follows: 46 1) Parallel plates with serrated surfaces (microscopic pyramidal indents) were used for all experiments. 2) Tests conducted under N2 3) Start heating to 275 oC . Takes approximately 10 min. 4) Press to make gap of 1.5 mm. Trim. The sample is then ready for the specific testing program type described in the section “1. experimental procedures”. For instance, for a type 2 (FTF) program conducted at T=225oC, the following sequence would apply: 5) Lower temp to 225 oC. Wait for temperature to stabilize. 6) Step 1: 1st frequency sweep from 0.1 to 40 Hz, 5% strain. 7) Step 2: conduct a time sweep at 10Hz-5% Strain for 20min at T=225 oC (as an example) 8) Step 3: 2nd frequency sweep under the same conditions as the 1st frequency sweep. 4.2: LLDPE Same procedure and methodology as described above for PC, except that drying was not necessary, and the molding temperature in the Carver Press was 225 oC. The test procedure for the type 4 (viscometry) experiments (Figs. 2a, 2b, and 14) was as follows: Serrated plates were used. Disk’s initial.thickness was ~2 mm. Tests were run under N2 -Start heating to the initial temperature (e.g. 190oC) and hold for 3 min, -Make gap of 1.6 mm. Trim the excess melt around the rim. -Re-heat to 190oC, wait for temperature to stabilize (approx.1min) -Start viscometry test with a shear rate of 1.0 sec-1, record for 30min . 4.3: PS The same procedure and methodology as described above for PC was used, except that drying was not necessary, and the molding temperature in the Carver Press was 200 oC. A single cavity mold was used; 3 min pre-molding time at 200 oC, 3 min under 4 Ton force during molding, 2 min cooling time by pressure contact with cold Aluminum plates. Specimens of thickness varying between 1200 and 200 microns were used. Tests were 47 conducted under N2 to avoid degradation (proven to exist by separate tests conducted under air atmosphere). 5. Definition of the Rheological Parameters to Analyze the Stability of the Melt. In the following, we present the dynamic rheology data in a way that, we believe, is most appropriate to reveal the difference between melt states. The classical presentation of the data is the use of log-log scales to display G’ and G” vs w at a given temperature, and the display of a cross-over point, defined by G’=G”, found at a frequency wx, the cross-over frequency, usually associated with the terminal time (to=1/ wx ). It is well known that increasing temperature or decreasing molecular weight shifts the value of wx towards larger numbers. wx also increases with Me, the molecular weight between entanglements, i.e. when “disentanglement” occurs, since the terminal time scales with (Me/M)a . Note that, according to classical views, as discussed in ref. [ 2 ), G’(w) and G”(w) are the product of Go,N, the plateau modulus (Go,N = r RT /Me , where T is absolute temperature and r the melt density), and a function of w and ti , where ti are the relaxation times. . Hence a complementary way to compare two melt states, besides the comparison of the wx, as explained above, is to plot G” vs G’ on a log-log scale for both melts and see whether they are shifted horizontally and/or vertically, and by what respective amount. The value of G’ at the cross-over, defined as G’x (also equal to G”x), can also easily be found from such a plot at the intercept of the curve G” vs G’ and of the straight line G”=G’. At equal T and r, the value of G’x should be compared for the two melts. 48 A convenient way to find the cross-over [2] is to plot (G’/G*)2 vs log w, as shown in Fig. 10 Fig. 10 Comparison of two states of a PS melt at the same temperature 190 oC. The un-sheared “original melt before treatment” (dots) has a lower wx. The “treated” melt (triangles) will be described later on. It has a higher frequency at the cross-over point. wx is found for (G’/G*)2 =0.5, so the comparison of the wx for two frequency sweeps is straightforward. The use of the ratio (G’/G*) offers other advantages. First, it is the stored energy per cycle, so it is a representation of the state of the bonds and of their interaction to bear stress (assuming that a totally relaxed system will not bear any stress). A second benefit for using the ratio of two moduli as a rheological parameter is to provide, at least partially, a response to certain scientists, such as Freidrich and coworkers [60,61], who assume that the decrease of modulus or viscosity with time is always due to the decrease of the area of contact at the surface between the polymer melt and the plate. While it is correct to state that pealing off the surface would decrease the area of contact being sheared and would, therefore, decrease 49 the modulus proportionally, it should be added that G’, G” and G* would be affected in exactly the same way , which would translate mathematically to DG”(t)= DG’(t), and the ratio (G’/G*) would remain strictly constant. This is a test that is easy to do, as illustrated in Figs 11a and 11b . Fig. 11a This is the same PS as in Fig. 10. The ratio (G’/G*)2 is plotted against time, as the melt is strained at various larger amplitudes 5%, 10%, 15%, 20% (the curve corresponding to 20% is not shown. The frequency of oscillation is 87 Hz. One sees that (G’/G*)2 is not constant, it can decrease or increase, following the same pattern as viscosity changes . This observation appears to contradict the argument that time dependence of moduli or viscosity is created by a surface effect [60,61]. 50 Fig. 11b The x-axis is the complex modulus. The melt is a linear PC (Mw=32,000) submitted to time sweeps at given frequency and strain %, as indicated in the insert box. This results in the decrease of G* which becomes time dependent (in the Figure, the starting point for each temperature is the point located at the extreme right, then follow the curve leftward). One sees that (G’/G*)2 decreases a small amount as G* decreases, then increases sharply at the end of the time sweep. This is in contradiction with an interpretation based on a surface fracture to explain the time dependence of G* (and therefore of viscosity). Freidrich et al [60,61] mention the possible increase of tan d (corresponding to a decrease of (G’/G*)2 in their experiments (on PS only), due to a bifurcation of the propagating crack inside the material, but how could such an interpretation explain an increase of the elasticity after the melt has presumably released the energy input from the oscillation? It is true that for some polymers, e.g. PS, under certain conditions of frequency and strain during time sweeps, (G’/G*)2 remains constant, or quasi constant as G’(t) and G”(t) vary, as reported by Freidrich et al. [60,61]. This is the case for PS in Figs 3a and b. But this might be a viscoelastic property of melts, totally un-related to a surface effect; for instance, describing the re-organization of the bonds’ interaction occurring internally, not at the surface, making 51 both G’ and G” vary in a way that makes the ratio (G’/G*) constant, or appear relatively constant. We favor this interpretation and will argue why it is so later in this paper. Finally, the usefulness of the ratio (G’/G*)2 as a rheological parameter to characterize the state of a melt stems from its simple relationship to tan d = G”/G’, since cos d = (G’/G*) and cos2 d = 1/(1+tan 2 d) . A plot of tan d vs log w displays a minimum, for a certain value of w, classically viewed as the onset of the plateau of rubber elasticity, starting from the viscous end. In fact, as an empirical rule, the value of Go,N is taken as the value of G’ at the minimum of tan d. Because of the relationship between cos d and tan d, a plot of (G’/G*)2 vs log w displays a maximum. The value of (G’/G*)2 at the maximum scales like (M/Me)0.8 according to the Marvin-Oser theory of entanglements [69]. While this relationship is empirical and applies to mono-dispersed melts, it is nevertheless another useful parameter to characterize the entanglement state of a melt, and can easily be found from plots of (G’/G*)2 vs log w to compare melts, in particular to know whether disentanglement occurred or not, as illustrated in Fig. 12. 52 Fig. 12 Same PS as in Figs 10 and 11a. T is 160 oC. The curve at the top (triangles) corresponds to the unsheeare melt and is the Reference. The curve with squares applies to the state of the melt after it has been through a first” treatment”, a time sweep of 10 min at 50 rad/s, 25% strain (the strain % is increased gradually by steps of 5% every 3 min) . The lower curve (dots) corresponds to the state of the melt after it has gone through TWO treatments and one “recovery” (time sweep at w= 1 rad/s, 2% strain, one hour). Note the large increase of wx between the original curve (obtained by extrapolation) and the other two. Also, the value of w for the maximum of (G'/G*)2 is approximately the same for all the curves, but the height at the maximum value is clearly different for the original and treated melts. RESULTS 1. Linear PC (Lexan 141). Time sweeps at various temperatures, frequencies, 50% strain. 53 The types of experiments performed correspond to Type 1A and 1B, as defined in the section on Procedure. The results were first reported in refs. [16, 43, 45]. The RDA 700 from Rheometrics was used. Fig. 13a Fig. 13b Fig. 13c Fig. 13d Fig. 13 Time sweeps for PC-1 at T=220 oC under various frequencies (157, 31.4, 12.56, 6.28, 3.39 rad/s) and 50% commanded strain (Figs. 13a, b, d). Fig. 13c shows the effect of time sweeps under those conditions on the No-Flow curve (temperature cooling sweep) performed afterwards (at 1 Hz, 5% strain). 54 Fig. 13a shows that as soon as the time sweep started, at a given temperature (here T=220 oC), frequency (157, 31.4, 12.56, 6.28 or 4.39 rad/s) and 50% strain, a transient behavior was observed, the complex modulus G* (and thus viscosity, G*/w) decaying in time from an initial value (increasing with frequency) towards a value that looks like a steady state value, that is function of strain and temperature. The transient kinetics is a strong function of w, the steady state being reached faster at higher frequency. The dynamic modulus G* is "pumped-up" by the sudden application of an oscillation at 50% amplitude, more so as w is increased. For example, in Fig. 13a, the start up G* varies from 0.01 MPa to 0.05 MPa ( a 5 fold increase) when w varies from 4.39 rad/s to 157 rad/s. The initial value of G* divided by frequency is the initial dynamic viscosity that decreases as w increases, illustrating that the initial state is controlled by shear-thinning. Figure 13b is a plot of (G’/G*) vs time for the same various frequencies during the time sweep. One sees that the stored energy increases as frequency increases, but slowly decreases as G*(t) decays. The apparently stronger relative decrease of (G’/G*) for w=12.56 and w=6.28 rad/s is actually due to the inability of the RDA700 temperature controller to maintain temperature strictly constant at the high strain amplitude applied (50%). Once the effect on the modulus of the small temperature rise is taken into account, the corrected variation of (G’/G*) becomes minimal at lower frequencies. The reason why the high frequency w= 157 rad/s does not seem to show an even stronger effect of temperature rise due to forced oscillation at high amplitude is explained by Fig. 13d. The RDA700 is unable to keep the strain equal to the value of the commanded strain, 50%, even at the lower frequencies where 15.7% strain is reached and remains constant. At higher frequency, see w=31.4 rad/s and worse w=157 rad/s in Fig. 13d, the strain is not constant and continues to gradually ramp up during time sweep, from 5% to 55 15.7% at T=220 oC. This is due to limitations imposed by the maximum torque permitted by the RDA700. Because of the strain ramp up, the temperature rise was non-existent, explaining the result. In the case of w=157 rad/s the decay of (G’/G*) is clearly visible and not due to temperature rise. Modern instruments are not plagued by the same problems as the RDA700, and are capable of maintaining temperature strictly constant (by better convective cooling inside the rheological chamber). Much higher torques are also provided in the new versions of rheological instruments now commercially available. Figure 13b shows that the modulus increased with frequency at the start-up of Fig. 13a is in accord with an increase of the stored elastic energy, G’/G*, from 0.3 to 0.8 ( a 2.7 times . increase), which explains shear-thinning [66, 70]. Also notice that for T=220 oC and w =157, the value of (G'/G*) is above the value of the cross-over (0.707), and, noticeably, this is for this frequency that we observe the strongest decay of G*(t) in Fig. 13a and the strongest departure of the No-Flow curve in Fig. 13c, which is discussed in the next paragraph. Despite the experimental difficulties of keeping temperature and strain constant, which required careful corrections during analysis, the RDA700 was capable of providing evidence for the first time that time sweep treatments, operated under dynamic conditions that rendered the moduli transient, could give rise to new states of a melt; in other words that melts could be made rheologically unstable (in the same sense that a glass can be brought out of equilibrium). This is shown in Fig. 13c. This graph corresponds to a Type 1B experiment described earlier. It plots the complex viscosity against temperature for a temperature ramp down (at cooling rate -1 oC/min) under oscillation at 1 Hz ( 6.28 rad/s), 5% strain, done right after the 10 min of time sweep “treatment” (such a procedure is called “a no-flow curve” and is routinely done by 56 scientists performing Mold-Flow simulations) . The purpose was to reveal the state of the melt after its treatment by comparing the No-Flow curves between a Reference melt, not submitted to any time sweep treatment, and a treated melt, submitted to a time sweep at given temperature, frequency and 50% commanded strain. It is clear from Fig. 13c that the No-Flow curves are different, depending on the frequency chosen during time sweep. The top No-Flow curves of Fig. 13c, obtained for the lowest w during time sweep, are identical to the Reference, but the No-Flow curve obtained for a treatment at w=157 rad/s is definitely lower, indicating a lower viscosity melt [16, 43, 66]. Many tests were conducted to study the effect of temperature of the time sweeps, their duration, the grade of the polymer, the gap thickness, and the strain %. Each of these variables play a significant role in determining the success of modifying the state of the melt, as indicated by the No-Flow curves that revealed the difference. The details of these experiments are reviewed elsewhere [45]. 2. Viscosimetric experiments on LLDPE 2,1 Pure Rotation. Experiment of Type 4. The rheometer used was an ARES, operated with a parallel plate geometry according to the Type 4 experiment described in the Procedure section. The sample was LLDPE. Temperature was measured during a run to check that it remained constant. N2 was flowing in the rheometer, and a separate TGA showed that the sample was totally chemically stable at these temperatures for more than 1 hour, i.e. the observations made in the figures to follow were not due to, or influenced by, degradation. In Fig. 14, a given strain rate (given in the graph insert) was "instantaneously" imposed on the melt and held constant for about 30 min. The strain rate was chosen to be in the vicinity of the reptation time calculated from the cross57 over time (1/wx) times the ratio of (M/Me), which turned out to be between 2 to 3 sec. The melt jumped to a certain stress (left box) and normal force (right box) level, and these started to decay in time towards a steady state value which was barely a function of the strain rate imposed. The initial value of the stress and normal force, as well as the relaxation times, strongly depended on the strain rate, as can be seen in Fig. 14. The top curve, corresponding to a strain rate of 1 sec-1, was already presented in Figs. 2a and b. Fig. 14 Viscosity vs time (left) and Normal Force vs time (right) for pure viscometry at constant strain rate. The melt is LLDPE at T=190 oC. The rates are indicated in the inserts. Notice the presence of a little hump at ~400 sec in the viscosity/stress-time curve corresponding to 1 sec-1(this hump does not exist on the normal force decay curve). It is also visible for the 2 sec-curve, but not for the 3 sec-1 strain rate. This feature, which we hardly notice in the case of Fig. 14 but is more visible for other conditions presented later, is almost always visible for melts for a certain range of strain rates. It might reveal the influence of the 58 stress on the relaxation times, at least the first relaxation time, initially accelerating the relaxation decay, and, thereafter, slowing it down (even to the point of a local reversal, see later) as the total stress itself decreases and no longer accelerates the decay of the first exponential term (in a mathematical sense, the potential barrier is lowered by stress which itself decays with time). The relationship between stress and normal force is analyzed in Fig. 15 , expanding further on the influence of stress on the relaxation time. Fig. 15 Normal Force vs Shear Stress for the data of Fig. 14 Figure 15 eliminates time and cross-plots normal force vs shear stress measured during the transient stage that consists of a continuous decay of both shear stress and normal force. The 3 curves were obtained at 3 strain rates, 1, 2 and 3 sec-1. The starting point to follow the evolution is on the upper right of each curve, the uppermost point corresponding to the shortest time. . One can extrapolate the curves of Fig. 14 to obtain the initial value of the viscosity, and 59 thus of the stress, at t = 0. One can draw a line, shown as the tilted dotted line in Fig. 15, passing through these t = 0 points extrapolated for the 3 strain rates shown in Fig. 14. This line cuts the zero normal force x-axis at a stress of ~5,700 N. For any strain rate below 1 sec-1 , which is the lowest curve in Fig. 15, the t=0 point would be moving down on the dotted line; eventually we would reach the Newtonian value (corresponding to strain rate0), and, in such a case, there would be no normal force, and no time dependence, so the shear stress should vary along the horizontal dashed line in the Newtonian regime. In other words, the cross-overpooin between the two dash-lines is the beginning of non-linearity, the start of non-Newtonian flow for higher stress. This is the point where the elastic contributions from the deformed melt start to come into play. Figure 15 suggests a shear stress criteria for the onset of transient behavior, rather than a strain rate criteria as advocated by others [8, 9]. Notice the initial pronounced curvature in Fig. 15 for plots of normal force vs shear stress, followed by subsequent apparent linearity between these two parameters. In the initial stage (upper right), the curve is “flatter”, i.e., after the establishment of the rotation the shear stress variation was larger than the normal force change, whereas in a subsequent stage it appears to vary more linearly with normal force. This behavior is clearly seen for the lowest curve of Fig. 15, but also for the other two curves, although linearity is confined to the lower region and a log-log plot (not shown) would be more appropriate. The point raised by these observations regards the influence of stress on the relaxation times, as already mentioned for Fig. 14. Stress decay and normal force decay do not appear to decay in phase in the non-linear region, at the initiation of the deformation, the decay of normal force being simpler (one relaxation exponential decay instead of two, for instance). It could be that the transient stress 60 decay starts to phase-in with the normal stress decay (where the two parameters would be linearly related) only after an extra relaxation term, only present in the decay of stress, has relaxed (its relaxation time being a function of stress), in a recursive way. In terms of an activated process to describe deformation, one term for the stress is created by a pro-active change of the conformation statistics of the conformers as a response to deformation; this defines the potential energy of isomeric rotation, which is plasticized by the total stress, creating the recursive process. As the stress rises, at the onset of the transient relaxation, the relaxation time is as small as it will ever be, since the stress is at its maximum. When the total stress relaxes, due to an orientation mechanism, the pro-active stress decay is slowed down, providing the hump seen in Fig. 14, already mentioned, and the strong non-linearity between stress and normal force at the beginning of the transient stage in Fig. 15. This interpretation also explains the effect of strain rate on the viscosity transient kinetics (Fig. 14), since a faster strain rate produces a larger stress, decreasing the relaxation times. The normal force does not have this pro-active term, because the mechanism that generates it is the same as that which produces the second term of the total stress, the orientation of the conformers allowing relaxation of the deformed conformers statistics by diffusion. When the pro-active term of the stress has decayed, stress and normal force are in-phase and their time dependence is described by the same relaxation times. This corresponds to the linear (lower left) portion of Fig. 15. Figures 16 (a) and (b) are similar to Fig. 14, but add two more strain rates, 0.1 sec-1 and 3.58 sec-1, two of the other curves being reproduced as references. There are two interesting pieces of information: 61 (a) (b) Fig. 16 Viscosity (a) and Normal Force (b) vs time for pure viscometry at constant strain rate (indicated in inserts) at T= 190 oC. LLDPE. First, transient behavior is observed at all shear rates, even for 0.1 sec-1, for which the normal force remains close to zero. This plot confirms the decrease of relaxation time with increasing imposed strain rate discussed previously. The steady state would be reached after an extremely long time for the 0.1 sec-1 strain rate and in less than 50 sec for the 3.58 sec-1 rate. Second, the value of the steady state viscosity and of the steady state normal force seem to be raised for the largest strain rate, 3.58 sec-1. Such a behavior corresponds to shear-thickening of the melt and is unexpected in pure shear. Note in Fig. 16b that normal force is also raised to a steady value of 47.5 g (4.75 N) corresponding to a normal pressure of 9,677 Pa. Figures 17 to 28 expose well, in our opinion, the remaining challenges of rheology, in particular with respect to melt entanglement stability, and the nature of entanglements. The following examples apply to LLDPE, but similar results were obtained (not shown) with a (M/Me=17) PS grade, and the results are thought to be general. 62 Fig. 17 Viscosity vs time for 3 successive Type 4 experiments conducted with the same melt. The successive strain rates and their time of application are written in the inset. The melt was LLDPE at T=220 oC. Figure 17 shows the results of 3 successive type 4 experiments for LLDPE. The LLDPE melt was here at 220 oC. Initial viscosity, measured at strain rate 0.1 sec-1 , was quite stable for at least 15 min, a sign that it was the steady state value: 7,400 Pa-s. The viscosity became time dependent for a strain rate change from 0.1 to 1 (also note that, after extrapolation, viscosities match at the transition between the 2 rates). The viscosity decrease corresponds to a transient behavior that lasted 30 min. As the melt was reaching its new steady state value for the new strain rate (the step 2 curve shows that it had not fully stabilized, but that it was very close), the strain rate was then reversed back to 0.1 sec-1, where one would expect the melt viscosity to return to the initial viscosity of 7,400 Pa-s. Instead, it evolved, through a transient recovery behavior, to only 3,500 Pa-s. 63 The question is: was the initial viscosity of 7,400 Pa-s a steady state value or was steady state, instead, the value given by the plateau on the step 3 curve? If the initial viscosity at 0.1 sec-1 was a non-equilibrium viscosity, what makes it so stable for 15 min that one has the impression that it was a steady state viscosity? When does one know if viscosity is the steady state one or not? After all, at a lower temperature, 190 oC in Fig. 16, it was shown that a strain rate of 0.1 sec-1 resulted in a transient decay. Should we not expect a faster decay at a higher temperature? What is the origin of the transient decay? The polymer melt was polyethylene; it was linear, without long branches, its entanglement density was 170 (M/Me), it had no polarity, it was at a temperature 216 oC above its solidification temperature (37 oC; crystals are unlikely to be present). It is one of the most simple polymer macromolecules that one could think of, and yet, a simple experiment such as the one presented here, and in the following figures, seems to be a challenge to traditional views regarding the understanding of what causes this behavior. If entanglements are responsible for the transient behavior, what do these results teach us about the meaning of what entanglements really are? The following figures deepens the level of our questioning of classical rheology. 64 Fig. 18 Viscosity vs time for a series of constant strain rate segments performed sequentially (the rate is indicated in the insert). The insert in Fig. 18 describes the sequence of strain rate jumps. Notice that, contrary to Fig. 17, the "junctions" of viscosity at the various shear rate jumps are not perfect. (This point, though, once said, is considered insignificant in comparison to the other comments to follow). Also notice the presence of the little hump in the step 2 curve (for 1 sec-1), even more pronounced than in Fig. 14. Finally, and most importantly, the step 3 (0.1 sec-1), step 4 (0.01 sec-1) and step 5 (0.001 sec-1) curves created a continuous tendency towards a return to the initial value of 7,400 Pa-s, the starting value for the 0.1 sec-1 strain rate. Since strain rate continued to decrease from step to step in each recovery section, the final extrapolated value of viscosity must correspond to the Newtonian value at that temperature. Now there are two assumptions one can make: 65 1. the value of 3,500 Pa-s, observed for the plateau on recovery at rate 0.1 sec-1, in Fig. 17 must be a shear-thinned value for that strain rate at that temperature. The fact that initially, in Fig. 17, the initial melt responded to a strain rate of 0.1 sec-1 by providing the Newtonian value and not the shear-thinned value for that rate indicates metastability of the initial state, i.e. a phenomenon reminiscent of glasses in a state of thermodynamic instability with respect to their phase transition, such as water which can be frozen below the freezing temperature to become metastable, in a frozen glassy state with no crystals, or glassy polymer produced by quenching through Tg (see Kovacs's work in Ref. [71}). 2. A second conclusion would challenge the first one. Suppose that the initial viscosity at the rate 0.1 sec-1 is the real Newtonian value, but that, as the melt has been deformed at a rate faster than the reptation time for a duration long enough, a DIFFERENT MELT is produced, with different bond-interaction characteristics (let's call it a different entanglement state), then the application of the 0.1 sec-1 shear strain rate to THAT new melt would result in a new steady state viscosity value (3,500 Pa-s). Thus, based on the second conclusion, a melt can have several steady states at the same temperature and strain rate, depending on its state of entanglement, and it appears that shear can modify the entanglement state at will: this is the basis of “shear-refinement”. If entanglements can be kept in an unstable state long enough, it is possible to produce "disentangled polymers" that, in terms of viscosity decrease are attractive commercial 66 “grades”. The challenging question is how to retain in a metastable state (that we could control) the lower viscosity melt produced at the end of a transient "treatment' and then recover the original properties after processing. Another conclusion seems to emerge from these experiments: shear-thinning might just become time dependent, under certain strain rate conditions. In other words, what ever causes shear-thinning produces a melt state that is not stable under certain conditions. The transient behavior observed would be the reflection of that time dependence of shear-thinning, and the molecular motions involved in shear-thinning and in the transient decay might be closely related, if not identical. Figure 19, shows the effect of annealing the melt in the middle of a transient decay to see if the melt would reconstruct its internal structure to provide the original viscosity after annealing. The shear rate history shown in the box of Fig. 19a was applied to the melt (the temperature was 215 oC). The difference with Fig. 17 is that the melt was rested (un-sheared) for 30 minutes, at the end of the transient decay induced by shear rate 1 sec-1. Then the melt was sheared with rate 0.1 sec-1. Figure 19b shows the variation of viscosity with time, Fig. 19c shows the variation of normal force, and Fig. 19d presents details of (c) around the zero normal force line. It is clear (Fig. 19b) that the melt nearly re-gained its original viscosity after the time of rest when no mechanical deformation was applied. This is evidence that the equilibrium state for strain rate 0.1 sec-1 was the original viscosity. The normal force was almost zero for the initial strain rate (Fig. 19c, left curve), went up and decayed when the strain rate was changed to 1 sec-1, and was zero for the second application of 0.1 sec-1 strain rate. Zooming on the zero line region of box (c) shows that normal force decay during transient 67 behavior actually converged to a small negative value (step 2 curve), but that after annealing (step 4 curve), the normal force had returned to zero (a) (b) (c) (d) Fig. 19 Same type of experiments as in Fig. 18 but with a different mechanical history. T is here 215 oC. See text for details To check whether the small tensile force on the melt in steady state conditions (Fig. 19d step 2 curve) was also observed for the strain rates of Fig. 18, Fig. 20 shows the variation of the normal force with time, confirming that the steady state melt obtained after application of 68 the 1 sec-1 strain rate was, indeed, under a small tension. Switching the strain rate to a lower value released the tension towards zero. The phenomenon seems real, repeatable and requires an explanation (see discussion). Fig. 20 This normal force vs time history applies to the deformation described in Fig. 18.A close-up view shows a small attractive normal force in the melt (~ -5g) obtained in the steady state for the 1 sec-1 strain rate (step 2 curve). At each “instantaneous” step strain rate decrease (step 3 and 4 curves ) a small initial negative jump of the normal force occured before normal force relaxed back towards zero. Each change of strain rate resulted in another small elastic tension of the melt. 69 Fig. 21 Same type of experiments as in Fig. 18. The successive strain rates are indicated in the insert. T = 220 oC Figure 21 is another exhibition of the difficulty of using classical rheological tools (and the classical understanding of the concept of entanglements) to characterize simple rheological experiments. In this set of conditions, very similar to those of Fig. 17, the melt was deformed first at very low strain rate, at 0.001 sec-1, and then at 0.01 sec-1, both for 15 min, before the initial conditions set in Fig. 17 were reached (0.1 sec-1 for 15 min followed by 1 sec-1). The longer stay at 220 oC at very low shear rate magnifies the hump discussed earlier to the extent that it now looks like a true partial recovery of the viscosity at one point. After the instantaneous drop of viscosity due to shear-thinning, at the switch of rate between 0.1 and 1, the melt viscosity droped sharply at first, then hesitated between increasing or decreasing, with 70 decreasing finally prevailing. The hump was no longer barely visible, it was a full feature of the melt’s rheological behavior (incidently, another small hump is also visible in step 2). 2,2 Pure Rotation followed by Frequency Sweep. Experiments of Type 5. Figure 22 shows the result of an experiment of type 5, a viscometry at two shear rates followed by a frequency sweep to characterize the state of the melt at the end. The strain rate at 0.1 sec-1 was performed as a first step to establish a baseline for “the un-sheared melt” and compare with the viscosity obtained from the frequency sweep under similar conditions. Figure 22a shows the viscosity vs time history, including the viscosity during the frequency sweep. The viscosity was slightly transient in step 1, but the transient decay was much more pronounced for step 2. Notice that we waited 4,500 sec before triggering the frequency sweep, i.e. we waited for steady state to be well established under these strain rate and temperature conditions (215 oC and 1 sec-1). Figures 22 b,c and d compare frequency sweeps for the “unsheeare melt” (the melt before it was submitted to viscometry at 1 sec-1 strain rate), and the melt after it had reached steady state, which we call "sheared" in these graphs. Frequency sweeps were done for both melts in the linear viscoelastic range ( 2% strain). Graph 22b compares the complex moduli. Graph 22c plots G' and G" vs w for both the un-sheared (top) and sheared melts. Graph 22d refers to (G’/G*)2 vs log w, showing identical stored elasticity up to the cross-over point (G’/G*)2=0.5), but a more elastic sheared-melt at higher frequencies, which might be surprising in view of the fact that both moduli G’(w) and G”(w) (Fig. 22c) were substantially reduced for the sheared melt. 71 (a) (b) (c) (d) Fig. 22 The graphs apply to an experiment of type 5, pure viscometry at constant rate immediately followed by a frequency sweep in the linear viscoelastic range. See text for details In Fig. 22b, for the un-sheared melt, the extrapolated value of G* was 800 Pa for w = 0.1 rad/s giving a complex viscosity of 8,000 Pa-s, agreeing with what we obtained in pure viscometry (top left in Fig. 22a). However, for w= 1 rad/s the value of G* was 6,000 Pa (giving a viscosity of 6,000 Pa-s), which was the initial value obtained for strain rate 1 sec-1 in pure 72 viscometry (explaining the initial instantaneous decrease of viscosity in Fig. 22a at the change of rate between 0.1 and 1 sec-1). However, a big difference between pure viscometry and dynamic viscosity measurement is that there is no transient, no time dependence, created by the oscillation at this small strain (2%), and, therefore, we were unable to obtain the equivalent of the steady state viscosity value arrived at under strain rate 1 sec-1 (i.e. 354 Pa-s). We will show below (Figs. 27, 28), for this same polymer melt, that it waspossible to create a transient viscosity in pure oscillating conditions, by just increasing the strain % amplitude and the frequency at which we operated. Figure 22c shows that the magnitude of the modulus at the cross-over was18 times smaller for the sheared melt; the shape of the G’(w) and G”(w) were also very different (Fig. 22c), yet the cross-over point seems to be the same, ~ 71 rad/s (Figs. 22c and d). In Fig. 22c we attempted to determine the Maxwell’s time (1/wo) for both the sheared and un-sheared melts. It is not certain that this procedure makes any sense at all, since the respective slopes of G' vs w and G" vs w were not 2 and 1, as they should be according to the Maxwell’s model. Nevertheless, it is seen that the extrapolated cross-over-points are the same for both the sheared and un-sheared melts and about 2 times the cross-over value wx. This result questions the use of the cross-over point to depict the melt characteristics. One might argue that artifacts, such as slip or surface fracture might have occurred in the case of the sheared melt during transient viscometry (Fig. 22a, step 2 curve). Figure 22d suggests otherwise. Although (G'/G*)2 remained the same for both sheared and un-sheared melt at low w, which could go along with a surface effect explanation, the fact that at higher w the ratio (G'/G*)2 was greater for the sheared melt (the round dots) is a remarkable proof that there was something rheological going on, and that it 73 cannot be due to a surface or a slip effect (which would maintain the ratio (G’/G*)2 constant, not increase it). Actually, the upturn of (G'/G*)2 at high w implies a more pseudo-plastic melt (it shear-thins more), which is also demonstrated in Fig. 22b by G* becoming nearly constant for the sheared-melt beyond w ~ 10 ra/s whereas the modulus of the un-sheared melt continues to rise with w (viscosity is G*/w). Fig. 23 G’/w vs w for the sheared and unsheared LLDPE melt at T=215 oC. The unsheared melt is the “normal” frequency sweep for a melt without prior shear history. The sheared melt is that described in Fig. 22a, prior to the subsequent frequency sweep. Fig. 23 is a classical plot of (G’/w) vs w for the samples in Fig. 22. For a “normal” melt, i.e. responding at low w according to the Maxwell’s equations (see discussion on this subject in [2]) the value of w at the maximum of G'/w should be the inverse of the terminal time (wo=1/to), the same as that which is found at the cross-over. It is expected that the sheared melt would have a higher wo (a smaller terminal time) than the un-sheared melt, since its viscosity is much lower, but we find the opposite, wo for the sheared melt is 3 times lower 74 than that of the un-sheared one. Also, the value found for wo, from the maximum of G’/w, does not agree with the value found from extrapolation of the slopes of G’ and G” in Fig. 22c, nor with wx. The plot in Fig. 23 does not make any sense, or, perhaps, it illustrates the limitations of the traditional approach when analyzing melts which have been submitted to non-linear mechanical histories. Yet, one can hardly describe the sheared melt of Fig. 23 as a special nonlinnea melt, since it was just sheared at 1 sec-1 for a long time in order to reach its steady state. A GPC measurement conducted on the resin frozen from the steady state did not reveal any apparent difference in molecular weight or its distribution with the original melt. The conclusion seems to point towards the formation of a differently structured melt, presenting different rheological properties. 2,3 Experiments of Type 4 on Melts with Prior Mechanical History. We have previously reported extensively that shear-refinement modifies the rheological properties of melts [28-54]. Obviously, when one has succeeded preserving in a pellet form the viscosity drop observed during shear-refinement processing, one can mold disks from the treated pellets and perform a type 4 (pure viscometry) experiment and compare the results obtained with those from a reference melt. This is done in Fig. 24. Alternatively, the treated melt (from compression-molded treated pellets), which we designate “mechanically disentangled” in the following figures, can be analyzed by a simple frequency sweep done in the linear region, so that there is no possibility of any artifact or rheological effect due to the application of larger strain. The frequency sweep of such a disentangled melt is compared with that of a virgin melt in Fig. 25, studied under identical conditions. 75 Figure 24 compares the transient behavior obtained in pure viscometry (T=190 oC 1 sec-1) for an un-sheared melt (round dots) and a pre-sheared melt corresponding to a disentanglement treatment (squares). The resin is the same LLDPE as before. It is clear from this figure that there was no transient decay for the disentangled sample. The viscosity "hesitated" between decaying and rising. This phenomenon of oscillation is the result of the recursive character of the effect of stress on the relaxation times, as discussed in previous sections. When stress decreases, activation energy increases, slowing down the process of decay. When a melt is successfully brought out of equilibrium, such as in the case of a disentangled melt made out of treated pellets, the relaxation time spectrum is modified (their stress dependence of the activation energies is not the same), the dynamics of deformation is disturbed, and, as in Fig. 24, melt viscosity appears to remain steady at its low value, as if the new entanglement state was quasi-stable. This quasi-stability of the melt is due to a balance between two opposite drives, one leading to a time dependent shear-thinning transient controlled by the melt elasticity, and the other by the kinetics of return to a thermodynamics equilibrium state of the interactions between the conformers. The treatment defines the out of equilibrium initial conditions that governs the kinetics of “re-entanglement”, as well as the rheological properties of the treated melt, under linear viscoelastic testing mode. 76 Fig. 24 Comparison of viscosity vs time for a mechanically disentangled melt (with the apparatus of Fig. 5b) and a virgin (unsheared) melt with no prior shear history. The same testing conditions (strain rate, temperature) are used for the two samples. It is crucial to understand the stability of a disentangled melt from a theoretical point of view, not simply because it will reveal the true nature of entanglement, but also for commercial perspectives, in order to put shear-refinement benefits under control. The understanding of the stability of disentangled melt refers to the stress and temperature conditions that result in its return to equilibrium, and the prediction of its induction time, i.e. how long it can remain at a low viscosity before returning to equilibrium. An example of re-entanglement triggered by prolonged shear is given in Fig. 25: Engage 8180 T=140 oC M2: 60 RPM 22 24 26 28 30 32 34 36 38 40 0 200 400 600 800 1000 1200 1400 1600 1800 Tor qu eAm p77 Fig. 25 A shear-refined LLDPE was sheared at 60 RPM, T=140oC. The torque (in Amp) was stable at the low initial value of 26-25 Amp for 500 sec, then, without any change of any input (RPM, temperature), it suddenly rose to another value, 34 Amp, which is the reference torque at that temperature. The shearing conditions (60 RPM, T= 140 oC) are associated with the induction time to trigger recovery of a more stable melt (other conditions would result in a different induction time). The 4 times initial viscosity difference seen in Fig. 24 between reference and disentangled samples is not simply due to a change of the density of entanglements, but also due to some collateral damage to the chain molecular weight during the disentanglement treatment, as observed by GPC. We show in Fig. 26 the frequency sweep for both melts, after correction for the Mw change as decribed below. There still remains an important viscosity decrease, due to disentanglement. 78 Fig. 26 Comparison of (G’/G*)2 vs w for a Virgin/unsheared melt and a mechanically disentangled melt (the data have been corrected to account for the change of Mw. See text). In the case of the treated LLDPE presented in Fig. 24, some collateral damage was due to the shear-refinement process, resulting in a decrease of Mw. The data must be corrected on both the horizontal and vertical scale to account for a change of Mw. The x-axis is corrected by multiplying w by the ratio of (Mw/Mwref)3.4 , assumed to be the amount of viscosity drop corresponding to a Mw change. A small correction on the y-axis is neglected. The net result of the correction on the x-axis (log scale) is the shifting of the raw data to the left. The resulting curves are shown in Fig. 26. It is clear that the shear-refinement process produced an important modification of the rheological behavior, even after correction for the Mw change. One sees, in particular, a substantial increase of wx. The situation is very similar to that depicted in Fig. 10 for a PS melt “treated” at high strain, high w in a dynamic rheometer. The Melt Flow Index of the treated pellets can be determined and compared to the virgin reference pellets. After 79 correction of the results for the Mw reduction, 55% MFI increase remained for the treated pellets. There is no possibility of attributing this lasting viscosity reduction to an artifact, surface slippage, or degradation. The analogy between Figure 10 and Fig. 26 is striking. Fig. 10 is for a melt submitted to a non-linear dynamic treatment in a dynamic rheometer, Fig. 26 relates to a resin submitted to a shear-refinement treatment. Other interpretations than those proposed by Freidrich et al [60, 61] must be found to explain the new results (see the Discussion section) 2,4 Transients created in dynamic conditions by increase of strain. We saw in section 2.1 that step strain rate viscometry can cause transients resulting from the application of strain rates greater than certain values, yielding very large decreases of viscosity, from 8500 to 55 Pa-s in the case of LLDPE in Fig. 14. We also confirmed in section 2.2 (Fig. 22a and b) a common observation of rheology, the correspondence between viscosity values obtained from pure viscometry and dynamic viscosity measurements, except for the absence of transient behavior in the case of dynamic results. The difference was attributed to working at low strain, in the linear visco-elastic region. Figures 27 and 28 summarize schematically the experimental procedure to create a transient with a dynamic rheometer, avoiding melt fracture. In the figures, a parallel plate configuration was used, but a cone and plate combination is also a valid option, providing essentially the same results. The resin was the same LLDPE, the temperature 155 oC, the rheometer, the ARES from Rheometrics. The gap was chosen between 1.2 and 2 mm. 80 Fig. 27 Frequency and strain % history (plotted against time) for the data analyzed in Fig. 28 81 Fig. 28 Dynamic viscosity vs time for the 3 steps of Fig. 27a Figures 27a and b describe the frequency and % strain history. Figure 28 plots dynamic viscosity against time. The first and last segment, called “initial” and “recovery” in Fig. 27 represent the baseline, the value of viscosity under linear viscoelastic conditions, i.e under very low frequency and amplitude (here 1 rad/s, 1% strain). The so-called « treatment zone » in Figs 27 and 28 was initiated by a jump of the frequency, from 1 to 47 rad/s, which created, in Fig. 28, an instantaneous drop of viscosity from 57,000 Pa-s to 10,000 Pa-s, due to shearthinnning The jump was then followed by a gradual stepwise increase of the strain amplitude, from 1% to 25%. Figure 28 shows that for the first 2 steps of increase of strain, the viscosity held constant at 10,000 Pa-s, its shear-thinned value at that temperature and frequency, but that starting at strain = 13 %, the viscosity started to become transient declining from 10,000 to a steady state value of 3,100 Pa-s. This operation took about 25 min. Then the frequency and 82 strain amplitude were changed back to their low values of the linear range (1%, 1 rad/s), and one observes an instantaneous partial loss of the effect of shear-thinning combined with strain softening, i.e. the viscosity jumped back to 38,000 Pa-s. Recovery of viscosity occured over the following 20 minutes, viscosity increasing slowly and finally regaining its original Newtonian value, 57,000 Pa-s. In other words, the state of the melt produced by the transient treatment (let’s call it disentanglement to simplify) was unstable when the energy that produced the transient behavior was released: this is why viscosity slowly increased in time and returned back to the original value for the melt. Nevertheless, it took 20 minutes for recovery, and this time is 60 times longer than the terminal time at that temperature, making it possible to exploit the benefits of a smaller viscosity during recovery if the melt were to be processed at that stage. One can define the viscosity benefit by comparing the initial Newtonian viscosity (57,000) and the Newtonian viscosity before recovery after the shearthinnnin elastic loss (38,000), a ratio of 1.5 in this treatment (« 50% disentanglement »). Notice that a processor could still benefit from shear-thinning of the treated resin (Fig. 28), and work under much greater viscosity reduction (3,100 Pa-s versus 57,000 Pa-s, an improvement of over 1,700 % !). The experimental procedure described in Fig. 27 has several variations: the time duration between strain amplitude step-ups can vary, the strain amplitude increment itself can be changed as can the temperature of the melt and the frequency of operation during treatment. The treatment could also be done differently, by increasing at low frequency the strain to 25%, say, and step wisely increase the frequency from 1 rad/s to 47 rad/s. All these changes contribute to the final % disentanglement, which can be as small as 20%, to as large as 83 3,000%. The wrong procedure can also produce artifacts or surface effects,. as will be explained in the discussion section of the paper. In our interpretation of the results, strain softening, known to decrease the modulus at higher strain, combines with shear-thinning due to the effect of frequency to render the melt unstable in its original entanglement network configuration; thus the transient behavior occurs. In a step strain experiment conducted in the molten state, a softening factor is defined, h = G(strain)/G(LVE), where G(strain) is the melt modulus for a given strain and G(LVE) refers to the strain independent Linear Viscoelastic Value (h <1). At low strain, the modulus is only time dependent, and an increase of strain produces an increase of stress proportionally. Pure viscometry experiments have demonstrated that above certain strain rates, corresponding to a certain stress level, a transient decay towards steady state released the elastic energy stored during initialization. It was suggested earlier in this paper that the dynamics of this process could be viewed as a recursive effect of the stress on relaxation times (also see the discussion).. As stress continues to grow, due to increased strain, strain softening is the first revealing sign of the modification of the structure due to the stress dependence of the relaxation time. Figure 28 reveals that under dynamic conditions, the softening factor h can become time dependent, which translates into a transient behavior. The advantage of producing transient behavior with a dynamic viscometer is that G' and G" become time dependent, so it is possible to analyze these curves individually and also follow how (G'/G*)2 varies during transient stress decay. The transient decay can be produced in-situ in the rheometer, and a frequency sweep performed before the transient and after it, allowing an easy way to analyze the differences due to the stay in the non-linear regime. This type of experiments, of type 2 in our definition (FTF), allows to analyze the influence of strain and frequency during time sweep (“the treatment”). 84 3. Dynamic Experiments of Type 2 (FS-TS-FS) on PC The resin was the Makrolon PC with Mw =32,000 described in section 3 “Materials”, with the corresponding procedure to dry it and running the rheological tests. A typical experiment was as follows: Step1 was a frequency sweep from 0.1 to 40 Hz at 275 oC, with 5% strain. The test lasted about 120 sec (squares). In step 2, a time sweep done at the same temperature at w=0.1 Hz, 5% strain was done for approximately 1,000 sec (dots curve). For step 3 (triangle curve), we repeated step 1, i.e. we reran a frequency sweep using the same conditions, from 0.1 Hz to 40 Hz, 5% strain T=275oC. Fig. 29 is a plot of the complex viscosity in Pa-s versus “consolidated time”, meaning the global time, starting from the beginning of the first frequency sweep, step1. In this section, we vary the conditions of strain % and/or frequency during step2, and examine the difference between the frequency sweeps. We successively study the effect of strain % at constant low angular frequency (w = 0.1 Hz), and of frequency at constant strain %. In the next section, we also vary the temperature at which the various steps are conducted. 3.1 Effect of strain at constant low frequency (0.1 Hz). One of the purposes for using a low frequency for the oscillation was to avoid any possible artifact. The resin chosen was a “virgin” PC, provided by the manufacturer as presenting a “mild thermo-mechanical history” due to its extrusion conditions after the reactor’s phase. We purposely chose this resin in this section of the article because of this 85 particular feature. The reasons will become apparent as we study the effect of the various parameters. For the present purpose, let’s categorize this melt as “mildly disentangled” due to its thermal-mechanical history. We will present results of increasing strain during step 2, all other variables, including the time of time sweep, remaining the same. 3.1.1 5% strain Fig. 29 is a consolidated plot of the 3 steps. For step 1 one sees that viscosity increased a little bit at the beginning (the low w values of the frequency sweep), but that increasing frequency reversed the tendency, showing the classical display of shearthinnning viscosity drops by about 400 Pa-s. In step 2, one sees that viscosity started at around 1,050 Pa-s-which is incidentally the extrapolated value for the very beginning of the black square curve, corresponding to the low w range of the frequency sweep, then continued to rise to reach a plateau value of 1,200 Pa-s. Viscosity gained 275 Pa-s in step 2, i.e. 30% of its initial value. For step 3, shear-thinning started from the beginning of the frequency sweep, no longer did we observe a time dependent behavior at low w; viscosity decreased as w increased to reach approximately the same viscosity as for step1 for 40 Hz. The conditions used during the time sweep were extremely “soft”, in terms of energy input. This corresponds to letting the melt “anneal”, and “taking pictures” of its evolution, as G’ and G” are measured simultaneously. Since viscosity increased during 86 step 2, no surface artifact was possible under those very soft conditions [60, 61]; thus we conclude that the true steady state value of viscosity, 1,200 Pa-s, was only obtained after 15 minutes of “annealing time”, i.e for a time 210,000 greater than the value of the terminal time responsible for molecular relaxation at this elevated temperature (to=0.0055 sec). We speculate that the original melt was in a non-equilibrium state, not because the molecular motions do not have time to occur (like for a glass below Tg), but because “the entanglement network” had been brought out of equilibrium by a previous thermal-mechanical history that created the situation. Annealing the melt let the entanglement network parameters return to their thermodynamic value, re-adjusting along the “framework” of the molecular motions and instantaneously reaching a new steady state value (in time to), as return to equilibrium of the network proceeded. All these concepts are used here without precise definition, as a way to introduce them, and with the knowledge that a quantitative description will be required. 87 Fig. 29 Dynamic viscosity vs time. 3 steps: Frequency Sweep-Time sweep (0.1 Hz, 5% strain)-Frequency Sweep. PC-2. T=275 oC 88 Fig. 30 Same data as in Fig. 29 but plotted against w Fig. 30 is a traditional log-log viscosity-w graph for the same data presented in Fig. 29. The lower curve corresponds to step 1, the upper curve to step 3. Step 2 occured at constant w=0.1 and is the short vertical segment. As already revealed in Fig. 29, the initial viscosity at the beginning of step 2 was higher than the original viscosity at the same frequency on the lower curve; this is because the initial melt had a “lower entanglement” level, due to a previous thermo-mechanical treatment, and that “reentangglement occurred during the step 1 frequency sweep. In other words, the melt entanglement network was initially in a disentangled state produced by a previous shearrefinnemen treatment, and some recovery already took place during step 1 resulting in a higher viscosity at the beginning of step 2. It is interesting to point out that, although 89 higher w values shear-thined the step 1 melt, as clearly evidenced for the square curve in Fig. 29 by a downturn of viscosity, some re-organization of the melt occurred, at the same time, to render its entanglement state closer to its thermodynamic equilibrium. This observation proves that one can obtain a frequency sweep curve but be uncertain that it represents the true stable state of the melt. Classical views and equations describe a melt rheology as if it was in equilibrium. Figure 30 provides two different frequency sweeps of the same polymer, under the same rheological conditions, the same temperature, proving that the equations of rheology must incorporate the state of entanglement of the melt in its formulation. The next figure explores this issue. Figure. 31 applies to the same data as those of Figs. 29 and 30. G”(w) is plotted vs G’(w) for the two frequency sweeps, step 1 (squares) and step 3 (dots). Fig. 31 G”(w) vs G’(w) for step 1 and step 3. Same data as in Fig. 29 90 As explained in part I of this series [2], in traditional visco-elastic theories that express G' and G" as a function of a spectrum of relaxation times, it is represented that G' and G" both scale with the plateau modulus GoN, which itself can be expressed as a function of rT/Me where Me is the molecular weight between entanglements. As pointed out in the Introduction, if Me increases (disentanglement) or decreases (re-entanglement) as a function of annealing, or as a function of the treatment conditions, and the spectrum of relaxation times remains unchanged, then a plot of G" vs G' on a log-log scale should show a shift of G’ and G” by the same amount. In Fig. 31, the data points appear to be shifted so that they remain on the same line. The data points are numbered 1, 2, 3 etc. The same number applies to the same frequency, 1r and 1b, which should be compared, or 2r and 2b, etc. One sees that the squares and dots were shifted to almost stay on the same curve. The problem is that the slope of that curve is 0.57, not 1, so that the amount of shift on the horizontal and vertical axes are different, a significant departure from a classical change of Me. What is also important to notice is the fact that the squares and dots curves superpose as a result of annealing, i.e. that the effect of re-equilibration of the network of entanglements resulted in the same horizontal and vertical shifting as the effect of frequency on G’(w) and G”(w). When this is the case (we will see later that it is not always true), the return to the equilibrium state of the entanglement network occurs without any modification of the network framework. This is the simplest kinetics to analyze, all changes being due to the re-orientation of the entanglement framework. Incidentally, as already mentioned, and shown in Fig. 31, the effect of this re-orientation on G’ and G” seems to be similar to that described by shear-thinning as a result of changing frequency. 91 3.1.2 20% strain In this section, we repeated the same type of experiments (FS=step 1, TS=step 2, FS=step 3) except that the "annealing treatment" occurred under a larger strain, 20% instead of 5% (at the same low frequency of 0.1 Hz and the same temperature 275 oC). The initial melt was the one produced at the end of step 3 in the previous section. The same overall behavior was observed, but the effect of increasing strain in the annealing step triggered interesting differences. (a) (b) Fig. 32 Fig. 32a and 32b should be compared with Figs. 29 and 30, respectively. The initial state of the melt before the 1st frequency sweep (black square curves) corresponds to that obtained after step 3 of Fig. 29. The dots curve correspond to a time sweep under a strain amplitude of 20% . The triangles are for step3, the 2nd frequency sweep. 92 In Fig. 32a, viscosity at the beginning of step 2 started at almost the same value found for the same frequency (0.1 Hz, first data point) of the step1 curve, indicating that the frequency sweep producing shear-thinning did not occur simultaneously with a modification of the state of the entanglement network due to annealing. This is in line with the fact that the melt of Fig. 29 appeared stable at the end of step 2. Yet, in Fig. 32a, the 15 min time sweep at 20% strain did produce a new instability of the melt, visible by the viscosity which starts to rise again towards a new stable value of 1,575 Pa-s. Also notice in Fig. 32b that, contrary to what is observed in Fig. 30, for which the annealing treatment was done under 5% strain, the 20% annealing treatment produced a shift that seemed to affect equally the low frequency and high frequency regions (compare Figs. 30 and 32b in the high w region). 93 Fig. 33 Comparing the storage and loss modulus vs w for step 1 (1st frequency sweep) and step 3, performed after 15 min of time sweep treatment at 0.1 Hz and 20% strain. The result of “annealing” under 20% strain was to shift the moduli upward. The amount of shift was different for G’ and G” but remained constant as w increased. Figure 33 shows G' and G" versus the radial frequency on a log-log scale. This is a classical representation of the data, useful to determine the "cross-over" point, the value for which G'=G". All G'(w) and G"(w) for step 3 melt (after treatment) are in dots and up triangles, located above the G' and G" for step 1 melt. The cross-over frequency for the more viscous melt was lower (181 vs 231), which makes sense for a stiffer melt, but the modulus was lower (0.231 MPa vs 0.268 MPa), which does not make sense if one would assign the increase of viscosity to an increase of the entanglement density (Me decreases). Traditional theories consider the cross-over point a characteristic parameter, the transitional change between a viscous and elastic behavior. The cross-over is considered the reciprocal of the terminal relaxation time. Figure 33 suggests that classical interpretations of melt behavior are too simplistic and not necessarily helpful to understand phenomena related to entanglement instability induced by mechanical treatment. Figure 34 provides some preliminary insight of our new concepts proposed to understand visco-elastic deformation of polymer melts, in particular to separate out what relates to changes occurring to the entanglement network. In this approach [66, 67, 70, 72], the analysis of the variation of (G'/G*)2 versus w ( or G*) is assumed to be related to the number of active strands (bearing stress by a mechanism of conformation statistics activation), whereas (1-(G'/G*)2) would scale with the amount of relaxation-diffusion 94 taking place simultaneously, and would require a stress computed from such diffusion mechanism. Polymers are assumed to have a dual-phase structure not only locally (to characterize the coupling between adjacent conformers), but also globally, induced by the interpenetration of the macro-coils [72 ], which produces the entanglement network phase. The mechanism(s) of activation and relaxation of strands is an interplay between the local dual structure due to the conformers interaction and the global dual structure due to the existence of the entanglement phase, which can itself be sketched as a channeling pipeline deformable network. More and more strands are activated as w is increased. Depending on molecular weight, there is a maximum of active strands that can be activated. The deformation of the entanglement network is described by the number of strands that can be activated, and re-oriented towards the flow direction by relaxdifffusio after activation has occurred. The deformation of the strands themselves involves a modification of the local dual structure of the conformer interaction, the more elongated trans-conformers being favored in the direction of flow. The viscous regime deformation is dominated by the variation of the number of active strands as a function of w, strain rate, T and P, with the simultaneous orientation of the entanglement network dual phase in the direction of flow resulting from the concomitant stress relaxationdifffusio mechanism. Molecular weight affects the amount of entanglement phase available, and therefore increases the amount of orientation possible of the entanglement phase, which, in essence, explains the spreading of the width of the rubbery plateau modulus when molecular weight increases. When the orientation of the entanglement phase is completed (ending the “entropic character” of the strand network deformation), the local conformational changes become the dominant mechanism, visible as we 95 approach the transition zone. These concepts will be elaborated in the discussion, but having been briefly presented here will allow their use in the description of the figures, as compared to a classical description. Fig.34 Comparison of (G’/G*)2 vs w for step 1 and step 3 after time sweep at T=275oC with 0.1 Hz and 20% strain In Fig. 34 one sees that the net result of the time sweep “treatment” was to increase, at each w, the number of activated strands (the dots correspond to step 3). This is due to a re-orientation of the existing network of strands during the time sweep step because of the larger strain deformation demand (20 % instead of 5%). All of this occured at T= 275 oC, for which the terminal relaxation time was about 5 ms (1/wx), but the molecular re-arrangements were 200,000 times faster than a re-alignment of the 96 entanglement network responsible for the stability of the rheological parameters in time. We conclude that the original melt had an initial oriented entanglement network structure, corresponding to a metastable local conformer structure equivalent to a larger free volume content, thus a lower viscosity. As a thermodynamically more stable entanglement network was re-established-favored by an increase of strain % in step 2-the local dual conformer interaction structure lost some free volume, resulting in an increase of viscosity. Fig. 35 (G’/G*)2 (a) and Normal Force (b) vs time for the data of Fig. 32 Figure 35 (a) shows that the number of activated strands (G'/G*)2 increased as w increases in a frequency sweep. The annealing treatment was done under conditions of deformation (at 0.1 Hz, 20% strain) that do not activate the network of strands (G'/G*)2 was almost zero), yet, as we have seen in Fig. 34, there was a modification of the melt entanglement structure, yielding to a step 3 melt showing more activated strands during a new frequency sweep. This is due to the interactive character between the local structure 97 of the conformers’ interaction and the definition of the entanglement phase itself [72] In Fig. 35b the y-variable is now the normal force. The analogy with Fig. 35a is striking. Also notice that during step 2, there was a tendency for the normal force to decrease slightly, to become negative. This same observation was made for the sheared LLDPE melt after pure rotation at high strain (Figs 19d, 20). In summary, shearing the melt at 0.1 Hz at T=275 oC under 20% strain does not involve enough energy input to activate the entanglement network, but it produces enough strain in the strands to modify the local conformational structure which interactively defines the orientation of the entanglement network. The best sign that this is the case appears to be the increase of the tensile force (negative normal force) acting perpendicular to the shearing direction. This tendency will be even more visible in the next section, where the strain was increased to 500% during step 2. 3.1.3 500% strain We now study the same melt (at the end of step 3 of the previous section) and perform the same type of successive step 1, step 2 and step 3 at T=275 oC, with a time sweep treatment under 500% strain, still at 0.1 Hz. A large strain amplitude forces the melt to be deformed faster, 100 times faster than it was when it was deformed at 5%. Figure 36 shows that under such conditions of large deformation, the melt viscosity decreased with time during the time sweep treatment. 98 (a) (b) Fig. 36 Same conditions as in Fig. 32 but the time sweep (step 2) is done with 500% strain ( 0.1 Hz). At the beginning of step 2 (dots), in Fig. 36, viscosity had a lower value than at the beginning of step 1 (squares). There was no frequency change between these two points, only a strain amplitude change between 5 % to 500%. This illustrates strain softening, as is well demonstrated and known in step strain experiments done at high strain. The reverse of strain softening triggered the small viscosity increase observed between the end of step 2 (dots) and the beginning of step 3 (triangles) in Fig. 36a. This small viscosity "jump" is like the spontaneous increase of viscosity observed upon suddenly decreasing frequency from a higher value to a lower one. The drop of viscosity in step 2 is quite significant, from 1,575 Pa-s (beginning) to 864 Pa-s (steady state), these 2 values being extrapolated from a regression fit of the available data. This time dependence of viscosity is reminiscent of a transient behavior in a viscometry test at constant strain rate, here triggered by an increase of strain. 99 Figure 36b should be compared with Figs. 32b and 30. The increase of strain to 500% during the time sweep step produced a step 3 melt with lower viscosity, even in the Newtonian region, demonstrating that a new entanglement state was generated by the time sweep “treatment”. Figure 36b shows that the new entangled melt had a lower viscosity at all frequencies. The frequency sweep shown as the lower curve in Fig. 36b (step 3) is, in fact, very similar to the frequency sweep for step 1 in Fig. 30, corresponding to the initial melt, which we characterized as a melt with a thermalmechaanica history. The 500% step 2 treatment in the rheometer induced similar modification to the entanglement network (a) (b) 100 (c) (d) Fig. 37 Analysis of the results for the 3 step FS-TS-FS experiment with step 2 corresponding to 0.1 Hz 500 % strain. See text. Figure 37a shows the data from Fig. 36, plotted as in Fig. 34. It is clear that Fig. 37a shows the reverse of that in Fig. 34, as expected from the reversal of the viscosity change during step 2. Using the language introduced in the previous section to interpret visco-elasticity, the number of activated strands of the entanglement network was less for melt 3 (the dots in Fig. 37a) than for melt 1 (the squares), at a given frequency. The time sweep treatment reduced the number of activated strands as a result of the re-structuration of the local dual conformer interactions. Figure 37b shows that both G’ and G” were lowered for step 3, at each w, the respective curves appearing shifted on the vertical axis. Fig. 37c denies the objectivity of such shifting attempt procedure (also see Ref. [2]). In this figure, we plot the ratio (G’3/G’1) and (G”3/G”1), each established at the same w, versus w. The subscript 3 and 1 refers to step 3 and step 1 data points. There are two important conclusions from this plot: 101 -the time sweep treatment affects the storage modulus G’ much more than the loss modulus, G”; this would contradict any explanation of the time sweep viscosity drop due to a surface effect [60, 61], for which G’ and G” would be modified identically. -the ratios are frequency dependent, being more pronounced in the Newtonian region. Besides, the ratio for the storage moduli varies faster with frequency than the ratio for the loss moduli. This is confirmed in Fig. 37d, a plot of the ratio of (G’/G*)2 with w for step 3 and 1, where it is seen that the loss of the stored elasticity, as high as 35% at low w, quickly plateaus to 12% beyond w=25 rad/s. It is conceivable that the entanglement state induced by the time sweep treatment (step 2) is thermodynamically instable, and that the melt’s return to a more stable state is accelerated by the increased stress generated by the increased w during the step 3 frequency sweep. This decrease by the stress of the relaxation times of the entanglement network has already been mentioned earlier in the case of pure viscometry at constant strain rate (section 2.2 of RESULTS). 102 Fig. 38 Normal Force is plotted as a function of the cumulative time, showing their respective variation for step 1 (black squares), step 2 (red dots) and step 3 (blue triangles). Time sweep is done under the following conditions: T= 275 oC, 0.1 Hz 500% strain. The graph of normal force vs time in Fig. 38 should be compared with the graph in Fig. 35b for which step 2 was done at 20% strain. The same behavior was observed for the frequency sweeps, but what is interesting is the oscillating decay of the normal force observed for step 2. We observed in Fig. 35b, during step 2 under 20%, a tendency of the normal force to become negative, indicative of a pulling melt, but the magnitude of the effect is much more pronounced in Fig. 38, with a persistence of the oscillating character in the negative range. Also note in Fig. 38, at the end of the time sweep, the jump back of the normal force from -10 g to 0 corresponding to a release of the strain amplitude from 500% to 5%. Additionally, normal force at the beginning of step 2 was the same as that at the end of step 1. This might be strange, in view of the difference in frequency between the two points, 40 Hz for the last point of step 1 (with 5% of strain) and 0.1 Hz for the 1st point of step 2 (with 500% strain). But, as shown above, if a release of strain from 500% 103 to 5%, at 0.1 Hz, results in a differential of normal force by 10 g, it is expected that such a build up of normal force would compensate for the decrease of frequency, when strain increases from 5% to 500% from step 1 to step 2: the odd behavior seems actually to be in line with the conclusion that strain softening, in many ways, behaves like shearthinnning i.e. like the influence of shear rate on the stress and the normal force. Yet, the oscillating nature of the normal force decay, and the origin for becoming attractive (negative), must be addressed as a specific feature of time dependent strain softening and explained quantitatively. 3.1.4 0.1 Hz 5% strain using a “disentangled melt” obtained by controlled shearrefinnement In the previous example of analysis of the melt entanglement instability of a PC, the initial entanglement state was unknown. All we knew was that some thermalmechaanica history produced a resin which required a certain degree of pre-annealing to stabilize. In the following example, a PC grade of smaller Mw/Me (9.4 instead of 12.8 in the previous example) was mechanically disentangled in a disentangling machine (a twosttag processor, as described in Fig. 6), achieving a very large change in the entanglement state, as will be revealed in the following figures. The same 3 step procedure was used, corresponding to a first frequency sweep (at T=275 oC), followed by an annealing treatment for 20 min under "mild" oscillating conditions (0.1 Hz and 5% strain), followed by another frequency sweep (0.1 Hz to 40 Hz, 5% strain). Because the initial melt was disentangled mechanically to a very large degree (relatively speaking, i,e, compared to what can be produced in a lab rheometer), the changes were most 104 spectacular and significant, yet in line with what we have observed for lab induced “melt disentanglement”. (a) (b) Fig. 39 Same type of experiments as in Figs. 29 and 30, with the same conditions for the 3 steps, but the polymer melt corresponds to a “disentangled polymer” processed by the apparatus in Figs. 5a and 5b Figure 39 displays the two plots we have been using to describe the evolution of the entanglement state. The first frequency sweep (the squares) has the general features of a frequency sweep of a disentangled melt: first an increase of viscosity at low w, the presence of a maximum at a certain frequency and a decrease of viscosity due to shearthinnning Note in Fig. 39a the very low initial viscosity 300 Pa-s, and the short span of variation due to shear-thinning (a gain of about 100 Pa-s for w between 0.1 to 40Hz), indicative of a melt with very little elasticity. Step 2, annealing without any "strong" strain, displays a spectacular viscosity recovery in a short time: viscosity increased by a factor of 3, almost linearly. 105 Between step 2 and step 3, although frequency and strain remained the same, respectively 0.1 Hz and 5% strain, one observes a drop of viscosity by 170 Pa-s. This situation is extremely challenging to explain by the current theories which do not consider the thermodynamic stability of entanglements. The drop of viscosity was not induced by a change of strain or frequency, but by time alone, the time it took in the rheometer to switch from a time sweep mode to a frequency mode, altogether about 30 sec. During that time, the entanglement network reorganized without any external stress on it. Also notice that the 2nd frequency sweep (the triangles in Fig. 39a, and Fig. 39b) has a much "longer" length, due to increased shear-thinning: this is because the melt regaiine some elasticity during annealing, and this directly affected its number of active strands, thus the shear-thinning attributes. Figure 39b plots the same data against frequency w, showing the 3 steps. The use of the log-log scales changes the perspectives, but nevertheless shows the large change in the Newtonian viscosity obtained after "recovery" of entanglement produced by annealing. log ho*= 2.65 instead of 2.45, a gain of 0.2 on the log scale. It is also interesting to note, in passing, that the use of the log scale minimizes the manifestation of shear-thinning at low frequency. In Fig. 39a, it is clear that viscosity continuously decreased with w, even if for a short range, but in Fig. 39b the behavior looks Newtonian. Fig. 40 is a plot of (G’/G*)2 vs time for the 3 steps. 106 Fig. 40 (G’/G*)2 vs time for the data of Fig. 39 There are two important comments to be made for this figure: 1. It confirms the large increase of the number of activated strands for melt 3, after the recovery which occurred during annealing (step 2). The curve length for the triangles is twice as long as the squares one, for the same span of frequency. This increase of (G'/G*)2 is essentially the reason for the increased shear-thinning of the step 3 melt. 2. During annealing treatment (dots), a slight but visible increase of the number of active strands occured, although the rheological variables (w and strain) were very soft (0.1 Hz and 5%). This demonstrates a particular feature of a disentangled melt: an increased sensitivity to rheological parameters, such as strain and strain rate. Usually, for a stable virgin melt, there is no visible change of (G'/G*)2 during annealing at high 107 temperature under soft treatment conditions. The drop of the stored elasticity between the end of step 2 and the beginning of step 3 is intriguing (it corresponds to the decrease of viscosity observed in Fig. 39a). The system probably overshot in trying to recover elasticity in step 2, and quickly re-adjusted in the short time between step 2 and step 3. Figure 41 is a plot of G" vs G' on a log-log scale for step 1 and step 3. It is interesting in comparison to Fig. 31 obtained on a quasi-stable entangled melt strained under the exact same conditions. Fig. 41 G”(w) vs G’(w) for step 1 and step 3. Same data as in Fig. 39 Step 1 data correspond to the squares, numbered 1b, 2b, 3b etc, as w increased. Step 3 data are the dots, shown as 1r, 2r, 3r etc. This plot also displays the G'=G" straight line, to determine the cross-over point by interception with the G" vs G' lines. The important 108 aspect of this plot is the huge discrepancy in behavior between the shift on the G' or the G" axis. The difference between points 1b and 1 r, 2b and 2r, 3b and 3r etc. is clear: variations occurred with a much larger amplitude on the G' scale than on the G" scale. There is no longer a correspondence, as we observed in Fig. 31, between the effect of frequency and the effect of annealing on the value of G’ and G”. Time of annealing shifted G’ much faster than G” (in comparison with the shift produced by w on G’ and G”). This observation is important, because it points to the deficiency of the traditional approach in its attempt to describe entanglement density by a single parameter Me, which scales both the G' and G" in the same way. The reality is that the influence of entanglement on G' and G" seems different. Traditional incorporation of Me in the expression of G' and G" via the introduction of GoN (the plateau modulus) must be revisited since it does not describe experimental results. Another point can be brought up from Figs. 41 and 42 regarding the value of the crossovve and its physical meaning. Identical G'x were obtained for melt 1 and melt 3 (this is seen in Fig. 41 by the same value of the intercept of the straight line G”=G’ with the square and dot lines), but a lower wx characterized the annealed (re-entangled) melt, as clearly demonstrated in Fig. 42. Again, unless the cross-over must be determined differently, it appears that the classical understanding of the cross-over is defective. 109 Fig. 42 The number of active strands (G'/G*)2, for a given frequency w, was much larger for the reentaangle melt, after the annealing treatment, than for the original disentangled melt. It can be predicted from this graph that wx for step 3 (the dots) is lower than wx for the squares (step 1). wx is obtained for (G'/G*)2=0.5. 3.2 Effect of Frequency during Time Sweep (at constant strain of 5%) We study 1 Hz, 10 Hz and 40 Hz for PC (Mw=32,000) T=225 oC, all for strain of 5% (considered low, i.e. melt in the linear range). 3.2.1 -1 Hz Figures 43a-d show the results. Fig. 43a compares the dynamic viscosity vs w curves before and after the time sweep. In Fig. 43a one observes a slight increase of viscosity at low w but no change of the slope of the log-log curve (the “pseudo-plasticity index”) beyond w~20 rad/s. The dots apply to step 2 in both Figs 43a and b showing that 110 there was a very small increase of viscosity occurring during time sweep, but that it did not have a lasting effect since the value of viscosity at the beginning of time sweep (step 2 frequency is 1 Hz) was the same as the value found for 1 Hz (i.e. w=6.28 rad/s) on the step 3 curve. The increase of the Newtonian viscosity was actually due to changes that occurred during step 1, the initial viscosity at 1 Hz at the beginning of step 2 being greater than the value found on step 1 for 1 Hz (Fig. 43a). (a) (b) (c) (d) Fig. 43 Effect of a time sweep at 1 Hz 5% T= 225 oC for 20 min on the frequency sweep at T=225 oC , 5% 0.1-40 Hz. The figures compare a frequency sweep done before and after the time sweep step. 111 Figure 43c, a plot of (G’/G*)2 vs w, confirms the absence of any visible significant effect on the value of the cross-over point (or on the number of activated strands) of the time sweep stage done under these “soft” oscillating conditions (1 Hz, 5% strain). However, Fig. 43d is interesting in that regard because some features due to annealing (which we said mostly occurred during step 1) become apparent when different variables are used to analyze the dynamic data. The two curves in Fig. 43d correspond to linear scale plots, versus w, of the ratio of G” for step 3 and step 1 (squares), and of the ratio of the G’ (open dots), respectively. The fact that some recovery occurred after steps 1 and 2 is quite visible in Fig. 43d, which distinctively impacts G’ and G”; it is clear that both G’ and G” increased respectively (step 3 vs step 1) but that the elastic modulus increased to a larger extent. The increase of modulus was especially effective at low w (+30% for G’, +16% for G” at 0.1 Hz) and almost non-existent (+3% for both moduli) at higher w . Fig. 43d is another demonstration that the interpretation of Friedrich and coworrker [60, 61], that the observed changes during time sweep are due to edge fracture or surface of contact effects, does not make sense. As already mentioned several times before, if Friedrich was correct, both moduli G’ and G” would be modified by the same ratio; thus Fig. 43d would not consist of two distinct curves, but a single one. 3.2.2 -10 Hz The same experiments as those in section 3.2.1 were now done with a frequency of 10 Hz during step 2, every other parameter remaining the same. This is a 10 times increase of the frequency and should trigger important changes. The results are shown in Figs. 44 a-d. 112 (a) (b) (c) (d) Fig. 44 Effect of a time sweep at 10 Hz 5% T= 225 oC for 20 min on the frequency sweep at T=225 oC , 5% 0.1-40 Hz. The figures compare a frequency sweep done before and after the time sweep step. Figure 44a shows that the viscosity curve corresponding to step 1 (squares) is located above the one for step 3 (triangles) for all w, and that the imparted viscosity decrease observed for step 3 is due, unlike in Fig. 43a, to the viscosity change occurring in step 2 (the dots), which was preserved. Figure 44b shows G”(w) vs G’(w) for all the steps 1 to 3 (the scales are linear on both axes) demonstrating two aspects of the effect of the treatment: 113 -1. G’ and G” appear to have decreased more intensely as w increased, meaning that the melt not only preserved its new viscosity attributes but even became more sensitive to frequency (or strain rate) than the original melt. -2. the time sweep treatment in Fig. 44b is shown as a straight line of G” vs G’, (the dots) approximately passing through the origin. The regression of that line gives a slope of 0.96 and an intercept of 12,475 Pa. In other words tan d = G”/G’ was almost constant during the time sweep, a conclusion that Friedrich et al [60, 61] would attribute to a surface defect. In fact, the ratio G’/G’ was not constant because the intercept is not zero, and Figs 44c and d also contradict Friedrich’s proposal. Fig. 44c is the same type of plot as Fig. 43d, showing the ratio between step 3 and step 1 of the G” and the G’, respectively. Fig. 44c clearly suggests that the effect of the time sweep treatment on G’ and G” was much more complex than just a change of the surface area of contact. Comparison between Figs. 43d and 44c also points to the same conclusion, favoring a modification of the viscoelastic properties of the melt due to a change of the melt entanglement state. The increase of frequency during step 2 not only reduced the value of (G”3/G”1) and (G’3/G’1), for a given w of the frequency sweep, but the ratio for G’ became smaller than 1 at higher w, indicative of a softer melt (the ratio for G” is always smaller than 1). The percentage of change of G’ (between step 3 and 1) is plotted against the percentage of change for G” in Fig. 44d. A straight line is drawn through the data (as frequency is increased , going downward on the line), and it is quite clear that, although a correlation existed between the changes occurring to the loss and elastic moduli, the slope was not 1 (it was 1.65), which would be the case if a surface defect was responsible for the viscosity decrease observed during step 2 (Fig. 44a). The apparent complexity of 114 behavior seen in Fig. 44c, is simply explained by the straight line in Fig. 44d: the moduli ratio varied more for G’ than for G”, which means that the treated melt became more sensitive to frequency, i.e.it was a more pseudo-plastic melt. Increasing frequency in the treatment stage, at constant strain, qualitatively yielded the same result as an increase of strain at constant frequency (compare Figs. 36b and 44a; also Figs. 37c and 44c): viscosity decreases and the changes are preserved for times long enough to be visible in subsequent frequency sweeps. Notice, however, the interesting differences between Figs. 37c and 44c, probably related to the difference in the operating temperature (Fig. 37 is at 275 oC, Fig. 44 at 225 oC): in Fig. 37c the ratios are increasing with w, and in Fig. 44c they are decreasing. The stability of the treated (disentangled) melt is a function of the frequency, the strain and the temperature during the treatment. Like in the case of a glass brought out of equilibrium by an up-quench or a down-quench thermal treatment [71], showing an excess or a lack of free volume with respect to its equilibrium value, a melt can be brought out of its entanglement equilibrium value by a dynamic mechanical treatment, the frequency, strain and temperature determining the mechanical history. The melt properties are no longer uniquely determined, as current models would predict. 3.2.3 -40 Hz Figures 45 a to f show the results obtained when the frequency was 40 Hz (251 rad/s) during step 2. All other parameters remained identical to those in sections 3.2.1 and 3.2.2. 115 (a) (b) (c) (d) (e) (f) 116 Fig. 45 Effect of a time sweep at 40 Hz 5% T= 225 oC for 20 min on the frequency sweep at T=225 oC , 5% 0.1-40 Hz. The figures compare a frequency sweep done before and after the time sweep step. Fig. 45a shows the viscosity-w curves before (step 1) and after treatment at 40 Hz, to be compared with 44a (10 Hz) and 43a (1 Hz). The treatment (step 2) is shown at the right end side, corresponding to the dots. The Newtonian viscosity was higher for step 3 than for step 1 (13,100 vs 11,000 Pa-s) despite a very large decrease of viscosity occurring during step 2 (viscosity was equal to 750 Pa-s at the end of step 2). The viscosity decrease obtained during treatment does “not stick”, it even reverted to an increase at low w in a manner similar to what is observed in Fig. 43a. Yet, also visible in Fig. 45a, when w was about 30 rad/s and beyond, a similar behavior to that observed in Fig. 44a characterized the flow properties: the step 3 melt was much more pseudo-plastic and its viscosity decreased much faster with an increase of w. Extrapolation of the two curves in Fig. 45a, using equation (5) of ref. 2, predicts a 400% decrease of viscosity at w = 1,000 rad/s, which would approximately correspond to the range of strain rate used in injection molding. In the case of Fig. 45a, the MFI of melt 3, the melt after treatment, would be smaller than the original melt, which could be interpreted as an unsuccessful attempt to decrease viscosity, but its fluidity at high rate of shear would be much improved. This shows that the impact of a history treatment on the final properties of the melt is not straightforward to elucidate. It is remarkable to point out that the only difference between Figs. 43a, 44a and 45a was a change of frequency during step 2. It suggests the important sensitivity of the entanglement state to frequency at T= 225 oC for this PC grade, even at low strain ( 5%). 117 Figure 45b is the equivalent of 44b; it shows the same trend, with noticeable differences though. The G” vs G’ straight line (dots) corresponding to step 2, has a slope of 0.77 (vs 1.56 for 10 Hz) and an intercept of 2,921 (vs 12475 for 10 Hz), which is very close to zero, thus (G’/G*)2 remains constant during treatment (~ 0.62). It is also important to notice in Fig. 45b how the step 2 straight line crosses the step 3 line (for G’~ 275,000 Pa) and continues towards the left bottom corner as time proceeded during treatment (the values of G’ and G” after 20 min treatment were 129,000 and 105,000 respectively). If the treatment had fully “stuck”, like would be the case for a 100% plastic deformation, these values of G’ and G” at the end of step 2 would be the ones found on a step 3 curve for w= 40 Hz. The difference is due to an elastic mechanism of retraction which we need to understand and control in order to optimize the technology developed from this type of work [46]. In Fig. 44b, for instance, the treatment seems to be more efficient, i.e. most of the changes of G’ and G” induced by step 2 were preserved and recovered on step 3. One needs to understand why this is so. Figure 45c shows the comparison for steps 1, 2 and 3 of (G’/G*)2 vs w and the determination of the cross-over for (G’/G*)2 =0.5. This graph confirms that (G’/G*)2 remained constant to 0.62 for step 2 (triangles), and reveals that the cross-over w for step 3 ,wx3, was smaller than the one for step 1, wx1 (67 vs 103 rad/s). The number of active strands was greater for the melt after treatment, for all w. As we shall explain in the discussion, this means that cooperativity between conformers was increased, which is the reason for the increased shear-thinning ability, i.e. for the increased pseudo-plasticity. The treated melt behaved as if we had increased its entanglement density, not decreased 118 it. A plot of G’/w vs log w (not shown) indicates for step 1 a maximum at wx1= 22.4 rad/s and for step 3 at wx3 = 14.6 rad/s which would be consistent with that conclusion. Figure 45d is the equivalent for this 40 Hz treatment frequency of Figs 44c (10 Hz) and 43d (1 Hz). In Fig. 45d the ratio for the G’ varied between 1.47 down to 0.82 and extrapolated to 0.75 at infinite w. The ratio for the G” varied between 1.17 and 0.75 and may have almost reached an asymptotic value for the largest w value of the frequency sweep . The curves in Fig. 44c cross at w~ 3 rad/s, but they never cross in Fig. 45d, which might be a key observation to understand the retention of the properties after treatment. The spread of % change of G’ and G” was greater for the 40 Hz treatment than for the others at 1 Hz and 10 Hz. This is confirmed in Fig. 45e, which should be compared with Fig. 44d (the corresponding figure is not shown for the 1 Hz treatment). The slope was 1.524 and the intercept 20% in Fig. 45e, compared to 1.65 and 11.6 %, respectively, in Fig. 44d. The increase of the G’ and G” changes was thus essentially due to a shift of the intercept, from 11.6% to 20%, which may be related to the increased stored elasticity of the strand network, as shown in Fig. 45c. Figure 45f shows a plot of G* (left vertical axis) and of the normal force (right axis) versus time during step 2. Both parameters can be fitted with a double exponential function with a constant term. For instance, the normal force fit provides: -32.5 -25.95 exp(-t /18.4) +58.87 exp(-t /498.03) where t is time in sec. Fig. 45f is quite intriguing: why would the normal force become negative beyond t= 250 sec, and why would this negative excursion continue to be in full agreement with the decay of G*? The asymptotic value found for the normal force was -32 g, which is an attractive normal force of magnitude 16,000 Pa.. For a “normal” melt, the induced elasticity by the 119 torsional shear deformation creates a push against the plates of the rheometer, corresponding to positive normal force. In the case of Fig. 45f, it appears that the treatment reduced both the shear stress, G* and the corresponding normal force, and that the excursion into the negative normal force region is the mere continuation of the process that reduced G*(t). We do not see any discontinuity in the decay of these functions, nor in the ratio of (G’/G*)2 which remained equal to 0.62 beyond t=250 sec (not shown), nor in the variation of G”(t) vs G’(t) in Fig. 45b. We conclude that the occurrence of the “attractive” normal force was real and describes some real changes occurring in the melt. Such negative normal forces during transient behavior was already reported earlier, not only for pure rotational flow experiments (Type 4), see Figs. 19d and 20, but also for dynamic experiments (Figs. 35b and 38). The “structuring” of the melt into laminated layers might be responsible for these negative normal forces, as has already been mentioned when describing those figures. Incidentally, the structuring into layers might also be responsible for the partial lack of retention of the viscosity reduction, as we shall discuss later. 3.3 Effect of increased energy input during Time Sweep: T= 225 oC, Frequency=5 Hz and g=20%. In this section, the frequency was 5 Hz and the strain was raised to 20% during step 2, all other conditions remained the same as in section 3.2 The frequency sweeps were done with 5% strain. Figs. 46a to f show the results. Figure 46a is the now familiar plot on linear scales of viscosity vs time across steps 1, 2 and 3. The comparison between step 1 and step 3 is very significant: there was 120 a huge drop of the Newtonian viscosity from 12,000 to 3,500 Pa-s due to the step 2 treatment at 5 Hz, 20% strain for 20 min. The viscosity decrease is also visible at high w, although Fig. 46b shows it better (the viscosity at 40 Hz on the step 3 curve was still 3 to 4 times smaller than the value found at 40 Hz on step 1). 121 Fig. 46 Effect of a time sweep at 5 Hz 20% T= 225 oC for 20 min on the frequency sweep at T=225 oC , 5% 0.1-40 Hz. The figures compare a frequency sweep done before and after the time sweep step. It is noticeable in Figs. 46a and b that the step 2 curve started at nearly the same viscosity level as at the end of the step 1 curve. Yet, frequency was 40 Hz at that point for the step 1 curve, and only 5 Hz for the step 2 curve. Viscosity should be higher than what was observed, based on shear-thinning due to strain rate effect. The lower viscosity observed at the beginning of step 2 is due to strain-softening obtained by the increase of strain, from 5% to 20% in this instance. It has been already noted that strain plays a thinning role, in many ways similar to the effect of strain rate. Actually, based on simple considerations, one can expect such a similarity: for a dynamic experiment, the strain rate is not w, but wg, where g is the strain. Figure 46b clarifies further the effect of changing the frequency and the strain at the end of step 1. The position on the w axis of the step 2 vertical line indicates the frequency of work during the step 2 treatment. As already mentioned for Fig. 46a the step 2 curve initial viscosity approximately coincided with the value obtained at the end of the 122 step 1 curve, i.e for 5 % 40Hz. This is a pure coincidence. The important observation is the difference between the step 1 curve (top) and the beginning of the step 2 curve on the vertical line corresponding to 5 Hz. That difference, due to strain softening at 5 Hz T=225 oC, was preserved in the step 3 melt. Notice that the two frequency sweep curves seem to remain parallel, in particular that they are shiftable on the log h* axis. Notice also that the step 3 curve passes through the exact same point that originated the viscosity decay for step 2. In other words, the melt PRESERVED the same value of viscosity that was the result of coupling the effect of shear-thinning and strain softening at the beginning of step 2. There is apparently no incidence on the step 3 melt curve of the large decay of viscosity occurring during step 2 (the log h* decreasing from 3.2 to 1.9!). All of the viscosity decrease in step 2 must have recovered in the lapse of time it took to switch from the experimental conditions of step 2 to those of step 3, about 20 sec. Figure 46c compares the number of activated strands bearing stress (proportional to (G'/G*)2 for the original melt (step 1) and the treated melt (step 3), showing that this is not the parameter that was mainly modified by the treatment under those conditions. In Figure 46c the step 3 curve (dots) is located a little bit above the step 1 curve (squares) in the frequency region below the treatment frequency (5 Hz). However, there was no change observed above the treatment frequency. This lack of change of (G'/G*)2 is significant in view of the large decrease of viscosity observed for melt 3. The vertical line in Fig. 46c corresponds to step 2 done at 5 Hz. One observes for step 2 a little portion of (G'/G*)2 values located above the step 1 and 3 curves. This is explained in Fig. 46d Figure 46d is a plot of (G'/G*)2 vs time during step 2, showing the initial maintenance of the number of activated strands at approximately 0.3 for about 450 sec, 123 followed by large fluctuations, an attempt to maintain the integrity and the cohesion of the initial entanglement network, followed by the construction of a new entanglement network of strands with a higher number of activated strands, approximately corresponding to (G'/G*)2 =0.42. The final melt had a higher elasticity; this corresponds to the small tail, the portion of points for step 2 located above the step 1 and step 3 curves in Fig. 46c. A small fluctuation of the signal is perceived in Fig. 46d; it is not related to the structural instability, it was due to a small temperature fluctuation imposed on the melt to allow a fine analysis of the mechanical deformation details [72]. A rheological criteria must be defined to account for the instability of the initial network under the excessive energy application induced by the parameters of deformation in step 2. Time obviously plays a crucial role, since it took 450 sec before the instability of the entanglement network created its re-structuring into a different network, with higher activated strands sustaining the deformation. Figure 46e is a plot of normal force vs time across the three steps. The normal force value went up to 40 g in the first frequency sweep. That normal force decayed in step 2, in a way that mimics what happened to (G'/G*)2 in Fig. 46d, i.e. the decay was "normal" until about 450 sec when some large fluctuations appeared for the first time, seemed to stabilize somewhat, and then there was a slight rise of the normal force at the end, beyond 1200 sec. The step 3 melt had very little normal force, which only went up to 10 g, 1/4th the value found for step 1; the step 3 melt had lost 75% of its elasticity. 124 Figure 46f is a plot of G" vs G' on a log-log scale comparing melt 1 and melt 3. This plot should be compared with Figs. 31 and 41 for melts whose treatment during step 2 was done at higher temperature (T=275oC) and lower frequency (0.1 Hz). In Fig. 46f the G' and G" values at each frequency was considerably higher for the untreated melt, the treated melt being located well below the initial melt, and the data collected onto parallel lines. Interestingly, the amount of change on the G" axis was about twice as large as what is observed on the G' axis, and this ratio remained approximately constant as w varied. This is different from what we observed for other treatment conditions, for which the changes were greater for the elastic modulus (Figs. 44d, 45e). An important question arises from the results of Figs. 46a to f: what caused the viscosity decrease to “stick” ? Is it because the melt went into a new cohesive network of entanglement during step 2, which would be the equivalent of going through a plastic deformation (thus freezing the state –shear-thinning plus strain softening-that it had acquired before such freezing step)? One observes in the middle of step 2 (Figs. 46d and e), a large scattering of data, as if the melt had lost its cohesion at one point. This is not melt fracture because there was no apparent modification of the MWD, as checked by GPC, and the stress was too low to produce melt fracture. We speculate that this feature corresponds to the renewal of the network of entanglement, a re-organization of the cohesive network of interactive conformers, the Dual-Phase “EKNET network” as we call it [73]. This is due to the amount of energy stored in the strained networked of strands reaching a critical value. In terms of the deformation of the dual-phases of the EKNET network, using the analogy of a pipeline network of branched rivers to represent the entanglement phase, this is as if 125 new branches had to be created due to an overflow situation. The cohesion and stability of the entanglement network can be brought to their limit, to the equivalent of the onset of melt plastic yielding, beyond which new viscoelastic properties of the melt are expected. The decohesion and renewal of the entanglement network is essential to understand. It is quite possible that the success of preserving into a pellet form the viscosity changes induced by mechanical deformation will depend on whether the melt has crossed its plastic yielding criteria. 3. 4 Effect of Annealing the melt after treatment and experiments of Type 3 In this section we review published data [13, 14, 23, 50] obtained to characterize shear-refined (treated) PC by the technology described in Figs. 5a and b . This is the same PC grade as in sections 3.1 and 3.2 above. The experimental procedure was described as a Type 3 experiment in section 1 “Experimental Procedures” and in section 4.1 of “Initial State and Sample Molding Procedure”. The difference with sections 3.1 and 3.2 is that the “disentanglement” treatment was not done inside the rheometer but through a disentangling processor and pellets of the treated melt was produced. We already studied in section 3.1.4 the properties of a melt produced out of such treated pellets. The two graphs of Fig. 47 compare the complex viscosity – radial frequency w curves at T= 275 oC (obtained in the linear viscoelastic range, with 5% strain) for a reference melt (prepared from the virgin pellets) and for a treated (disentangled) melt prepared from pellets obtained from the shear-refinement treatment. The symbols in Fig. 47 correspond to the frequency sweep data points, the continuous lines are fits with the 126 Carreau’s equation [Eq. (5) of Ref. 2] and their extrapolation to w = 1,000 rad.sec-1. As mentioned before, this value corresponds to a strain rate in the range of what occurs in an injection molding machine. Figure 47 shows that the treated melt had a slightly lower Newtonian viscosity than the virgin melt. This was confirmed by an MFI test performed on both the virgin and treated pellets: the MFI of the treated pellets was only 20% higher than the virgin pellets. However, the situation was very different at high w, due to a spectacular increase of the pseudo-plasticity of the treated melt. Fig. 47 indicates a 5 fold increase of fluidity at w = 1,000 rad/s Fig. 47 Comparison of the frequency sweeps at T=275oC for the Virgin and the treated (disentangled) pellets made with apparatus in Figs. 5a and 5b. 127 Figure 48 compares the G’ and G” between the reference and treated samples. It is clear that the difference between the respective moduli (treated vs virgin) was only significant and increasing at higher w, confirming an increased shear-thinning ability at higher shear rates. Figure 49 compares the viscosity-w curves of a treated melt before (1st pass), and after annealing it at T= 275 oC for 10 minutes (2nd pass) The frequency sweeps were conducted at T= 225 oC (the melt was cooled down to T=225 oC after its annealing period. The treated melt is represented by the dots (the lower curve). Annealing here was a true thermal treatment, with no mechanical deformation on the sample. 128 Fig. 48 G’ and G” vs w for the data of Fig. 47 Fig. 49 Comparison of Dynamic viscosity vs w for a treated (dots) and a treated-annealed (square) melt. See text. Figure 49 shows that the Newtonian behavior was unchanged by annealing. Both curves coincided at low w. However, annealing converted the high frequency behavior back to its original virgin status: the extra-shear-thinning observed for the 1st pass, i.e the increase of pseudo-plasticity, was gone for the 2nd pass. The improvement of the pseudoplastticit of the treated polymer melt appears to be temporary. Figure 50 attempts to determine how fast the recovery takes place. For this test we operated at T= 275 oC for all steps, the 1st pass, the annealing step and the 2nd pass, in order to avoid the intermediary times of heating and cooling. Annealing was only for 5 129 minutes. Figure 50 shows the virgin melt, the 1st pass for the treated sample and pass 2 for the annealed sample. The instability of the treated melt is clearly evidenced: the melt had already started to revert back to its equilibrium (virgin) properties after only 5 minutes of annealing. Note, however, that the destruction of the benefits of an increased pseudo-plasticity by the 5 minute exposure at T=275 oC was far from complete. Considering that this temperature is 130 oC above the Tg, it is already remarkable that the melt could exhibit such “long” period of metastability (with respect to its terminal time). Yet this annealing test reveals another difficulty in producing treated disentangled melts, with regard to their time and temperature stability. If the time of exposure at a high temperature “re-entangles” the melt too fast, it will restrict the type of applications feasible with the use of such melts 130 Fig. 50 Comparison of frequency sweeps (dynamic viscosity vs w) for a Virgin, a disentangled and an annealed disentangled melt. See text. Figures 51a and b compare the respective ratio of elastic (G’3/G’1) and loss (G”3/G”1) moduli vs w for a treated sample (step 1) and after annealing (step 3) on one hand (Fig. 51a) and for a reference virgin melt (Fig. 51b) that was annealed similarly. All steps were conducted at T= 275 oC including annealing. The annealing time was 10 min. . Fig. 51a Fig. 51b Comparison of the respective ratio of elastic and loss moduli vs w for a treated sample (“as is” and after annealing) and for a reference virgin melt. The frequency sweeps before and after annealing, and annealing were all done at T= 275 oC. Annealing time 10 min. An horizontal line, corresponding to a ratio of 1, is also drawn on the graphs as a way to indicate the behavior expected for a melt that would not change before and after 131 annealing. Figure 51b demonstrates that it was, indeed, the case for the virgin sample: the ratio for G’ and for G” both remained the same and randomly equal to 1, respectively. Fig. 51a applies to the shear-refined (treated) sample and one can see that the ratio for G’ and for G” were different. The ratio for G” remained quasi-constant at ~0.925 whereas the ratio for G’ varied with w, decaying from 1.27 to 0.925. This behavior resembles that of a boosted pseudo-plastic melt, as shown earlier for melt treatment of type 2 (Figs. 43d and 45d). This analogy of viscoelastic behavior between a disentangled melt processed by a disentanglement machine that produces pellets and by a time sweep treatment inside a lab dynamic rheometer may constitute a convincing proof that no credit should be given to an edge fracture mechanism to explain the time dependence of viscosity in the case of the lab dynamic experiments [60.61]. For Fig. 52 we ran an experiment of Type 3 (specified in Section 1 “Experimental Procedures”) on a shear-refined PC sample of Mw=35,000. The first frequency sweep (“1st pass”) was done at T= 225 oC (dots), then the temperature was raised to 275 oC to run a frequency sweep at that temperature (“1st pass@275”, triangles). The temperature was then lowered to 225 oC where a second frequency sweep was run at that temperature (“rt at 225”, filled squares). Finally, the temperature was raised to 275 oC and a new frequency sweep (“rt @275oC”, open squares) was done. All the frequency sweeps were done in the linear range (5% strain), so there is no question of a surface artifact whatsoever under such conditions. Figure 52 forcefully illustrates many features observed throughout this Section 3 about the rheological behavior of melts brought out of equilibrium. The comparison of the 1st and 2nd pass at T= 225 oC, after raising the melt 132 temperature to 275 oC and running the 1st pass frequency sweep at 275 oC, is quite spectacular. The viscosity difference (decrease) at w =250 rad/s between these two curves was 10 folds. “Annealing” at 275 oC did make the original treated melt lose a great deal of its pseudo-plasticity benefits, but not all of it, as can be deduced by comparing the 1st pass and the rerun at the higher temperature of T= 275oC. Only the rerun at T=275 oC was identical to the virgin at that temperature, meaning that there was still an important amount of boosted pseudo-plasticity remaining in the 1st pass at T=275 oC, and therefore in the 2nd pass at T=225 oC. In other words, the melt had only entirely recovered its entanglement equilibrium state after the 12 minutes it took to run the 1st pass at 225 oC, the 1st pass at 275 oC and the 2nd pass at 225 oC. Fig. 52 Comparison of frequency sweeps for experiments of Type 3. The initial melt is disentangled by the apparatus in Figs. 5a and 5b. See text. 133 Figure 53a gives the variation of G’(w) and G”(w) for the two frequency sweeps done at T=225 oC, step 1 and step 3 (after “annealing” at T=275 oC). For the treated melt (step 1), both G’ and G” go through a maximum for w~20 rad/s. After “annealing” at 275 oC, the rerun shows that both G’ and G” gained a decade in magnitude and that the value of the maximum of G’ and G”, still present, was shifted to w~100 rad/s. This is a situation very similar to that depicted in Fig. 22c for another polymer, LLDPE, sheared in a type 4 experiment (pure viscometry) before running a frequency sweep. Figure 53b plots (G’/G*)2 vs w for the initial (treated) melt (dots) and the melt after annealing (squares). It should be compared with Fig. 22d. For both the sheared LLDPE of Fig. 22d and the shear-refined treated PC sample in Fig. 53b, the higher w behavior is matched by an increase of (G’/G*)2, which we attribute to an increase of the “internal stress” of the active strands, not to an increase of their number. This causes the pseudo-plasticity boost responsible for the excess viscosity decrease. As shown in another paper [71], the degree of shear-thinning is directly correlated with (G’/G*)2, thus an increase of its value results in a decrease of viscosity. This represents one way to produce a decrease of viscosity and, as shown in Fig. 52, this method can be very effective. 134 Fig. 53a Fig.53b Analysis of a disentangled melt before and after annealing. (a): G’ and G” vs w; (b): (G’/G*)2 vs w However, as pointed out above, the relatively short term stability of the boosted melt might be a limitation for preserving its benefits. Long term stability arises when the shear-refinement process has focused (and succeeded) in modifying the number of active strands bearing stress: this is demonstrated by the lowering of the value of (G’/G*)2 at low w. When this is the case, the Newtonian viscosity is substantially lowered as well (see below in Fig. 55 an example with PMMA). The goal is, of course, to find shearrefinnemen processing windows that combine a controlled modification of the number of active strands with the modification of the strand internal stress, resulting in “smart processing”. 135 Fig. 54 Comparison of frequency sweeps (dynamic viscosity vs w 1st pass) at the same temperature for a series of disentangled melts processed under different conditions. Fig. 54 is a collection of 1st pass curves, such as the 1st pass curve in Fig. 52. They all correspond to shear-refined pellets molded into disks analyzed in the same rheometer, at the same temperature, following the same procedure, by the same operator. We showed in ref. 2 that such conditions yield a 0.5 % reproducibility between samples. Also eliminated from the collection in Fig. 54 were all samples which had a Mw different from the reference by more than 3% (as measured by GPC). According to traditional views of the molten state, all curves of Fig. 54 should be one single curve. The result is quite revealing: thermal-mechanical history, which is what differentiates these samples, can alter very significantly, by as much as 20 times, the value of the viscosity at any given point. In summary, the fundamental viscoelastic properties of a PC melt can be modified at will by entanglement manipulation. In Fig. 54 we demonstrate that we can create melt 136 entanglement states which yield lower viscosity than the reference (the filled squares), presumably corresponding to thermodynamic conditions, but also greater viscosity than the reference (all curves located above the black squares). One of the melts of Fig. 54 was the starting melts (step 1) studied in section 3, which could be heated and/or mechanically annealed in step 2 to induce viscosity recovery, back to the thermodynamic entanglement state. This is general. The melt entanglement state is like a glass state and can be brought out of equilibrium by thermal-mechanical means, such as pure viscosimetry or pure oscillation, or by a combination of those means. 4. Long Term Entanglement Network Instability for a PMMA melt Fig. 55 Comparison of dynamic viscosity vs w curves obtained for a disentangled PMMA sample before annealing (dots) and after annealing (squares). See text. 137 Fig. 56 (G’/G*)2 vs w for the data of Fig. 55 Figures 55 and 56 apply to a PMMA random copolymer of 95% methyl methacrylate and 5% ethyl acrylate with Mw=78,000, Mn= 40,000 and Tg=104 oC. Figure 55 is a plot of complex viscosity vs w on log-log scales, Fig. 56 is a plot of (G’/G*)2 vs log w. The squares correspond to a frequency sweep performed at T = 215 oC (0.1 Hz to 40 Hz, 2% strain) on a melt made out of pressed, disentangled pellets. Shear-refinement was performed using the disentangling two-stage processor described in Fig. 5b, producing pellets showing a 70% decrease of its Newtonian viscosity (as measured by MFI). This disentangled melt was very stable (compared to the PC melts of section 3, for instance). Annealing at T=215 oC for 1 hour under N2 conditions did not produce any sign of recovery of the viscosity drop induced by the treatment. It took 24 hours of 138 annealing time in the rheometer (under no stress) to finally obtain the dots curve in Figs. 55 and 56, which compares well with the initial untreated (virgin) melt frequency sweep. Figure 55 clearly shows the decrease of the Newtonian viscosity for the treated sample as well as its lower viscosity at all frequencies. Fiure 56 compares the number of activated strands for the disentangled sample and the sample annealed for 24 hours, which we called “re-entangled”. The disentangled melt had less activated strands than the re-entangled (and the virgin) melt. This is the reason, we suggest, why the Newtonian viscosity was lowered. This is perhaps also one of the reasons for the stability of the disentangled melt which required no less than 24 hours to recover its equilibrium entanglement network state. One may wonder why this disentangled melt became so stable. Could it be that for PMMA, under the conditions of operation of the two-station disentangler (Fig. 5b), a new entanglement network was created, in the sense of what we assumed to have occurred for the PC sample treated in step 2 at T=225 oC, 5 Hz 20% strain (section 3.3, Fig. 46d ) This new entanglement network might be much more stable than just a disentangled melt produced by "orientation" of the entanglement network (note that this orientation is different but driven by the molecular orientation that is controlled by the terminal time). The type of entanglement network orientation and decoheesio we are talking about is modulating the local interactions between the bonds which are occurring much faster, with rate 1/to. 139 Fig. 57 Comparison of G’ vs w plots for a virgin sample, a treated (disentangled) sample and a reentaangle sample. See text. In Fig. 57 G' is plotted against w for 3 types of melt. The virgin PMMA (diamonds) corresponds to a melt prepared out of virgin PMMA pellets (the same PMMA as in Fig. 55), the squares correspond to pellets from a shear-refined (treated) melt, and the triangles apply to a "re-entangled" melt after disentangled pellets are dissolved in a solvent, the solvent evaporated, and new pellets produced to be melted and studied by frequency sweep. Figure 57 shows the shifted respective positions of the elastic moduli at all frequencies for the treated (disentangled) melt, and the return of G' to the reference curve, after re-entanglement through solvent dissolution had taken place. Fig. 57 is an excellent proof that disentanglement and re-entanglement are reversible phenomena that do not involve MWD changes. The same experiments were also reported by Hanson for PE [ 28 ] and by Stange et al. [42 ] for PP when those polymers were submitted to shearrefinnement 140 5. Entanglement Network Instability for a Polystyrene melt. 5.1 PS 1070 Fig. 58a Fig. 58b Fig. 58c Error! Objects cannot be created from editing field codes. Fig. 58d Fig. 58 Transient behavior observed in a dynamic rheometer with PS (Figs. 58a, b, c) for conditions given in the text. Fig. 58d compares frequency sweeps for different states of stability of the entanglement network, created by the previous time sweep “treatment” history. Figure 58a to d relates to PS1 from the section 3 “material” list. It is the same PS already described in Figs. 10, 11a and b and 12. Figure 58a displays G’ and G” vs time during a time sweep done at 8 Hz (w=50 rad/s), g= 25%, T=160 oC to induce a transient decay. The strain was gradually raised to 22% by steps of 5% done every 3 minutes (as 141 explained before, this ramp was to let the melt relax the amount of built-up elasticity at each step increase to avoid melt fracture). Fig. 58a is called "1st treatment". It lasted 10 minutes. Both G' and G" started to decay. The ratio (G'/G*) also decayed (not shown), a good indication that the transient was not due to a surface effect or slip. A second “treatment “of 10 min (a repeat of step 1) was done just after the 1st one was finished, with an interruption of 2 min (rest) in between. Then a partial “recovery” was conducted (at w=1 rad/s 2% strain) for 67 min. Neither of those two steps curves are shown. Fig. 58b corresponds to a 3rd treatment (using the same oscillation conditions w= 50 rad/s g=25%). The magnitude of the change of the modulus G’ and G” should be compared with those in Fig. 58a: the initial value for both was decreased by ~25 times at the end of Fig. 58b. Figure 58c shows a new recovery step conducted at the end of the thermal history, lasting 6,000 sec, with w= 1 rad/s 2% strain, where it can be seen that G' and G" increased with time steadily but slowly, at a pace much slower than the decreases observed during the initial treatments. The difference of kinetics between treatment timescale and recovery may be related to the influence of frequency on the magnitude of the stress (by elasticity build up) which influences the barrier of the activated processes involved in the interactions between the conformers, as mentioned several times in this article. Interestingly, in Fig. 58c the recovery shows at t ~ 2,250 sec a sort of shift of the curve; this may be related to a memory effect for the transient network of strands, similar to what was observed by Kovacs [71] for a glass returning to equilibrium. The increase of the rate of recovery might very well reflect the incidence of either the 1st recovery step or 142 the interruption of 2 minutes between the first two treatments, and demonstrate the kinetic aspect of the entanglement network. A melt behaves like a glass with respect to its entanglement network; it is capable of memory effects. This statement has profound consequences to understand what entanglements really are: static topological interpretations of entanglement cannot, in our view, account for the results presented here and throughout this paper. Figure 58d provides the complex viscosity-w curves (on a log-log scale) at various states of the melt evolution after the successive time sweep treatments. This plot should be analyzed along with the results of Fig. 12 which provide (G’/G*)2 vs w for the same frequency sweeps (for the same polymer). The curve at the top of both Figs 58d and 12 (triangles) corresponds to the un-sheared melt, the Reference. The squares curve applies to the state of the melt after it was through the first 10 min treatment. The viscosity decrease incurred during the time sweep treatment was almost totally preserved (“the treatment stuck”). We saw in Fig. 12 that the extrapolated curve for the un-sheared melt cut the 0.5 horizontal line at a wx~ 0.01. The cross-over for the 1st treatment curve was located at wx ~ 0.1, so 10 times bigger. This is the reason for the melt viscosity benefits “to stick”: the number of entanglement strands were significantly reduced by the 1st 10 min treatment. The dots curve in Fig. 58d (and in Fig. 12) corresponds to the state of the melt after it had gone through two treatments of 10 min each and the partial “recovery” (time sweep at w= 1 rad/s 2% strain 67 min). One sees that the viscosity curve was no longer parallel to the reference, the recovery step affecting the higher frequency relaxation times faster than the slow ones. This observation relates to the complexity of the kinetics of the return to 143 equilibrium of a metastable network of entanglements. Also, note the correspondence between the changes occurring to the viscosity and to the value of (G'/G*)2 after each step, the repositioning of these curves with respect to the reference curve being similar. As already mentioned for Fig. 12 the height at the maximum value of (G’/G*)2 was less for the treated melts. The maximum number of activated strands possible decreased for the sample that went through a transient decay. 5.2 PS2: Thermal-Mechanical History to Create Out-of-Equilibrium Melt Properties. We present in this section another example of thermal-history to help understand the stability of the entanglement network and the various facets linked to its deformation. Figure 59 is a (G’/G*)2 vs w plot for PS2 (specified in section 3 of Experimental procedure). The frequency sweep was done at 2% strain, T=155 oC, i.e. in the linear range. 144 Fig. 59 (G’/G*)2 vs w for PS-2 in the linear regime (1%) for T= 155 oC One reads a value of 0.80 and 0.844 for w = 1 rad/s and 50 rad/s respectively. For w= 100 rad/s (G’/G*)2 was also equal to 0.8. Note that these three radial frequencies are located on two sides of the maximum, 50 and 100 rad/s being on the same side. A succession of steps, 1 to 8, corresponding to various time sweep “treatments” makes up what we called the “Thermal-Mechanical History”. The objective was to follow the evolution of the network of entanglement and the “internal stress” build up of the activated strands, for instance by studying what happens to the curve in Fig. 59 after the melt has been submitted to step treatments in the non-linear range. This is explained in Fig. 60. The strain history is shown in Fig. 60a. Steps 1, 2 and 3 were done at w= 100 rad/s, The other steps were done at w= 50 rad/s except step 8 for which w= 1 rad/s. The 145 strain for steps 6 and 8 was 1%. Fig. 60b displays the evolution of the complex modulus G*(t) and provides the frequencies used during the various steps. Figure 60c shows (G’/G*)2 vs time across all steps (this is the reason for the word “consolidated”). Fig. 60a Strain% history for 8 steps 1 to 8. The insert of Fig. 60b indicates the frequency and strain % for each step. 146 Fig. 60b G*(t) for the various steps 1 to 8. The insert indicates the frequency and strain % for each step. Fig. 60c (G’/G*)2 vs time for the various steps 1 to 8. The insert indicates the frequency and strain % for each step. 147 The first observation is that (G’/G*)2 in Fig. 60c is a network parameter, as much as G*(t) is in Fig. 60b; it decreased, changed rate of change, reversed direction, increasee. The changes occurring to these two parameters, (G’/G*)2 (t) and G*(t), must be correlated to understand which part of (G’/G*)2 describes a change of the number of activated strands bearing stress, and which part relates to a modification of “the internal stress” of the strands. Obviously, as mentioned for PC, their respective influence on the retention ability of the viscosity reduction benefit is crucial to understand. The boosting of the pseudo-plasticity of the melt, responsible for the high frequency behavior, is due to an increase of (G’/G*)2 caused by an increase of the strands’ “internal stress”. The low frequency behavior, i.e. the Newtonian viscosity changes, is correlated to the modification of the number of active strands of the entanglement network. Changing the treatment frequency from 16 Hz (w=100 rad/s) in steps 1, 2, 3 to 8 Hz (steps 4,5,6,7), and at the same time changing strain % (Fig. 60a) produced different interplay between shearthinnnin and strain softening effects. For instance, for steps 1, 2, and 3 (G’/G*)2 remained constant at the linear value of 0.8 found for w=100 rad/s (Fig. 59), The corresponding G*(t) in Fig. 60b declined with a faster rate as strain was increased from 10% to 18% (Fig. 60a). The situation between step 3 and step 4 is quite significant. The decrease of w from 100 to 50 rad/s resulted in the expected increase of (G’/G*)2 seen in Fig. 59 (on the right end side of the maximum). However, the increase of strain, at the same time, from 18% to 20% in step 3 to 4, and to 22 % for step 5 resulted in increased strain-softening, which triggered a transient for both G*(t) and (G’/G*)2. Step 6 was a strain step down 148 recovery done under forced oscillation (w stays at 50 rad/s). One sees that the value of (G’/G*)2 was only slightly lower than at the beginning of step 4 and remained constant. G*(t) increases, showing the time dependency of strain-softening. This step 6, which only lasted 10 min, had a spectacular effect on the subsequent decay of both G*(t) and (G’/G*)2 observed for step 7. At one point (G’/G*)2 had declined from 0.844 to 0.775 and the corresponding decrease of G*(t) was more than 10 times its initial value. Figure 60d is a masterplot of “ELAS”, equal to G’/G*)2 , vs ETA*, the complex viscosity, across all steps, 1 to 8. The open dots correspond to the frequency sweep done in the linear region of viscoelasticity, for 2% strain. Fig. 60d (G’/G*)2 vs dynamic viscosity (ETA*) for the 8 steps of the mechanical history 149 One sees that steps 1,2,3 were right on the linear region curve (the open dots), although the strain was increased to 18%. The deviation from the linear region curve occurred for viscosity values (steps 4 to 7) that became transient and inferior to their linear counterpart value for the same (G’/G*)2; this is why the curve for these steps is located above the linear range curve (dots). The viscosity at the beginning of step 8 (w= 1 rad/s 1% strain) was equal to 12,000 Pa-s and should be equal to 100,000 Pa-s on the open dots curve. We thus conclude that the effect of Thermal-Mechanical History on the entanglement network stability can conveniently be studied with a dynamic rheometer and applied to industrial shear-refinement practice to produce retainable viscosity reduction benefits. . 150 DISCUSSION The question of the origin of the time dependency of the visco-elastic parameters. In pure viscometry (at constant rate of shear), a transient behavior is expected before the melt reaches its steady state. Questions regarding the origin of this transient are still experimentally and theoretically investigated and debated [7-9]. We showed in section 2.1 that the stability of the steady state could be a function of the previous thermo-mechanical history of the melt, which could be a sign that either “sustainable orientation” could be the result of a structured stratification of the network of entanglements inside the gap or the result of “disentanglement”, or that, actually, “disentanglement” meant in reality “sustainable network orientation”. Additionally, we suggested that the total stress could be split into an active stress and a relaxing stress, explaining some kinetic features obtained during transients (e.g. Fig. 21) and the negative normal force observed at the end of the transient behavior (e.g. Figs. 19d and 20). In order to study the instability of the melt under conditions that separate the effects of strain and strain rate, we proposed to investigate the triggering of time dependence of the moduli by strain in dynamic experiments performed in the non-linear range. Section 3 of the paper presents the effects of various “treatment” parameters, that of frequency, strain amplitude and temperature. In all these experimental tests we observed the same phenomenon: as strain was increased beyond a certain critical value (which is a function of frequency and temperature), the melt starts to become transient, i.e., for instance, its viscosity changed with time. The time dependence of moduli in relaxation and creep experiments performed near Tg (~Tg +30 oC), are well known [e.g. Figs. 1a to 1d], but the relaxation times are extremely small (10-3 to 100 sec, depending on molecular weight) at these low temperatures; thus, far above Tg. (~Tg +150 oC), 151 the melt is always considered to be in equilibrium after, say, 2 min of relaxation, even for the highest molecular weights. One could argue that in certain cases, for branched polymers in particular, the longest relaxation time could reach 10 minutes at T ~Tg +150 oC. Perhaps. But, what we are talking about in this paper are linear polymers, with relatively low M/Me (say 5 to 20), capable of transients which last 24 hours (see PMMA in Fig. 55). This is obviously not the same relaxation process involved as that in Figs 1a to 1c, or, if it is the same process (and we will suggest in sections of this discussion that it is), something is missing in the present understanding of what entanglements are and how they actively determine the long term relaxation properties of melts. The first thing we do in this discussion section is review the challenging interpretations of the time dependence of the moduli under non-linear dynamic conditions. Challenging Interpretations. In presenting the type of experimental data illustrated in Figs. 4 and 28 to the scientific community, a number of interpretations of the results emerged: · The viscosity reduction is due to shear viscous heating. · The viscosity reduction is due to shear degradation (Mw is decreased). · The viscosity reduction is due to plasticization (Tg is decreased), caused by the production of monomers by shear degradation. · The viscosity is reduced because drooling occurs at the edge. · Slippage occurs. Viscosity reduction is due to a surface fracture effect and does not apply to the bulk of the specimen. · The viscosity reduction is due to shear-thinning, which is a well known phenomenon. 152 These we explore in more detail below. Viscous Heating: Shear generated heating is real and could explain some results (e.g. see the explanation regarding Fig. 13b) obtained with the use of first generation rheometers. If the heat generated is not controlled by cooling, the viscosity will decrease because of the temperature rise. However, the experimental procedure requires that one work at constant temperature. Early results using the RDA 700 were duplicated using more modern instruments, the ARES from Rheometrics, the Bohlin SVO200, and the AR 2000 from TA Instruments, which are known to have improved isothermal control of their furnace. Temperature does not rise more than 0.2 oC, as measured by a thermocouple placed right underneath the sample. Such a small temperature change is not capable of producing the large viscosity change observed during the transients triggered by non-linear shear oscillation. In the type of shearrefinnemen processor described in Figs. 5a and b, cooling conduits (element 240, in Fig. 5a) are built in the static and rotor sections to dissipate out the heat generated by the shear oscillation at large amplitude. The temperature of the melt is directly measured by contact with the melt, and remains constant during the process. In conclusion, viscous heating is not responsible for the time dependency of viscosity, in particular for the decrease of viscosity. Shear Degradation. In the torsion experiments done in a lab rheometer (such as those of Figs. 27 and 28), the specimens did not show any sign of degradation after the time sweep “treatment”. For all the dynamic results presented in this article, GPC tests were systematically conducted on samples extracted before and after the time sweep stage to ensure that the decrease of viscosity was not due to chain breakage or degradation. A GPC measures the molecular weight distribution, providing the various molecular weight averages: Mn, Mw, Mz and Mz+1. For all 153 disentanglement experiments done in the lab rheometer, we did not observe shear degradation of the samples within 3% variance (which also equals the accuracy of GPC measurements). However, when shear-refinement processors were used to produce disentangled pellets, the level of degradation was visible and depended heavily on the treatment duration, the temperature, the amount of anti-oxidant present and mostly on the nature of the polymer. For PMMA, for instance, the degradation could be kept low, between 1 to 5% depending on the extent of disentanglement obtained. For polyolefins, the degradation could be as high as 25%. Despite these molecular weight changes, which could be accounted for by a correction factor, shear-refined pellets displayed an extra viscosity decrease that could be as high as 50% to 400%, measured by re-heating the pellets in a Melt Flow Indexer or by rheometry. Figure 61 shows the Refractive Index (RI) measured by GPC as a function of molecular weight for 3 types of PC sample processing: one sample is the virgin pellet, another sample is a pellet after it had been disentangled by a disentanglement processor [Figs. 5a and b], and the third sample is the extruded virgin, i.e. the sample after the virgin pellets were extruded through the MFI process at 300 oC. The value for Mw and Mn are given in the figure for the 3 types of pellets. It is clear that the weight and number average molecular weights are practically the same for these 3 samples. The decrease of Mw for the treated PC is 5%, i.e. 2% more than the decrease corresponding to the virgin extrudate (3% degradation). A decrease of Mw by 5% corresponds to a viscosity drop of 16% (calculated from (Mw/Mwref) 3.4 = 0.95 3.4 = 0.84). This correction was applied to the MFI results which, after correction, still displayed an increase of 70% between the virgin pellet and the treated PC pellet. Note that we differentiate, in Fig. 61, the MFI results obtained for “dried” or “undried” pellets (whether they are treated or virgin): the undried treated pellets indicate an improvement of the MFI by +140% (with respect 154 to the undried virgin), twice the value obtained for the dried treated pellets (dried at 110 oC for 4 hours under vacuum). All MFI results were compared after respective correction for the Mw small decrease. The difference between the MFI improvement when treated pellets were dried or not is perhaps indicative of the true reason for the viscosity changes. See below. In any case, the decrease of viscosity due to the triggering of a transient state by increasing strain under shear-thinning conditions is not caused by shear-degradation. Fig.61 Refractive Index (RI) vs log M from GPC comparing the molecular weight distribution for a virgin pellet (top curve), a shear-refined (“treated”) pellet displaying a +140% (undried) or +70% (dried) increase in MFI value after treatment (middle curve), and a virgin sample after it went through the extrusion process in a MFI measurement process (lower curve “Virgin PC extrudate”). The polymer is PC. 155 Drooling of the melt outside of the rheometer plates. On certain occasions, drooling of the melt was visible by opening the door of the furnace right at the end of the time sweep step. We observed that drooling occurred for time sweeps done at high frequencies, high strains, and for thicker samples (2.5 to 3 mm thick). When drooling occurred, the results were discarded. Besides, an easy way to prevent drooling is to use a bottom plate shaped like a cup, preventing the melt from spilling out. Nevertheless it is interesting to briefly analyze how drooling could occur. Let us consider the centrifugal force acting on a sliced ring located at distance r of thickness (dr). It is equal to k*dm *V2/r with dm = density*thickness*2p*r*dr and V is the local velocity. The constant k results from the integration over a period of the angular speed, which is not constant in a periodic deformation. The integration over the full specimen radius shows that total centrifuge force is proportional to the cube of the radius and to the square of the frequency. Additionally, the velocity V depends on the layer position in the gap since it is proportional to the strain rate times the gap between the moving layer and the static plate. We suggest that drooling is possible when the magnitude of the normal (lateral) force, proportional to g2 , due to the shear-deformation in the perpendicular direction, is overcome by the centrifugal force pulling the melt out of the parallel plates. When a transient occurs, the normal forces decrease (see examples in Figs. 38 and 45f for dynamic experiments and in Fig. 20 for pure viscometry), reducing the pull-in retractile force in the direction perpendicular to the shear deformation, permitting drooling to result. In other words, drooling is a sign that an imbalance of the forces maintaining the integrity of the melt in the gap occurred. This imbalance is due, 156 we suggest, to gradients of velocity across the gap structuring the Dual phase layers differently (the strain rate is assumed to be constant across the gap in laminar shear flow defomation). The imbalance could also be due to gradients existing co-centrically. In summary, the shear vibration induces a great deal of extensional stress between concentric rings as well as a gradient of forces between the layers of the gap due to the dependence of the centrifugal forces with the position of the layers. The decrease of the magnitude of the normal forces results from this internal structuring, i.e. from the anisotropic distribution of the “entanglement phase” which we called the orientation of entanglement network. Fig. 62 is a picture of an oriented dual-phase melt according to the Dual-phase model [73]. 157 Fig. 62 In this cartoon sketch of the Dual-phase model [73] the “entanglement phase” is shown to align with the direction of flow (bottom-up direction) This figure represents one entanglement network layer of the gap (one virtual slice). For a circular motion, such as in a classical plate-plate rheometer, the entanglement phase line-up would form rings. The number of rings would be function of the radius r and of the layer position in the gap, creating an orientation pattern characteristic of the non-linear viscoelastic deformation, explaining the “sustained orientation” of the entanglement network. See later. It is possible to eliminate drooling completely by working with thinner samples (~500 to 1000 m thick) which might lessen the gradients across the gap. Furthermore, experiments repeated with samples using serrated plates, with the sample’s gap adjusted at the high temperature, before lowering T to its treatment value, did not display any drooling at all, for frequencies up to 40 Hz. Additionally, a 1mm wide drooling ring would correspond to a viscosity correction of the order of 10%, nothing of the order of magnitude of the viscosity reduction seen as a result of melt disentanglement (50% to 1300%). Finally, transients are still observed when the melt is confined to a closed chamber without the possibility to escape, such as in a dynamic disentanglement processor (Fig. 5a). The effect of combining strain and frequency on the viscosity decay appears to be very similar in a such a confined setting and in an open-edge plate plate rheometer. In conclusion, drooling cannot explain the large viscosity changes observed in dynamic experiments triggered by an increase of strain at (high) frequency. Plastification due to an increase of the monomer concentration by the shear process. For PMMA, it was observed that the concentration of monomers increased from 1000 ppm (for the virgin pellet) to 2000 ppm (for the “disentangled” pellet) after shear-refinement. Could this increase result in the observed viscosity changes observed in Fig. 55?. It is well known that an increase of concentration of small molecules decreases the Tg, and that a decrease of Tg, at a given temperature, reduces the viscosity. So, the question is legitimate. 158 The influence of the concentration of plasticizers on Tg is given in textbooks [79} and corresponds to a decrease of Tg by ~0.5 oC for the doubling of the concentration between 1000 ppm and 2000 ppm in PMMA. The WLF equation can be used to approximate the corresponding decrease of viscosity (see ref. [2], eq. (3)). For PMMA, we find that Log aT is decreased by 0.03 when Tg is lowered by 0.5 oC. This corresponds to an increase of the Melt Flow Index by 7%, not the +70% reported for the “disentangled” PMMA pellet in Fig. 55. Two other arguments against the plasticizing effect of monomers can be added. First, pellets were dried for a long time (17 hours) under vacuum at approximately Tg-40 oC before the MFI measurements are done. It can reasonably be assumed that the more volatile components, present in the pellets at ppm level, would not survive such a drying step. Second, the GPC lower tail, which focuses on the low molecular weight fractions, did not show any visible modifications for the samples reported in this paper. This is evidenced, for instance, for the PC samples shown in Fig. 62. In conclusion, the changes of viscosity observed by shear-refinement are not due to an increase of the monomer concentration Shear-thinning. “Shear-thinning” describes the reduction of viscosity induced by an increase of the strain rate, thus by frequency in a dynamic experiment. This is quite clear in Fig. 28, for instance. Shearthinnnin occured as soon as the frequency of oscillation was increased from 1 to 47 rad/s: viscosity droped from 57,000 to 10,000 Pa-s . This means that the melt became less viscous when it was vibrated at 7.5 Hz frequency (47 rad/s). However, to induce this benefit, vibration must be applied to the melt and maintained. As soon as vibration was stopped, so did the shear159 thinning effect on viscosity and the melt recovered instantaneously its original Newtonian viscosity. The value of shear-thinned viscosity was stable at low strain (up to 13% in Fig. 28). The viscosity became time dependent thereafter, the rate of viscosity change increasing with the strain (see, for instance, Fig. 60b). The triggering of the time dependent (transient) behavior and the holding of the melt in that state influences the post-treatment visco-elastic properties: in Fig. 28 the melt no longer sprang back to its initial Newtonian viscosity, it only sprang back to 38,000 Pa-s and not 57,000 Pa-s. The remaining viscosity difference was recovered over the next 20 to 30 minutes. This melt behavior is different from the classical shear-thinning characteristics. The longest relaxation time was apparently increased 60 times. We suggested that strain-softening coupled with shear-thinning was responsible for that situation. This, obviously, needs quantification. The point, however, is that the transient behavior triggered by non-linear strain displays marked differences with shear-thinning effect. What we called “disentanglement” corresponds to this “sustained” shear-thinning. Note that we previously introduced, relative to Fig. 20, the notion of “sustained orientation” to describe the orientation of the network of entanglement, .and its possible stability above Tg, as opposed to the orientation of local bonds .that relax very fast above Tg. Obviously, the local deformation interloock with the deformation of the network which still needs to be defined. The inter-lock must also be quantified. Edge fracture explanation. In this section we examine the proposal made by Friedrich et al. [60, 61] that the time dependency of viscosity triggered by an increase of strain in dynamic experiments is due to an edge fracture effect propagating inward. We have said many times in this paper that, in our opinion, such an explanation was not correct. This conclusion was derived from the analysis of 160 several figures (Figs. 11a, 37c, 43d, 44c) which show that G’(t) and G”(t) did not vary in the way a surface contact decrease would affect the results. When the ratio G”/G’ (equal to tan d) was apparently constant (thus (G’/G*)2 was ~ constant), we suggested that the time dependence of G’ and G” was due to the orientation of the network of strands, which occurs at constant total number of active strands. This is the same basic mechanism of deformation that controls shear-thinning and shear strain softening, with specific variants determined by the value of frequency, strain and temperature. What these time sweep experiments essentially teach us is the fact that the expression of G’(w) and G”(w) should also include a time dependent term which becomes noticeable under non-linear conditions of deformation. The “static” (time independent) expressions used in linear rheology (see for instance Eq. (15) of Ref. 2) have limitations, being only applicable to a small range of strain for which the entanglement network is stable in its current structure. For instance, shear-thinning at low strain corresponds to an increase of the number of activated strands with the increase of frequency. The transient behavior classically admitted to occur for constant shear rate viscometric experiments is the consequence of strain (which increases linearly with time) reaching a critical value that puts the network of strands in the time dependent (non-linear) visco-elastic region where it starts to deform, first, and then to structure. If the new network structure is relatively stable, one observes what we call “disentanglement”. Like for pure viscometry, this situation can only be achieved in dynamic experiments above a certain strain (e.g. Fig. 28). Thus it does not seem unexpected (and we do not need a surface artifact explanation) to find for dynamic experiments, conducted beyond critical conditions of strain and frequency (Fig. 28), a similar transient behavior to that which we observe in fast shear rate viscometry (Fig. 2a). 161 In this paper we have seen several examples of time dependence of G’ and G” occurring at either increasing (Figs.11b, 40 (step 2), 46d, 60c (end of step 7) ) or decreasing (Fig. 60c (steps 4, 5)). (G’/G*)2 . When the transient occurs at constant (G’/G*)2, the network of strands deforms but does not structure. When structuring occurs, the network of activated strands orients and can assume new stable structures. The stability of the new network entanglement structure depends on the way it was established, thus on the thermal-mechanical history. An elaborate combination of strain softening and shear-thinning can be set up to create thermal mechanical histories capable of defining at will, it seems, the future visco-elastic behavior of the melt. Examples are given in Figs. 60a to d. The sustainability of the new network describes the stability of the new inter-lock between the local bonds and their organization as a system, under stress. A new “terminal time” must be defined to account for the stability of the network. Based on our experience, it can be 100,000 times greater than the local to that is supposed to define the longest relaxation time of the melt. Figure 63a. below is the same as Fig. 11a. of the introduction section, with a full scale disclosure of the effect of the largest strain amplitudes (15% and 20%) on the time dependence of (G’/G*)2. Fig. 63b displays the decrease of viscosity occurring at the same time. 162 Fig. 63a Fig. 63b 163 Fig. 63 4 time-sweep steps done with increasing strain % at each step, triggering a transient of both (G’/G*)2 (a) and dynamic viscosity (b). See text. The sample in Figs. 11a, and 63a and b was a film of thickness 484 m. The time sweep occurred at T=235 oC, under a relatively high frequency (87 Hz). The transient decay of both h* and (G’/G*)2 became very pronounced after the strain reached 15%. The dynamic viscosity (Fig. 63b) continued to decrease but leveled off at 20 Pa-s ( a 750% decrease) for a strain of 20%, whereas the stored elasticity, which had dropped from 0.775 to 0.15 during the transient decay at strain =15%, showed an initial drop to approximately zero when the strain reached 20%, followed by an increase of its value afterwards (Fig. 63a). Friedrich and collaborators [60, 61] acknowledge that tan d increases at one time of the time sweep under strain but suggest that the fracture mechanism (which they say remains confined to the surface up to that point) has somehow started to penetrate inside the sample. They also report that the stress and/or strain signals become distorted as soon as tan d starts to increase. Figure 64 shows the stress and strain signals (which are displayed continuously by the AR 2000 dynamic rheometer) at a point near (G’/G*)2 ~0. in Fig. 63a. These signals are not distorted. It is true that Friedrich uses thicker samples (2 to 3 mm) and that Fig. 64 applies to a film; the gap thickness makes a significant difference with respect to the question of integrity of the gap, as clearly evidenced by Wang [8, 9]. As mentioned earlier, the structuring of the gap into an anisotropic entanglement network layers depends on the gap thickness. It is quite possible that Friedrich’s experimental set up triggers effects described by Wang, which are in no way responsible for the transient behavior itself but interfere with it. The best proof is that for thinner samples, for which the integrity of the gap is more preserved, the transient behavior is more pronounced (Figs. 65a to c), for reasons that we explain below. This result appears to 164 contradict Friedrich’s conclusions regarding the effect of the gap thickness on the intensity of the transient behavior [61]. Fig. 64 Signals observed for strain and stress in the region where transients of (G’/G*)2 and G* are visible. Friedrich et al. mention that the thickness of the gap influences the onset of the increase of tan d (corresponding to a decrease of (G’/G*)2), i.e., in their case, the beginning of the distorted signals. These authors did not explore the use of films (as in Fig. 64, showing no signal distortion) or the use of a cup bottom plate which eliminates the openness of the melt at the edge, and thus edge fracture, yet still showing a transient behavior triggered by higher strains.. 165 Fig. 65a Compare the transient viscosity decay (Log h*(t) in Poises vs time) for two successive time sweeps done on the same melt, changing the value of the gap (from 2mm to 1.5 mm) after the first run. The sample is a branched PC; T=230 oC, w=157 rad/s and the commanded strain is 30%. Figure 65a shows the transient decay of the dynamic viscosity obtained for a branched PC from GE Plastics (PK 2870) triggered by the application of a commanded strain of 30% with a frequency of 25 Hz (157 rad/s) at a temperature of 230 oC. The rheometer was the RDA 700 already mentioned relative to Fig. 13. The gap was initially 2mm. (Run 1). At the end of run 1, we squeezed the gap to 1.5 mm, checked by opening the furnace door to determine whether there was a need to trim an expanded bulge from the edge (there was a little trimming necessary), and rerun a new time sweep using the same parameters, lasting another 1,800 sec (Run 2). This experiment is very interesting for several reasons. First, one observes that the viscosity at the start of run 2 was the same as the viscosity at the start of run 1. This could be interpreted as a clear demonstration that the transient decay of run 1 was an artifact. In other terms, if the viscosity remained unchanged, after squeezing the gap, it is because the transient behavior was due to a surface effect or drooling or some other artifact. This was the 166 interpretation given for Fig. 65a by a majority of scientists and technicians, when these transient tests were first introduced by us in 1996. However, let us study the results more closely. Although the viscosities for run 1 and run 2 at the beginning of the time sweeps are almost identical in Fig. 65a, the transient path lines look very different for the two gaps. The decay is much more pronounced for run 2. Figure 65b provides more insight to the reasons. Fig. 65b (G’/G*)2 vs time (left axis) and strain % vs time (right axis) for the data of Fig. 65a In Fig. 65b we have two types of graphs corresponding to either the vertical axis on the left or on the right. The left vertical axis is (G’/G*)2 and the right vertical axis is the strain %. The data are extracted from the same time sweeps experiments of Fig. 65a for run 1 (gap=2 mm) and for run 2 (gap=1.5 mm). The x-axis is the time (in sec). One sees that, although the 167 commanded strain was constant (and equal to 30%) for both runs 1 and 2, the actual strain was increasing with time and only reached 30% in the case of run 2. The value of (G’/G*)2 decreased slightly at the beginning of the time sweep, for about 200 sec, then stabilized and remained constant, starting to drop only when the strain reached 16% for both run 1 and 2. The final decrease of (G’/G*)2 is very small for run 1 since the strain only increased to 22 % before the end of the 1800 sec time sweep. For run 2, the 16% strain, for which (G’/G*)2 started to decrease, was reached much sooner (for t~550 sec) compared to t~1,500 sec for run 1. The kinetics are totally different for these two gaps. Fig. 65c Variation of the melt temperature for run 1 in Figs 65a and b. The asymptotic temperature is 229.4 oC. The rheometer was a RDA 700, a first generation rheometer with limited cooling capabilities in the non-linear visco-elastic range. Fig. 65c explains the reason for the initial decrease of (G’/G*)2 for the first 200 sec. It is a plot, for run 1 (the plot for run 2 is not shown), of the melt temperature against time during time sweep. The temperature rose by 0.5 oC (from 228.7 to 229.2 oC) in 200 sec, as a consequence of the application of the oscillation at 25Hz. As already mentioned, the RDA 700 168 used for the experiment was a first generation rheometer, quite satisfactory to work with in the linear visco-elastic range, but with insufficient cooling capabilities to maintain the temperature of the melt constant while working under non-linear conditions. Figure 65b shows that, after correction for the small increase of temperature at the beginning, (G’/G*)2 remains constant for both runs 1 and 2 until the strain reaches 16%. As mentioned in the previous section, when (G’/G*)2 remains constant, the network of strands is not even deformed. The transient response of G’ and G” (and therefore of the viscosity) is elastically driven, due to the local reorganiizatio of the bond interactions to accommodate the imposed strain. There is no structuring of the network of strands possible under such conditions, i.e. no possibility of sustained orientation. Hence, it does not seem surprising that, as run 1 ended, the viscosity change did not “stick”, i.e. the melt had the same entanglement state (with the same to) as at the beginning of run 1. We can consider that run 1 did not create a thermal history for run 2 because strain was not above the critical value 16% long enough, and the squeezing of the gap (from 2mm to 1.5 mm) destroyed whatever small changes of the network of strands there were, from t =1,500 to 1,800 sec, visible by a slight decrease of (G’/G*)2 in that time range. Run 2 had a different transient dynamics than run 1 because the gap was thinner, not because it was a second run. The controlling parameter is the strain, g, which varied towards the commanded strain gc much faster for run 2. In fact, a log-log plot of h*(t) vs g(t)/gc ,not shown, proves that melts 1 and 2 had the same transient behavior up to 16%, diverging beyond that strain, where strain alone was no longer the controlling parameter. One sees in Fig. 65b that (G’/G*)2 steadily decreased for a strain between 16% and 29%, reaching a value of 0.575 at which it leveled off for about 100 sec, then continued to significantly decrease at an even steeper rate to finally reach the value of 0.3 for a strain of 30%. 169 Following Friedrich’s explanation (61) of the increase of tan d (i.e. a decrease of (G’/G*)2), the propagation of the edge fracture inside the sample should be much faster in the case of the thinner sample (run 2). This appears to contradict Friedrich’s own findings regarding the effect of gap thickness (61). One could argue that the effect of the gap on the viscosity response is well known to rheologists studying wall slippage [78] and that run 2 has a lower viscosity in time due to an increase of the wall slippage velocity. This explanation is discussed later in the section dealing with the effect of the plate surface on the transient results, in particular the value of the steady state viscosity, but was unlikely in the present situation (Figs. 65a and b) because the initial value of the stress was much less than the critical stress for initiating the no-slip violation (~ 100,000 Pa). The stress was 41,192 Pa at t=0 for run 1 and 58,521 Pa for run 2. In the explanation we propose to explain Figs. 65a and b, and all the other figures in this paper, it is clear that we concur with Wang’s results [7-9] pointing to the limitation, as we enter the non-linear range, of the basic assumption of rheology regarding the scalability of the rheological parameters (stress and deformation tensors) in terms of viscosity, strain and strain rate to describe the effect of the gap thickness. The definition of viscosity (the ratio of stress and strain rate) and of strain rate (the gradient of the velocity profile across the gap) requires an homogeneous melt., or, as we further add, an homogeneous, unstructured entanglement network, which is a valid and justified concept only for certain conditions of deformation, for instance in the linear viscoelastic range. In the non-linear region, as strain increases, the network of entanglements first deforms without structuring (at constant (G’/G*)2 , this is the only range for which the separation of the effect of time and strain is valid), followed by the orientation/structuration of the network of entanglements itself, finally yielding to its 170 instability, and eventually its rupture and re-organization into a new network (Figs 46c and d). All these manifestations of “entanglement instability” must be well defined molecularly, and correlated with the macroscopic variables, torque and global strain. The assumptions regarding the affine correlation that exists between local deformation and global strain must be reviewed, refined and revised when working in the non-linear region. Figs 65a and b are important because they show that the gap plays another role than just defining the strain (g = a R/h, where a is the radial angle, R the radius and h the gap). Not just the velocity gradient across the gap is important in the non-linear deformation range, but also the velocity of the layers, leading to the structuring of a dynamic network of interactions for which the interplay between entropic and enthalpic forces account for the stability of the network in time and under stress. Simple concepts borrowed from the linear range (Fig. 65a) can mislead the understanding of the physics behind non-linear effects (Fig. 65b). The gap plays another role, in the non-linear range, when no slip occurs, than what can be predicted from the concepts developed in the linear-range. Melt Fracture Initiation: Vinogradov’s criteria Edge fracture is an instability of cone-plate and parallel plate flows reported for low molecular weight viscoelastic liquids and suspensions, characterized by the formation of a `crack' or indentation at a critical shear rate on the free surface of the liquid [76]. As mentioned in the Introduction section, certain authors [60,61] suggested that, at least for PS, an edge crack formed on the free surface of the bulge of the melt between the parallel plates which propagated inwards, concentrically, in effect gradually peeling off the melt from the surface of contact to cause the observed decay of viscosity. One needs to understand how an 171 edge fracture would initiate in the case of a highly viscous polymer, not a low molecular weight liquid or a grease, for which an inertia explanation has been advanced [76]. A possible answer might be provided by examining the Vinogradov’s melt fracture criteria applicable to high molecular weight polymers [74] , as reported and modified by van Krevelen [75]. Van Krevelen uses Bueche’s dimensionless strain rate number, G, and specifies the critical value for melt fracture to occur according to Vinogradov’s experimental results. The equations below define the parameters: where g is the strain, r the melt density, w the radial frequency, M the weight average molecular weight, Me the molecular weight between entanglements, ho the Newtonian viscosity at temperature T, R the perfect gas constant, a the maximum angular displacement per cycle, Go,N the plateau modulus defining the entanglements, s the shear stress, and h* the complex viscosity. For instance, for the PC of Fig. 46, by plugging both melt fracture criteria 172 into the above equation of the dimensionless strain rate, and the known values for Me and Go,N, respectively 2,500 g/mole and 1.5 MPa [6], one can compute the stress causing the melt to fracture at that temperature: 0.987 MPa. Figure 46b shows that the stress at the beginning of the time sweep (at 5 Hz, 225 oC) was only 49,791 Pa, corresponding to a viscosity of 103.2. The critical stress for melt fracture is 20 times greater than the actual stress at the onset of the time sweep showing transient behavior: why would an edge fracture occur, a fracture process nevertheless, under the present low stress conditions? Even if Vinogradov’s fracture stress criterion was too large by a factor 2, which has been found by Archer [78] for some polymers, one would need such a large stress concentration factor to reach the critical level (10 times), that the likelihood of its occurrence appears remote for high molecular weight liquids. Friedrich et al. [60, 61] show that once the edge fracture crack is initiated (for whatever unexplained reason), their results can be quantitatively explained by the propagation of the crack or indentation, using the same formula used by several authors studying edge fracture in low molecular weight viscoelastic liquids and suspensions, in particular grease and toothpaste [76]. According to Keentok and Xue, “the Tanner-Keentok theory of edge fracture in secondorrde liquids can be extended to cover the Criminale-Ericksen-Filbey (CEF) model” [76]. They used a finite volume method program to simulate the flow of a simple viscoelastic liquid, and obtained the velocity and stress distribution in parallel plate flow in three dimensions. The simulation, specifically applicable to lubricating grease and toothpaste, showed that edge fracture in viscoelastic liquids depends on the Reynolds number, and is broadly consistent with the CEF model, allowing to simulate its dependence on the physical dimensions of the flow (i.e. parallel plate gap or cone angle), on the surface tension coefficient, on the critical shear rate and on the critical second normal stress difference. The simulation [76}explains how stress 173 concentrations of the second normal stress difference (N2) can be found in the plane of the crack; how the velocity distribution could show a secondary flow tending to aid crack formation if N2 was negative, and how a secondary flow could tend to suppress crack formation if N2 was positive. In summary, the effect of inertia on edge fracture of these low molecular weight viscoelastic liquids was predicted by the simulation. Furthermore, a video camera was used [76] to record the inception and development of edge fracture in four viscoelastic liquids and two suspensions. All these findings on low viscosity liquids probably influenced the authors who believe [60-65] that a similar behavior could result for high molecular weight polymer melts. The extrapolation attempt to polymers was/is, indeed, a credible approach and could apply to certain processing conditions (as we have, indeed, observed ourselves at high frequency and high strain, for instance, using thick samples). However, the validation of this assumption fails badly, in our opinion, to explain the transient evidence within the conditions presented in this paper; in particular we conclude that a surface contact deficiency is not compatible with the unequal transient variation of DG’(t) and DG”(t) observed in our work. Other criteria of the paper by Keentok and Xue [76] also do not seem to apply to the conditions of transient behavior observed for our polymer melts, such as the value of the Reynolds number for the validation of the inertia criteria. Finally, the experimental evidence presented by Gonnet and collaborators [77], explained in the next section, gives further credibility to the suggestion that the integrity of the interface is not responsible for the transient decay of the moduli. Simultaneous Dielectric and Dynamic Mechanical Measurements in the Molten State If the protagonists of an edge artifact were correct regarding the inward propagation of a surface fracture initiated at the edge of the melt [60-65], a simultaneous measurement of the 174 melt dielectric properties would reveal such a peeling of the polymer from the metallic surface of contact. In particular, space charges would be created and an increase of the noise level would be expected. Gonnet et al. [77] published an article about the behavior of a polymer melt during large strain sweep experiments performed in a modified dynamic rheometer equipped with dielectric measurement means. The strain amplitude was increased to beyond the linear viscoelastic regime, in the domain where we would expect “disentanglement manifestations” to take place (a transient behavior). The decrease in the mechanical signals G’ and G” corresponding to disentanglement activity was indeed observed by Gonnet et al. [77], yet the dielectric probe response proved that these changes were not surface artifacts but truly bulk property events, which could be characterized dielectrically. In particular, there is no mention in ref. 77 of an increase of noise due to space charges. The dielectric signal was coherent with the mechanical signal, although a transient decay was observed. The polymer studied by Gonnet (PVDF) was different from those studied by either Friedrich [60, 61] or by us in this article. Yet, the triggering of the transient decay by an increase of strain at low frequency provided a similar response to those shown in Figs. 37a to d for PC. There is no reason to believe that the nature of the polymer would require a different explanation when the rheological response to the same type of deformation yields the same result. We suggest Gonnet and collaborators’ article provides an elegant and definitive answer to the question whether the effects observed with a dynamic rheometer are due to a bulk viscoelastic response or artifacts generated by some surface effect; they are, indeed, due to bulk properties. Effect of the nature of the surface melt contact 175 Figures 66a and b suggest that the interaction of the melt with the surface of the dragging layer (the top parallel plate) influences the steady state viscosity, thus the melt structure that gives rise to that steady state. Figure 66a plots the viscosity (experiment of type 4) versus time for the LLDPE of Figs 14-23. Figure 66b plots the normal force vs time for the same data. Three different types of surface were used: serrated, smooth and rough. The material used for the disk plate was Aluminum. The smooth surface was polished to a very fine finish, the rough surface was sand-paper treated to leave some scratches across it, and the serrated disk surface was densely sparkled with a multitude of homogeneously distributed pyramid-shaped clits of height 150 m. Both the stationary and moving surfaces had the same surface treatment, for a given test. The experiment with the rough surface was repeated twice using a different sample, to assess repeatability. Temperature was 190 oC, the strain rate was 3.0 sec-1. The gap was the same for all tests, 1.6 mm. Repeatability was, indeed, excellent in Figs. 66a and b, shown by the perfect superposition of the viscosity and normal force curves for the rough sample and the rough repeat one. We assumed that the serrated plates created a better contact, a better interfacial grip, due to the microscopic indents at the surface. It appears from Fig. 66a that the more the melt grips to the moving surface, the lower the steady state viscosity. The smooth surface gave the top curve with a steady state viscosity of 800 Pas-s. The second lowest steady state viscosity value was obtained for the rough surface (200 Pa-s), and the lowest steady state viscosity corresponds to the serrated surface (almost zero). The same order is seen for the normal force in Fig. 66b, 75, 10 and -15 g for the smooth, rough and serrated surfaces, respectively. The nature of the surface of the disk also influences the transient decay relaxation time, as is clearly shown in Figs 66a and b, the serrated plates providing the slowest decay. 176 The effect of the surface on the viscoelastic response is not new [81] and is usually considered to be caused by wall slippage [78, 80, 81]. It is commonly established that above a certain critical stress (~100,000 Pa for most melts) slippage occurs at the stationary wall, reducing the velocity of all layers all the way up to the dragging surface. Polymer viscosities measured in pressure-driven and drag flows have been reported to systematically decrease as the dimension of the flow channel is reduced [78, 80]. According to Larcher [78]: “Work by several groups…clearly indicates that fundamental understanding of polymer adsorption and interactions between polymer chains near the polymer-solid interface are important for resolving the molecular scale processes responsible for slip violations.” Hence, in Figs 66a and b, one could conclude that the results reflect the strength of adhesion between the mobile plate and the melt, the slip being more pronounced for the smooth surface. This explanation, however, is unlikely to be the correct one in view of the value of the stress at the initiation of the transient behavior with respect to the critical stress for slippage. The extrapolated viscosity is ~ 10,000 Pa-s for a strain rate of 3 sec-1, giving a stress maximum of 30,000 Pa, three times less than the critical stress to initiate slip. The solution must be found somewhere else. The established view considers that in planar Couette shear flow, driven by one mobile surface, the strain rate in the gap, alone, characterizes the rheology, and that, above a critical shear stress, some correction of the apparent strain rate is necessary to account for the effect of the gap thickness and the nature of the contact with the wall on the slip velocity. We suggest that this is a simplification which is only valid within certain conditions of laminar flow and that results such as those in Figs 66a and 66b are indications that the polymer melt organizes its structure across the gap in ways which are not simply predicted by macro-variables independent of the nature of the polymer or its state of entanglement. In the non-linear range 177 that we talk about, such as in Figs 66a and b, the different moving layers across the gap are dragged at different speeds from top to bottom. The maximum stress is at the stationary surface and there is no slip. If and when the transient decay is due to orientation of the active strand network in the flow direction, the success of the orientation is not just a function of the strain rate (assumed constant in the gap), but also on the stress, which varies across the gap. Since we do not reach the critical stress criteria for slip in Figs. 66a and b, we suggest that smooth plates are not capable of creating an orientation pattern across the gap which penetrates deep enough, serrated plates appear to be the best, the rough surfaces being intermediary. In other words, “disentanglement” is not uniform across the gap. Fig. 66a Viscosity vs time for different surfaces. The conditions are found in the inserts 178 The structuring of the entanglement network occurs both concentrically and across the gap, with the orientation of the entanglement phase in circular rings, the number of rings varying from layer to layer, and the structuring being influenced by the state of adhesion with the stationary and dragging surfaces. Fig. 66b Normal Force vs time for different surfaces. The conditions are found in the inserts In Fig. 66b, the serrated plates were the only ones capable of producing a steady state melt with negative force. All other plates had a positive remaining normal force (10 g for the rough surface, 75 g for the smooth surface). These are significant clues to what was happening during transient decay and could be interpreted by a layered orientation structure of an active strands network. 179 If the degree of disentanglement is not uniform across the gap, it is expected that squeezing of the gap after the transient stage (like was done in Figs. 65a to b between run 1 and run 2) will result in at least the partial destruction of the structure. This is particularly important when the benefits of the viscosity drop are sought to be preserved after shearrefinnemen into pellets. Melt Flow Index of Disentangled Pellets and in-line Viscosity of Disentangled Melts. To explain the transient decay of polymer melts and results such as those in Figs 3, 7a and b, 28, 58a to d, the most crucial and convincing evidence in favor of the “disentanglement hypothesis”, is to measure the viscosity of the melt obtained by the disentanglement treatment after it has been treated and ensure that the decrease of viscosity was not due to chain breakage or degradation by measuring its molecular weight distribution with a GPC. There were two methods that we used to perform those convincing tests. They were both described in the introduction section of this paper. One method (Fig. 8) consisted in measuring the viscosity of the melt at the exit of the disentanglement processor by side-dispatching a small amount of the treated melt into a capillary viscometer working in the linear range. This corresponds to an inliin viscosity measurement done between 2 to 5 min after the melt left the treatment section (depending on the throughput rate). Another method consisted in measuring the Melt Flow Index (MFI) of the pellets produced by passing the treated melt through a strand die and a pelletizer. MFI is, roughly speaking, the inverse of viscosity. We consistently compared the in-line viscosity with the MFI measurements (Fig. 9). Results of 1996 on PC were published in 1999 [16], and several papers followed suit in subsequent years covering a decade of experiments [12-14,18, 43-54]. In fact, the entire lab activity of the author (9 persons) was 180 dedicated to the characterization by MFI and GPC of disentangled samples produced by the disentanglement processors described in Figs. 5a and b. Figures 67a and b provide another example of good correlation between the MFI of the disentangled pellets and the in-line viscosity measurement at the exit of the disentanglement processor. Fig. 67a This plot is similar to the one in Fig. 9 except that it applies to a different polymer, PMMA, already described in Figs. 55-57. The reference MFI (for the virgin) was 16.3. The various points correspond to changing the processing conditions in the 2 stations of Fig. 5b. Degradation due to the treatment was between 1.5 and 4%. The MFI values given are corrected for the small Mw degradation and are expressed in g/10 min at T=230 oC under 3.8 Kg. Pellets were dried at 60 oC for 17h before performing the MFI test. For the in-line rheometer, temperature was 225 oC, strain rate was 36.5 sec-1 corresponding to a flow rate of 5.8 cc/min. A picture of the in-line rheometer screen for this PMMA treated melt is shown in Fig. 67b. 181 Fig. 67b In-line viscosity measurement at the end of the disentanglement processor. Thousands of experiments were conducted with samples sent to the testing laboratories of large resin manufacturers and to universities. To summarize, time sweep treatments done in “disentanglement processors” (Figs. 5a and b) under a combination of shear, shear oscillation and extensional flow appeared to produce what we call "disentanglement", that can be characterized by the % improvement of MFI of the pellets produced by the shear-refining flow after correction of the viscosity by the Mw change (which affects viscosity as Mw3.4 ). The improvement of viscosity was also measured by the in-line viscometer which followed the state of the melt as we varied the treatment parameters. We conclude that it is, indeed, possible to submit polymer melts (branched or linear) to specific thermal-mechanical treatments that not only favor (immensely) the “in-line” conditions of flow inside the disentangling processor but also permit to capture in pellet form at least a part of the viscosity benefits imparted during the in-line viscosity reduction. Such “inpelllets sustained viscosity reduction improvement was reported by us for PC, PETG, LLDPE, 182 PP, EVOH and PMMA [43-54]. Is this technology applicable to all resins? The limitation seems to be related to: -the collateral degradation of Mw caused by the length of the treatment in the Shear-Refinement processor ( from 3% to 25% depending on the type of polymer and the amount of antioxidant additives). -the cost of the shear-refinement processor and the cost of the research to find the appropriate processing windows for each new resin. -the issues related to the control of the re-entanglement kinetics (too fast for certain conditions and polymers, too slow for others), i.e. the stability of the new entanglement network. -the apparent increase of the sensitivity to thermal degradation of the disentangled resin -the lack of quantitative theoretical understanding of the results, and, as a consequence, the disbelief that such experiments can be integrated with the current established understanding of polymer science. As already mentioned in the introduction, there is no apparent problem in combining the effect of strain softening and shear-thinning to boost the viscosity reduction of melts during the in-line disentanglement process to very large values (say +1500%) with very little degradation present (1-3%). However, the capture of, say, +100% viscosity reduction in the pellet appears to be a much more difficult task. It is true that the use of small concentrations of additives during the disentanglement processing, in combination with the thermal-mechanical treatment [82], has opened up new prospects of success that have rendered the in-pellet technology much more efficient (+300% ). 183 For instance, an extrusion grade (higher Mw) can be converted by this method into an injection molding grade (lower Mw) with boosted flow properties (+300%) compared to the same molecular weight untreated grade [82]. Manifestation of properties of disentangled polymers is not new Prevorsek and De Bona [83] prepared, by a solution process, unentangled polymers to establish whether the effects of chain entanglement persisted also in the glassy state. The polymers investigated were prepared by a solution process which, in the purification step, involved precipitation from dilute solutions. In the course of this study, we discovered that the melt viscosity of highly entangled polymers isolated from dilute solutions exhibits behavior which suggests that with such polymers it takes considerable amount of time for the molecules to attain equilibrium interpenetration and entanglement. This phenomenon allowed the preparation of samples where the chain entanglement could be varied without changing the chemical composition. This, in turn, provides the possibility to study the role of chain entanglement on properties belowTg without an interfering effect of chemical composition [83]. . Prevorsek and De Bona determined the melt viscosity of these precipitated polymers using a capillary rheometer. Their reported “unusual behavior” is reproduced below in Fig. 68. 184 Fig. 68 Melt viscosity vs time for a precipitated PCT and comparaison with a re-extruded melt (after Prevorsek and De Bona [ref. 83, Fig.4]. Reproduced with permission. Compare the transient viscosity increase in this figure with that of Fig. 58c attributed to the re-entanglement of disentangled PS. The melt viscosity of the polymers precipitated from solutions increased slowly towards their steady state level (the lower curve in Fig. 68). Depending on the temperature of the melt, the time to reach equilibrium could be between 10-100 min. When the polymer extruded from the steady state was re-extruded, the melt viscosity reached its steady state in a few minutes, as shown by the upper (dashed) curve in Fig. 68. Prevorsek and De Bona report [83] that chemical analyses and molecular weight determinations showed that no significant changes in composition or molecular weight occurred during the transient increase of viscosity for the melts produced from precipitation. . Furthermore, these authors characterized the extrudates by optical and electron microscopy and showed that no difference existed between the control and the transient melt. Prevorsek and De Bona showed that the transient response of the “precipitated melt”could be varied by changing the “solution history” and concluded: 185 In view of the results presented below on the effects of solution history on chain entanglement… it appears that only a systematic study could resolve the question whether the observed differences between predicted trend and experimental data should be attributed to inadequate theory or inaccurate experiments [83]. S. Rastogi and collaborators [84-86] explored the role of entanglements in obtaining a homogeneous product of ultra high molecular weight polyethylene (UHMW-PE). In this original approach to produce stable disentangled polymers, “the disentangled state is obtained directly from the reactor by controlling the polymerization conditions or in the solid state when there is enhanced chain mobility along the c-axis of a unit cell” [84]. Rastogi et al. claim [85] that their novel approach to synthesize disentangled polymers is applicable to polymers in general as long as three criteria are met during polymerization: -homogeneous polymerization, the catalyst sites being separated from each other as far as possible. -low reaction temperature to work in the range in which the rate of crystallization is faster than their synthesis. -living polymerization system to achieve a narrow molecular weight distribution. Rastogi and collaborators show that the disentangled state can be maintained in the melt over a long period of time, “invoking implications in polymer rheology” [84]: “Flow behavior of polymers through confined geometry is of fundamental and technological relevance having implications in fiber spinning or extrusion processes. Presence of entanglements and their realization in polymer melt is a basis of the flow behavior dunng polymer processing, crystallization and thus the mechanical properties. So far studies have been performed extensively on the entangled polymers in the thermodynamically stable melt state because of the non-availability of disentangled polymers. The availability of the disentangled polymers will provide an opportunity for the first time, to address the influence of disentangled (or partially entangled) melt state on chain orientation, relaxation time, viscosity and its implications on polymer crystallization”[85]. 186 Talebi [86} studied the kinetics of the re-entanglement process starting from well characterized disentangled UHMWPE synthesized by Rastogi’s method [84]. Like we did for the mechanically disentangled LLDPE .(Fig. 28 (recovery zone), Talebi used a time sweep experiment at low strain (1%) and low frequency (10 rad/s) to follow the growth of the moduli G’ and G” with time, slowing returning to the equilibrium entanglement value. The recovery curves presented by Talebi ( Figs. 4.12 and 4.13 of ref. [86]) are very similar to what we observed for mechanically made disentangled melt, see Fig. 28 (recovery zone) for LLDPE or Fig. 58c, for PS. Talebi also found the same increase of the strain softening ability for disentangled melts, showing that the critical strain to trigger time dependent effect (transient viscosity) is lower for disentangled melts [86]. In summary of what we learned from the work of Prevorsek et al. [83] and Rastogi et al. [84-86], one can say that one of the most demonstrative proofs that the effect of melt disentanglement by mechanical treatment is, indeed, to disentangle the macromolecules is evidenced in post-treatment thermally induced viscosity « recovery » experiments which look so much like what other authors find for their chemically synthesized or solvent precipitated disentangled polymers. One clearly sees in Fig. 28, for instance, that the viscosity of the initial specimen, which had been decreased by melt disentanglement treatment, was slowly and kinetically growing back to its initial viscosity value at the corresponding temperature, as the system was left alone in the rheometer chamber and the entanglements allowed to recombine to their stable thermodynamic level. The same behavior was observed when we operate the treatment at different temperatures. The thermally induced recovery behavior observed in Fig. 28 is kinetically driven and an activation energy can be determined for the process. These recovery experiments are most spectacular and convincing of what is taking place during the 187 treatment: disentanglement. In Fig. 60b (step 6), for PS, the recovery experiment was triggered by just reducing the strain %, keeping frequency the same (50 rad/s). This is clearly a demonstration that the decrease of viscosity was not the result of a mechanism of slippage at the surface of the Rheometer, nor a mechanical degradation of the chain macromolecules, but rather due to a viscoelastic effect in the bulk, which manifests the thermo-kinetic nature of the network of interaction (dynamic entanglements), and the possibility to modify it by mechanical means. For instance, Figs. 14 to 24 show that transients caused by pure rotational shear at high shear rate and strain are the same manifestation of this re-organisation of the dynamic entanglement network. Viscosity recovery curves are clearly triggered by a decrease of the strain rate in Fig. 18, in a way similar to what causes the recovery step in Fig. 28. We studied the inducement of non-equilibrium states for the entanglement network by dynamic solicitations (oscillatory) in the non-linear range (beyond a critical strain), separately analyzing the effect of increasing strain at given low frequency (Figs. 29-42), the effect of increasing frequency at given low strain amplitude (Figs. 43-45) or combining both (Figs. 46, 60a to c). We showed that sophisticated disentanglement processors (Figs 5a to b) could induce a lasting modification of the network of entanglement to the point that pellets could be extruded with sustained viscosity decrease that could last for long times, say tens of minutes or even hours at elevated temperatures far above Tg, say 150 oC above it. These pellets could be pressed into samples that could be reheated in a rheometer and studied in the linear range (Figs 39-42, 47-57) or in the non-linear range (Fig.25). 188 We also explained that it was not straightforward to succeed in obtaining in-pellets a “sustained orientation (i.e. disentanglement)”. When in-pellet disentanglement is not successful, it is either because the shear conditions are not strenuous enough to exhaust the cooperative mechanism responsible for shear-thinning (via the increase of the number of activated strands), or because the elasticity of the melt is too high, the shear stress at the wall is over the fracture stress, causing degradation, melt instability and possibly slippage. So, it is true that several experimental conditions could cause adverse effects, preventing disentanglement to take place. The art and science of disentanglement technology resides in obtaining the largest disentanglement possible, in the minimum amount of time, and with as little degradation and melt fracture as possible. After the disentanglement processing window has been found, the best re-entanglement method and conditions must also be found. The real problem is the understanding of the nature of entanglement and of the entropic character of polymer melt deformation. In this section, we present the results of an investigation carried out on disentangled pellets of PC. This study is quite revealing, in our opinion, of what causes “disentanglement”, i.e. of the reasons why pellets of treated melts (processed by the disentanglement processors of Figs 5a and 5b) sustain viscosity changes at elevated temperature for much longer times than what is predicted by the value of their to at that temperature. 189 Fig. 69a MFI (g/10 min) vs “flag” time for a virgin PC (Reference) and a disentangled pellet. T= 300 oC, 1.2 kg. The pellets were not dried before running the MFI test. The MFI testing equipment (from Dynisco) was fully automated and determined the starting time and the duration of the test, which were both dependent on the fluidity of the melt in the barrel. There were 8 measurements (“flags”) done to provide a given average of the MFI value. A computer was attached to the output of the MFI tester so that all MFI values for all flags could be recorded, giving the data in this figure. 190 Fig. 69b Same as in Fig. 69a but for different thermo-mechanical treatments in the disentanglement processor. The numbers in the insert give the % increase of MFI with respect to the reference MFI for the virgin (11.5). Different processing conditions yield different magnitudes of “improvement”. Figure 69a compares the MFI measurements for undried pellets of “disentangled” PC and the reference (the virgin pellets). The MFI remains constant during the time it takes the melt to pass through the capillary (the flags correspond to specific “indexed” measuring intervals). The MFI of the disentangled sample is 10 times greater than the reference at the beginning but drops steeply with time, from 120 to 85. The rate of passage through the capillary is so large for the disentangled sample that the 8 flags are accomplished in less than 15 seconds whereas it takes a minute and a half for the reference test. In Fig. 69b, several treatment conditions (changing the speed of rotation of the shaft, the frequency and amplitude of oscillation, the temperature profile of the zones, etc.) provided pellets with a variety of MFI response, but all show the same trend of a steep initial drop of the MFI followed by a stable plateau value. Figure 69b gives the impression that, given a certain grade (MFI=11.5), we can choose the MFI we want, from 120 (Fig. 69a) to 20. This may look like a very powerful asset to polymer processors. However, these results apply to undried pellets. Table 1 analyses the difference of the MFI obtained for undried and dried pellets (treated and virgin). The drying 191 conditions are described in the Table’s caption. The 1st column identifies the pellets (2 lots are considered, with slightly different MFI as shown for Virgin PC1 and Virgin PC2, although it is the same grade from the same manufacturer), the next two columns give the absolute value for the plateau MFI for the undried and dried sample, the next two columns convert those results to % MFI increase (with respect to the respective virgin MFI for the same lot), and the last two columns compare the undried and dried pellets after the correction for the amount of Mw degradation has been accounted for, as explained before. One sees, for instance, that the Treated-1 sample, which showed a +106% increase of MFI when undried and uncorrected has only +3 % left after drying and correction for the Mw decrease. Likewise, Treated -5 sample, which showed +434 % improvement has only left +77% after drying and Mw correction. Is this behavior “normal”? 1 2 3 4 5 6 7 Sample ID MFI MFI % MFI Increase % MFI Increase % MFI Increase after Degradation correction undried DRIED undried DRIED undried DRIED Treated -1 23.00 12.39 +106 +22 + 85 +3 Treated -2 33.89 20.15 +151 +59 + 150 +57 Treated -3 41.52 25.98 +208 +105 + 185 +91 Treated -4 25.02 18.23 +86 +44 + 85 +44 Treated-5 59.52 22.97 +434 +127 + 315 +77 Treated-6 61.57 26.89 +357 +112 + 335 +103 Virgin PC1 13.48 12.69 Virgin PC2 11.50 10.13 Table 1 Column 2 and 3: MFI measurement (in g/10 min at 300 oC , 1.2 Kg) of “disentangled” PC pellets (Mw of virgin=23,000). The reference MFI is for the virgin pellets (2 lots are shown for the same grade). Pellets were dried (4h @120oC and MFI done under dried N2) or undried before the MFI test. Columns 4 and 5 display the result in % MFI increase with respect to the reference (virgin). The last two columns, 6 and 7, show the final % MFI increase (which we call “% disentanglement” for 192 convenience) after the MFI have been corrected for the effect of the small % of degradation due to the treatment (the Mw of the treated and reference pellets were measured by GPC). Sample ID Tg oC DCp @Tg Pellet density g/cc % moisture content Treated -1 146.43 0.163 1.19851 0.198 Treated-2 145.87 0.272 1.19339 0.273 Treated-3 146.52 0.238 1.19684 0.206 Treated-5 147.08 0.244 1.19529 0.192 Treated-6 virgin PC1 virgin PC2 148.76 147.45 149.22 0.244 0.225 0.240 1.19318 1.19712 1.19855 0.116 0.265 0.183 Table 2 The moisture content % was measured with the Mark2 Moisture Analyzer from Omnimark Instrument Corp. The Tg data were obtained by DSC. The density of the pellets was according to ASTM D1238 The change of MFI between the undried and dried virgin pellets is what defines normality. One sees that the drying step does decrease the MFI of virgin PC1 by 6% and that of virgin PC2 by 13%. But this magnitude of change is 10 to 20 times less than what is observed for the undried vs dried treated pellets, from +434 % MFI increase to +127% only for Treated-5 sample, for instance. The difference is quite significant. This is particularly intriguing in view of the results of Table 2 which displays the moisture content, the density and the glass transition characteristics (Tg and the DCp at Tg) for the undried samples. It was originally expected that a large increase of moisture content would be observed for the undried treated pellets, explaining the MFI increases of Figs. 69a and b due to degradation by hydrolysis. But this was not the case: as Table 2 clearly indicates, the moisture content (expressed in % of weight loss) of the treated pellets and of the virgin pellets do not differ significantly. The same can be said of the density, which we measured to be sure that the treated samples were not less dense. The Tg and 193 the change of the heat capacity at Tg were also the same for the treated and the virgin undried samples. . One must conclude from Table 2 that the disentangled pellets and the virgin pellets have the same AVERAGE density and moisture content, although it should also be realized that any sample anisotropicity would not be revealed by such measuring techniques. Since we have hypothesized that “disentanglement” (the viscosity decrease retention) could be due to the formation of a structured multi-level orientation of the entanglement network of active strands, showing significant anisotropicity, the results of Figs. 69a and b and of Tables 1 and 2 lead us to believe that it is not the average functions that might be responsible for the extraordinary different flow behavior of the undried treated and virgin pellets, but, precisely, their anisotropic character. In more specific terms, and as a way of illustration, let us talk about the distribution of free volume in a polymer melt. It is well known that the free volume content influences the viscosity of polymers [3], an increase of free volume decreasing viscosity. The free volume is considered to be a local property which is isotropically distributed across the bulk of the sample. Diffusion of small molecules, such as water molecules, into the free volume of the polymer would be isotropic. However, what would happen to that diffusion process if we had succeeded in creating structures where the free volume was heavily anisotropically localized?. The water molecule local concentration would actually follow the pathways created by the channels of free volume. This may be the situation for the undried PC pellets, explaining many features observed for the treated pellets in Figs. 69 a and b). In summary, the “sustained orientation” of disentangled pellets could be the result of a modification of the free volume distribution in the melt, not simply its amount but also its 194 orientation. If the thermo-mechanical deformation history has resulted in an increase of the average free volume, one would expect a drop of the Newtonian viscosity because of the corresponding influence of the free volume on Tg. But one could also conceive cases where, say, for the same average free volume, a reorganization of free volume distribution would result in zones of layered concentration increase of excess free volume alternating with zones of lower than mean free volume. Such a vision could be describing Fig. 62. See later. In the following figures, we use the technique of TMA (Thermal Mechanical Analysis) to test the hypothesis of high anisotropic sustained orientation in treated pellets of PC and PMMA. In a TMA experiment a thin sample slice is placed on a plate and a probe touches it connected to an LVDT, constantly measuring the increment of thickness due to a small force on the probe (1 to 5 g). A constant heating rate (+ 10 oC/min) raises the temperature of the sample linearly in time. The temperature holds constant at the programmed maximum temperature for two minutes, and then the sample is cooled down at constant cooling rate. A pellet of polymer is made by cutting at regular intervals (with a pelletizer) a set of strands slowly pulled out of a strand die, at the exit of the extrusion process, after the strands have been cooled by immersion in a cooling bath. In Fig. 6b, the treated melt goes through a strand die and pellets of “disentangled” polymer are collected. The pellet is a short piece of the cooled strand, cut across by the pelletizer blade. To obtain a TMA sample we cut a small slice from the pellet itself. We can cut the pellet across the strand pull out direction or make a slice in the direction parallel to the strand flow direction. The final cut is about 1 to 1.5 mm thick flatly disposed on the lower plate of the TMA cell. For a virgin pellet, we also cut it in the crosssecctio (“cs” sample) or in the parallel direction (“parallel”), the pellet being a small cylinder 195 longer in the direction of strand pull out. Figure 70a plots % L/Lo vs temperature for a PC virgin pellet. Fig. 70a Lo is the initial thickness of the sample, at room temperature, L is the thickness calculated by the instrument as L=Lo-DL, where DL is measured by an LVDT attached to the probe applying a small weight on top of the sample as temperature is linearly increased. The maximum temperature was 300 oC where the sample was held for 2 min, then was cooled down to room temperature at constant cooling rate. Figure 70a is typical of what was observed for a virgin PC pellet. Either a “cs” or a “parallel” slice gave the same TMA response. The Tg of the PC sample was observed at a temperature of 143 oC, for which a very small deflection is visible. The steeper decrease of L started around T= 170 oC and continued until L collapsed to practically zero. The cooling curve looks like a straight line not very far above 0 (~1%). Figures 70b and 70c are the TMA responses for two different treated PC samples, each figure showing the distinct response obtained for a “cs” section and a “parallel” section. 196 Fig. 70b TMA curves for cs and parallel sections of PC disentangled pellets obtained after treatment by a single station in Fig. 5b (the melt exited after the first station and was pelletized). Figure 70b applies to a treated PC after treatment through a single disentangling processor (“single” station), and Fig. 70c shows the result for a pellet from a melt that went through 2 successive stations, as described in Fig. 5b. Additionally, for the pellet of Fig. 70c, the rotation of the shafts in the first and the second stations were reversed in order to “comb” the melt in one direction in station 1 and in the other direction in station 2. Let us examine the features of Fig. 70b first (the melt obtained with a single station). We have indicated 4 zones (1 to 4), and there are two curves, one for the cross-section sample (triangles) and the other for the parallel cut, which shows an up-turn just above Tg. Zone 1 corresponds to the glassy region, it is identical for both cs and //pellets. In zone 2, comparing with the virgin (Fig. 70a) and comparing the cs with the //sample, the //curve pushes upward and the cs curve 197 downward. This is typical of the response of an oriented sample which retracts in one direction and contracts in the other, just above Tg. The steep decrease of the thickness (in zone 3) is slightly different for both cuts, and, likewise, the cooling curves (zone 4) display some differences, but not in a very significant way. Fig. 70c TMA curves for cs and parallel sections of PC disentangled pellets obtained after treatment by 2 successive stations as depicted in Fig. 5b (the melt exited after the 2nd station and was pelletized). Additionally, the shaft rotation was reversed for station 1 and 2. The two TMA curves of Fig. 70c are strikingly different than those in Fig. 70b. First of all, zone 1 and 2 are the same for both the cs and //cuts: there is apparently no sign of orientation above Tg. However, a marked difference between the samples arise in zones 3 and 4. In zone 3, the cs sample appears to push upward, especially above T=200 oC, resulting in a slow down of the decrease of L with temperature. The final value of the thickness ratio is not zero but +10%.in zone 4. In the case of the parallel sample (//), the opposite trend is visible, the sample 198 appearing to pull L downward, which results in the further decrease of L towards negative values, the final thickness ratio being -15% in zone 4. We suggest that Fig. 70b corresponds to a typical behavior of local entropic orientation, for which chain segments have been oriented and return to their random equilibrium position as soon as Tg is reached. However, Fig. 70c is not typical of a traditional orientation process and displays the relaxation of a sustained oriented entanglement network with a strong anisotropicity between the transverse and parallel flow directions, and a high temperature stability of the network resulting from the compensation (the coupling interlock) between entropic and enthalpic interactions between the conformers. When such a situation occurs, the pellet shows the ability to retain at high temperature, far above Tg , its new “state of entanglements” responsible for the viscosity improvements shown in Figs. 47-54. In Fig. 70a, the orientation is not sustained at high temperature and collapses as soon as Tg is reached. The ability to retain orientation is, therefore, due to 1. the orientation of the entanglement network and 2. its stabilization (lock-down) by enthalpic forces. This determines the success whether viscosity decrease benefits will “stick” and for how long. In Fig. 70c, the final % L/Lo levels are +10% for the cs sample and to -15% for the //sample. How is that possible? As we said, the LVDT in the TMA instrument measures increments of thickness variation, not the absolute value (which is calculated). When the initial sample cut has frozen-in orientation below Tg, the initial thickness Lo does not correspond to the stable state; heating above Tg relaxes out the frozen strain, freeing up the internal motions to coordinate their interactions to obtain a stable state. The first motions to occur are those triggered by the presence of the available local free volume allowing a local re-organization of the conformal state of the bonds, showing entropic effects such as those observed in Fig. 70b. 199 The small force on the TMA probe is sufficient to flatten-out the thickness to almost zero. When the network of active strands has been oriented and stabilized by an enthalpic-entropic compensation mechanism, the release of the internal orientation not only occurs at a higher temperature than Tg (Fig. 70c) but also induces structures which resist the further relaxation by the small weight on the probe (case of the cs sample), or, conversely, favor it in the transverse direction (parallel sample), depending on the contribution of the enthalpic forces in establishing the distorted coil structure. In Fig. 70c the enthalpic contributions appear to have been less for the parallel sample since the final level of strain is 5% lower (in absolute value of % L/Lo), i.e -15% vs 10%. Figures 71a to c, Figs. 72a to b relate to the PMMA sample already described in Figs. 55-57 and Figs. 67a and b. Figures 71a to c display the TMA response for a cross-section cut of three types of pellet, a virgin sample, a +70% (MFI increase) disentangled sample and a +100% disentangled pellet. The three figures focus on different temperature ranges, comparing the behavior of the virgin and the disentangled pellets in zones 1, 2 , 3 and 4. The first observation (in Fig. 71a) concerns the decrease of the Tg for the disentangled sample, especially for the +100% disentanglement. This ~10 oC difference in the Tg can be associated with an increase of free volume due to the treatment. The respective position of the curves in the T > Tg region is, overall, controlled by this increase of free volume (Fig. 71a), but Fig. 71b shows an interesting feature of the treatment at temperatures above T=225 oC: the curve for the virgin (indicated by the label “3” on the graph), which was located above the other two curves for T< 255 oC, is now located underneath them (note that the +100% disentangled pellet is designated as “1”). This apparent greater stiffeness of the disentangled melts at higher temperature is maintained all the way through cooling, resulting in a higher value for the 200 %L/Lo at the end of the experiment (Fig. 71c). This result is intriguing in view of the fact that if the free volume was the only parameter modified by the treatment, a shift along the temperature axis would be expected, for all temperatures, hence the disentangled melt should be less stiff, not stiffer. Here, it appears that the free volume increase is just one of the several features altered by the disentanglement treatment, and that there is, in addition to it, an effect of modulus stiffening in the rubbery and rubbery flow region, in other words, the signs of a weaker but more stable network of entanglement. This is the same situation as in Fig. 70c for PC. However, in Figs. 72a and b, the effect of free volume increase superimposes on top of the phenomenon of sustained orientation and thus of extended stability of the network of entanglements. Thus the viscosity decrease can be accounted for by the decrease of Tg and the stability of the shift of time scale is maintained at high temperature because of the lock down between enthalpic and entropic contributions permitting the sustained orientation to occur. Fig. 71a 201 This is the same PMMA studied in Figs. 55-57 and Figs. 67a and b. The Virgin pellet is the curve on the top for T=175 oC, below it is the +70% disentangled pellet, and below it is the +100% disentangled pellet, showing a substantially lower Tg. These TMA curves correspond to cross-section cuts. Fig. 71b Detail of Fig. 71a focusing in the higher temperature region. 202 Fig. 71c Detail of Fig. 71a in region 4 (cooling), showing the respective final level of % L/Lo present at the end of the heating-cooling cycle. The top curve corresponds to the +100% disentangled pellet, followed by the +70% disentangled pellet, the virgin pellet being the bottom one. Figures 72a and 72b give the rate of change of the TMA signal as a function of temperature, obtained by differentiating the virgin and the +100% disentanglement curves in Fig. 71a. The study of the rate permits clarification of the respective role of free volume excess and of the increase of stability of the network of entanglement on the relaxation behavior. For the comparison we refer to the values given in the respective graphs which point to certain features of the relaxation process, such as the onset of the thickness decrease (associated with Tg) or the maximum of the rate, etc. The general features observed for both the virgin (Fig. 72a) and the disentangled (Fig. 72b) pellets are the presence of two peaks, one smaller at lower temperature, the other one of greater magnitude (their sign is negative because the thickness 203 decreases), and of a plateau in the high temperature region of the melt before the rate goes to zero. These features are characteristics of how the changes due to processing affect the relaxation due to the small force on the TMA probe. It is clear that the information in Figs. 72a and b are complementary to the rheological analyses of Figs. 55-56. Fig. 72a This graph corresponds to the rate of change of the TMA signal for the virgin pellet in Fig. 71a 204 Fig. 72b Rate of change of the TMA signal for the +100% disentangled pellet of Fig. 71a A first observation is that the Tg onset, the temperature at the first minimum and the temperature at the second minimum are all shifted to lower temperature, by 10 oC, 14 oC, and 15.7 oC, respectively. This is the consequence of the free volume excess. The rate at the first minimum is 56% higher for the disentangled sample than for the reference (-0.54 vs -0.34), but is only 5% lower at the major peak (where the rate is maximum). The second observation concerns the kinetics beyond the 2nd maximum, at T > 150 oC, comparing Figs. 72a and b. In this temperature range, the rate for the disentangled melt spreads towards the right, in a way which appears to slow down or even reverse the effect of the free volume (which shifts temperatures towards the left for the disentangled sample). This is quite visible when one looks at the temperature values for the “slow down” of the relaxation process, shown as a plateau in Figs. 72a and b. The onset of the plateau occurs at the same 205 temperature of 200 oC for both the reference and the disentangled samples, although one would have expected a shift of -10 to -15 oC or so for the disentangled melt because of the free volume excess shifting Tg by this amount. Furthermore, one sees that the end of the slow down occurs for a temperature 15 oC higher for the disentangled melt, 225.6 oC vs 210.7 oC. This is a +25 oC to +30 oC shift difference from the temperature value expected after the free volume excess is taken into consideration. The value of the rate at the plateau is -0.55 for the virgin and -0.31 (average) for the +100% disentangled sample. In other words, the melt remains stable for a longer time, to a higher temperature and varies at a slower rate for the disentangled pellet. This is quite a crucial observation which explains the stability of the disentangled network at high temperature. As we mentioned previously for Fig. 55, the viscosity frequency sweep of the disentangled PMMA melt took 24 hours at T=225 oC to recover its original shape (that of the reference). The above result appeared as an extraordinary challenge to existing theories of molecular motions in polymer melts. The explanation of the results, we suggest, is related to a new understanding of the concept of entanglements of long chain molecules and of its impact on the mechanism of deformation in the rubbery and rubbery flow region. In this paper we have shown that transients were triggered by the combination of strain rate and strain, whether it was in pure shear (rotational viscometry), in pure dynamic oscillatory shear, or in the combination of the two (Figs. 7a and b). Transient responses reveal how bond interactions evolve as a result of an imposed deformation. There are different mechanisms of response which are related to the initial state of interaction at the initiation of the deformation process. Depending on “the severity” of the deformation, i.e. on the magnitude of “the demands” (speed of deformation, magnitude of strain), chain segments are able to freely diffuse in 3 D (in the 206 Newtonian region) or actively interactively cooperate to determine how many of them are stretched together as a strand unit, and for how long (before they relax by cooperative diffusion). When the deformation conditions have reached a level where all the strands are activated simultaneously (at the maximum of (G’/G*)2), then the network of entanglement starts to orient by a mechanism of cooperative interaction between enthalpic and entropic forces. This situation may result in the formation of a stable oriented network of activated strands and result in the long term viscosity retention behavior observed in this paper. The anisotropicity of the network is probably linked to its stability, and vice-versa. Working in the proper range of frequency (or strain rate) and strain amplitude represents the first set of conditions specifically needed to create a new oriented network of entanglement, but the lock down of this entanglement network (resulting in the sustainability of orientation) is due to another condition, only realized by the concomitant orientation of the laminar flow layers into a stratified structure where both entropic and enthalpic contributions “compensate”. Both entropic (orientation) and enthalpic (changes of the conformation distribution along the chain) forces must influence one another to result in the lock-down of the entanglement structure. When this is realized, melts can behave rheologically in extraordinary new ways, and new applications can be derived, as further publications will reveal. SUMMARY To summarize some of the findings and thoughts expressed in this paper: -Transients and steady states must be described by a unique theory of the deformation of interactive conformers. We suggest it is necessary to understand non-linear effects first and to have linear viscoelasticity derived by extrapolation to infinite time. In other words, time, frequency (or strain rate) and strain should be involved in the 207 mathematical description of the deformation process (in the quantification of the moduli). -A melt can be brought out of equilibrium with respect to its entanglement state. The return to equilibrium explains the transient properties. New entanglement states can be made quasi-stable, even at high temperature in the melt, by coupling entropic and enthalpic effects produced under specific conditions of melt processing. -The currently accepted descriptions of rheology only apply to a stable entanglement state, which is not general enough. For instance, the WLF-Carreau equation of viscosity-strain rate does not correctly describe the rheology of an unstable entanglement network. The modelization of the influence of a network of entanglement on the melt deformation mechanism in terms of parameters introduced in linear viscoelasticity (t, GoN, Me) provides the wrong answers when the entanglement network has become transient. -The influence of strain on the rheological equations is currently not addressing the issue of its influence on the stability of the network of entanglement, and therefore is incomplete. -The interpretation of the phase angle between stress and strain in terms of a dissipative and an elastic component represents an over-simplification of the mechanism of deformation which, we believe, mischaracterizes the relative influence of a network of strands on the elasticity /relaxation process versus the influence of the local bond orientation (the conformer statistics). The difference between the two permits to define the amount of interactive coupling reorganization due to entropic vs enthalpic drives and under what conditions of strain rate and strain they occur. An entropic driven 208 coupling mechanism of deformation can be viewed as an activation, then orientation process of the active network of strands. We have made the suggestion, in this paper, that the active number of system strands (defining the EKNET network) is proportional to (G'/G*)2. In fact, the active number of strands is not exactly proportional to (G'/G*)2 but can be calculated from (G’/G*)2 , and is almost exactly equal to (G’/G*)2 shifted by a constant when its value is approximately less than 80% of the maximum of (G'/G*)2 .The enthalpic contribution starts beyond that.point and corresponds to the orientation of the network. We suggest that only certain compensations of enthalpic and entropic contributions result in stable “sustained oriented entanglement states”. This set of conditions would be the equivalent of “plastic yielding” and implies highly anisotropic samples. -An increase or decrease of G* (t) and thus of viscosity can be produced when the network of strands is unchanged (Figs 1a to d) and local orientation/relaxation is responsible for the transient behavior, and the relaxation times relate to the properties of this network. In order to obtain a modification of the network, one needs to add energy to it until it yields. Strain rate or frequency are capable of reaching that point for any strain % deformation, but the value of the strain % allows to decrease the frequency or strain rate at which the network starts to deform. CONCLUSION The deformation of a polymer melt in shear mode is the main subject of interest in the science of rheology of such materials. It is a crucial topic for successfully processing these materials. As illustrated in part I of this series [2] and in the above examples, it is a complex 209 and rich subject which is far from being fully understood. In part I of this series [2], we suggested that even the linear visco-elastic behavior of polymer melts (at low strain rate and low strain) was not satisfactorily described by the accepted theoretical models, when carefully comparing experiments and theoretical predictions. In the non-linear range, at high strain rate and strain, the subject of this part II, it is generally admitted that the current theoretical developments that successfully predict the main characteristics of polymer melts in the linear range come short but merely need improvements. The improvements proposed generally consist in tweaking certain assumptions of the linear viscoelastic model to be able to extrapolate to the non-linear behavior. There is no current theoretical challenge to the dominant reptation model of melt deformation in polymer physics. The aura this model has reached among polymer scientists makes it more difficult to search for other explanations for viscoelastticit and rubber elasticity. Yet, as we suggest, it is possible that the experiments described in this paper challenge the reptation school to its limits, to the edge of usefulness. As already concluded in part I of this series of papers dedicated to flow, the theory seems to be fine in the linear range in appearance only. The “devil is in the details” says the old saying. The present understanding of the physics of macromolecules is based on an analysis of the properties of a single chain. The presence of the other chains is perceived as a mean field influence on the properties of that chain. The reptation school considers that this mean-field can be described as a topology, an homogeneous field of obstacles restricting the motion of the single chain and explaining the molecular weight dependence of viscosity. The mobility is constrained within an imaginary tube and the chain “reptates” within that tube. The shortcomings of the predictions of that model made the initial static tube evolve into a more dynamic tube, capable of evolution, in time and as a consequence of the various modes of deformation of the melt. 210 The tube was therefore thought to have a stability of its own, it could fluctuate in length, and, to address some of the non-linear issues, it could get thinner and elongate in length. In other words, the tube itself had evolved into a “super macromolecule” capable of deformation very similar to what early polymer scientists would assign to macromolecular chains themselves. Perhaps, at the horizon of the reptation school, also lies the concept of entanglement of the tubes themselves!. We are not suggesting this idea totally ironically, because it illustrates another concept that we will develop in a follow up article of this series, that of the need to not only define the scale of the basic unit that participates in the deformation process, but also to determine the link and the modulation between cooperative scales. In explaining several figures of this paper, we made reference to a “network of strands” to describe the cooperative interactive process resulting from the macroscopic deformation. We obviously referred to a basic unit of deformation that involved the cooperative motion of a group of bonds responding as a set [87]. We must define what cooperation means, how many bonds cooperate in an active strand and where they are located, on a single chain or on several chains?. The physics of dealing with all the chains at once is the model that we have adopted to describe the deformation of polymer melts and solids, above Tg and below Tg, [72, 87]. The theory not only addresses the interaction between the conformers of a single chain to assume the shape of a macro-coil (which can be deformed), but also defines why entangled macro-coils exhibit the response of a network of active strands when all the chains participate cooperatively in the deformation process. The link between the deformation of a conformer, of a macro-coil and of a network of strands must be fully described 211 To be useful the new model should understand the influence of chain molecular weight to predict a change of behavior below and above a critical molecular weight, in other words the characteristics of “entanglements” and their influence on the dynamic melt properties G’(w,T) and G”(w,T). It must predict shear-thinning and strain-softening in shear mode, and strainharddenin in extensional mode. It should also successfully describe the transitional behavior at Tg, from a solid-like to a liquid-like behavior. 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