Slides for Lecture #3 Instabiliity of the Entanglement Network

Instability of the Entanglement Network studied in a Dynamic Rheometer WIZIQ Lecture #3 April 9th 2011 J. P. IbarWe present evidence, in this presentation, of the instability of the entanglement network, characterized by Go,N , to, and ways to trigger it. Go,N= r RT/Me where Go,N is the rubbery plateau modulus, r is melt density, R the gas constant, T absolute temperature and Me the mass molecular weight between entanglements. ho = Go,N to k with to the reptation time, ho the Newtonian viscosity and k a constant which depends on the nature of the polymer. INTRODUCTIONIn a dynamic rheometer (parallel plate configuration), we perform a 3 steps experiment 1. Frequency sweep at constant T in the linear region (low g%): step 1 2. Time sweep (“treatment” step 2) 3. Rerun step 1: Frequency sweep step 3 4. Compare G’, G” for steps 1 and 3 Note that in step 2, from one experiment to the next, we vary the frequency and the g % amplitude, or time. QUESTION: Are we expecting the results for step 1 and step 3 to be different? Why would they be different? How do they vary with the parameters of step 2?. EXPERIMENTAL PROTOCOLEPREAMBLE STUDY: -I Step strain rate experiment in pure viscometry à Hints that the steady state viscosity can be unstable. -II Dynamic data at increasing strain: time dependence of strain softening. NOTE: The Figure numbers on the slides refer to Figures in the paper: “The Great Myths of Rheology, part II” downloadable from My Content at www.wiziq.com/NewSchoolPolymerPhysics977161Fig. 2aFig. 2bFig. 16aFig. 16bFig. 17Fig. 18Fig. 19aFig. 19bFig. 19cFig. 19dFig. 20Fig. 22aFig. 22bFig. 22cFig. 22dFig. 23CONCLUSION For this LLDPE melt, the transient triggered by a step strain rate is composed of a short term relaxing component and of a long term relaxation, which, we suggest, is associated with the instability of the steady state itself, this instability increasing with the value of the shear stress. G(t) = A GoN h (t/to,N) *(1+Aexp-(t/to)n)) h is a strain softening function (between 1 and 0) toN = tooN exp(-(DH-k s)/RT with s= G . g These are recursive equations As the stress s decreases due to relaxation, the network relaxation toN increases, but as strain rate increases, s increases that lowers toNTriggering Entanglement Network instability by effect of strain In dynamic experimentsFig. 27a Fig. 27bFig. 28Shear-thinning reduces viscosity from 57,000 to 10,000 Pa-s Strain-Softening, done under those shear-thinning conditions, decreases modulus by a factor h=0.31 After release of the stress, the remaining viscosity decrease is 0.6574, compared to the original Newtonian value. This is as if the MFI of the melt had increased by 52%. Dynamic experiments permit to create specific strain softening conditions that control the final viscosity drop ratio and the kinetics of recovery. NOW WE ARE READY TO EXPLORE THE THREE STEPS EXPERIMENTSThe polymer resin is a PC (Mw=32,000à M/Me~13 At T=275 oC (Tg+133 oC) We study the effect of different step 2s on frequency sweeps 1. Time sweep at T275, 0.1 Hz, 5% strain 20 min 2. Time sweep at T275, 0.1 Hz, 20% strain 20 min 3. Time sweep at T275, 0.1 Hz, 500% strain 20 min • We suspect that this resin has received a prior mechanical history that has destabilized its entanglement state, corresponding to a slight initial disentanglement. • The problem with the present state of understanding of polymers is that there is no “Entanglement Index” which would quantify whether the resin is at its equilibrium entanglement state value or not.Fig. 29 5% strainFig. 30Fig. 32a 20% strainFig. 32bFig. 33Fig. 34Fig. 35aFig. 35bFig. 36a 500% strainFig. 36bFig. 37aFig. 37bFig. 37cFig. 37dFig. 38New case study: Disentangled PC (220% MFI improvement)Fig. 39aFig. 39bFig. 40Fig. 42New study at lower temperature T=225 oC • 1 Hz 5% strain • 10 Hz 5% strain • 40 Hz 5% strain And 5 Hz 20% strainFig. 43a 1 HzFig. 43bFig. 43cFig. 43dFig. 44a 10 HzFig. 44bFig. 44cFig. 44dFig. 45a 40 HzFig. 45bFig. 45cFig. 45dFig. 45eFig. 45fFig. 46a 5 Hz, 20% strainFig. 46bFig. 46cFig. 46dFig. 46eFig. 46fFig. 50Fig. 52Fig. 53aFig. 53bFig. 54CONCLUSIONS Current understanding of viscoelasticity of melt is only valid if the entanglement network is stable. Then the concept of a scalar Me to describe entanglement might be acceptable. Under conditions of dynamic conditions (strain rate and strain) that makes the entanglement network unstable, shearthinnnin and strain softening combine in a way that makes the concept of a single Me unacceptable. Strain softening factors are different at various w and are different for G’ and G”. Me can no longer be a scalar. Likewise, the concept of a terminal time (1/wx) is not representative of the variety of changes occurring to the interactions between the conformers describing the evolution of the network of entanglements when the melt is deformed in the non-linear regime. We must find new expressions for G’ and G” that not only describe the results of linear viscoelasticity but also apply to understand the results shown in this presentation. The concept of entanglement must be readdreessed