Viscoelasticity concentration dependence

The effects of interaction on viscoelastic properties at low concentrations depend on the Simha parameter. For example, Ferry has pointed out the importance of c[jj] for the transition from Zimm-like to Rouse-like behavior in the dynamic properties and in the observed values of J (15). The shear rate dependence of viscosity undergoes a corresponding transition as a function of... 

Williams has derived the molecular weight and concentration dependence of a viscoelastic time constant t0 (actually the characteristic time governing the onset of shear rate dependence in the viscosity) from his theory (217-219). Employing a dimensional argument, he equates the parameters which control the shear rate dependence of chain configuration and the intermolecular correlation function. The result agrees with the observed form of characteristic relaxation time in concentrated systems [Eq.(6.62)] ... 

As an example of the concentration dependence of viscoelastic properties in Fig. 16.11 the shear creep compliance of poly(vinyl acetate) is plotted vs. time for solutions of poly(vinyl acetate) in diethyl phthalate with indicated volume fractions of polymer, reduced to 40 °C with the aid of the time temperature superposition principle (Oyanagi and Ferry, 1966). From this figure it becomes clear that the curves are parallel. We may conclude that the various may be shifted over the time axis to one curve, e.g. to the curve for pure polymer. In general it appears that viscoelastic properties measured at various concentrations may be reduced to one single curve at one concentration with the aid of a time-concentration superposition principle, which resembles the time-temperature superposition principle (see, e.g. Ferry, General references, 1980, Chap. 17). The Doolittle equation reads for this reduction ... 

The bis-urea thin filaments can be very long in non-polar solvents such as 1,3,5-trimethylbenzene. Consequently, these solutions show a high viscosity r]/r]Q = 8 at a concentration C = 0.04 molL and at T = 20 °C) and a high concentration dependence of the viscosity (ri/rio C ) [43]. As in the case of UPy based supramolecular polymers, the value of this exponent is in agreement with Cates s model for reversibly breakable polymers [26,27]. However, the solutions are not viscoelastic, even at concentrations well above the overlap concentration [43]. Consequently, the relaxation of entanglements, probably by chain scission, must be fast (r < 0.01 s). 

Michon, C., Cuvelier, G., and Launay, B. 1993. Concentration dependence of the critical viscoelastic properties of gelatin at the gel point. Rheol. Acta 32 94-103. 

Stable particle suspensions exhibit an extraordinarily broad range of rheological behavior. which depends on particle concentration, size, and shape, as well as on the presence and type of stabilizing surface layers or surface charges, and possible viscoelastic properties of the suspending fluid. Some of the properties of suspensions of spheres are now reasonably well understood, such as (a) the concentration-dependence of the zero-shear viscosity of hard-sphere suspensions and (b) the effects of deformability of the steric-stabilization layers on the particles. In addition, qualitative understanding and quantitative empirical equations... 

Although motional averaging might occur in ways other than that envisioned by Cates, temperature-jump experiments have yielded values of Tbr that indicate Tbr < in the region where the relaxation is nearly monoexponential, in agreement with Cates theory. In addition, Cates theory offers distinctive predictions for the concentration-dependencies of the viscoelastic behavior these allow the theory to be tested rather stringently. To obtain these predictions, we note that in the semi-dilute regime, the mean-field reptation time is L 4>, where 0 is the volume fraction of surfactant. Hence, from Eqs. (12-31) and... 

It is expected that the same picture that gives a good account of the linear viscoelastic behavior of polymer melts should also hold for semidilute and concentrated solutions. In the case of semidilute solutions some conclusions can be drawn from sealing arguments (19,3, p. 235). In this way, concentration dependence of the maximum relaxation time tmax the zero shear rate viscosity r Q, and the plateau modulus G% can be obtained, where t is the viscosity of the solvent. The relevant parameters needed to obtain Xmax as a function of concentration are b, c, N, kgT, and Dimensional analysis shows that... 

The long delayed responses of the fuel cell to changes in load have been attributed to mechanical property changes in the polymer. We have initiated measurements of polymer stress relaxation. The stress relaxation and viscoelastic creep of Nafion is both temperature and water concentration dependent. Response times vary from 1 s to 10 s, which can give a wide range of characteristic response times for PEM fuel cells. 

Figure 7.7b shows the concentration dependence of the plateau modulus obtained from the fitting of the viscoelastic spectra. We have also calculated GL from Tls and 770 by using the relation... 

In addition to the free volume [36,37] and coupling [43] models, the Gibbs-Adams-DiMarzo [39-42], (GAD), entropy model and the Tool-Narayanaswamy-Moynihan [44—47], (TNM), model are used to analyze the history and time-dependent phenomena displayed by glassy supercooled liquids. Havlicek, Ilavsky, and Hrouz have successfully applied the GAD model to fit the concentration dependence of the viscoelastic response of amorphous polymers and the normal depression of Tg by dilution [100]. They have also used the model to describe the compositional variation of the viscoelastic shift factors and Tg of random Copolymers [101]. With Vojta they have calculated the model molecular parameters for 15 different polymers [102]. They furthermore fitted the effect of pressure on kinetic processes with this thermodynamic model [103]. Scherer has also applied the GAD model to the kinetics of structural relaxation of glasses [104], The GAD model is based on the decrease of the crHiformational entropy of polymeric chains with a decrease in temperature. How or why it applies to nonpolymeric systems remains a question. 

The concentration dependence of blends viscosity (at constant T and additivity rule. In rj = S<(>j In Hj, as showing a positive deviation, PDB, negative, NDB, or mixed, PNDB or NPDB. Treating blends as emulsions of viscoelastic liquids, leads to prediction of PDB (found in 60% of blends). The mechanism that explains NDB is the interlayer slip, caused by the thermod3mamically... 

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