Viscoelasticity molecular weight dependence

It appears that the formal theories are not sufficiently sensitive to structure to be of much help in dealing with linear viscoelastic response Williams analysis is the most complete theory available, and yet even here a dimensional analysis is required to find a form for the pair correlation function. Moreover, molecular weight dependence in the resulting viscosity expression [Eq. (6.11)] is much too weak to represent behavior even at moderate concentrations. Williams suggests that the combination of variables in Eq. (6.11) may furnish theoretical support correlations of the form tj0 = f c rjj) at moderate concentrations (cf. Section 5). However the weakness of the predicted dependence compared to experiment and the somewhat arbitrary nature of the dimensional analysis makes the suggestion rather questionable. 

Hayashi,S. Theory of viscoelasticity in temporarily crosslinked polymers. IV. Relaxation spectrum and molecular weight dependence of viscosity. J. Phys. Soc. Japan 19,2306-2312 (1964). 

If the general features of the viscoelastic behaviour are well depicted, the experimental molecular weight dependence of these parameters is ... 

Coffman JP, Naumann CA (2002) Molecular weight dependence of viscoelastic properties in two-dimensional physical polymer networks amphiphilic lipopolymer monolayers at the air-water interface. Macromolecules 35 1835-1839... 

V.R. Raju, E.V. Menezes, G. Marin, W.W. Graessley, and L.J. Fetters, "Concentration and Molecular Weight Dependence of Viscoelastic Properties in Linear and Star Polymers," Macromolecules, 1, 1668 (1981). 

At this point the reptation theory makes some strong predictions about the viscoelastic response in the linear regime, viz, the viscosity varies as and the ratio of Js°/Gn = 6/5 = 1.2. Note that the molecular weight dependence of the viscosity has already been discussed above, and recall that, experimentally, the viscosity varies as N -. In addition, the ratio is observed experimentally... 

We have already met this particular molecular weight dependence, in Eqs. (5.119) and (5.120), when formulating the average viscoelastic relaxation time f of polymer melts. Roughly speaking, r gives the time required by a chain for a complete conformational reorganisation. This also implies a full reorientation of the end-to-end distance vector of the chain. It is exactly this motion which shows up in the dielectric normal mode. 

In any case, whatever the model, since tube-renewal is more important (compared to reptation) and accelerates the motion more efficiently for short chains than for long chains, it introduces additional molecular weight dependences of the dynamical quantities, and certainly contributes to the experimental deviation of the viscosity/molecular weight exponent from the reptation value 3. All treatments, including tube renewal, exhibit such deviations which vanish for asymptotically long chains. Detailed quantitative tests are, however, very difficult to perform when tube-renewal is taken into account, polydispersity becomes an essential parameter (the shortest mechanism, reptation and tube-renewal, dominates the relaxation process). No complete set of experiments, either for diffusion or for viscoelasticity, with constant polydispersity at all molecular weights, are presently available. 

This molecular weight dependence of D has been seen experimentally in melts by Klein (1978) and in concentrated solutions by Legeretal. (1981). Reviews of diffusion behavior are available (Tirrell, 1984 Kausch and Tirrell, 1989). One can also deduce the molecular weight dependence of the viscosity by a nonrigorous but plausible argument. Suppose the entire fluid behaves as a simple viscoelastic solid (Maxwell element) then its relaxation time would be... 

With these generally accepted, but not necessarily accurate, conceptual models in hand, major efforts are going into molecular modeling of more complex real behavior. This is the state of the art. Some important areas of current work include nonlinear viscoelasticity, branched polymers, blends of different molecular weights, and chemical composition. E)eep problems remain, such as the definitive explanation of the 3.4 power law for the molecular weight dependence of melt viscosity and proper description of concentrated solution rheology. 

Tanaka K, Taura A, Ge SR, Takahara A, Kajiyama T. Molecular weight dependence of surface dynamic viscoelastic properties for the monodisperse polystyrene film. Macromolecules 1996 29 3040-3042. 

This chapter removes the hmitations described by Ferry and Pearson. Section 13.2 supplies an ansatz that correctly predicts the shapes of major viscoelastic functions. Comparison with experiment shows that the ansatz describes experiment well. Material-dependent viscoelastic parameters determined from actual measurements have simple concentration and molecular weight dependences, as is reasonably expected for rational physical properties, leading to a description for the c and M dependences of the viscoelastic functions, and thus to a coherent description of the variations in the shapes of the viscoelastic functions when polymer concentration and molecular weight are changed. 

Raju, V. R., Menezes, E. V., Marin, G., Graessley, W. W. Concentration and molecular weight dependence of viscoelastic properties in linear and star polymers. Macromol (1981) 14, pp. 1668-1676... 

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