Polyisoprene Damping function

Figure 13.22 Damping functions hf y) and hs y) for the fast and slow relaxation processes of a 15 wt% solution of a micelle-forming polystyrene-polyisoprene diblock copolymer (molecular weights, respectively, of 14,000 and 29,000) in a low-molecular-weight (A/ = 4,000) polyisoprene. Damping functions for linear and star polymers and for silica dispersion are shown for comparison. (From Watanabe et al. 1997, with permission from Macromolecules 30 5905. Copyright 1997, American Chemical Society.)...

The damping function, g(s), in Eq. (6.30) accounts for lack of proportionality between stress and strain. The product, g(e)e, quantifies the nonlinear elasticity (g(e) = 1 for linear viscoelastic behavior). Separability of time and strain is illustrated for 1,4-polyisoprene in Figures 6.4 and 6.5 the time-dependence of the stress relaxation is the same for shear strains of varying amplimde and for different modes of deformation (Fuller, 1988). 

In polymers, due to the constraint resulting from the connectivity of the chain, the local motions are usually too complicated to be described by a single isotropic correlation time x, as discussed in chapter 4. Indeed, fluorescence anisotropy decay experiments, which directly yield the orientation autocorrelation function, have shown that the experimental data obtained on anthracene-labelled polybutadiene and polyisoprene in solution or in the melt cannot be represented by simple motional models. To account for the connectivity of the polymer backbone, specific autocorrelation functions, based on models in which conformational changes propagate along the chain according to a damped diffusional process, have been derived for local chain... 

The importance of errors in the short time dynamics can be explained with reference to Figs. 4 and S. The initial drop in the correlation functions shown in Fig. 4 would likely occur on a faster time scale in a more realistic simulation. These high frequency motions are too severely damped by the BD equation of motion. Likewise, it is expected that the separation of time scales shown in Fig. 5 is even more striking in reality. NMR experiments on polyisoprene support this conclusion. They indicate that motion on two time scales contribute to the correlation function decay, in qualitative agreement with the simulation results [67]. The separation of these two time scales, however, is larger in the experiments than in the simulations. 

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