Chain conformations in blends

Thus it is of interest to check the accuracy of eq. (7.39) by testing the basic assumption that the mean square gyration radii are independent of the state of the mixture (Fig. 7.30). It is seen that for T Tc this assumption still is a reasonable approximation, since deviations from this approximation are in the order of several percent only. However, considering a mixture of asymmetric composition ( j A 4 b) as done in Fig. 7.30, one notes that 

The behavior in Figs 7.30(b) and 7.31 signifies a serious breakdown of the simple RPA, of course-remember that the simple RPA would imply hor- 

As already discussed in Section 7.2.6, studies of interdiffusion have focused on the nonequilibrium behavior where in a compatible (AB) system a layer of pure A-polymers is brought on a layer of pure B-polymers, and one studies the broadening of the resulting interfacial profile between A- and B-monomers with time (Fig. 7.22). These studies have attempted to address theoretical ideas about the relation between interdiffusion (Dint) and self-diffusion constants (Dj) in blends, and to check for the so-called thermodynamic factor . In fact, if one extends simple mean-field concepts to the dynamics of interdiffusion in polymer mixtures, one finds that the 

Here the right-hand side of the equation is simply the thermodynamic factor which hence should be linear in the variable Nx- The Monte Carlo test of eq. (7.41) revealed a rather pronounced curvature of this ratio Ant(x)/Ant(x = 0) as function of x, however also the short chains accessible (N = 10,20, and 40, respectively) did not conform to the expected scaling in terms of the variable Nx- This problem certainly deserves further study, however, since the chain lengths used are very short, and there are also possible systematic errors in principle, one should deduce Ant(x) from interdiffusion of layers which differ in their concentrations 4 A, i A only a Uttle (rather than having = 0,4 A /i i A + = 1, as done in the avail- 

Similar restrictive comments need to be made about the existing simulations of spinodal decomposition in polymer blends. First studies addressed the two-dimensional case. In this case, there is no chain interpenetration, and since polymer mixtures in d =2 dimensions are not predicted to become mean-field-like for AT — oo, one expects the same behavior as in small molecule mixtures, and this is what has been found. Using the slithering snake algorithm, the dynamics of the model is neither realistic at short times (where the chain dynamics should be described by Rouse-model type motions ) nor at late times (where hydrodynamic effects play a role, as discussed above, at least in d=3 dimensions). 

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