Concentration fluctuation model polymer blends

Kamath, S. K., R. H. Golby, S. K. Kumar, K. Karatasos, G. Floudas, G. Fytas, and J. E. L. Roovers. 1999. Segmental d5mamics of miscible polymer blends Comparison of the predictions of a concentration fluctuation model to experiment./. Chem. Phys. 111 6121-6128. 

The simulation result for the time evolution of structure factors as a function of the scattering vector q for an A/B 75/25 (v/v) binary blend is shown in Fig. 9 where time elapses in order of Fig. 9c to 9a. The structure factor S(q,t) develops a peak shortly after the onset of phase separation, and thereafter the intensity of the peak Smax increases with time while the peak position qmax shifts toward smaller values with the phase-separation time. This behavior suggests that the phase separation proceeds with evolution of periodic concentration fluctuation due to the spinodal decomposition and its coarsening processes occurring in the later stage of phase separation. These results, consistent with those observed in real polymer mixtures, indicate that the simulation model can reasonably describe the phase separation process of real systems. 

Concentration fluctuations are prevalent at some compositions of polymer blends, resulting in spatial heterogeneity and broadening of the frequency dispersion of the segmental a-relaxation in polymer blends (Shears and Williams, 1973 Zetsche et al., 1990). This factor was the center of attention in models by blend dynamics by Zetsche and Fischer (1994) and Katana et al. 

Leroy, E., Alegria, A., and Colmenero, J. 2003. Segmental dynamics in miscible polymer blends Modeling the combined effects of chain connectivity and concentration fluctuations. Macromolecules 36 7280-7288. 

Equations for Tg based on the free-volume concept have been proposed for miscible polymer blends and they are similar to the Kelly-Bueche equation given above for polymer-diluent systems. Likewise, this description in terms of a single Tg over-simplifies the dynamics of the components in the blend and neglects some important elements. An important element for interpreting the relaxation behavior of blends is fluctuations in concentration or composition [102]. Models have been... 

Polymer Alloys. Perturbation of meltlike conformation upon transfer to a multicomponent environment is not understood. The influence of proximity to phase boundaries, coupled density and concentration fluctuations, and mixture composition on both single-chain dimensions and miscibility are problems that have begun to be addressed within the PRISM formalism for the simple symmetric blend model by Singh and Schweizer and symmetric diblock copolymer model by David and Schweizer,"" and other more coarse-grained field-theoretic approaches. Comparisons with the few available simulations " have also... 

In the preceding chapter we have, based on the Flory-Huggins theory, discussed the basis for the phase behavior of polymer blends. Miscible polymer blends and polymer solutions have, even in the mixed one-phase system, spatial variations in the polymer concentration. These concentration fluctuations reflect the thermodynamic parameters of the free energy, as described in the Flory-Huggins model. 

Simulations of polymer blends or block copolymers involve two rather distinct aspects one aspect is the generation of equilibrium configurations of dense polymer melts and the relaxation of the configurations of individual chains this aspect is not essentially different from simulations that deal with one-component polymer solutions and melts, as treated in other chapters of this book. The work described in the present chapter has used dynamic Monte Carlo methods such as combinations of kink jump and crankshaft rotation algorithms (Fig. 7.5(a)) " or simple hops of effective monomers in randomly chosen lattice directions (in the case of the bond fluctuation model " ) or the slithering snake technique. 52-54,55,80,81 algorithms need a nonzero concentration of vacancies,... 

It is essential to first briefly review the model for the dynamics of concentration fluctuations in the absence of shear, first derived by Cahn and Hilliard [39] for binary alloys, later modified by Cook [40] to include thermal noise, and more recently adapted by deGennes [41] and Pincus [42] for describing phase separation in polymer blends. 

Doi and Onuki [50] (DO), extended the models to polymer blends in which both components are entangled. The key aspect to address is how to incorporate stress into the equation of motion for concentration fluctuations. Effectively, by determining the conditions for force balance, it was shown that the stress enters the equation of motion at the same level as the chemical potential. Such an approach enabled the development of a framework that coupled the dynamics of concentration fluctuations to the flow fields and stress gradients however, only the simplest form of constitutive relation for the stress was treated. In entangled polymer solutions, the tube model predicts that the relaxation of an imposed stress is well described by a single exponential decay, with the characteristic time-scale being that required for... 

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