Stationary dynamics approach to analytical approximations for polymer coexistence curves

Phase separation in polymer blends is an important process. However, the compositions of the coexisting phases can only be predicted by numerical methods. We provide simple analytical expressions which serve as good approximations for the compositions after phase separation of binary homopolymer blends. These approximations are obtained by a stationary dynamics approach: we calculate the compositions of two polymer mixtures such that the stationary diffusion between these distinguishable mixtures vanishes. For the diffusion equations we employ composition-dependent diffusion coefficients, as derived according to the slow- and fast-mode theory from the Flory-Huggins free energy. The analytical results are in good agreement with exact (numerically calculated) binodal compositions. Our coexistence curves are more accurate than some conventional approximations. Another advantage of the stationary dynamics approach is that it is not only applicable to binary polymer blends or polymer solutions, but also to symmetrical multicomponent blends. The same diffusion coefficients may be used to obtain the exact spinodal compositions in multicomponent systems.