Kinetics of phase separation in ramified polymer blends of arbitrary topology

We present here a theoretical study of kinetics of phase separation within a mixture made of two chemically incompatible ramified polymers. For simplicity, we assume that they have the same topology. We are interested in the variation of the relaxation rate, tau(q), versus the wave number q, in the vicinity of the spinodal temperature. The kinetics is governed by local (Rouse) and reptation motions (faster and slower modes). For qR(G) >> 1 (R-G being the gyration radius), kinetics is entirely controlled by local motions where each chain moves inside its own tube, and we show that the corresponding characteristic frequency, tau(-1)(q), scales as tau(-1)(q) similar to KGq(6), where K-G is a known topological factor. For qR(G) << 1, however, kinetics is rather dominated by long-wavelength (reptation) motions where unlike ramified polymers creep inside a long tube. For this case, we find that tau(-1)(q) similar to Lambda(0) q(2) (chi(c) - chi), where Lambda(0) is another known topological factor that represents the total mobility of free monomers belonging to connected chains and reticulation points, and chi(c) accounts for the critical value of the segregation parameter. Finally, the derived relaxation rate must be compared to that relative to a linear polymer mixture.