Collective diffusion, nucleation, and spinodal decomposition in polymer mixtures

Abstract

The dynamics of concentration fluctuations in binary polymer mixtures AB, A and B being long and flexible chains, is studied near the critical point of unmixing. A ‘‘hydrodynamic’’ theory in close analogy to the treatments of Cahn–Hilliard and Cook for the dynamics of unmixing alloys is developed, and its validity is carefully analyzed. It is shown that homogeneous nucleation for long chains is negligible except in a narrow region of volume fraction φ0 near the spinodal curve φs0 of width (φs0−φ0)/φ0∝N−1, where N is the number of subunits of the chains. For N→∞ the spinodal curve hence is well defined, in contrast to mixtures with short-range forces, and also the linearized theory of spinodal decomposition is predicted to have wider validity. The collective relaxation in the one-phase region is described by a characteristic time involving the collective diffusion constant Dcoll τq=(Dcoll q2)−1, if the wave vector q is smaller than the inverse correlation length ξ−1coll, while in the range ξ−1coll≪q≪R−1 (R being the polymer coil radius) rates τ−1q∝q4 and in the range R−1≪q rates τ−1q∝q2 are predicted. Both the Rouse model and the reptation model for single-chain relaxation are considered, and a comparison with previous treatments is made. One central result, namely that the wave vector qm of maximal growth in spinodal decomposition is typically of the order of qm∼R1, agrees with the results of Pincus. Experimental consequences are briefly discussed.