Collective diffusion, nucleation, and spinodal decomposition in polymer mixtures

摘要

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 lsquo;lsquo;hydrodynamicrsquo;rsquo; theory in close analogy to the treatments of Cahnndash;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 fgr;0near the spinodal curve fgr;s0of width (fgr;s0minus;fgr;0)/fgr;0prop;Nminus;1, whereNis the number of subunits of the chains. ForNrarr;infin; the spinodal curve hence is well defined, in contrast to mixtures with shorthyphen;range forces, and also the linearized theory of spinodal decomposition is predicted to have wider validity. The collective relaxation in the onehyphen;phase region is described by a characteristic time involving the collective diffusion constantDcolltgr;q=(Dcollq2)minus;1, if the wave vectorqis smaller than the inverse correlation length xgr;minus;1coll, while in the range xgr;minus;1collLt;qLt;Rminus;1(Rbeing the polymer coil radius) rates tgr;minus;1qprop;q4and in the rangeRminus;1Lt;qrates tgr;minus;1qprop;q2are predicted. Both the Rouse model and the reptation model for singlehyphen;chain relaxation are considered, and a comparison with previous treatments is made. One central result, namely that the wave vectorqmof maximal growth in spinodal decomposition is typically of the order ofqmsim;R1, agrees with the results of Pincus. Experimental consequences are briefly discussed.