THEORY OF THE ORDER-DISORDER PHASE-TRANSITION IN CROSS-LINKED POLYMERBLENDS

We consider the system of a network formed by crosslinking a polymer b lend. In such a system there is a competition between monomer-monomer interactions and elastic energy which may result in a microphase separ ation. We first treat the problem by adapting a model due to de Gennes to include the effect of concentration fluctuations 'frozen in' by th e crosslinking process. This yields an expression for the scattering s tructure factor which gives finite scattering in the limit of low wave number (this has been observed in experiments on crosslinked blends). The expression also shows that the frozen-in fluctuations 'seed' the p hase transition, so that the structure factor diverges as (chi(s) - ch i)(-2) on approaching the spinodal. We then reconsider the problem at a molecular level. We model the network as a blend of interacting chai ns anchored at either end to fixed points in space. The system is trea ted using a variant of the Random Phase Approximation (RPA) which deal s with the quenched chain-end variables but which does not resort to r eplica methods. The resulting structure factor has an identical form t o that obtained by modifying the de Gennes model, but allows us to inv estigate the effect of varying composition, crosslink density, and app lied strain. We find that the characteristic lengthscale for the early stages of microphase separation is controlled by the least concentrat ed component or the one with the shortest chain length between crossli nks, depending on which parameter shows the strongest difference betwe en the two chain types. We also find that strain produces a phase sepa ration with wavevectors in the direction(s) of least stretching (or gr eatest compression).