SINGLE-CHAIN STATISTICS AND THE UPPER WAVE-VECTOR CUTOFF IN POLYMER BLENDS

We derive the equation for the single-chain correlation function in polymer blends. The chains in the incompressible blend have a radius of gyration smaller than the radius of gyration for ideal chains. The chains shrink progressively as we approach the critical temperature T-c. The correction responsible for shrinking is proportional to 1/root N, where N is the polymerization index. At T=T-c and for N = 1000, the size of the chain has been estimated to be 10% smaller than the size of the ideal coil. The estimate relies on the appropriate cutoff In the limit of N --> infinity the chains approach the random walk limit. Additionally, we propose in this paper a self-consistent determination of the radius of gyration and the upper wave-vector cutoff. Our model is free from any divergences such as were encountered in the previous mean-field studies; we make an estimate of the chain size at the true critical temperature and not the mean-held one.