On the miscibility of chemically identical linear homopolymers of different size

The effects of asymmetry due to the chain-size differences on the miscibility of linear polymer blends composed from the same monomers are studied by means of an analytical theory. The partition function of the blend and the resulting free energy are obtained through the summation of the series of the one-loop diagrams at any dimensionality d. From the stability conditions, no macrophase separation is found at d=3 for any size disparity or volume fractions in agreement with other recent theoretical calculations. At d=2, the effective repulsions between the two different species are much larger leading to macrophase separation. This result strongly indicates that a way to observe de-mixing of chemically identical homopolymer, is to increase the two-dimensional character of the chains like in the cases of strong adsorption or ultra-thin polymeric films.