Swelling and shrinking of polymer chains in homopolymer blends
The radius of gyration, R, of polymer chains in homopolymer blends is studied in the framework of a self-consistent one-loop approximation. We show that the polymer chains can shrink or swell in comparison to the Gaussian chain. Swelling of the polymer chains in a region far away from the critical point is caused by the steric repulsive forces that were included in the model as the constraint of incompressibility. The chains shrink progressively, as we approach the critical region passing through the Gaussian limit, R0 = sqrt(N/6) l, far away from the critical point (N − degree of polymerization, l − length of monomer). The correction responsible for the swelling and the shrinking is small when the concentrations of components ϕ are comparable (N = 1000, <ϕ> = 0.5, (R02-R2)/R02 = ±0.02%). This effect, although small, leads to a local demixing, a sharp shrinking of chains in both components accompanied by a strong change of the global inter-monomer distance, which should be observable experimentally. When the local demixing occurs there is a sudden increase in the scattering intensity (of the order of 30% for N = 1000, and ϕA = 0.2). The increase of the degree of polymerization of the same type of chains leads to an increase of the swelling-shrinking effects. In addition, the critical concentration of the shorter chains component is smaller in comparison to the value obtained in the Flory-Huggins theory. The self-consistent determination of the radius of gyration and the upper wave-vector cutoff make our model free from any divergences. In the limit of N → ∞ this theory reduces to the random phase approximation (RPA) of de Gennes.