Effective Interaction Parameters of Star/Star, Ring/Ring, and Ring/Linear Chemically Identical Blends

The effects of chain size and architectural asymmetry on the miscibility of chemically identical polymer blends composed of star/star, ring/ring, and ring/linear chains are studied by means of an analytical theory. The free energy of these blends is obtained through the summation of the series of the one-loop diagrams at any dimensionality d. From the spinodal equation, we find that for the same total molecular weights the effective repulsions between ring/ring species are higher than those of linear/linear blends and higher than those of the symmetrical star/star blends of four branches but smaller than the respective interactions of star/star blends where both species have five arms. At d = 3 no phase separation is found for blends composed of ring/ring and ring/linear chains at any size disparity or volume fraction. The same is true in the case of blends composed of star/star or star/linear chains with a few or a moderate number of arms in agreement with recent experimental and theoretical results.