Second virial coefficient of AxBy miktoarm star copolymers in common Θ, common good, and selective solvents

The mutual second virial coefficient A(2) between two identical ideal miktoarm star copolymer chains A(x)B(y) composed of A and B branches is determined up to the first order of the small parameter epsilon = 4 - d (d is the space dimensionality) by means of simple perturbation theory. Analytical expressions corresponding to various macroscopic states, as those are defined by the prevailing binary intermolecular interactions, are obtained as a function of the arm lengths N-A, N-B, their corresponding numbers x, y, and the interaction parameters, between units of similar or dissimilar kind u(AA), u(BB), and u(AB). The effect of the copolymer architecture is also studied in detail by calculating g(A), the ratio of the virial coefficient of a miktoarm star with respect to that of a linear diblock copolymer with the same number of A and B units; g(A) is dimensionless and experimentally accessible.