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

The mutual second virial coefficient A₂ between two identical ideal miktoarm star copolymer chains A_xB_y, composed of A and B branches is determined up to the first order of the small parameter ε = 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.