Crossover behavior of star polymers in good solvents

We perform Monte Carlo calculations for the mean-square center-to-end dista nce, mean-square radius of gyration, and second virial coefficient of f = 3 to 41 arm star polymers composed of rigidly bonded hard spheres of varying diameters. As with linear chains, there are two different crossover regime s: (i) crossover from the Gaussian chain to the Kuhnian chain limit, where the penetration function Psi (f) increases monotonically with increasing po lymer molecular weight, and (ii) crossover from the rigid-rod to the Kuhnia n chain limit, where the penetration function decreases with increasing mol ecular weight. We propose a phenomenological approach for the extension of our previous crossover theory for linear polymers to star polymers. We show that the theoretical crossover function obtained earlier by Douglas and Fr eed [Macromolecules 16, 1854 (1984)] fails to reproduce the simulation data for the penetration function with f greater than or equal to6, while the p henomenological crossover model is in good agreement with the simulation da ta up to f less than or equal to 41. We also obtain a generalized crossover equation for the penetration function for linear and star polymers in good solvents. The crossover equation is able to accurately describe the variat ion of the infinite molecular weight limit of the penetration function Psi* (f) with the number of arms f on the star polymer, and it predicts that Psi *(f) approaches 2.39 in the limit f --> infinity. (C) 2001 American Institu te of Physics.