Crossover behavior of star polymers in good solvents

Abstract

We perform Monte Carlo calculations for the mean-square center-to-end distance, 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 regimes: (i) crossover from the Gaussian chain to the Kuhnian chain limit, where the penetration function Ψ(f) increases monotonically with increasing polymer molecular weight, and (ii) crossover from the rigid-rod to the Kuhnian chain limit, where the penetration function decreases with increasing molecular 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 Freed [Macromolecules 16, 1854 (1984)] fails to reproduce the simulation data for the penetration function with f⩾6, while the phenomenological crossover model is in good agreement with the simulation data up to f⩽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 variation of the infinite molecular weight limit of the penetration function Ψ*(f) with the number of arms f on the star polymer, and it predicts that Ψ*(f) approaches 2.39 in the limit f→∞.