Crossover behavior of star polymers in good solvents

摘要

We perform Monte Carlo calculations for the mean-square center-to-end distance, mean-square radius of gyiation,and second virial coefrcie.nt of f= 3 to 41 arm star polymers composed of rigidly onded hard spheres of va!'fing diameters. As with linear chains, there are two different crossover ~gimes: (i) crossover from the Gaussian chain to.'the K~hnian chain limit,Cwhere the penetration Ilnction 'I'(n increases monotonically with i~creasing polymer molecular weight, and (ii) rossover from the rigid-rod to the Kuhnian chain limit, where the penetration function decreases rith increasing molecular weight. We propose a phenomenological approach for the ex;tension of ur previous crossover theory for linear polymers to star polymers. We show that the theoretical rossover function obtained earlier by Douglas and Freed [Macromolecules 16, 1854 (1984)] fails ) reproduce the simulation data for the penetration function withf~ 6, while the phenomenological rossover model is in good agreement with the simulation detaup data p to f <=41.We also obtain a eneralized crossover equation for the. penetration function for linear and star polymers in good olvents. The crossover equation is able to accurately describe the variation of the infinite molecular reight limit of the penetration function 'I' * (I) with the number of arms Ion the star polymer, and it predicts that #psi#~*(f) approaches 2.39 in hte limit f—>infinity.