Crossover scaling in semidilute polymer solutions: a Monte Carlo test

Abstract

Extensive Monte Carlo simulations are presented for the bond-fluctuation model on three-dimensional simple cubic lattices. High statistics data are obtained for polymer volume fractions Φ in the range $0.025 \leqslant \Phi \leqslant 0.500$ and chain lengths N in the range $20 \leqslant N \leqslant 200$, making use of a parallel computer containing 80 transputers. The simulation technique takes into account both excluded volume interactions and entanglement restrictions, while otherwise the chains are non-interacting and athermal. The simulation data are analysed in terms of the de Gennes scaling concepts, describing the crossover from swollen coils in the dilute limit to gaussian coils in semidilute and concentrated solution. The crossover scaling functions for the chain linear dimensions and for the decay of the structure factor are estimated and compared to corresponding theoretical and experimental results in the literature. Also the dynamics of the chains is studied in detail, and evidence for a gradual crossover from the Rouse model to a D ∼N-2 law for the diffusion constant is presented. This crossover is consistent with scaling only if a concentration-dependent segmental “friction coefficient" is introduced. Within this framework general agreement between these data, other simulations and experiment is found