Dynamics of entangled flexible polymers. Monte Carlo simulations and their interpretation

Abstract

Monte Carlo simulations have been reviewed for several models of dense polymer systems: (i) a system of very short (N= 16 links) freely joined chains with Lennard-Jones interactions in the continuum, (ii) self-avoiding walks on a diamond lattice with up to N= 200 links and (iii) pearl-necklace chains with up to N= 98 hard spheres. The cases of both a mobile and a frozen-in environment have been considered. The dynamics of displacements and the structure factors have been studied and interpreted in terms of the Rouse model and the reptation model, paying particular attention to the crossover between these models. Only for the frozen-environment case is reptation fully verified, while for models (i) and (ii) simple Rouse behaviour is found and for model (iii) relaxation with a diffusion constant D∝N^{–2.0 ± 0.2} and disengagement time τ_d∝N^{3.4 ± 0.4} is found, but the monomer displacements are in disagreement with reptation laws. A brief comparison with pertinent experiments has been made, and the crossover between the Rouse model and the Zimm model is considered briefly.