Brownian Dynamics of Nondilute Solutions of Rodlike Polymers. 1. Low Concentrations

We report the results of Brownian dynamics simulations for solutions of rodlike polymers with an aspect ratio of 50 at moderate concentrations (5–50 rods/L³, where L is the molecular length). Account for direct two-body interactions was sufficient for the description of the equilibrium properties over the range of concentrations we simulated. Correspondingly, the energy was adequately approximated by a density expansion through the second virial coefficient and the pair distribution function, which exhibited very weak concentration dependence, was well approximated by the Boltzmann factor. Despite the potentially nondiffusive character of rotation in concentrated systems of axisymmetric particles, the rotational motion could be described by a rotational diffusion equation in our simulations, due to the strong decorrelating effect of the solvent-polymer interaction. The translational diffusivity normal to the rod axis, despite its sharp decrease with concentration, did not freeze up to the highest concentration simulated, demonstrating in this way that the cage renewal mechanism postulated by the Doi-Edwards theory is inappropriate in this concentration regime. On the contrary, a model proposed by Fixman was found to be perfectly adequate since it reproduced very well our simulation results for the rotational diffusivity. These simulation results are the first to achieve quantitative agreement with experiment. The success of Fixman's model originates from the simple two-body nature of the polymer local structure and the strong solvent-induced decorrelation that weakens the intrinsically many-body character of the polymer-polymer interaction.