Simulation of polymer dynamics. I. General theory

Abstract

Methods are presented for the simulation of conformational relaxation processes in polymer chains. The chains interact with the solvent through frictional and Langevin forces, have constrained bond lengths and angles, and smooth rotational energy functions. Relationships are obtained between the stochastic difference equations that form the basis for computer simulation, and equivalent Langevin differential equations and Smoluchowski diffusion equations. The presence of constraints and the associated action of potential forces and Langevin forces on the same time scale leads to somewhat intricate algorithms and correction terms. However, the time increment during a simulation step can be increased by a factor of 1000 or more over what is required if vibrational potentials are used to preserve the primary chain structure. Computation time is proportional to chain length in the absence of hydrodynamic interaction and excluded volume forces.