STATISTICAL-MECHANICALLY EXACT SIMULATION OF POLYMER CONFORMATION IN AN EXTERNAL-FIELD

A mathematically exact method is presented for sampling conformations of polymer molecules in an external field with fixed energy or energy range in accord with the formulation of statistical mechanics for a mi crocanonical ensemble. As a consequence, conformations of negligible B oltzmann weight can be selectively eliminated from simulations for eff icient calculation of macroscopic polymer properties. The method is ap plicable for conformations that are described by a stochastic differen tial equation along the contour length in the field-free situation. It is based on the concept of a stochastic bridge process for which a ne w stochastic differential equation is derived that has stipulations at both ends of the process. This idea is exploited on a pair of stochas tic differential equations in the conformation vector X and an augment ed variable Z which represents the running Boltzmann weight in the giv en field, transforming to a new pair of equations for which the termin al Boltzmann weight can be arbitrarily stipulated. The stochastic equa tion for the bridge involves solving the Fokker-Planck equation for th e original stochastic pair. We demonstrate the method on the conformat ion of a ''Brownian'' polymer in a quadratic external field of varying strength. The stochastic differential equations for the bridge proces s in this case can be derived analytically. Sample conformations are d isplayed that satisfy exactly energy constraints either at fixed value s or within a stipulated range. It is shown that polymer properties ca n be computed more efficiently and accurately with the bridge process simulations than by unconstrained process simulations. The bridge proc ess approach presented here must be distinguished from other approache s such as umbrella sampling methods because of the former's ability to sample conformations exactly with stipulated energy constraints. (C) 1997 American Institute of Physics.