Principles for coarse-graining polymer molecules in simulations of polymer fluid mechanics

Abstract

Recent increases in computer speed now allow fast Brownian dynamics simulations to be carried out on large ensembles of bead–spring and bead–rod models of polymer chains in flow fields. For these simulations to be realistic representations of real polymers, accurate coarse-graining must be carried out whereby the relevant physics of real polymers can be expressed in terms of bead–spring and bead–rod models, including development of force laws for nonlinear elastic springs, and assignment of model parameters, such as spring constants, bead friction coefficients and hydrodynamic coupling parameters to represent the strength of the hydrodynamic interaction (HI). Discussed here are the principles by which this coarse-graining can be carried out, methods for assignment of coarse-grained parameter values, and the conditions under which coarse-graining is likely to break down. Examples of long polystyrene molecules (PS) in a theta solvent and long DNA molecules in water are discussed in detail, especially including the effects of HI, which is weak in DNA solutions, but strong for high molecular weight PS. We find that accurate description of hydrodynamic interactions requires a detailed description of the distribution of friction within the chain, which limits the degree of coarse-graining possible. This necessitates the use of large numbers of beads to represent high molecular weight polymers. Because the computation involved in simulations with HI scales with the number of beads is to a large power (3 or higher), such simulations are expensive, but are now feasible with fast computer clusters.