Molecular dynamics simulation of a polymer chain in solution

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Abstract
Results of a molecular dynamics simulation of a single polymer chain in a good solvent are presented. The latter is modeled explicitly as a bath of particles. This system provides a first‐principles microscopic test of the hydrodynamic Kirkwood–Zimm theory of the chain’s Brownian motion. A 30 monomer chain is studied in 4066 solvent particles as well as 40/4056 and 60/7940 systems. The density was chosen rather high, in order to come close to the ideal situation of incompressible flow, and to ensure that diffusive momentum transport is much faster than particle motions. In order to cope with the numerical instability of microcanonical algorithms, we generate starting states by a Langevin simulation that includes a coupling to a heat bath, which is switched off for the analysis of the dynamics. The long range of the hydrodynamic interaction induces a large effect of finite box size on the diffusive properties, which is observable for the diffusion constants of both the chain and the solvent particles. The Kirkwood theory of the diffusion constant, as well as the Akcasu et al. theory of the initial decay rate in dynamic light scattering are generalized for the finite box case, replacing the Oseen tensor by the corresponding Ewald sum. In leading order, the finite‐size corrections are inversely proportional to the linear box dimensions. With this modification of the theory taken into account, the Kirkwood formula for the diffusion constant is verified. Moreover, the monomer motions exhibit a scaling that is much closer to Zimm than to Rouse exponents (t2/3 law in the mean square displacement; decay rate of the dynamic structure factor ∝k3). However, the prefactors are not consistent with the theory, indicating that (on the involved short length scales) the dynamics is more complex than the simple hydrodynamic description suggests.