Dynamics of short polymer chains in solution

– We present numerical and analytical results describing the effect of hydrodynamic interactions on the dynamics of a short polymer chain in solution. A molecular dynamics algorithm for the polymer is coupled to a direct simulation Monte Carlo algorithm for the solvent. We give an explicit expression for the velocity autocorrelation function of the centre of mass of the polymer which agrees well with numerical results if Brownian dynamics, hydrodynamic correlations and sound wave scattering are included. Introduction. – The aim of this paper is to present numerical and analytical results describing the effect of hydrodynamic interactions on the dynamics of a short polymer chain in solution. Modelling a dilute polymer solution is a difficult task. This is because the dynamical behaviour of the polymer can be dominated by hydrody-namic interactions between different parts of the polymer chain. These interactions are long-ranged and develop very slowly compared to the time scale of the Brownian fluctuations of individual monomers. Thus if a molecular dynamics time-step is chosen to correctly follow the Brownian dynamics it becomes prohibitively expensive in computer time to also model the dynamics of enough solvent molecules for sufficient time to allow hydrodynamic correlations to develop. To move towards overcoming this problem we introduce a hybrid numerical approach. The dynamics of the chain is treated exactly (within the limitations of a finite time step) by a molecular dynamics solution of Newton's equations of motion. The solvent is modelled using a direct simulation Monte Carlo algorithm [1]. The algorithm is constructed in such a way that energy and momentum are conserved and that at equilibrium the system is described by a microcanonical distribution. However, molecular details of the solvent are not included: it acts as a momentum-conserving heat bath which can support hydrodynamic modes. The physical quantity we choose to measure in the simulations is the velocity autocorrelation function of the centre of mass motion of a polymer chain. This provides clear evidence of a fast exponential decay at early times which results from collisions in which the solvent particles are uncorrelated and a slow algebraic decay at later times arising from hydrodynamic interactions that develop in the fluid. We propose a theory which reproduces the behaviour of the velocity autocorrelation function and demonstrate that both limits arise naturally from a simple equation of motion which incorporates the solvent–polymer interaction as a viscous drag term. We also argue that, as …