MOLECULAR-DYNAMICS INVESTIGATION OF DYNAMIC SCALING FOR DILUTE POLYMER-SOLUTIONS IN GOOD SOLVENT CONDITIONS

A molecular dynamics (MD) investigation of dynamic properties of a single freely jointed N mer (N = 6,9,20,30) in explicit solvent at high dilution and in good solvent conditions is presented. Our aim is to establish the validity of scaling laws for short chains so that all experiments are performed at the same temperature and overall density. In order to unravel the periodic boundary conditions (PBC) artifacts of standard MD, we first consider a nine beads chain in solvent and compare data obtained for various cubic boxes of edge L in the range 0.1 < R(g)/L < 0.3, where R(g) is the chain radius of gyration. In this range, static properties of the chain do not present PBC effects, while global dynamical properties, such as the chain intermediate scattering function S(k,t) in the low k regime, are strongly box size dependent. This effect, ascribed to hydrodynamic interactions (HI) due to image chains, does not show up on the local chain fluctuations (high k regime), because the typical relaxation times are shorter than the time HI need to spread a distance d almost-equal-to (L - 2-pi/k). This explains our earlier observation of the high k universal behavior of S(k,t)/S(k) for different chain lengths and box sizes [C. Pierleoni and J.-P. Ryckaert, Phys. Rev. Lett. 61, 2992 (1991)], the limits of which are now discussed in detail. In the small k regime, the important finite size effect can be identified as an increase of the center of mass diffusion with the box size. As recently pointed out [B. Dunweg and K. Kremer, Phys. Rev. Lett. 61, 2996 (1991)], this dependence can be predicted with the aid of the Kirkwood formula for the chain diffusion coefficient after suitable modification to incorporate image chains influence. In the present range of chain lengths and box sizes, we observe a very good quantitative agreement between Kirkwood formula predictions and direct measurements of the diffusion. Finally, as the main outcome of this work, we find a consistent dynamic scaling picture emerging from our low and high k regimes analyses: our MD experiments yield nu = 0.584 +/- 0.002 and nu' = 0.52 +/- 0.01 for the static and the dynamic exponent, respectively.