Mean free volume and self-diffusion coefficient of short polymer chains: Computer simulations and statistical mechanical theory

We report a comprehensive investigation on computing thermodynamics and diffusion coefficients of short linear and ring polymer chains using statistical mechanical theories and molecular dynamics (MD) simulations. The polymer chain lengths of five and ten are taken into account. We first compute the location of fluid phase envelope using the equilibrium MD simulations. Then the diffusion coefficients are computed via two different methods: 1-computing the mean squared displacement using MD simulation and 2- free volume theory method. We utilize the Generic van der Waals theory to compute the mean free volume and apply the results in the modified Cohen-Turnbull theory to obtain the diffusion constant and compare the results to the MD simulation outcomes. The virial minimization method is used to compute the effective site diameters and the results are applied as the repulsion-attraction splitting distance of the interaction potentials within the theory. We show that the logarithm of the mean free volume versus density is almost linear at densities above the critical point independent of the chain length. We analyzed the self diffusion coefficient results of the theory and computer simulations in detail.