(13i) Prediction of Self-Diffusion Coefficients of Polymer Melts Using Modified Free Volume Theory and MD Simulation

MD simulation of polyethylene melts with different chain lengths is performed. Crossover in the center-of-mass self-diffusion coefficient (D) as a function of chain length (N) is observed: as N<N_c, D~N^-1 and as N>N_c, D~N^-2.2. The modified free volume theory is used to describe such crossover as observed in the MD simulation. The two parameters in the modified free volume theory, which are the critical free volume and mean free volume per repeat unit, can be determined from the pair correlation function by either solving PRISM equations for polymers or using the MD simulation data. This makes the modified free volume theory parameter-free. Voronoi tessellation of the MD simulation data are also performed for comparison with the statistical mechanical calculations. Such analysis gives us the exact distribution of free volume in the polymer melts, and therefore the probability for a repeat unit having free volume greater than that of critical free volume.