Diffusion and Friction Dynamics of Probe Molecules in Liquid n-Alkane Systems: A Molecular Dynamics Simulation Study

We present a molecular dynamics simulation study of the probe diffusion and friction dynamics of Lennard-Jones particles in a series of liquid n-alkane systems from C-12 up to C-400 at 318K, 418K, 518K, and 618K, to investigate the power law dependence of self-diffusion of polymer liquids on their molecular weights. Two LJ particles MY1 with a mass of 114g/mol and MY2 with a mass of 225g/mol are used as probes to model methyl yellow. We observed that a clear transition in the power law dependence of n-alkane self-diffusion on the molecular weight (M) of n-alkane, D-self approximate to M-, occurs in the range C-120 approximate to C-160 at temperatures of 318K, 418K, and 518K, corresponding to a crossover from the oligomer to the Rouse regime. We also observed that a clear transition in the power law dependence of the diffusion coefficient D-MY2 on the molecular weight (M) of n-alkane, D-MY2 approximate to M-, occurs at low temperatures. The exponent for D-MY2 shows a sharp transition from 1.21 to 0.52 near C-36 at 418K and from 1.54 to 0.60 near C-36 at 318K. However, no such transition is found for the probe molecule MY2 at temperatures of 518K and 618K and for MY1 probe at temperatures of 418K, 518K, and 618K, but the power law exponent for MY1 at 318K shows instead a linear or a rather slow transition. The dependence of the probe diffusion (D-MY2) on the matrix molecular weight (M) reflects a significant change of the matrix dynamics associated with the probe diffusion: a crossover from the solvent-like to the oligomer regime. As the molecular weight of n-alkane increases, the ratio of D-self/D-MY2 becomes less than 1 and the probe molecules encounter, in turn, two different microscopic frictions depending on M-MY/M-matrix and the temperature. It is believed that a reduction in the microscopic friction on the probe molecules that diffuse at a rate faster than the solvent fluctuations leads to large deviations of slope from the linear dependence of the friction of MY2 on the chain length of the n-alkane at 318K and 418K.