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 C12 up to C400 at 318 K, 418 K, 518 K, and 618 K, to investigate the power law dependence of self-diffusion of polymer liquids on their molecular weights. Two LJ particles MY1 with a mass of 114 g/mol and MY2 with a mass of 225 g/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, Dself∼M−γ, occurs in the range C120∼C160 at temperatures of 318 K, 418 K, and 518 K, 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 DMY2 on the molecular weight (M) of n-alkane, DMY2∼M−γ, occurs at low temperatures. The exponent γ for DMY2 shows a sharp transition from 1.21 to 0.52 near C36 at 418 K and from 1.54 to 0.60 near C36 at 318 K. However, no such transition is found for the probe molecule MY2 at temperatures of 518 K and 618 K and for MY1 probe at temperatures of 418 K, 518 K, and 618 K, but the power law exponent γ for MY1 at 318 K shows instead a linear or a rather slow transition. The dependence of the probe diffusion (DMY2) 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 Dself/DMY2 becomes less than 1 and the probe molecules encounter, in turn, two different microscopic frictions depending on MMY/Mmatrix 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 318 K and 418 K.
Molecular dynamics simulation study of self-diffusion for penetrable-sphere model fluids
