Diffusion of Probe Molecule in Small Liquid n-Alkanes: A Molecular Dynamics Simulation Study

The probe diffusion and friction constants of methyl yellow (MY) in liquid n-alkanes of increasing chain length were calculated by equilibrium molecular dynamics (MD) simulations at temperatures of 318, 418, 518 and 618 K. Lennard-Jones particles with masses of 225 and 114 g/mol are modeled for MY. We observed that the diffusion constant of the probe molecule follows a power law dependence on the molecular weight of nalkanes, DMY${\sim}M^{-\gamma}$ well. As the molecular weight of n-alkanes increases, the exponent $\gamma$ shows sharp transitions near n-dotriacontane ($C_{32}$) for the large probe molecule (MY2) at low temperatures of 318 and 418 K. For the small probe molecule (MY1) $D_{MY1}$ in $C_{12}$ to C80 at all the temperatures are always larger than Dself of n-alkanes and longer chain n-alkanes offer a reduced friction relative to the shorter chain n-alkanes, but this reduction in the microscopic friction for MY1 is not large enough to cause a transition in the power law exponent in the log-log plot of DMY1 vs M of n-alkane. For the large probe molecule (MY2) at high temperatures, the situation is very similar to that for MY1. At low temperatures and at low molecular weights of n-alkanes, $D_{MY2}$ are smaller than $D_{self}$ of n-alkanes due to the relatively large molecular size of MY2, and MY2 experiences the full shear viscosity of the medium. As the molecular weight of n-alkane increases, $D_{self}$ of n-alkanes decreases much faster than $D_{MY2}$ and at the higher molecular weights of n-alkane, MY2 diffuses faster than the solvent fluctuations. Therefore there is a large reduction of friction in longer chains compared to the shorter chains, which enhances the diffusion of MY2. The calculated friction constants of MY1 and MY2 in liquid n-alkanes supported these observations. We deem that this is the origin of the so-called“solventoligomer”transition.