Molecular size and shape effects: Rotational diffusion and the Stokes-Einstein-Debye relation

Abstract

Formulation of rotational diffusion coefficient and the Stokes-Einstein-Debye (SED) relation is presented for diatomic molecular liquids by molecular dynamics simulation with two-center Lennard-Jones (2CLJ) potentials. Shear viscosity ηsv and rotational diffusion coefficient Dr are expressed as a function of molecular mass and number density N/V, or moment of inertia, packing fraction, temperature T, interaction energy, and molecular elongation l∗ ≡ l/σ, where N is the number of molecules included in the system volume V, l the bond length in the diatomic molecules, and σ the size parameter used in the LJ potentials. The packing fraction and elongation are the variables expressing molecular size and shape, respectively. These results produce directly a molecular-basis SED relation as Drηsv/T ∝ vm∗1/3l∗−3(N/V), where vm∗ is the dimensionless molecular volume expressed as an analytical function only of elongation l∗. That is, this SED equation depends not on the size but on the shape. This is highly contrasted with the original SED relation based on the size, which suggests overall reconsideration of the relation on a molecular scale. The shape term accounts for a paradox that more spherical molecules such as N2 deviate more strongly from the original SED equation based on a spherical particle. In addition, the SED relation without the size is consistent with the Stokes-Einstein relation for both the Lennard-Jones and 2CLJ liquids expressed as Dηsv/T ∝ (N/V)1/3, where D is the translational self-diffusion coefficient.