Effect of Frequency-Dependent Viscosity on Molecular Friction in Liquids

TL;DR

This study links molecular friction in liquids to hydrodynamic properties using simulations and theory, showing the transient Stokes equation's validity at molecular scales and revealing hydration layer effects.

Contribution

It analytically and computationally connects frequency-dependent molecular friction with hydrodynamic theory, highlighting the importance of accurate viscosities and hydration layers.

Findings

Transient Stokes equation accurately predicts molecular friction.

Frequency-dependent shear viscosity requires finite-size correction.

Hydration layers significantly alter friction for non-spherical molecules.

Abstract

The relation between the frequency-dependent friction of a molecule in a liquid and the hydrodynamic properties of the liquid is fundamental for molecular dynamics. We investigate this connection for a water molecule moving in liquid water using all-atomistic molecular dynamics simulations and linear hydrodynamic theory. We analytically calculate the frequency-dependent friction of a sphere with finite surface slip moving in a viscoelastic compressible fluid by solving the linear transient Stokes equation, including frequency-dependent shear and volume viscosities, both determined from MD simulations of bulk liquid water. We also determine the frequency-dependent friction of a single water molecule moving in liquid water, as defined by the generalized Langevin equation from MD simulation trajectories. By fitting the effective sphere radius and the slip length, the frequency-dependent friction and velocity autocorrelation function from the transient Stokes equation and simulations quantitatively agree. This shows that the transient Stokes equation accurately describes the important features of the frequency-dependent friction of a single water molecule in liquid water and thus applies down to molecular length and time scales, provided accurate frequency-dependent viscosities are used. The frequency dependence of the shear viscosity of liquid water requires careful consideration of hydrodynamic finite-size effects to observe the asymptotic hydrodynamic power-law tail. In contrast, for a methane molecule moving in water, the frequency-dependent friction cannot be predicted based on a homogeneous model, which suggests, supported by the extraction of a frequency-dependent surface-slip profile, that a methane molecule is surrounded by a finite-thickness hydration layer with viscoelastic properties that are significantly different from bulk water.