Connection between Macroscopic Hydrodynamics and Molecular Friction in Liquids

Abstract

A fundamental problem in molecular dynamics is the relation between the frequency-dependent friction of a molecule in a liquid and the underlying hydrodynamic equations. We investigate this connection for the case of a water molecule moving in liquid water using all-atomistic molecular dy�namics simulations and linear hydrodynamic theory. For this we calculate the frequency-dependent friction of a sphere with finite surface slip moving in a non-Newtonian compressible fluid by solving the linear transient Stokes equation, including frequency-dependent shear and volume viscosities, which are determined from MD simulations of bulk liquid water. We investigate in detail the in�fluence of the volume viscosity on the sphere friction and find that the high-frequency decay of the volume viscosity crucially influences the friction. 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 in the solution of the Stokes equation, the two frequency-dependent frictions are shown to agree well. This shows that the transient Stokes equation describes 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. In particular the pronounced maximum of the sphere friction around 7 THz is shown to be caused by a pronounced maximum of the shear viscosity at the same frequency. We also find non-negligible slip effects for the motion of a water molecule, in quantitative agreement with a recent study of the translational and rotational diffusion of a water molecule in liquid water. For a methane molecule moving in water, the friction function cannot be predicted based on our simple hydrodynamic model, which suggests that a methane molecule is surrounded by a hydration layer with viscous properties that are very different from bulk water. Subject Areas: Soft Matter, Statistical Physics, Fluid Dynamics, Biological Physics, Complex Systems