Nature of Intrinsic Uncertainties in Equilibrium Molecular Dynamics Estimation of Shear Viscosity for Simple and Complex Fluids

TL;DR

This paper investigates the intrinsic uncertainties in estimating shear viscosity via equilibrium molecular dynamics, focusing on statistical errors and system size effects, and provides formulas and insights for accurate measurement in simple and complex fluids.

Contribution

It introduces uncertainty quantification formulas for shear viscosity estimation and analyzes the size-dependent behavior and Gaussianity of shear-stress fluctuations.

Findings

Gaussianity is more pronounced in shear-stress processes than in velocity processes.

Shear viscosity exhibits size-dependent behavior at high densities.

A characteristic length scale related to shear-stress correlation length determines reliable viscosity measurements.

Abstract

We study two types of intrinsic uncertainties, statistical errors and system size effects, in estimating shear viscosity via equilibrium molecular dynamics simulations and compare them with the corresponding uncertainties in evaluating the self-diffusion coefficient. Uncertainty quantification formulas for the statistical errors in the shear-stress autocorrelation function and shear viscosity are obtained under the assumption that shear stress follows a Gaussian process. Analyses of simulation results for simple and complex fluids reveal that the Gaussianity is more pronounced in the shear-stress process (related to shear viscosity estimation) compared with the velocity process of an individual molecule (related to self-diffusion coefficient). At relatively high densities corresponding to a liquid state, we observe that the shear viscosity exhibits complex size-dependent behavior unless the system is larger than a certain length scale, beyond which reliable shear viscosity values are obtained without any noticeable scaling behavior with respect to the system size. We verify that this size-dependent behavior is configurational and relate the characteristic length scale to the shear-stress correlation length.