Nature of intrinsic uncertainties in equilibrium molecular dynamics estimation of shear viscosity for simple and complex fluids

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, and 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.

Best Practices for Computing Transport Properties 1. Self-Diffusivity and Viscosity from Equilibrium Molecular Dynamics [Article v1.0]

“…Kim et al [47] demonstrate that a complex oscillatory relationship exists between the shear viscosity of dense fluids and V -1/3 , where the oscillations dampen with increasing system size (see Figures 8 and 9 of Ref. [47]). However, extrapolation to the infinite system size viscosity is not feasible due to the non-linear scaling behavior with respect to V -1/3 .…”

“…Finite size effects can arise in small, dense systems due to limited space for configurational rearrangements [47]. Kim et al [47] demonstrate that a complex oscillatory relationship exists between the shear viscosity of dense fluids and V -1/3 , where the oscillations dampen with increasing system size (see Figures 8 and 9 of Ref. [47]).…”

Best Practices for Quantification of Uncertainty and Sampling Quality in Molecular Simulations [Article v1.0]

“…However, care must be exercised to avoid integrating pure noise over too large of an interval, since this can generate Brownian motion; see, for example, Ref. [46] and references contained therein.…”

Thermodynamic and dynamical properties of the hard sphere system revisited by molecular dynamics simulation

“…The N-dependence of the self-diffusion coefficient has been the subject of investigations for a range of liquids. 28,[46][47][48][49][50][51][52][53][54][55][56] From these studies, it has been firmly established by hydrodynamic theory and simulations that the effects of periodic images for sufficiently large N can be represented by the following analytic expression,…”