Reliable Viscosity Calculation from Equilibrium Molecular Dynamics Simulations: A Time Decomposition Method

Abstract

Equilibrium molecular dynamics is often used in conjunction with a Green-Kubo integral of the pressure tensor autocorrelation function to compute the shear viscosity of fluids. This approach is computationally expensive and is subject to a large amount of variability because the plateau region of the Green-Kubo integral is difficult to identify unambiguously. Here, we propose a time decomposition approach for computing the shear viscosity using the Green-Kubo formalism. Instead of one long trajectory, multiple independent trajectories are run and the Green-Kubo relation is applied to each trajectory. The averaged running integral as a function of time is fit to a double-exponential function with a weighting function derived from the standard deviation of the running integrals. Such a weighting function minimizes the uncertainty of the estimated shear viscosity and provides an objective means of estimating the viscosity. While the formal Green-Kubo integral requires an integration to infinite time, we suggest an integration cutoff time tcut, which can be determined by the relative values of the running integral and the corresponding standard deviation. This approach for computing the shear viscosity can be easily automated and used in computational screening studies where human judgment and intervention in the data analysis are impractical. The method has been applied to the calculation of the shear viscosity of a relatively low-viscosity liquid, ethanol, and relatively high-viscosity ionic liquid, 1-n-butyl-3-methylimidazolium bis(trifluoromethane-sulfonyl)imide ([BMIM][Tf2N]), over a range of temperatures. These test cases show that the method is robust and yields reproducible and reliable shear viscosity values.

Multiscale thermal modeling of cured cycloaliphatic epoxy/carbon fiber composites

“…It is important to note that the error bars for the EMD method are larger than those of the NEMD method because of inherent computational difficulties associated with the EMD method. 47 Given the uncertainty levels, the results suggest that the two methods are in general agreement. This behavior is similar to that observed with MD modeling of the EPON862 system.…”

“…The error bars represent the standard deviations associated with the five models at each crosslink density. It is important to note that the error bars for the EMD method are larger than those of the NEMD method because of inherent computational difficulties associated with the EMD method . Given the uncertainty levels, the results suggest that the two methods are in general agreement.…”

Rheology of phosphonium ionic liquids: a molecular dynamics and experimental study

“…Therefore, the error is not too large if we use 96 ion pairs, which have been used unless otherwise mentioned. It should be noted there are some recent works 35,36 where reasonably accurate viscosities are obtained by using systems of 200-300 ion pairs. Finally, it should be noted that the charge scaling factors, used to compensate for the polarizability and the charge transfer in the present work and in the mentioned references to some extent compensate for the system size dependence as well.…”

“…A number of works on the rheology and viscosity of ILs have been reported during the last fifteen years. [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] In most cases, the ILs have been composed of a cation consisting of an imidazolium based core substituted with alkyl chains. These cations have been combined with a wide range of anions such as tetrafluoroborate, hexafluorophosphate, methylsulfate, trifluoromethylsulfonate, acetate, trifluoroacetate, and bis(trifluoromethylsulfonyl)amide.…”

Molecular dynamics simulation of the capillary leveling of viscoelastic polymer films

“…The former was initially calculated in the bulk state from the late-time value of the Green-Kubo formula: 55 = lim…”