Effect of kinetic and configurational thermostats on calculations of the first normal stress coefficient in nonequilibrium molecular dynamics simulations

Abstract

Thermostats for homogeneous nonequilibrium molecular dynamics simulations are usually designed to control the kinetic temperature, but it is now possible control any combination of many different types of temperature, including the configurational and kinetic temperatures and their directional components. It is well known that these temperatures can become unequal in homogeneously thermostatted shearing steady states. The microscopic expressions for these temperatures are all derived from equilibrium distribution functions, and it is pertinent to ask, what are the consequences of using these equilibrium microscopic expressions for temperature in thermostats for shearing nonequilibrium steady states? Here we show that the answer to this question depends on which properties are being investigated. We present numerical results showing that the value of the zero shear rate viscosity obtained by extrapolating results of nonequilibrium molecular dynamics simulations of shearing steady states is the same, regardless of the type of temperature that is controlled. It also agrees with the value obtained from the equilibrium stress autocorrelation function via the Green-Kubo relation. However, the values of the limiting zero shear rate first normal stress coefficient obtained from nonequilibrium molecular dynamics simulations of shearing steady states are strongly dependent on the choice of temperature being controlled. They also differ from the value of the first normal stress coefficient that is calculated from the equilibrium stress autocorrelation function. We show that even when all of the directional components of the kinetic and configurational temperatures are simultaneously controlled to the same value, the agreement with the result obtained from the equilibrium stress autocorrelation function is poor.

Density dependence of the stress relaxation function of a simple fluid

“…Calculation of the first normal stress coefficient using their method with EMD simulations is computationally expensive, even with modern computers, because it requires stress autocorrelation function data of extremely high precision. Recently, Daivis [14,22] used the Coleman-Markovitz method to calculate the zero-shear normal stress coefficient of a simple liquid. He also calculated the zero-shear viscosity and first normal stress coefficient using NEMD by extrapolating the shear-rate dependent viscosity and first normal stress coefficient to zero-shear rate, for a range of densities.…”

“…While the equilibrium and nonequilibrium calculations of the viscosity agreed in the limit of zero-shear rate, the values of the first normal stress coefficient did not. A detailed understanding of this discrepancy is still lacking, but it is clear that the choice of thermostat has a strong influence on the values of nonlinear rheological properties calculated in NEMD simulations [22].…”

Non-equilibrium molecular dynamics simulations of the thermal transport properties of Lennard-Jones fluids using configurational temperatures

“…It has also become possible to measure configurational temperatures in systems with discontinuous potentials [28,32], and to employ thermostats that act only on the configurational degrees of freedom [33]; while it is well established that linear transport coe cients (such as viscosity and thermal conductivity) do not depend significantly on the choice of thermostat, it has been shown that nonlinear properties, such as normal stress coe cients, can do [34]. There is no reason a priori that any one temperature should be a better choice than others; in fact, Ayton et al [35] established that in systems experiencing spatially varying strain rates, only Rugh's dynamical temperature is able to correctly account for the resulting heat fluxes.…”

Effects of nanoscale density inhomogeneities on shearing fluids

“…Likewise, reduced density inhomogeneities still form when the thermostat is used to eliminate kinetic temperature inhomogeneities. Therefore, as well as thermal expansion, other factors such as inhomogeneities in the configurational temperature or normal stress differences [36], must be involved in the relationship between the temperature and density profiles. Figure 2 shows the velocity, density and temperature profiles for the set of system 1 simulations summarized in Table I.…”