Nonequilibrium Methods for Computing Transport Properties

An alternative to using equilibrium MD for computing transport coefficients is to use nonequilibrium molecular dynamics (NEMD) in which a modified Elamiltonian is used to drive the system away from equilibrium. By monitoring the response of the system in the limit of a small perturbation, the transport coefficient associated with the perturbation can be calculated. There is a rich literature on the use of NEMD to calculate transport coefficients the interested reader is referred to the excellent monograph by Evans and Morriss and the review article by Cummings and Evans.The basic idea behind the technique is that a system will respond in a linear fashion to a small perturbation. The following linear response theory equation is applicable in this limit  

An alternative NEMD method has been developed that is much simpler to implement than is the SLLOD method, particularly for charged systems such as ionic liquids. The method is called reverse nonequilibrium molecular dynamics (RNEMD) and was first developed as a means for computing thermal conductivity but has also been applied to viscosity. It differs from conventional equilibrium and nonequilibrium methods where the cause is an imposed shear rate and the measured effect is a momentum flux/stress. RNEMD does the opposite it imposes the difficult to compute quantity (the momentum flux or stress) and measures the easy to compute property (the shear rate or velocity profile). The method is very simple to implement because it only requires periodic swapping of momenta between atoms at different positions in the box. These swaps set up a velocity profile in the system (i.e., a shear rate). By tracking the frequency and amount of momentum 

The RNEMD method has also been used to compute the thermal conductivity of l-ethyl-3-methylimidazolium ethylsulfate ([C2mim] [EtS04]) as a function of water content using the simple point charge (SPC) model for water.We are unaware of any experimental thermal conductivity data for this system, and we have not seen any previous thermal conductivity simulations for any other ionic liquids. Table 1 shows the computed values at 348 K. Note that the experimental thermal conductivity of pure water at this temperature is 0.66 W/(m K). Thus the SPC model overpredicts the thermal conductivity of pure water by nearly 30%. 

Only a few experimental measurements of ionic liquid thermal conductivity exist. For example, [C2mim][BF4] has a value of 0.193 0.006 W/(m K) at 350K, ° while [C4mim][PF6] has a thermal conductivity of 0.147 0.007W/ (m K) at 335 The computed values for [Cimim] [EtS04] thus appear to be reasonable. Note that the thermal conductivity of the pure ionic liquid is much lower than that of water, and, it remains low even at a water mole fraction of 0.75. 

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