PHYSICAL REVIEW A VOLUME 45, NUMBER 4 15 FEBRUARY 1992 Heat Sow and mass difFusion in binary Lennard-Jones mixtures Sten Sarman and Denis J. Evans Research School of Chemistry, Australian National University, Canberra, Australian Capital Territory 260l, Australia (Received 14 February 1991; revised manuscript received 24 October 1991) We have applied the Evans-Cummings (EC) nonequilibrium molecular-dynamics (NEMD) heat-flow algorithm for liquid mixtures to an equimolar Lennard-Jones (LJ) mixture where the potential parame- ters and the state point have been chosen to model an argon-krypton mixture at its triple point. We have calculated the thermal conductivity and the Soret coefficient for one 108-particle system and one 1024- particle system. In order to check the results we have used the color conductivity algorithm to obtain the mutual diffusion and the Dufour coefficients. According to the Onsager reciprocity relations the Dufour and the Soret coefficients should be equal, and this has also been found to be the case within the statistical uncertainty. The thermal conductivity and the diffusion coefficient increase slightly with the system size, but the statistical error makes it impossible to discern any size dependence of the cross- coupling coefficients. We also computed the Soret coefficient for three hypothetical types of LJ mix- tures. A consistency control was done by evaluating the Green-Kubo (GK) relations for the different transport coefficients by performing an equilibrium molecular-dynamics simulation. The GK thermal conductivity and the diffusion coefficient agree very well with the NEMD results but GK cross-coupling coefficients are very noisy and the error is probably about 15%. The EC algorithm is a NEMD algo- rithm that violates adiabatic incompressibility of phase space, but this does not cause any difficulties. PACS number(s): 44. 30. + v, 44. 10.+ i I. INTRODUCTION In a liquid mixture, a temperature gradient does not only give rise to a heat flow but also to chemical-potential gradients. These gradients induce mass currents of the various components in the mixture. This phenomenon is known as the Soret effect [1] and the cross-coupling coefficients relating the temperature gradients and the mass currents are known as Soret coefficients. Converse- ly, a chemical-potential gradient also causes heat flow, which is known as the Dufour effect with a correspond- ing Dufour cross-coupling coefficient. According to the Onsager reciprocity relations (ORR) the Dufour and the Soret coefficient should be equal. There have been vari- ous attempts to calculate these coefficients by applying molecular-dynamics (MD) methods. There are basically two categories of MD methods for computing transport coefficients, namely synthetic homogeneous nonequilibri- um molecular-dynamics (NEMD) methods and equilibri- um molecular-dynamics (EMD) methods. In the first case one couples the system to an external field and the transport coefficient is obtained in the limit of zero field. In the latter case the Green-Kubo (GK) relation for the transport coefficient in question is evaluated. A successful effort to calculate cross-coupling coeffi- cients was made by McGowan and Evans [2] in 1986. They devised a NEMD heat-flow algorithm for ideal rnix- tures, which will be referred to as the ME algorithm in the rest in this article, and they applied it to an equimolar Lennard-Jones (LJ) mixture where the different potential parameters and the state point were chosen to model an argon-krypton mixture at its triple point. Their results were confirmed by Paolini and Ciccotti [3], who used the same algorithm augmented with a subtraction noise- II. THEORY A. Macroscopic theory In a two-component mixture the thermodynamic for- ces and fluxes are formally related by the following rela- tion: (J, ) =L„X, +L, gXg, ( Jg ) = Lg, X, + L00X0, (2. 1) where ( J, ) is the macroscopic mass current density of component 1, (J& ) is the macroscopic heat flux vector, reduction method [4]. Apart from these two works most other attempts have been based on END evaluations of GK integrals. The first of these simulations tried to re- peat the NEMD results [4,5], but later works have covered different systems like hard-sphere systems [6] and a wider range of LJ fluids [7 — 9]. The main drawback with the ME algorithm is that it is only strictly valid for ideal mixtures. In order to be able to calculate transport coefficients of more realistic mix- tures a more general algorithm is required. A solution to this problem was suggested by Evans and Cummings (EC) [10]. They devised a completely general NEMD al- gorithm for heat flow in a mixture of simple fluids. Their algorithm makes it possible to unambiguously calculate both the thermal conductivity and the Soret coefficient. In this paper we will test this method for the same system as in Ref [2] which . is almost an ideal mixture, so we ex- pect the results to be similar. In Sec. II we present the necessary theory, in Sec. III the results are presented, and finally in Sec. IV there is a conclusion. 2370 1992 The American Physical Society