Thermal Flux through a Surface of n-Octane. A Non-equilibrium Molecular Dynamics Study Jean-Marc Simon,* ,² Signe Kjelstrup, ‡ Dick Bedeaux, ‡,§ and Bjørn Hafskjold ‡ Laboratoire de Recherches sur la ReactiVite des Solides, UMR 5613 du CNRS, UniVersite de Bourgogne, BP 47870, 21078 Dijon Cedex, France, Department of Chemistry, Norwegian UniVersity of Science and Technology, NO-7491 Trondheim, Norway, and Leiden Institute of Chemistry, PO Box 9502, 2300 RA Leiden UniVersity, Leiden, The Netherlands ReceiVed: NoVember 24, 2003; In Final Form: February 24, 2004 We show using non-equilibrium molecular dynamics that there is local equilibrium in the surface when a two-phase fluid of n-octane is exposed to a large temperature gradient (10 8 K/m). The surface is defined according to Gibbs, and the transport across the surface is described with non-equilibrium thermodynamics. The structure of the surface in the presence of the gradient is the same as if the interface was in equilibrium, as measured by the variation across the surface of the pressure component that is parallel to the surface. The surface is in local equilibrium by this criterion and because the equation of state for the surface was unaltered by a large heat flux. The surface has a small entropy and is thus more structured than a surface of argon particles. The excess thermal resistance coefficient and the coupling coefficient for transport of heat and mass were calculated and found to be smaller than corresponding coefficients from kinetic theory and for argon-like particles, probably because molecular vibrations contribute to heat transfer. Away from the triple point, the heat of transfer was more than 30% of the value of the enthalpy of evaporation, which means that the surface has a large impact on the heat flux across it. This will be of practical importance in non-equilibrium models for phase transitions. The results support the basic assumptions in non-equilibrium thermodynamics and enable us to give linear flux force relations of transport with surface tension dependent transfer coefficients. 1. Introduction The region between two phases, the surface, has physical properties that are different from those of the homogeneous phases. The thermodynamic description of the surface in terms of excess variables was worked out already by Gibbs. 1 The excess variables of the surface between a vapor and a liquid are the excess density, entropy, and energy. On a microscopic scale, the surface has a thickness ranging from a few molecular diameters (at the triple point) to infinity (at the critical point of the fluid). On the thermodynamic scale, the surface thickness is integrated out. While methods and techniques for calculations of equilibrium properties of a surface are well established; such methods are hardly available for a surface in a system that is not in equilibrium. The major aim of this paper is to contribute to the establishment of such methods. Questions of fundamental importance, that shall be addressed in the paper, are: Can we define a surface in the absence of global equilibrium in the system? Can we define local thermodynamic properties also in the case that there are large gradients across it? How can we define the transport properties of the surface? Of course, we are also interested in the values of the transport coefficients. A first effort to answer these questions was made by Røsjorde et al. 2 using non-equilibrium molecular dynamic simulations (NEMD). The authors studied the liquid-vapor interface in a simple fluid of Lennard-Jones spline particles exposed to large temperature gradients and to pressures that differed from the saturation pressure. An important finding was that the surface tension at global equilibrium in the system was the same as the surface tension in a temperature gradient, for the same surface temperature. The surface temperature was defined using the kinetic energy of the interface layer. In other words, the surface was in local equilibrium. The hypothesis of local equilibrium is central to non-equilibrium thermodynamics. Once it is valid, we can use this theory to set up transport equations for the system. Heat and mass transfer coefficients were found for the argon-like particles, specific for the surface. Near the triple point they compared well with results from kinetic theory. However, the coefficients did not agree with experimental results reported by Fang and Ward. 3,4 These authors measured large temperature jumps at an evaporating surface of water, octane, and methyl- cyclohexane. These temperature jumps were an order of magnitude larger than those predicted by kinetic theory and NEMD. The molecular structure may be important in this respect. It has been proposed that the rotational degree of freedom in the molecule determines its probability of condensa- tion. An important aim of this article is thus to see if vibrational and rotational degrees of freedom in the molecule alter the conclusions above or account for the discrepancy between non- equilibrium molecular dynamics simulations and experiments. This gives the background for choosing n-octane as a case study. The same molecule was used in the experiments of Ward et al. 3,4 Transport properties for the liquid and vapor phases of linear n-alkanes are known from experiments as well as from simulations. 5-10 NEMD is an excellent tool to study the questions raised above. It can be used to find transport properties as well as to * Corresponding author. E-mail: jmsimon@u-bourgogne.fr ² Universite de Bourgogne. ‡ Norwegian University of Science and Technology. § Leiden University. 7186 J. Phys. Chem. B 2004, 108, 7186-7195 10.1021/jp0375719 CCC: $27.50 © 2004 American Chemical Society Published on Web 05/06/2004