Non-Equilibrium Thermodynamics for surfaces and Local Equilibrium for the Liquid-Vapor Interface
D. Bedeaux

Department of Chemistry, Norwegian University of Science and Technology, Trondheim Norway

Abstract: Experiments done in the last ten years have found temperature differences across the liquid-vapour interface of the order of 10 degrees Celsius during evaporation in one- component systems. These temperature differences are much larger than expected on the basis of kinetic theory. The challenge is to describe these results in a clear macroscopic context, on the one hand, and to understand them on a microscopic level, on the other hand. We will show how non-equilibrium thermodynamics for surfaces provides the needed macroscopic description for multi-component systems. Catalytic surfaces are considered. The description uses, as Gibbs did for equilibrium interfaces, excess densities. This implies that the surface is a separate thermodynamic system. When the system is not in equilibrium the surface will even have a temperature and chemical potentials different from the temperatures and chemical potentials in the adjacent phases. Using balance equations and the Gibbs relation one obtains the excess entropy production of the surface and are thereby able to give force-flux relations (boundary conditions) for transport into and through the surface. An important assumption in this analysis is that the surface is in local equilibrium. We have simulated such transports using molecular dynamics [1-5]. On the basis of these simulations we were then able to verify that the description using non-equilibrium thermodynamics is correct. In order to investigate the validity of local equilibrium in more detail we have used the square gradient model for the surface in one- component systems [6] and for binary mixtures [7,8]. The square gradient contribution to the free energy density shows that there is no local equilibrium in the interfacial region in the continuous description. On the basis of numerical results we have been able to show that in the description using excess densities, obtained by integration over the continuous profiles, the assumption of local equilibrium is valid. We conclude that the use of non-equilibrium thermodynamics for surfaces, using excess densities, is appropriate for many systems.

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