Time-dependent density functional theory and the kinetics of lattice gas systems in contact with a wall

• Published in: The Journal of chemical physics 1998-02, Vol.108 (7), p.3028-3037
• Main Authors: Fischer, H. P., Reinhard, J., Dieterich, W., Gouyet, J.-F., Maass, P., Majhofer, A., Reinel, D.
• Format: Article
• Language: English
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.475690

We develop an improved mean-field theory which allows us to describe the diffusive dynamics near phase transformations in condensed systems. Starting from a master equation for a stochastic lattice gas we obtain evolution equations on the single-particle level, whose stationary solutions in principle are consistent with the exact equilibrium statistics. Our method, which generalizes an approach proposed earlier, is based on a combination of a local equilibrium assumption and the lattice version of classical density functional theory. In the continuum limit, which is worked out for attractive interactions, generalized Cahn–Hilliard-type equations are recovered. Microscopic kinetic coefficients can be identified, which in general depend on the instantaneous local correlations in the nonequilibrium state. Moreover we study semi-infinite systems interacting with a planar wall and derive the appropriate boundary conditions to be imposed on the continuum equations. Applications to problems of the kinetics of phase changes influenced by a near wall are pointed out.