Mean field curvature corrections to the surface tension

Abstract

Expressions for the surface tension σ, Tolman length δ, and for the rigidity constants k and k̄ of a curved liquid-vapor interface in mean field approximation are presented. The local free energy comes from the Carnahan-Starling equation of state in mean field, and the usual square gradient term is replaced with a more general, integral nonlocal term. The surface tension and the Tolman length are calculated numerically, and the behavior as the critical temperature is approached is discussed; this behavior is compared with results from a molecular dynamics simulation. Two appendices are included; the first presents derivations of alternative expressions for σ and δ, and the second gives an analytical calculation of the value of δ at the critical point. The Tolman length is found to be negative and approximately 0.2 molecular diameters in magnitude for all temperatures investigated. It is also found to approach a constant value of −0.20263 molecular diameters at the critical point, in agreement with previous results.