Mean field curvature corrections to the surface tension

Expressions for the surface tension sigma, Tolman length delta, and for the rigidity constants k and (k) over bar 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 rind 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 sigma and delta, and the second gives an analytical calculation of the value of delta at the critical point. The Tolman length is found to be negative and approximately 0.2 molecular diameters in magnitude far 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. (C) 1998 American Institute of Physics. [S0021-9606(98)50603-4].