Microscopic integral relations for the curvature dependent surface tension in a two-phase multi-component system

In this paper we discuss the thermodynamics and statistical mechanics of a curved fluid interface, in a system containing several chemical components. We derive microscopic integral relations for the Tolman-length, the spontaneous curvature and rigidity constants in a multi-component system. A thorough discussion is given of the dependence of the various relevant quantities on the choice of the dividing surface. Also some choice invariant characteristics quantities are given. We furthermore discuss the small-curvature correction to the Clausius-Clapeyron condition