A statistical-mechanical theory of surface tension

A system is studied which consists of a large number of molecules contained in a rectangular parallelepiped with rigid walls. Volume and surface area are taken as two principal coordinates, and pressure and surface tension are considered as isothermal derivatives of the free energy. It is shown that, for a one-phase system, the thermodynamic pressure so obtained depends on the values, at the centre of the container, of the number density and the pair-distribution function. Two types of surface tension are considered as derivatives of the free energy, that at the walls of the container and that at the surface between liquid and vapour. For the latter, the formula obtained agrees with that of Kirkwood & Buff (1949), who treated surface tension from the point of view of a stress, and it is shown how their treatment may be shortened considerably. The virial of the forces exerted by the container on the molecules is shown to include terms involving the surface tensions referred to above, and it is proved that the quantities, pressure and surface tensions, occurring in the expression of the Clausius virial theorem, agree with the corresponding thermodynamic quantities. For the tension of a plane surface between phases, an approximate formula is obtained which depends on a suggested approximate form for the pair-distribution function.