The Statistical Mechanical Theory of Surface Tension

  • Kirkwood J
  • Buff F
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Abstract

A general statistical mechanical theory of interfacial phenomena is developed and expressions are derived relating the surface tension and other superficial thermodynamic functions to the potential of intermolecular force and molecular distribution functions. On the basis of a reasonable approxi-mation to the superficial density of molecular pairs, the Lennard-Jones potential and the Eisenstein-Gingrich radial distribution function, the surface tension, surface energy, and the superficial density of matter, referred to the surface of tension, are calculated for liquid argon at 90 0 K and compared with experiment. The positive value which is obtained for the superficial density, referred to the surface of tension, confirms the results of Tolman's quasi-thermodynamic theory and leads to the conclusion the surface tension of small drops decreases with increasing curvature. I. T HE most recent statistical mechanical analysis of the relation between surface tension and the intermolecular forces acting at an interface between two fluid phases is due to R. H. Fowler.! However, as in earlier and more primitive analyses of the problem, Fowler introduces, almost at the beginning, the approximation of a mathematical surface of density discontinuity between the two phases. The formulation of a general theory of surface tension, free from this simplification wiH be presented here. Following the deduction of a general expression for surface tension in terms of the potential of intermolecular force and molecular distribution functions, the use of the mathematical surface of density discontinuity for the purpose of approximate calculation will be discussed. In the formulation of the theory we shall need two molecular distribution functions, p(l)(R) and p(2) (RI' R 12), the statistical mechanical theory of which will be presented in Section II. The singlet density p(l)(R) specifies the average number of molecules p(1)dv in volume element dv at a point R in the fluid. The doublet or pair density p(2) (Rit R 12) specifies the average number of molecular pairs p(2)dvldv12, one member of which is situated in volume element dv at point RI and the other in dV12 at point R12 in the relative configuration space of the pair. The pair correlation function g(2)(RJ, R 12) is defined by the relation, p(2) (Rl' R 12) =p(I) (Rl)p(1) (R 2)g(2) (Rl' R I2). (1)

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Authors

  • John G Kirkwood

  • Frank P Buff

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