Further Development of Scaled Particle Theory of Rigid Sphere Fluids

A new approach to the scaled particle theory of fluids is developed which is based on detailed consideration of the reversible work required to create a fixed spherical cavity of radius r in a rigid sphere fluid. The new results depend only on the mechanical concept of work and the classical virial theorem. A cycle greatly facilitates the necessary detailed analysis. A new integral equation for G(r), the primary function in scaled particle theory, culminates the new results. Approximation schemes may be employed relatively easily in this integral equation. The series approximation G(r) =  ∑ n = 0∞ Gn(r−1)n, which is asymptotically correct as r → ∞, is discussed. A new set of exact conditions on the coefficients Gn in this asymptotic expansion, the most striking of which is G3 ≡ 0 in three dimensions, is derived. These exact conditions relate to surface properties. The infinity and integral exact conditions on G(r) are shown to be truly independent. The jump condition on the second derivative of G(r) is in...