表面張力の統計力学

抄録

Statistical mechanics of surface tension. It is shown that we can derive the expression of surface tension in terms of disrtribution functions from purely statistical considerations regarding surface tension as the increase in free energy for an increase of unit area of the interface between the liquid and vapor phases.
The expression obtained is
γ=1/2∫∫…∫dφ₁₂/dR₁₂x²₁₂-Z²₁₂/R₁₂ρ_S⁽²⁾(Z, R₁₂)dZ₁dv₁₂,
where γ is the surface tension, φ₁₂ is the intermolecular potential and ρ_S⁽²⁾ (Z, R₁₂) is the excess pair density reckoned relative to an arbitrary Gibbs dividing surface. The above expression can be transformed into
γ=∫(p_N-p_T)dZ₁
where
p_N(Z)=kTρ⁽¹⁾(Z₁)-1/2∫∫…∫dv₁₂∫Z₁Z₁-Z₁₂dφ₁₂/dR₁₂Z₁₂/R₁₂ρ⁽²⁾(ζ, R₁₂)dζ,
p_T(Z₁)=kTρ⁽¹⁾(Z₁)-1/2∫∫…∫dv₁₂dφ₁₂/dR₁₂x₁₂²/R₁₂ρ⁽²⁾(Z₁, R₁₂).
The results coincide with those of kirkwood and Buff which were derived by calculating stresses directly.