Scaled Particle Theory of Fluids

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Abstract
A statistical thermodynamic theory has been developed employing distance scaling as a coupling procedure. This is an extension to real fluids of the technique applied by Reiss, Frisch, and Lebowitz to rigid‐sphere systems. One considers molecules interacting with pair potential u(r), except for one particle which interacts with potential u(r/λ). This single particle, essentially a scaled version of a normal molecule, is termed a λ‐cule. It is convenient to restrict discussion to potentials with rigid cores at r=a and cutoffs at γa. Attention is focused on a function, θ(λ, ρ, T), which reduces to G of footnote reference 1 in the case of rigid spheres. The pressure, chemical potential, and work of expanding a λ‐cule are simply related to θ. One can write θ exactly for λ<1/2γ and simple connection conditions hold at λ=1/2γ. An integral condition and λ=∞ condition on θ also exist. While θ is not completely specified, the foregoing conditions determine much of its behavior.

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