Scaled Particle Theory of Fluids

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 λ1/2γ 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.