Extension of Scaled Particle Theory for Rigid Disks

Abstract

Geometric information about rigid disk arrangements in the plane, not previously used, is assembled and incorporated into scaled particle theory. In particular the close packed density limit for the contact correlation function G(λ) has been obtained exactly. The revised theory provides substantially better agreement than its predecessor with molecular dynamics results for rigid disks in the fluid phase. Although high density G(λ) curves develop nonmonotonic behavior as expected of crystalline packings, the corresponding pressure isotherms manifest no freezing transition in the present version. Suggestions for rectifying this shortcoming are included.