ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTA simple numerical method for solving complex equilibriaJerald A. Devore Cite this: J. Chem. Educ. 1988, 65, 10, 868Publication Date (Print):October 1, 1988Publication History Received3 August 2009Published online1 October 1988Published inissue 1 October 1988https://doi.org/10.1021/ed065p868RIGHTS & PERMISSIONSArticle Views160Altmetric-Citations3LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (2 MB) Get e-Alerts Get e-Alerts
A closure for the two-particle BGY equation is formulated by coupling the three-particle distribution functions for the superposition approximation and the exact expression for rigid rods through a density and angle dependent quantity f( ρ,θ)=Ψ( ρ)χ(θ). Given the angle dependence, one can determine Ψ( ρ) by requiring that the virial theorem and the compressibility relation yield the same equation of state (pressure consistency). Fourth through tenth virial coefficients for rigid disks and spheres are calculated using this closure.
The equations of state for rigid disks and spheres are discussed. Alder and Hoovers’17 approximants are found to yild compressibility factors close to those of Woodcock1 and Baram and Luban2. (AIP)
Modified distribution functions are defined by F*n(r1,⋅⋅⋅,rn) = Fn(r1,⋅⋅⋅,rn) ⋅ exp[Un(r1,⋅⋅⋅,rn)/kT], where Fn(r1,⋅⋅⋅,rn) is the distribution function and Un(r1,⋅⋅⋅,rn) is the mutual potential energy for a set of n molecules. These modified functions are equivalent to those of empty domains (cavities) and are used to derive several general zero-separation relations for rigid particle fluids.
