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Title: Combined temperature and density series for fluid-phase properties. I. Square-well spheres

Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B{sub 2}(β) η + B{sub 3}(β) η{sup 2} + B{sub 4}(β) η{sup 3} + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B{sub i}(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the B{sub i} coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the B{sub i} coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial seriesmore » converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.« less
Authors:
 [1] ; ;  [2]
  1. Chemical and Biomolecular Engineering Department, The University of Akron, Akron, Ohio 44325-3906 (United States)
  2. Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200 (United States)
Publication Date:
OSTI Identifier:
22489594
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 11; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CALCULATION METHODS; COMPARATIVE EVALUATIONS; COMPRESSIBILITY; DENSITY; FUNCTIONS; INTEGRALS; LIQUIDS; PERTURBATION THEORY; POWER SERIES