Three-body interactions, scaling variables, and singular diameters in the coexistence curves of fluids

M. W. Pestak, Raymond E. Goldstein, Moses Hung-Wai Chan, J. R. De Bruyn, D. A. Balzarini, N. W. Ashcroft

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Abstract

Evidence is presented that the pair-potential model of fluids is insufficient in the critical region. In particular, data on the critical properties of Ne, N2, C2H4, C2H6, and SF6 are shown to exhibit well-defined trends in the variation of certain nonuniversal critical amplitudes with the critical temperature Tc. Both the slope of the coexistence-curve diameter far from the critical point, and the deviations from linear behavior which appear closer to Tc, increase systematically with Tc, and are directly correlated with the molecular polarizability. These trends are explained on the basis of the increasing importance of three-body dispersion (Axilrod-Teller) forces in the more polarizable systems, and a simple mean-field theory is developed which accounts for the observed correlations. The possibility of incorporating the effects of three-body interactions into an effective pair potential is explored within the context of perturbation theory in the grand canonical ensemble, and it is shown that such an interaction is explicitly a function of fugacity. In the critical region, this is equivalent to a thermal scaling field which depends on the bare chemical potential of the system, and ultimately leads to a breakdown in the classical law of the rectilinear diameter. The magnitude of this field mixing, and hence of the diameter anomaly, scales with the product of the particle polarizability and the critical number density, in agreement with experiment.

Original languageEnglish (US)
Pages (from-to)599-614
Number of pages16
JournalPhysical Review B
Volume36
Issue number1
DOIs
StatePublished - Jan 1 1987

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scaling
fluids
curves
trends
interactions
critical point
critical temperature
perturbation theory
breakdown
anomalies
slopes
deviation
products

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Cite this

Pestak, M. W., Goldstein, R. E., Chan, M. H-W., De Bruyn, J. R., Balzarini, D. A., & Ashcroft, N. W. (1987). Three-body interactions, scaling variables, and singular diameters in the coexistence curves of fluids. Physical Review B, 36(1), 599-614. https://doi.org/10.1103/PhysRevB.36.599
Pestak, M. W. ; Goldstein, Raymond E. ; Chan, Moses Hung-Wai ; De Bruyn, J. R. ; Balzarini, D. A. ; Ashcroft, N. W. / Three-body interactions, scaling variables, and singular diameters in the coexistence curves of fluids. In: Physical Review B. 1987 ; Vol. 36, No. 1. pp. 599-614.
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Pestak, MW, Goldstein, RE, Chan, MH-W, De Bruyn, JR, Balzarini, DA & Ashcroft, NW 1987, 'Three-body interactions, scaling variables, and singular diameters in the coexistence curves of fluids', Physical Review B, vol. 36, no. 1, pp. 599-614. https://doi.org/10.1103/PhysRevB.36.599

Three-body interactions, scaling variables, and singular diameters in the coexistence curves of fluids. / Pestak, M. W.; Goldstein, Raymond E.; Chan, Moses Hung-Wai; De Bruyn, J. R.; Balzarini, D. A.; Ashcroft, N. W.

In: Physical Review B, Vol. 36, No. 1, 01.01.1987, p. 599-614.

Research output: Contribution to journalArticle

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AB - Evidence is presented that the pair-potential model of fluids is insufficient in the critical region. In particular, data on the critical properties of Ne, N2, C2H4, C2H6, and SF6 are shown to exhibit well-defined trends in the variation of certain nonuniversal critical amplitudes with the critical temperature Tc. Both the slope of the coexistence-curve diameter far from the critical point, and the deviations from linear behavior which appear closer to Tc, increase systematically with Tc, and are directly correlated with the molecular polarizability. These trends are explained on the basis of the increasing importance of three-body dispersion (Axilrod-Teller) forces in the more polarizable systems, and a simple mean-field theory is developed which accounts for the observed correlations. The possibility of incorporating the effects of three-body interactions into an effective pair potential is explored within the context of perturbation theory in the grand canonical ensemble, and it is shown that such an interaction is explicitly a function of fugacity. In the critical region, this is equivalent to a thermal scaling field which depends on the bare chemical potential of the system, and ultimately leads to a breakdown in the classical law of the rectilinear diameter. The magnitude of this field mixing, and hence of the diameter anomaly, scales with the product of the particle polarizability and the critical number density, in agreement with experiment.

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Pestak MW, Goldstein RE, Chan MH-W, De Bruyn JR, Balzarini DA, Ashcroft NW. Three-body interactions, scaling variables, and singular diameters in the coexistence curves of fluids. Physical Review B. 1987 Jan 1;36(1):599-614. https://doi.org/10.1103/PhysRevB.36.599