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TMF, 2000, Volume 123, Number 3, Pages 500–515 (Mi tmf619)  

This article is cited in 1 scientific paper (total in 1 paper)

Distribution functions of binary solutions (exact analytic solution)

G. A. Martynov

Institute of Physical Chemistry, Russian Academy of Sciences

Abstract: We show that the general solution of the Ornstein–Zernike system of equations for multicomponent solutions has the form $h_{\alpha\beta}= \sum A_{\alpha\beta}^j\exp(-\lambda_jr)/r$, where $\lambda_j$ are the roots of the transcendental equation $1-\rho\Delta(\lambda_j)=0$ and the amplitudes $A_{\alpha\beta}^j$ can be calculated if the direct correlation functions are given. We investigate the properties of this solution including the behavior of the roots $\lambda_j$ and amplitudes $A_{\alpha\beta}^j$ in both the low-density limit and the vicinity of the critical point. Several relations on $A_{\alpha\beta}^j$ and $C_{\alpha\beta}$ are found. In the vicinity of the critical point, we find the state equation for a liquid, which confirms the Van der Waals similarity hypothesis. The expansion under consideration is asymptotic because we expand functions in series in eigenfunctions of the asymptotic Ornstein–Zernike equation valid at $r\to\infty$.

DOI: https://doi.org/10.4213/tmf619

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English version:
Theoretical and Mathematical Physics, 2000, 123:3, 833–845

Bibliographic databases:

Received: 11.11.1999

Citation: G. A. Martynov, “Distribution functions of binary solutions (exact analytic solution)”, TMF, 123:3 (2000), 500–515; Theoret. and Math. Phys., 123:3 (2000), 833–845

Citation in format AMSBIB
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\by G.~A.~Martynov
\paper Distribution functions of binary solutions (exact analytic solution)
\jour TMF
\yr 2000
\vol 123
\issue 3
\pages 500--515
\mathnet{http://mi.mathnet.ru/tmf619}
\crossref{https://doi.org/10.4213/tmf619}
\zmath{https://zbmath.org/?q=an:0968.82026}
\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 123
\issue 3
\pages 833--845
\crossref{https://doi.org/10.1007/BF02551037}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000088926700011}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Martynov, GA, “What is the structure of a liquid?”, Journal of Structural Chemistry, 43:3 (2002), 507  crossref  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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