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

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:

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
\Bibitem{Mar00} \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} 

• http://mi.mathnet.ru/eng/tmf619
• https://doi.org/10.4213/tmf619
• http://mi.mathnet.ru/eng/tmf/v123/i3/p500

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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
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