Distribution functions of binary solutions (exact analytic solution)
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 500-515
Cet article a éte moissonné depuis la source Math-Net.Ru
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 $r\to\infty$.
@article{TMF_2000_123_3_a10,
author = {G. A. Martynov},
title = {Distribution functions of binary solutions (exact analytic solution)},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {500--515},
year = {2000},
volume = {123},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a10/}
}
G. A. Martynov. Distribution functions of binary solutions (exact analytic solution). Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 500-515. http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a10/
[1] T. Morita, K. Hiroike, Progr. Theor. Phys., 23 (1960), 1003 ; 24, 317 ; 25 (1961), 537 | DOI | MR | Zbl | DOI | MR
[2] G. A. Martynov, TMF, 22:1 (1975), 85 ; G. A. Martynov, Mol. Phys., 42 (1981), 329 | DOI | MR
[3] G. A. Martynov, Fundamental Theory of Liquids. Method of Distribution Function, Adam Hilger, Bristol–Philadelphia–New York, 1992 | MR
[4] R. Evans, R. J. Leote de Carvalho, D. C. Hoyyle, J. Chem. Phys., 100 (1994), 591 | DOI