|
This article is cited in 2 scientific papers (total in 2 papers)
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 $r\to\infty$.
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
Linking options:
https://www.mathnet.ru/eng/tmf619https://doi.org/10.4213/tmf619 https://www.mathnet.ru/eng/tmf/v123/i3/p500
|
Statistics & downloads: |
Abstract page: | 371 | Full-text PDF : | 212 | References: | 55 | First page: | 2 |
|