Martynov Vompe
The Martynov-Vompe closure relation [1] [2] is given by:
where
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.y^{*}(r)\right.=\ln y(r)-\beta \Phi _{p}}
where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \Phi _{p}} is the perturbative part of the pair potential (Note: in the Weeks-Chandler-Andersen separation for the Lennard-Jones system, the `perturbative part' is the attractive part). Martynov and Vompe have used the Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle dp_{v}-dP_{c}} and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle dU-dP} thermodynamic consistencies in constructing their closures [3].
References
- ↑ G. A. Martynov and A. G. Vompe "Differential condition of thermodynamic consistency as a closure for the Ornstein-Zernike equation", Physical Review E, 47 pp. 1012-1017 (1993)
- ↑ A. G. Vompe and G. A. Martynov "The bridge function expansion and the self-consistency problem of the Ornstein–Zernike equation solution", Journal of Chemical Physics 100 pp. 5249-5258 (1994)
- ↑ #Lloyd L. Lee, Dhananjay Ghonasgi, and Enrique Lomba "The fluid structures for soft-sphere potentials via the zero-separation theorems on molecular distribution functions", Journal of Chemical Physics 104 pp. 8058-8067 (1996)