Uhlenbeck-Ford model
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Functional form
The Uhlenbeck-Ford model is given by :
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U_{UF}(r) = - \frac{p}{\beta} \ln \left(1-e^{-(r/\sigma)^2} \right)}
where
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p \geq = 0 } is a scaling factor
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta := (k_B T)^{-1} } is the well depth (energy)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|} is the interparticle distance.
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is a length-scale parameter
References
- Related reading
- Rodolfo Paula Leite, Rodrigo Freitas, Rodolfo Azevedo and Maurice de Koning "The Uhlenbeck-Ford model: Exact virial coefficients and application as a reference system in fluid-phase free-energy calculations", Journal of Chemical Physics 145, 194101 (2016)
- Rodolfo Paula Leite, Pedro Antonio Santos-Flórez, and Maurice de Koning "Uhlenbeck-Ford model: Phase diagram and corresponding-states analysis", Physical Review E 96, 032115 (2017)