Uhlenbeck-Ford model: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
{{Stub-general}} | {{Stub-general}} | ||
== Functional form == | |||
The '''Uhlenbeck-Ford model''' is given by : | The '''Uhlenbeck-Ford model''' is given by : | ||
:<math>U_{UF}(r) = - \frac{p}{\beta} \ln \left(1-e^{-(r/\sigma)^2} \right)</math> | :<math>U_{UF}(r) = - \frac{p}{\beta} \ln \left(1-e^{-(r/\sigma)^2} \right)</math> | ||
where | |||
* <math>p \geq = 0 </math> is a scaling factor | |||
* <math> \beta := (k_B T)^{-1} </math> is the well depth (energy) | |||
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> is the interparticle distance. | |||
* <math> \sigma </math> is a length-scale parameter | |||
Revision as of 20:33, 11 October 2017
|
This article is a 'stub' page, it has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add sufficient material to this article then please remove the {{Stub-general}} template from this page. |
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)