Lennard-Jones model: Difference between revisions
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* Density, <math> \rho^* \equiv \rho \sigma^3 </math>, where <math> \rho = N/V </math> (Number of particles <math> N </math> divided by the volume <math> V </math>.) | * Density, <math> \rho^* \equiv \rho \sigma^3 </math>, where <math> \rho = N/V </math> (Number of particles <math> N </math> divided by the volume <math> V </math>.) | ||
* Temperature; <math> T^* | * Temperature; <math> T^* \equiv k_B T/\epsilon </math>, where <math> T </math> is the absolute temperature and <math> k_B </math> is the [[Boltzmann]] constant | ||
==References== | ==References== | ||
Revision as of 17:57, 16 February 2007
Lennard-Jones Potential:
![{\displaystyle V(r)=4\epsilon \left[\left({\frac {\sigma }{r}}\right)^{12}-\left({\frac {\sigma }{r}}\right)^{6}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5256ed833acfbaa9f624a55f4be3f9fcb3c27e1a)
where:
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle V(r)} : Potential energy of interaction betweeen two particles at a distance r;
- : Diameter (length);
- : well depth (energy)
Reduced units:
- Density, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \rho ^{*}\equiv \rho \sigma ^{3}} , where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \rho =N/V} (Number of particles 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 N } divided by the volume 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 V } .)
- Temperature; 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 T^* \equiv k_B T/\epsilon } , 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 T } is the absolute temperature and 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 k_B } is the Boltzmann constant
References
J. E. Lennard-Jones "Cohesion", Proc. Phys. Soc. Lond. volume 43 pages 461 (1931)