Lennard-Jones model: Difference between revisions
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* <math> V(r) </math> : Potential energy of interaction betweeen two particles at a distance r; | * <math> V(r) </math> : Potential energy of interaction betweeen two particles at a distance r; | ||
* <math> \sigma </math> : | * <math> \sigma </math> : diameter (length); | ||
* <math> \epsilon </math> : well depth (energy) | * <math> \epsilon </math> : well depth (energy) | ||
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#J. E. Lennard-Jones "Cohesion", Proc. Phys. Soc. Lond. '''43''' pp. 461- (1931) | #J. E. Lennard-Jones "Cohesion", Proc. Phys. Soc. Lond. '''43''' pp. 461- (1931) | ||
[[Category:Models]] | |||
Revision as of 12:33, 27 February 2007
The Lennard-Jones potential 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 V(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}- \left( \frac{\sigma}{r}\right)^6 \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 V(r) } : Potential energy of interaction betweeen two particles at a distance r;
- 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 } : diameter (length);
- 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 \epsilon } : well depth (energy)
Reduced units:
- Density, 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 \rho^* \equiv \rho \sigma^3 } , 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 \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; , 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. 43 pp. 461- (1931)