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^* \equiv k_B T/\epsilon </math>, where <math> T </math> is the absolute temperature and <math> k_B </math> is the [[Boltzmann]] constant | * Temperature; <math> T^* \equiv k_B T/\epsilon </math>, where <math> T </math> is the absolute temperature and <math> k_B </math> is the [[Ludwig Eduard Boltzmann | Boltzmann]] constant | ||
==References== | ==References== | ||
Revision as of 18:24, 16 February 2007
Lennard-Jones Potential:
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; 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)