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> : Diameter (length);
* <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

  1. J. E. Lennard-Jones "Cohesion", Proc. Phys. Soc. Lond. 43 pp. 461- (1931)