Lennard-Jones model: Difference between revisions

Revision as of 18:56, 16 February 2007

Lennard-Jones Potential:

$V (r) = 4 ϵ [{(\frac{σ}{r})}^{12} - {(\frac{σ}{r})}^{6}]$

where:

$V (r)$ : Potential energy of interaction betweeen two particles at a distance r;

Reduced units:

Density, $ρ^{*} \equiv ρ σ^{3}$ , where $ρ = N / V$ (Number of particles $N$ divided by the volume $V$ .)

Temperature; $T^{*} = k_{B} T / ϵ $, w h r e $ T $ i s t h e a b s o l u t e t e m p e r a t u r e a n d < m a t h > k_{B}$ is the Boltzmann constant

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

@@ Line 5: / Line 5: @@
 where:
-V(r): 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;
-&sigma;: Diameter (length);
+* <math> \sigma </math> : Diameter (length);
-&epsilon;: well depth (energy)
+* <math> \epsilon </math> : well depth (energy)
-==References==
+Reduced units:
+* 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^* = k_B T/\epsilon$, whre $T$ is the absolute temperature and <math> k_B </math> is the [[Boltzmann]] constant
+==References==
 J. E. Lennard-Jones "Cohesion", Proc. Phys. Soc. Lond. volume 43 pages 461 (1931)