Strongly correlating liquids: Difference between revisions

Revision as of 15:18, 18 May 2011

Strongly correlating liquids are defined as those for whom $R\geq 0.9$ where (Eq. 6 ^[1])

R={\frac {\langle \Delta {\mathcal {V}}\Delta U\rangle }{\sqrt {\langle (\Delta {\mathcal {V}})^{2}\rangle \langle (\Delta U)^{2}\rangle }}}

where $\Delta U$ represents fluctuations of the potential in the NVT ensemble and ${\mathcal {V}}$ is the virial (see also Virial pressure).

The liquid phase formed by the Lennard-Jones model is an example of a strongly correlating liquid^[3].

@@ Line 1: / Line 1: @@
 '''Strongly correlating liquids''' are defined as those for whom <math>R \ge 0.9</math> where (Eq. 6 <ref>[http://dx.doi.org/10.1063/1.2982247 Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, and Jeppe C. Dyre "Pressure-energy correlations in liquids. I. Results from computer simulations", Journal of Chemical Physics '''129''' 184507 (2008)]</ref>)
-:<math>R=\frac{\langle \Delta V \Delta U \rangle}{ \sqrt{ \langle (\Delta V)^2 \rangle \langle (\Delta U)^2 \rangle  }  }</math>
+:<math>R=\frac{\langle \Delta \mathcal{V} \Delta U \rangle}{ \sqrt{ \langle (\Delta \mathcal{V})^2 \rangle \langle (\Delta U)^2 \rangle  }  }</math>
-where <math>\Delta U</math> represents [[Fluctuation theorem | fluctuations]] of the potential  in the [[Canonical ensemble | NVT ensemble]] and <math>V</math>
+where <math>\Delta U</math> represents [[Fluctuation theorem | fluctuations]] of the potential  in the [[Canonical ensemble | NVT ensemble]] and <math>\mathcal{V}</math>
-is the [[virial]] (see also [[Virial pressure]]).
+is the [[Virial theorem | virial]] (see also [[Virial pressure]]).
 ==Isomorphs==
 <ref>[http://dx.doi.org/10.1063/1.3265957 Nicoletta Gnan, Thomas B. Schrøder, Ulf R. Pedersen, Nicholas P. Bailey, and Jeppe C. Dyre "Pressure-energy correlations in liquids. IV. “Isomorphs” in liquid phase diagrams", Journal of Chemical Physics '''131''' 234504 (2009)]</ref>