Strongly correlating liquids: Difference between revisions
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'''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>) | '''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== | ==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> | <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> | ||
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*[http://dx.doi.org/10.1063/1.2982249 Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, and Jeppe C. Dyre "Pressure-energy correlations in liquids. II. Analysis and consequences", Journal of Chemical Physics '''129''' 184508 (2008)] | *[http://dx.doi.org/10.1063/1.2982249 Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, and Jeppe C. Dyre "Pressure-energy correlations in liquids. II. Analysis and consequences", Journal of Chemical Physics '''129''' 184508 (2008)] | ||
*[http://dx.doi.org/10.1063/1.3265955 Thomas B. Schrøder, Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, and Jeppe C. Dyre "Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance", Journal of Chemical Physics '''131''' 234503 (2009)] | *[http://dx.doi.org/10.1063/1.3265955 Thomas B. Schrøder, Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, and Jeppe C. Dyre "Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance", Journal of Chemical Physics '''131''' 234503 (2009)] | ||
*[http://dx.doi.org/10.1063/1.3685804 Trond S. Ingebrigtsen, Lasse Bøhling, Thomas B. Schrøder, and Jeppe C. Dyre "Communication: Thermodynamics of condensed matter with strong pressure-energy correlations", Journal of Chemical Physics '''136''' 061102 (2012)] | |||
[[category: Classical thermodynamics]] | [[category: Classical thermodynamics]] | ||
[[category: Statistical mechanics]] | [[category: Statistical mechanics]] | ||
Latest revision as of 17:18, 16 February 2012
Strongly correlating liquids are defined as those for whom where (Eq. 6 [1])
where represents fluctuations of the potential in the NVT ensemble and is the virial (see also Virial pressure).
Isomorphs[edit]
Lennard-Jones liquid[edit]
The liquid phase formed by the Lennard-Jones model is an example of a strongly correlating liquid[3].
References[edit]
- ↑ 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)
- ↑ 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)
- ↑ Thomas B. Schrøder, Nicoletta Gnan, Ulf R. Pedersen, Nicholas P. Bailey, and Jeppe C. Dyre "Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems", Journal of Chemical Physics 134 164505 (2011)
- Related reading
- Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, Thomas B. Schrøder, and Jeppe C. Dyre "Pressure-energy correlations in liquids. II. Analysis and consequences", Journal of Chemical Physics 129 184508 (2008)
- Thomas B. Schrøder, Nicholas P. Bailey, Ulf R. Pedersen, Nicoletta Gnan, and Jeppe C. Dyre "Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance", Journal of Chemical Physics 131 234503 (2009)
- Trond S. Ingebrigtsen, Lasse Bøhling, Thomas B. Schrøder, and Jeppe C. Dyre "Communication: Thermodynamics of condensed matter with strong pressure-energy correlations", Journal of Chemical Physics 136 061102 (2012)