Widom test-particle method: Difference between revisions
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:<math>\mu^{ex} = -k_BT \ln \langle e^{-\Phi/k_bT}\rangle_N</math> | :<math>\mu^{ex} = -k_BT \ln \langle e^{-\Phi/k_bT}\rangle_N</math> | ||
where <math>k_B</math> is the [[Boltzmann constant]], ''T'' is the [[temperature]], ''N'' is the number of particles within the system and <math>\Phi</math> is the | where <math>k_B</math> is the [[Boltzmann constant]], ''T'' is the [[temperature]], ''N'' is the number of particles within the system and <math>\Phi</math> is the interaction potential energy between the randomly placed test particle and the ''N'' particles that the system is comprised of. | ||
==References== | ==References== | ||
#[http://dx.doi.org/10.1063/1.1734110 B. Widom "Some Topics in the Theory of Fluids", Journal of Chemical Physics '''39''' pp. 2808-2812 (1963)] | #[http://dx.doi.org/10.1063/1.1734110 B. Widom "Some Topics in the Theory of Fluids", Journal of Chemical Physics '''39''' pp. 2808-2812 (1963)] | ||
Revision as of 12:24, 26 September 2007
The excess chemical potential is given by
where is the Boltzmann constant, T is the temperature, N is the number of particles within the system and is the interaction potential energy between the randomly placed test particle and the N particles that the system is comprised of.
References
- B. Widom "Some Topics in the Theory of Fluids", Journal of Chemical Physics 39 pp. 2808-2812 (1963)
- B. Widom "Potential-distribution theory and the statistical mechanics of fluids", Journal of Physical Chemistry 86 pp. 869 - 872 (1982)
- David S. Corti "Alternative derivation of Widom's test particle insertion method using the small system grand canonical ensemble", Molecular Physics 93 pp. 417-420 (1998)