Grand canonical ensemble

From SklogWiki
Revision as of 14:02, 30 July 2008 by Carl McBride (talk | contribs) (Added a reference)
Jump to navigation Jump to search

The grand-canonical ensemble is particularly well suited to simulation studies of adsorption.

Ensemble variables

Grand canonical partition function

The classical grand canonical partition function for a one-component system in a three-dimensional space is given by:

where:

  • N is the number of particles
  • is the de Broglie thermal wavelength (which depends on the temperature)
  • , with being the Boltzmann constant
  • U is the potential energy, which depends on the coordinates of the particles (and on the interaction model)
  • represent the position coordinates of the particles (reduced with the system size): i.e.

Helmholtz energy and partition function

The corresponding thermodynamic potential, the grand potential, , for the aforementioned grand canonical partition function is:

,

where A is the Helmholtz energy function. Using the relation

one arrives at

i.e.:

See also

References

  1. Richard C. Tolman "On the Establishment of Grand Canonical Distributions", Physical Review 57 pp. 1160-1168 (1940)