Mayer f-function formalism
E841012
The Mayer f-function formalism is a mathematical framework in statistical mechanics that expresses intermolecular interactions via cluster expansions to analyze the thermodynamic properties of fluids and gases.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
cluster expansion method
ⓘ
statistical mechanics formalism ⓘ |
| appliesTo |
classical fluids
ⓘ
gases ⓘ |
| assumes |
classical distinguishable particles in many applications
ⓘ
pairwise additive interactions in simplest form ⓘ |
| basedOn | intermolecular pair potential ⓘ |
| coreIdea |
express partition function as sum over clusters
ⓘ
represent interactions via products of f-functions ⓘ |
| defines | f(r) = exp[-β u(r)] - 1 ⓘ |
| developedBy |
Joseph E. Mayer
NERFINISHED
ⓘ
Maria Goeppert-Mayer NERFINISHED ⓘ |
| field | statistical mechanics ⓘ |
| generalizedTo | quantum cluster expansions ⓘ |
| influenced |
diagrammatic methods in many-body physics
ⓘ
integral equation theories of liquids ⓘ modern liquid state theory ⓘ |
| introducesConcept | Mayer f-function ⓘ |
| leadsTo |
cluster integrals
ⓘ
virial coefficients ⓘ |
| limitation | convergence issues at high density ⓘ |
| mathematicalTool | graph theory ⓘ |
| relatedConcept |
Mayer cluster expansion
NERFINISHED
ⓘ
diagrammatic cluster representation ⓘ |
| relatedTo |
canonical ensemble
ⓘ
grand canonical ensemble ⓘ |
| relatesQuantity |
interparticle distance r
ⓘ
inverse temperature β ⓘ pair potential u(r) ⓘ |
| representsBondsAs | Mayer f-functions ⓘ |
| representsClustersAs | graphs ⓘ |
| representsParticlesAs | graph vertices ⓘ |
| timePeriod | 1930s ⓘ |
| usedFor |
analysis of non-ideal gas behavior
ⓘ
calculation of chemical potential ⓘ calculation of free energy ⓘ calculation of pressure from microscopic interactions ⓘ calculation of thermodynamic properties ⓘ cluster expansion of the partition function ⓘ low-density expansions of fluids ⓘ virial expansion of the equation of state ⓘ |
| usedIn | derivation of virial equation of state ⓘ |
| usesSymbol |
f(r)
ⓘ
u(r) ⓘ β ⓘ |
| validRegime | low to moderate densities ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.