Mayer cluster expansion in statistical mechanics
E841011
The Mayer cluster expansion in statistical mechanics is a mathematical method that expresses the thermodynamic properties of interacting particle systems as a series in terms of cluster integrals, enabling systematic analysis of non-ideal gases and liquids.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Mayer cluster expansion | 0 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical method
ⓘ
series expansion ⓘ technique in statistical mechanics ⓘ |
| appliesTo |
classical fluids
ⓘ
interacting particle systems ⓘ liquids ⓘ non-ideal gases ⓘ |
| assumes |
classical point particles
ⓘ
pairwise interaction potential ⓘ |
| basedOn |
classical canonical ensemble
ⓘ
grand canonical ensemble ⓘ |
| convergesBestFor | low densities ⓘ |
| describedIn | classical liquid state theory ⓘ |
| developedBy |
Joseph E. Mayer
NERFINISHED
ⓘ
Maria Goeppert-Mayer NERFINISHED ⓘ |
| developedIn | 1930s ⓘ |
| expresses |
equation of state in terms of cluster integrals
ⓘ
grand partition function as a series in activity ⓘ pressure as a power series in density ⓘ |
| field | statistical mechanics ⓘ |
| generalizedBy | Ursell cluster expansion NERFINISHED ⓘ |
| hasComponent |
Mayer f-function f(r) = exp(-βu(r)) - 1
ⓘ
cluster integral B_n ⓘ diagrammatic cluster representation ⓘ |
| hasLimitation |
convergence problems at high density
ⓘ
difficulty of computing high-order cluster integrals ⓘ |
| involves |
combinatorics of particle labels
ⓘ
connected and irreducible diagrams ⓘ integration over particle coordinates ⓘ |
| purpose |
analyze deviations from ideal gas behavior
ⓘ
express thermodynamic properties as a series in terms of cluster integrals ⓘ relate microscopic interactions to macroscopic thermodynamics ⓘ |
| relatedTo |
diagrammatic methods in many-body theory
ⓘ
grand potential expansion ⓘ linked-cluster theorem NERFINISHED ⓘ virial expansion ⓘ |
| relates |
cluster integrals to virial coefficients
ⓘ
pair potential to thermodynamic quantities ⓘ |
| typicalApplication |
Lennard-Jones fluid
NERFINISHED
ⓘ
hard-sphere fluid ⓘ |
| usedFor |
computing virial coefficients from intermolecular potentials
ⓘ
deriving virial expansion of the equation of state ⓘ low-density expansions ⓘ studying gas-liquid phase behavior ⓘ |
| usesConcept |
Mayer f-function
NERFINISHED
ⓘ
cluster integrals ⓘ connected clusters ⓘ graphical representation of clusters ⓘ virial coefficients ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.