Ornstein–Zernike equation
E835194
The Ornstein–Zernike equation is a fundamental relation in statistical mechanics that links the total and direct correlation functions of a fluid, forming the basis for many liquid-state theories and approximations.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
equation in statistical mechanics
ⓘ
integral equation ⓘ theoretical physics concept ⓘ |
| appliesTo |
classical fluids
ⓘ
colloidal suspensions ⓘ liquid mixtures ⓘ polymer solutions ⓘ simple liquids ⓘ |
| assumes |
homogeneous fluid
ⓘ
isotropic fluid ⓘ |
| basisFor |
Percus–Yevick approximation
NERFINISHED
ⓘ
hypernetted-chain approximation ⓘ liquid-state integral equation theories ⓘ mean spherical approximation ⓘ mode-coupling theories of liquids ⓘ reference interaction site model NERFINISHED ⓘ |
| describes | relation between total and direct correlation functions in a fluid ⓘ |
| field |
condensed matter physics
ⓘ
liquid-state theory ⓘ statistical mechanics ⓘ |
| generalizedTo |
anisotropic fluids
ⓘ
molecular fluids with orientational degrees of freedom ⓘ multicomponent mixtures ⓘ |
| hasForm | h(r12) = c(r12) + ρ ∫ d r3 c(r13) h(r32) ⓘ |
| hasFourierSpaceForm | h(k) = c(k) + ρ c(k) h(k) ⓘ |
| historicalContext | introduced to explain long-range density correlations near the critical point of fluids ⓘ |
| implies |
S(k) = 1 + ρ h(k)
ⓘ
S(k) = 1 / [1 − ρ c(k)] ⓘ |
| involves |
convolution of correlation functions
ⓘ
number density ρ ⓘ |
| namedAfter |
Frits Zernike
NERFINISHED
ⓘ
Leonard Ornstein NERFINISHED ⓘ |
| relatedTo |
critical opalescence
ⓘ
fluctuation–dissipation theorem NERFINISHED ⓘ pair distribution function g(r) ⓘ |
| relates |
direct correlation function c(r)
ⓘ
total correlation function h(r) ⓘ |
| usedFor |
analysis of scattering experiments
ⓘ
calculation of pair correlation functions ⓘ calculation of structure factor S(k) ⓘ computation of thermodynamic properties of liquids ⓘ description of critical phenomena in fluids ⓘ description of density fluctuations ⓘ |
| usedIn |
X-ray scattering analysis of liquids
ⓘ
light scattering analysis of fluids ⓘ neutron scattering analysis of liquids ⓘ |
| yearProposed | 1914 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Kirkwood approximation