Tarazona's weighted density approximation: Difference between revisions
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Inspired by the exact solution known for the system of [[1-dimensional hard rods]], | |||
Pedro Tarazona proposed a series of models in the 1980's | |||
Inspired by the exact solution known for the system of [[ | <ref>[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]</ref> | ||
Pedro Tarazona proposed a series of models in the 1980's ( | <ref>[http://dx.doi.org/10.1103/PhysRevA.31.2672 P. Tarazona "Free-energy density functional for hard spheres", Physical Review A '''31''' pp. 2672-2679 (1985)]</ref> | ||
dependence of the [[Helmholtz energy function]] is weighted: | <ref>[http://dx.doi.org/10.1103/PhysRevA.32.3148 P. Tarazona "Erratum: Free-energy density functional for hard spheres", Physical Review A '''32''' p. 3148 (1985)]</ref> | ||
<ref>[http://dx.doi.org/10.1080/00268978700100381 P. Tarazona, U. Marini Bettolo Marconi and R. Evans "Phase equilibria of fluid interfaces and confined fluids: Non-local versus local density functionals" Molecular Physics '''60''' pp. 573-595 (1987)]</ref> | |||
in which the dependence of the [[Helmholtz energy function]] is weighted: | |||
:<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>, | :<math>A_{\mathrm {hard~sphere}}^{\mathrm {excess}} [\rho ({\mathbf r})] = \int \rho ({\mathbf r}) a_{\mathrm {excess}} [\overline\rho ({\mathbf r})]{\mathrm d}{\mathbf r}</math>, | ||
where <math>\overline\rho ({\mathbf r})</math> is an average of the | where <math>\overline\rho ({\mathbf r})</math> is an average of the | ||
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==References== | ==References== | ||
<references/> | |||
[[category:density-functional theory]] | [[category:density-functional theory]] | ||
[[category:hard sphere]] | [[category:hard sphere]] | ||
Latest revision as of 15:32, 18 August 2010
Inspired by the exact solution known for the system of 1-dimensional hard rods, Pedro Tarazona proposed a series of models in the 1980's [1] [2] [3] [4] in which the dependence of the Helmholtz energy function is weighted:
- ,
![{\displaystyle A_{\mathrm {hard~sphere} }^{\mathrm {excess} }[\rho ({\mathbf {r} })]=\int \rho ({\mathbf {r} })a_{\mathrm {excess} }[{\overline {\rho }}({\mathbf {r} })]{\mathrm {d} }{\mathbf {r} }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4bdbc32dbc4c8debc6281f94e1542daf759efc27)
where is an average of the density distribution and where A is the Helmholtz energy function. The function should vanish at low values of its argument (so that the excess vanishes and one is left with the ideal case), and diverge at some saturation density corresponding to complete packing.
References[edit]
- ↑ P. Tarazona "A density functional theory of melting", Molecular Physics 52 pp. 81-96 (1984)
- ↑ P. Tarazona "Free-energy density functional for hard spheres", Physical Review A 31 pp. 2672-2679 (1985)
- ↑ P. Tarazona "Erratum: Free-energy density functional for hard spheres", Physical Review A 32 p. 3148 (1985)
- ↑ P. Tarazona, U. Marini Bettolo Marconi and R. Evans "Phase equilibria of fluid interfaces and confined fluids: Non-local versus local density functionals" Molecular Physics 60 pp. 573-595 (1987)