Tarazona's weighted density approximation: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
No edit summary
m (Changed references to Cite format)
 
(3 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Stub-general}}
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 1D hard rods,
<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 80s, in which the
<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 free energy 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
Line 13: Line 15:


==References==
==References==
#[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]
<references/>
#[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)]
#[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)]
#[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)]


[[category:density-functional theory]]
[[category:density-functional theory]]
[[category:hard sphere]]
[[category:hard sphere]]

Latest revision as of 14:32, 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:

,

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]