Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in or
create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision |
Your text |
Line 1: |
Line 1: |
| Inspired by the exact solution known for the system of [[1-dimensional hard rods]],
| | Pedro Tarazona (Universidad Autónoma de Madrid) |
| Pedro Tarazona proposed a series of models in the 1980's | |
| <ref>[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1984)]</ref>
| |
| <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>
| |
| <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>,
| |
| where <math>\overline\rho ({\mathbf r})</math> is an average of the
| |
| density distribution and where ''A'' is the [[Helmholtz energy function]].
| |
| The function <math>a(x)</math> 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== | | ==References== |
| <references/>
| | #[http://dx.doi.org/10.1080/00268978400101071 P. Tarazona "A density functional theory of melting", Molecular Physics '''52''' pp. 81-96 (1985)] |
| | #[http://dx.doi.org/10.1103/PhysRevA.31.2672 P. Tarazona "Free-energy density functional for hard spheres", Physical Review A '''32''' pp. 2672 - 2679 (1985)] |
|
| |
|
| [[category:density-functional theory]] | | [[category:dft]] |
| [[category:hard sphere]] | | [[category:hard sphere model]] |