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Sandpit

2007-10-02T11:25:49Z

161.111.27.2: New page: You can make tests here....

You can make tests here....

Models

2007-05-21T15:45:44Z

161.111.27.2: /* 'Hard' models */

__NOTOC__
See also: [[force fields]].
==Lattice models==
*[[Ising Models]]
*[[Potts model]]
*[[Heisenberg model]]
*[[Lattice gas]]
*[[Hard hexagons]]
*[[Bond fluctuation model]]

=='Hard' models==
*[[Hard rods]]
*[[Hard disks]]
*[[hard sphere model | Hard sphere]]
*[[Two-dimensional hard dumbbells]]
*[[Three-dimensional hard dumbbells]]
*[[Tangent linear hard sphere chains]]
*[[Flexible hard sphere chains]] (aka. pearl-necklace model)
*[[Branched hard sphere chains]]
*[[Fused hard sphere chains]]
*[[Hard ellipsoids]]
*[[Hard spherocylinders]]
*[[Hard core Yukawa]]

==Piecewise continuous models==
*[[Square well]]
*[[Square shoulder]]
*[[Square shoulder + square well]]
*[[Ramp model]]

=='Soft' models==
*[[Gaussian overlap model]]
*[[Gay-Berne model]]
*[[Kihara potential]]
*[[Lennard-Jones model]]
*[[9-3 Lennard-Jones potential]]
*[[United-atom model]]
*[[Intermolecular Interactions]]
*[[Flexible molecules|Flexible molecules (intramolecular interactions)]]
*[[Confined systems]]

== Ionic models==
*[[Restricted primitive model]]

== Metals ==
*[[Sutton-Chen]]
*[[Embedded atom model]]
*[[Finnis-Sinclair]]
*[[Gupta potential]]

Flexible hard sphere chains

2007-05-21T15:45:11Z

161.111.27.2:

(Sometimes known as the '''pearl-necklace model''')
==References==
#[http://dx.doi.org/10.1063/1.1743034 A. Isihara and R. Koyama "Theory of Dilute High-Polymer Solutions (the Pearl Necklace Model)", Journal of Chemical Physics '''25''' pp. 712-716 (1956)]
#[http://dx.doi.org/10.1063/1.1322637 C. Vega, J. M. Labaig, L. G. MacDowell, and E. Sanz "The virial coefficients of the pearl-necklace model", Journal of Chemical Physics '''113''' pp. 10398-10409 (2000)]
[[category:models]]

De Broglie thermal wavelength

2007-05-21T15:34:56Z

161.111.27.2: /* References */

The '''de Broglie thermal wavelength''' is defined as

:<math>\Lambda= \sqrt{\frac{h^2}{2\pi mk_BT}}</math>

where

* ''h'' is the [[Planck constant]]
* ''m'' is the mass
* <math>k_B</math> is the [[Boltzmann constant]]
* ''T'' is the temperature.

==References==
#[http://www.ensmp.fr/aflb/LDB-oeuvres/De_Broglie_Kracklauer.htm Louis-Victor de Broglie "On the Theory of Quanta" Thesis (1925)]
#[http://dx.doi.org/10.1088/0143-0807/21/6/314 Zijun Yan, "General thermal wavelength and its applications", Eur. J. Phys. '''21''' pp. 625-631 (2000)]

Vega equation of state for hard ellipsoids

2007-04-24T09:25:04Z

161.111.27.2:

The '''Vega''' equation of state for an isotropic fluid of hard (biaxial) [[Hard ellipsoids |ellipsoids]] is given by (Ref. 1 Eq. 20):

:<math>
Z = 1+B_2^*y + B_3^*y^2 + B_4^*y^3 + B_5^*y^4
+ \frac{B_2}{4} \left( \frac{1+y+y^2-y^3}{(1-y)^3}
-1 -4y -10y^2 -18.3648y^3 - 28.2245y^4 \right)
</math>
where <math>Z</math> is the [[compressibility factor]] and <math>y</math> is the [[volume fraction]], given by
<math>y= \rho V</math> where <math>\rho</math> is the [[number density]].
The virial coefficients are given by the fits

:<math>B_3^* = 10 + 13.094756 \alpha' - 2.073909\tau' + 4.096689 \alpha'^2
+ 2.325342\tau'^2 - 5.791266\alpha' \tau',</math>

:<math>B_4^* = 18.3648 + 27.714434\alpha' - 10.2046\tau' + 11.142963\alpha'^2
+ 8.634491\tau'^2 - 28.279451\alpha' \tau'
- 17.190946\alpha'^2 \tau' + 24.188979\alpha' \tau'^2
+ 0.74674\alpha'^3 - 9.455150\tau'^3,</math>

and

:<math>B_5^* = 28.2245 + 21.288105\alpha' + 4.525788\tau' + 36.032793\alpha'^2
+ 59.0098\tau'^2 - 118.407497\alpha' \tau'
+ 24.164622\alpha'^2 \tau' + 139.766174\alpha' \tau'^2
- 50.490244\alpha'^3 - 120.995139\tau'^3 + 12.624655\alpha'^3\tau',
</math>

where

:<math>B_n^*= B_n/V^{n-1}</math>,

:<math>\tau' = \frac{4 \pi R^2}{S} -1,</math>

and

:<math>\alpha' = \frac{RS}{3V}-1.</math>

where <math>V</math> is
the volume, <math>S</math>, the surface area, and <math>R</math> the mean radius of curvature.

For <math>B_2</math> see [[B_2 for any hard convex body]].
==References==
#[http://dx.doi.org/10.1080/002689797169934 Carlos Vega "Virial coefficients and equation of state of hard ellipsoids", Molecular Physics '''92''' pp. 651-665 (1997)]
#[http://dx.doi.org/10.1016/j.fluid.2007.03.026 Carl McBride and Enrique Lomba "Hard biaxial ellipsoids revisited: Numerical results", Fluid Phase Equilibria (2007)]

Hard spherocylinders

2007-03-22T11:37:19Z

161.111.27.2:

[[Image:spherocylinder_purple.png|thumb|right]]
The molecular volume of the spherocylinder is given by

:<math>v_0 = \pi \left( \frac{LD^2}{4} + \frac{D^3}{6} \right)</math>

where <math>L</math> is the length of the cylindrical part of the spherocylinder and <math>D</math> is the diameter.
==References==
#[http://dx.doi.org/10.1063/1.2207141 Giorgio Cinacchi and Yuri Martínez-Ratón and Luis Mederos and Enrique Velasco "Smectic, nematic, and isotropic phases in binary mixtures of thin and thick hard spherocylinders", Journal of Chemical Physics '''124''' pp. 234904 (2006)]
#[http://dx.doi.org/10.1063/1.473404 P. Bolhuis and D. Frenkel "Tracing the phase boundaries of hard spherocylinders", Journal of Chemical Physics '''106''' pp. 666-687 (1997)]
#[http://dx.doi.org/10.1063/1.471343 S. C. McGrother and D. C. Williamson and G. Jackson "A re-examination of the phase diagram of hard spherocylinders", Journal of Chemical Physics '''104''' pp. 6755-6771 (1996)]
[[Category: Models]]