Tetrahedral hard sphere model: Difference between revisions

Revision as of 14:58, 12 May 2010

The tetrahedral hard sphere model consists of four hard spheres located on the vertices of a regular tetrahedron.

{\frac {B_{2}^{*}}{4V_{m}^{*}}}=1+{\frac {UL^{*}+VL^{*3}}{4}}

where $L^{*}$ is the reduced elongation, $V_{m}^{*}$ is the corresponding reduced volume, $U=0.72477$ and $V=4.730$ .

The equation of state is given by (^[1] Eq. 17):

{\frac {\beta P}{\rho }}={\frac {1+(1+UL^{*}+VL^{*3})y+(1+WL^{*}+XL^{*4})y^{2}-(1+ZL^{*3})y^{3}}{(1-y)^{3}}}

where $U=0.72477$ , $V=4.730$ , $W=1.3926$ , $X=24.78$ and $Z=7.69$ .

@@ Line 2: / Line 2: @@
 [[Image:HS_tetrahedron.png|thumb|right]]
 The '''tetrahedral hard sphere model''' consists of four [[hard sphere model | hard spheres]] located on the vertices of a [[Hard tetrahedron model | regular tetrahedron]].
+==Second virial coefficient==
+The [[second virial coefficient]] is given by (<ref name="AbascalBresme" >[http://dx.doi.org/10.1080/00268979200102181 J. L. F. Abascal and F. Bresme "Monte Carlo simulation of the equation of state of hard tetrahedral molecules", Molecular Physics '''76''' pp. 1411-1421 (1992)]</ref> Eq.5):
+:<math>\frac{B_2^*}{4V_m^*} = 1 + \frac{UL^* + VL^{*3}}{4}</math>
+where <math>L^*</math> is the reduced elongation, <math>V_m^*</math> is the corresponding reduced volume, <math>U=0.72477</math> and <math>V=4.730</math>.
 ==Equation of state==
-<ref>[http://dx.doi.org/10.1080/00268979200102181 J. L. F. Abascal and F. Bresme "Monte Carlo simulation of the equation of state of hard tetrahedral molecules", Molecular Physics '''76''' pp. 1411-1421 (1992)]</ref>
+The [[Equations of state | equation of state]] is given by (<ref name="AbascalBresme"> </ref> Eq. 17):
+:<math>\frac{\beta P}{\rho} = \frac{1+(1+UL^* + VL^{*3})y  + (1+WL^* + XL^{*4})y^2 - (1+ ZL^{*3})y^3}{(1-y)^3}</math>
+where  <math>U=0.72477</math>, <math>V=4.730</math>, <math>W=1.3926</math>, <math>X=24.78</math> and <math>Z=7.69</math>.
 ==References==
 <references/>