Tetrahedral hard sphere model

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

Second virial coefficient

The second virial coefficient is given by ([1] Eq.5):

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

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

Equation of state

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

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

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

References

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