Liu hard sphere equation of state

Hongqin Liu proposed a correction to the C-S EOS which improved accuracy by almost two order of magnitude :

$Z={\frac {1+\eta +\eta ^{2}-{\frac {8}{13}}\eta ^{3}-\eta ^{4}+{\frac {1}{2}}\eta ^{5}}{(1-\eta )^{3}}}.$

The conjugate virial coefficient correlation is given by:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle B_{n}=0.9423n^{2}+1.28846n-1.84615,n>3.}

The excess Helmholtz free energy is given by:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle A^{ex}={\frac {A-A^{id}}{Nk_{b}}}={\frac {188\eta -126\eta ^{2}-13\eta ^{4}}{52(1-\eta )^{2}}}-{\frac {5}{13}}ln(1-\eta ).}