Liu hard disk equation of state

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The Liu equation of state for hard disks (2-dimensional hard spheres) is given by Eq. 1, 9 and 13 of [1].

For the stable fluid:

Z_v = \frac{1 + \eta^2/8 + \eta^3/18 - 4 \eta^4/21}{(1-\eta)^2}

where the packing fraction is given by \eta = \pi \rho \sigma^2 /4 where \rho is density and \sigma is the diameter of the disks.

The EoS for the stable fluid, liquid-hexatic transition region and hexatic:

Z_{lh} = Z_v + \frac{b_1 \eta^{m_1} + b_2 \eta^{m_2}}{(1-c \eta)}

The global EoS for all phases:

Z=Z_{lh} , \eta <= 0.72

Z=Z_{solid} , \eta > 0.72

where: Z_{solid} = \frac{2}{\alpha} + 1.9 + \alpha - 5.2 \alpha^2 + 114.48 \alpha^4

and \alpha = \frac{2}{3^{1/2} \rho \sigma^2}


b_1 - 1.04191 * 10^8
b_2 2.66813 * 10^8
m_1 53
m_2 56
\frac{1}{c} 0.75

References[edit]