Difference between revisions of "Liu hard disk equation of state"

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<math>Z_{solid} = \frac{2}{\alpha} + 1.9 + \alpha - 5.2 \alpha^2 + 114.48 \alpha^4</math>
 
<math>Z_{solid} = \frac{2}{\alpha} + 1.9 + \alpha - 5.2 \alpha^2 + 114.48 \alpha^4</math>
  
where <math>\alpha = \frac{2}{3^{1/3 \rho}</math>
+
where <math>\alpha = \frac{2}{3^{1/3} \rho}</math>
  
 
==References==
 
==References==

Revision as of 21:01, 22 October 2020

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

For the stable fluid:

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

where the packing fraction is given by \eta = \pi \rho \sigma^2 /4 where \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

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

References