Liu hard disk equation of state: Difference between revisions
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The '''Liu''' [[Equations of state | equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model | hard spheres]]) is given by Eq. 1, 9 and 13 of | The '''Liu''' [[Equations of state | equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model | hard spheres]]) is given by Eq. 1, 9 and 13 of | ||
<ref>[https://arxiv.org/abs/2010.10624]</ref>. | <ref>[https://arxiv.org/abs/2010.10624 Hongqin Liu "Global equation of state and phase transitions of the hard disc systems", arXiv:2010.10624 (2020)]</ref>. | ||
For the stable fluid: | For the stable fluid: | ||
:<math>Z_v = \frac{1 + \eta^2/8 + \eta^ | :<math>Z_v = \frac{1 + \eta^2/8 + \eta^3/18 - 4 \eta^4/21}{(1-\eta)^2} </math> | ||
where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\sigma</math> is the diameter of the disks. | where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\rho</math> is density and <math>\sigma</math> is the diameter of the disks. | ||
The EoS for the stable fluid, liquid-hexatic transition region and hexatic: | The EoS for the stable fluid, liquid-hexatic transition region and hexatic: | ||
Line 32: | Line 32: | ||
| <math>m_2</math> || 56 | | <math>m_2</math> || 56 | ||
|- | |- | ||
| <math>c </math> || 0.75 | | <math>\frac{1}{c}</math> || 0.75 | ||
|} | |} | ||
Revision as of 03:59, 11 November 2020
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:
where the packing fraction is given by where is density and is the diameter of the disks.
The EoS for the stable fluid, liquid-hexatic transition region and hexatic:
The global EoS for all phases:
,
,
where:
and
53 | |
56 | |
0.75 |