Lennard-Jones equation of state

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The equation of state of the Lennard-Jones model.

[edit] Johnson, Zollweg and Gubbins equation of state

Johnson et al ^[1] proposed an equation of state based on 33 parameters, which accurately reproduces the vapor liquid equilibrium curve.

[edit] Kolafa and Nezbeda equation of state

The Kolafa and Nezbeda equation of state ^[2] provides us with the Helmholtz energy function: (Eq. 30):

A = A_HS + exp( − γρ²)ρTΔB_2,hBH +	∑	C_ijT^{i / 2}ρ^j
	ij

the compressibility factor (Eq. 31)

$z \equiv \frac{P}{\rho T}= z_{\mathrm{HS}} + \rho(1-2\gamma\rho^2) \exp (-\gamma \rho^2) \Delta B_{2,{\mathrm{hBH}}} + \sum_{ij} jC_{ij} T^{i/2-1} \rho^j$

and the internal energy (Eq. 32)

$U= {3(z_{\rm HS}-1)\over d_{\rm hBH}}\, {\partial d_{\rm hBH}\over \partial (1/T)} + \rho \exp(-\gamma\rho^2)\,{\partial \Delta B_{\rm2,hBH}\over\partial (1/T)} - \sum_{ij} \left({i\over2}-1\right) C_{ij}\, T^{i/2} \rho^j$

On the following page is the FORTRAN code for the Kolafa and Nezbeda equation of state.

[edit] Melting line

The solid and liquid densities along the melting line are given by the equations of Mastny and de Pablo (Ref ^[3] Eqs. 20 and 21):

$\rho_{\mathrm {solid}} = \beta^{-1/4} \left[ 0.908629 - 0.041510 \beta + 0.514632 \beta^2 -0.708590\beta^3 + 0.428351 \beta^4 -0.095229 \beta^5\right]$