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Density-pressure isotherms of the 2D Lennard Jones fluid between the triple point temperature and the critical temperature

Pressure-density isotherms of the 2D truncated-shifted Lennard-Jones fluid, with \(r_{c} = 2.5 \sigma\): \(V\left(r\right) = \begin{cases} U\left(r\right) - U\left(r_{c}\right) & \text{if } 0 < r < r_{c}\\ 0 & \text{if } r \geq r_{c} \end{cases}\) with \(U\left(r\right) = 4 \varepsilon \left(\left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^{6}\right)\) All thermodynamic quantities are reduced with respect to the Lennard-Jones parameters \(\sigma\) and \(\epsilon\) : <ul> <li>Number 2D density \(\rho^{*} = \sigma^{2}\rho\)</li> <li>2D pressure \(P^{*} = \frac{\sigma^{2}}{\varepsilon}P\)</li> <li>Temperature \(T^{*} = \frac{k_{B} T}{\varepsilon}\)</li> </ul> The temperatures of the isotherms are \(T^{*} = 0.40\), \(T^{*} = 0.41\), \(T^{*} = 0.42\), \(T^{*} = 0.43\), and \(T^{*} = 0.44\) which corresponds to the range of liquid-gas coexistence, between the triple point temperature (\(T_{t}^{*} \approx 0.40\)) and the critical temperature (\(T_{c}^{*} \approx 0.46\)). Here are reported the isotherms for the gas and liquid phases and the coexistence points. The liquid and gas isotherms are obtained by Molecular Dynamics with the LAMMPS software (<a href="https://lammps.sandia.gov/">https://lammps.sandia.gov/</a>). The density and temperature are imposed (Langevin thermostat) and the pressure is computed with the virial estimate. The simulations are performed for 2D systems of dimensions \(L_{x} = 44.9 \sigma\) and \(L_{y} = 46.7 \sigma\) containing between 1300 and 1900 particles in the liquid phase, and 4 to 200 particles in the gas phase. The systems are equilibrated over \(3 \cdot 10^{7}\) times steps. Then, the computation of the thermodynamic properties is performed over a variable number of time steps in order to reach a targeted accuracy (standard deviation of the pressure). The longest simulations (liquid approaching cavitation) require about \(10^{9}\) time steps of computation. The block averaging method is used to estimate the standard deviation of pressure. The data are provided in csv files named as follows : 'liq_TX.XX.txt' for the liquid at temperature \(T^{*} = X.XX\), and 'gas_TX.XX.txt' for the gas at temperature \(T^{*} = X.XX\). The first column is the inverse number density \(1/\rho^{*}\), the second column is the pressure \(P^{*}\), and the last column is the standard deviation of the pressure \(\Delta P^{*}\). The coexistence points are obtained by Gibbs ensemble Monte Carlo with an in house code. The temperature is imposed and the liquid and gas densities and the coexistence pressure (virial estimate) are computed. The csv file 'coexistence.txt' contains the coexistence data in the following order: the first column is the temperature \(T^{*}\), the second and third columns are the average and standard deviation of the inverse of the gas number density \(1/\rho_{gas}^{*}\) and \(\Delta\left(1/\rho_{gas}^{*}\right)\), the forth and fifth columns are the average and standard deviation of the inverse of the liquid number density \(1/\rho_{liq}^{*}\) and \(\Delta\left(1/\rho_{liq}^{*}\right)\), and the sixth and seventh columns are the average and standard deviation of the coexistence pressure \(P^{*}\) and \(\Delta P^{*}\). The files 'chart_gas.pdf' and 'chart_liq.pdf' provide graphical display of the data, for the gas and liquid phases respectively.

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Topics

2D Lennard Jones density-pressure isotherms