Density-pressure isotherms of the 2D Lennard Jones fluid between the triple point temperature and the critical temperature
<p>Pressure-density isotherms of the 2D truncated-shifted Lennard-Jones fluid, with <span class="math-tex">\(r_{c} = 2.5 \sigma\)</span>:</p>
<p><span class="math-tex">\(V\left(r\right) = \begin{cases} U\left(r\right) - U\left(r_{c}\right) & \text{if } 0 < r < r_{c}\\ 0 & \text{if } r \geq r_{c} \end{cases}\)</span> with <span class="math-tex">\(U\left(r\right) = 4 \varepsilon \left(\left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^{6}\right)\)</span></p>
<p>All thermodynamic quantities are reduced with respect to the Lennard-Jones parameters <span class="math-tex">\(\sigma\)</span> and <span class="math-tex">\(\epsilon\)</span> :</p>
<ul>
<li>Number 2D density <span class="math-tex">\(\rho^{*} = \sigma^{2}\rho\)</span></li>
<li>2D pressure <span class="math-tex">\(P^{*} = \frac{\sigma^{2}}{\varepsilon}P\)</span></li>
<li>Temperature <span class="math-tex">\(T^{*} = \frac{k_{B} T}{\varepsilon}\)</span></li>
</ul>
<p>The temperatures of the isotherms are <span class="math-tex">\(T^{*} = 0.40\)</span>, <span class="math-tex">\(T^{*} = 0.41\)</span>, <span class="math-tex">\(T^{*} = 0.42\)</span>, <span class="math-tex">\(T^{*} = 0.43\)</span>, and <span class="math-tex">\(T^{*} = 0.44\)</span> which corresponds to the range of liquid-gas coexistence, between the triple point temperature (<span class="math-tex">\(T_{t}^{*} \approx 0.40\)</span>) and the critical temperature (<span class="math-tex">\(T_{c}^{*} \approx 0.46\)</span>). Here are reported the isotherms for the gas and liquid phases and the coexistence points.</p>
<p>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 <span class="math-tex">\(L_{x} = 44.9 \sigma\)</span> and <span class="math-tex">\(L_{y} = 46.7 \sigma\)</span> containing between 1300 and 1900 particles in the liquid phase, and 4 to 200 particles in the gas phase. The systems are equilibrated over <span class="math-tex">\(3 \cdot 10^{7}\)</span> 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 <span class="math-tex">\(10^{9}\)</span> 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 <span class="math-tex">\(T^{*} = X.XX\)</span>, and 'gas_TX.XX.txt' for the gas at temperature <span class="math-tex">\(T^{*} = X.XX\)</span>. The first column is the inverse number density <span class="math-tex">\(1/\rho^{*}\)</span>, the second column is the pressure <span class="math-tex">\(P^{*}\)</span>, and the last column is the standard deviation of the pressure <span class="math-tex">\(\Delta P^{*}\)</span>.</p>
<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 <span class="math-tex">\(T^{*}\)</span>, the second and third columns are the average and standard deviation of the inverse of the gas number density <span class="math-tex">\(1/\rho_{gas}^{*}\)</span> and <span class="math-tex">\(\Delta\left(1/\rho_{gas}^{*}\right)\)</span>, the forth and fifth columns are the average and standard deviation of the inverse of the liquid number density <span class="math-tex">\(1/\rho_{liq}^{*}\)</span> and <span class="math-tex">\(\Delta\left(1/\rho_{liq}^{*}\right)\)</span>, and the sixth and seventh columns are the average and standard deviation of the coexistence pressure <span class="math-tex">\(P^{*}\)</span> and <span class="math-tex">\(\Delta P^{*}\)</span>.</p>
<p>The files 'chart_gas.pdf' and 'chart_liq.pdf' provide graphical display of the data, for the gas and liquid phases respectively.</p>
opencc-by-4.0Jul 2019View details →
