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nist-gov/www.nist.gov/chemical-informatics-research-group/sat-tmmc-liquid-vapor-coexistence-properties-trappe-ua-n-butane
Scott Williams 4063bef310 Initital commit.
2025-03-05 18:59:57 +00:00

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<h1 class="nist-page__title">SAT-TMMC: Liquid-Vapor coexistence properties - TraPPE-UA n-Butane (LRC)</h1>
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<p>Liquid-vapor coexistence properties of n-Butane, modeled by the TraPPE-UA Force Field <a href="#ref1">[1]</a>, obtained by grand-canonical transition-matrix Monte Carlo and histogram re-weighting. Mean values of the saturation pressure, density, and activity (chemical potential- see below) for each phase are reported.</p>
<table>
<tbody>
<tr>
<td>METHOD</td>
<td>Grand-canonical transition-matrix Monte Carlo and histogram re-weighting&nbsp;<a href="#ref2">[2, 7-12]</a></td>
</tr>
<tr>
<td>Fluid</td>
<td>n-Butane</td>
</tr>
<tr>
<td>Model</td>
<td>TraPPE-UA <a href="#ref1">[1]</a></td>
</tr>
<tr>
<td>V</td>
<td>91125 Å<sup>3</sup></td>
</tr>
<tr>
<td>TRUNCATION</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>&nbsp; Lennard-Jones</td>
<td>12 Å + analytic Long-range Corrections</td>
</tr>
<tr>
<td>Prob. of Disp. Move</td>
<td>0.15</td>
</tr>
<tr>
<td>Prob. of Rot. Move</td>
<td>0.15</td>
</tr>
<tr>
<td>Prob. of Ins/Del Move</td>
<td>0.6</td>
</tr>
<tr>
<td>Prob. of Regrowth Move</td>
<td>0.3</td>
</tr>
<tr>
<td>Biasing Function Update Frequency</td>
<td>1.0E5 trial moves</td>
</tr>
<tr>
<td>Simulation Length</td>
<td>4.0E9 trial moves</td>
</tr>
</tbody>
</table>
<p>&nbsp;</p>
<table>
<tbody>
<tr>
<td>
<p><strong>T (K)</strong></p>
</td>
<td>
<p><strong>ρ<sub>vap</sub> (kg/m<sup>3</sup>)</strong></p>
</td>
<td>
<p><strong>+/-</strong></p>
</td>
<td>
<p><strong>ρ<sub>liq</sub> (kg/m<sup>3</sup>)</strong></p>
</td>
<td>
<p><strong>+/-</strong></p>
</td>
<td>
<p><strong>p<sub>sat</sub> (Pa)</strong></p>
</td>
<td>
<p><strong>+/-</strong></p>
</td>
<td>
<p><strong>lnz<sub>sat</sub></strong></p>
</td>
<td>
<p><strong>+/-</strong></p>
</td>
</tr>
<tr>
<td align="right">260</td>
<td align="right">2.6744E+00</td>
<td align="right">9.7039E-04</td>
<td align="right">6.2214E+02</td>
<td align="right">1.1355E-01</td>
<td align="right">9.6039E+04</td>
<td align="right">4.4275E+01</td>
<td align="right">-6.6086E+00</td>
<td align="right">2.4816E-04</td>
</tr>
<tr>
<td align="right">270</td>
<td align="right">3.7733E+00</td>
<td align="right">6.1933E-04</td>
<td align="right">6.1120E+02</td>
<td align="right">1.5785E-01</td>
<td align="right">1.3921E+05</td>
<td align="right">3.4763E+01</td>
<td align="right">-6.2852E+00</td>
<td align="right">1.9620E-04</td>
</tr>
<tr>
<td align="right">280</td>
<td align="right">5.1859E+00</td>
<td align="right">2.8346E-03</td>
<td align="right">6.0021E+02</td>
<td align="right">1.6458E-01</td>
<td align="right">1.9584E+05</td>
<td align="right">1.1170E+02</td>
<td align="right">-5.9917E+00</td>
<td align="right">2.2783E-04</td>
</tr>
<tr>
<td align="right">290</td>
<td align="right">6.9726E+00</td>
<td align="right">4.8224E-03</td>
<td align="right">5.8850E+02</td>
<td align="right">1.6588E-01</td>
<td align="right">2.6864E+05</td>
<td align="right">1.4197E+02</td>
<td align="right">-5.7241E+00</td>
<td align="right">3.4159E-04</td>
</tr>
<tr>
<td align="right">300</td>
<td align="right">9.1961E+00</td>
<td align="right">3.9770E-03</td>
<td align="right">5.7660E+02</td>
<td align="right">2.1610E-01</td>
<td align="right">3.6014E+05</td>
<td align="right">8.9835E+01</td>
<td align="right">-5.4798E+00</td>
<td align="right">2.4639E-04</td>
</tr>
<tr>
<td align="right">310</td>
<td align="right">1.1928E+01</td>
<td align="right">4.5937E-03</td>
<td align="right">5.6426E+02</td>
<td align="right">1.2926E-01</td>
<td align="right">4.7296E+05</td>
<td align="right">7.6236E+01</td>
<td align="right">-5.2563E+00</td>
<td align="right">1.6644E-05</td>
</tr>
<tr>
<td align="right">320</td>
<td align="right">1.5260E+01</td>
<td align="right">6.8396E-03</td>
<td align="right">5.5140E+02</td>
<td align="right">1.0071E-01</td>
<td align="right">6.1021E+05</td>
<td align="right">1.0262E+02</td>
<td align="right">-5.0515E+00</td>
<td align="right">1.0540E-04</td>
</tr>
<tr>
<td align="right">330</td>
<td align="right">1.9292E+01</td>
<td align="right">4.9510E-03</td>
<td align="right">5.3792E+02</td>
<td align="right">1.1502E-01</td>
<td align="right">7.7477E+05</td>
<td align="right">2.3778E+02</td>
<td align="right">-4.8633E+00</td>
<td align="right">1.5064E-04</td>
</tr>
<tr>
<td align="right">340</td>
<td align="right">2.4156E+01</td>
<td align="right">1.1391E-02</td>
<td align="right">5.2384E+02</td>
<td align="right">1.4795E-01</td>
<td align="right">9.6947E+05</td>
<td align="right">2.7508E+02</td>
<td align="right">-4.6902E+00</td>
<td align="right">1.9397E-04</td>
</tr>
<tr>
<td align="right">350</td>
<td align="right">3.0013E+01</td>
<td align="right">1.4062E-02</td>
<td align="right">5.0883E+02</td>
<td align="right">9.2284E-02</td>
<td align="right">1.1976E+06</td>
<td align="right">3.6212E+02</td>
<td align="right">-4.5306E+00</td>
<td align="right">6.5465E-05</td>
</tr>
</tbody>
</table>
<p>&nbsp;</p>
<p><strong>Remarks:</strong><br>
Uncertainties were obtained from&nbsp;four independent simulations and represent 95% confidence limits based on a standard t statistic. Liquid-vapor coexistence was determined by adjusting the activity such that the pressures of the liquid and vapor phases were equal. Here, the pressure is not the conventional virial pressure <a href="#ref3">[3,4]</a> but is the actual thermodynamic pressure, based on the fact that the absolute free energies can be obtained from the distributions determined from simulation <a href="#ref5">[5]</a>. Alternative methods, for example Gibbs-ensemble Monte Carlo and combination grand-canonical Monte Carlo and histogram re-weighting, can be used to determine liquid-vapor coexistence. A review of standard methods of phase equilibria simulations can be found in Ref. <a href="#ref6">6</a>.<br>
<br>
As introduced in Refs. <a href="#ref3">3</a> and <a href="#ref4">4</a>, the activity, z, is defined as</p>
<p>z = Λ-3 exp(βμ)</p>
<p>where Λ is the de Broglie wavelength, β = 1/(k<sub>B</sub>T) (where k<sub>B</sub> is Boltzmann's constant), and μ is the chemical potential. It is sometimes more convenient to work with ln z in the simulations and in post-processing. The reported activity has units of Å<sup>-3</sup>.</p>
<h3>References</h3>
<ol>
<li><a href="http://dx.doi.org/10.1021/jp972543+">M. G. Martin and J. I. Siepmann, J. Phys. Chem. B, <strong>102</strong>, 2569–2577 (1998).</a></li>
<li><a href name="ref2"></a><a href="https://doi.org/10.1063/1.1572463">J. R. Errington, J. Chem. Phys. 118, 9915 (2003).</a></li>
<li><a href name="ref3"></a>M. P. Allen and D. J. Tildesley, <em>Computer Simulation of Liquids</em> (Oxford University Press, New York, 1989).</li>
<li><a href name="ref4"></a>D. Frenkel and B. Smit, <em>Understanding Molecular Simulation</em>, 2nd ed. (Academic, San Diego, 2002)., pp.37-38.</li>
<li><a href name="ref5"></a><a href="https://doi.org/10.1063/1.476652">J. R. Errington and A. Z. Panagiotopoulos, J. Chem. Phys., <strong>109</strong>, 1093 (1998).</a></li>
<li><a href name="ref6"></a><a href="http://dx.doi.org/10.1088/0953-8984/12/3/201">A. Z. Panagiotopoulos, J. Phys.: Condens. Matter, <strong>12</strong>, R25-R52, (2000).</a></li>
<li><a href="http://dx.doi.org/10.1063/1.4884124">V. K. Shen and D. W. Siderius, J. Chem. Phys., <strong>140</strong>, 244106, 2014.</a></li>
<li><a href="https://doi.org/10.1021/jp040218y">V. K. Shen and J. R. Errington, JPC B <strong>108</strong>, 19595, 2004.</a></li>
<li><a href="https://doi.org/10.1063/1.1844372">V. K. Shen and J. R. Errington, JCP <strong>122</strong>, 064508, 2005</a>.</li>
<li><a href="https://doi.org/10.1021/jp070374f">V. K. Shen, R. D. Mountain, and J. R. Errington, JPC B <strong>111</strong>, 6198, 2007.</a></li>
<li><a href="https://doi.org/10.1021/jp400480q">D. W. Siderius and V. K. Shen, JPC C <strong>117</strong>, 5681, 2013.</a></li>
<li><a href="https://doi.org/10.1021/ie800143n">A. S. Paluch, V. K. Shen, and J. R. Errington, Ind. Eng. Chem. Res. <strong>47</strong>, 4533, 2008.</a></li>
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