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SAT-TMMC: Liquid-Vapor coexistence properties - TraPPE Nitrogen (LRC)
Liquid-vapor coexistence properties of Nitrogen, modeled by the TraPPE Force Field [1], 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.
| METHOD | Grand-canonical transition-matrix Monte Carlo and histogram re-weighting [2, 7-11] |
| Fluid | Nitrogen |
| Model | TraPPE [1] |
| V | 27000 Å3 |
| TRUNCATION | |
| Lennard-Jones | 15 Å + analytic Long-range Corrections |
| Electrostatics | 15 Å + Ewald Summation |
| Prob. of Disp. Move | 0.3 |
| Prob. of Rot. Move | 0.2 |
| Prob. of Ins/Del Move | 0.5 |
| Biasing Function Update Frequency | 1.0E6 trial moves |
| Simulation Length | 1.0E9 trial moves |
T (K) |
ρvap (mol/L) |
+/- |
ρliq (mol/L) |
+/- |
psat (bar) |
+/- |
lnzsat |
+/- |
| 60 | 1.320E-02 | 2.913E-05 | 3.139E+01 | 2.695E-02 | 6.554E-02 | 1.550E-04 | -1.175E+01 | 1.682E-03 |
| 65 | 3.187E-02 | 4.646E-05 | 3.062E+01 | 2.263E-02 | 1.704E-01 | 2.137E-04 | -1.088E+00 | 1.093E-03 |
| 70 | 6.677E-02 | 5.359E-06 | 2.982E+01 | 1.315E-02 | 3.812E-01 | 2.081E-04 | -1.016E+01 | 6.977E-04 |
| 75 | 1.254E-01 | 5.677E-05 | 2.902E+01 | 1.710E-02 | 7.566E-01 | 4.228E-04 | -9.556E+00 | 2.925E-04 |
| 80 | 2.162E-01 | 1.842E-04 | 2.819E+01 | 1.328E-02 | 1.367E+00 | 1.975E-03 | -9.045E+00 | 1.188E-04 |
| 85 | 3.490E-01 | 2.612E-04 | 2.733E+01 | 5.513E-03 | 2.292E+00 | 7.282E-04 | -8.609E+00 | 1.317E-04 |
| 90 | 5.350E-01 | 3.202E-04 | 2.643E+01 | 6.082E-03 | 3.613E+00 | 1.232E-03 | -8.236E+00 | 9.897E-05 |
| 95 | 7.877E-01 | 1.683E-04 | 2.547E+01 | 6.292E-03 | 5.417E+00 | 1.912E-03 | -7.913E+00 | 3.013E-04 |
| 100 | 1.126E+00 | 9.197E-04 | 2.446E+01 | 3.585E-03 | 7.799E+00 | 3.164E-03 | -7.632E+00 | 1.040E-04 |
| 105 | 1.573E+00 | 3.986E-04 | 2.335E+01 | 2.676E-03 | 1.084E+01 | 2.220E-03 | -7.386E+00 | 1.019E-04 |
| 110 | 2.170E+00 | 9.582E-04 | 2.212E+01 | 5.095E-03 | 1.464E+01 | 5.494E-03 | -7.171E+00 | 4.862E-05 |
| 115 | 2.986E+00 | 1.758E-03 | 2.069E+01 | 4.816E-03 | 1.930E+01 | 1.583E-02 | -6.980E+00 | 2.904E-04 |
| 120 | 4.211E+00 | 8.209E-03 | 1.887E+01 | 1.035E-03 | 2.494E+01 | 2.616E-03 | -6.811E+00 | 1.217E-04 |
| 125 | 6.380E+00 | 1.881E-02 | 1.618E+01 | 1.862E-02 | 3.176E+01 | 1.280E-02 | -6.661E+00 | 8.894E-05 |
Remarks:
Uncertainties were obtained from 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 [3,4] but is the actual thermodynamic pressure, based on the fact that the absolute free energies can be obtained from the distributions determined from simulation [5]. 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. 6.
As introduced in Refs. 3 and 4, the activity, z, is defined as
z = Λ-3 exp(βμ)
where Λ is the de Broglie wavelength, β = 1/(kBT) (where kB 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-3.
References
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- J. R. Errington, J. Chem. Phys. 118, 9915 (2003).
- M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1989).
- D. Frenkel and B. Smit, Understanding Molecular Simulation, 2nd ed. (Academic, San Diego, 2002)., pp.37-38.
- J. R. Errington and A. Z. Panagiotopoulos, J. Chem. Phys., 109, 1093 (1998).
- A. Z. Panagiotopoulos, J. Phys.: Condens. Matter, 12, R25-R52, (2000).
- V. K. Shen and D. W. Siderius, J. Chem. Phys., 140, 244106, 2014.
- V. K. Shen and J. R. Errington, JPC B 108, 19595, 2004.
- V. K. Shen and J. R. Errington, JCP 122, 064508, 2005.
- V. K. Shen, R. D. Mountain, and J. R. Errington, JPC B 111, 6198, 2007.
- D. W. Siderius and V. K. Shen, JPC C 117, 5681, 2013.