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SAT-TMMC: Liquid-Vapor coexistence properties - TraPPE Carbon Dioxide - 12Å LFS
Liquid-vapor coexistence properties of Carbon Dioxide, 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 | Carbon Dioxide |
| Model | TraPPE [1] |
| V | 27000 Å3 |
| TRUNCATION | |
| Lennard-Jones | 12 Å + Linear Force Shift |
| Electrostatics | 12 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 |
+/- |
| 230 | 8.561E-01 | 2.852E-04 | 2.424E+01 | 6.074E-03 | 1.383E+01 | 8.010E-03 | -7.882E+00 | 2.303E-04 |
| 235 | 1.028E+00 | 5.896E-04 | 2.372E+01 | 4.841E-03 | 1.654E+01 | 7.744E-03 | -7.741E+00 | 1.875E-04 |
| 240 | 1.229E+00 | 9.578E-04 | 2.318E+01 | 4.076E-03 | 1.963E+01 | 8.486E-03 | -7.610E+00 | 2.079E-04 |
| 245 | 1.466E+00 | 2.150E-03 | 2.261E+01 | 4.470E-03 | 2.313E+01 | 2.137E-02 | -7.486E+00 | 1.407E-04 |
| 250 | 1.744E+00 | 1.194E-03 | 2.200E+01 | 3.482E-03 | 2.707E+01 | 1.847E-02 | -7.370E+00 | 2.524E-04 |
| 255 | 2.074E+00 | 1.530E-03 | 2.135E+01 | 2.026E-03 | 3.149E+01 | 5.843E-03 | -7.260E+00 | 1.945E-04 |
| 260 | 2.472E+00 | 3.582E-03 | 2.063E+01 | 6.449E-03 | 3.643E+01 | 1.463E-02 | -7.157E+00 | 1.923E-04 |
| 265 | 2.962E+00 | 3.386E-03 | 1.981E+01 | 5.863E-03 | 4.191E+01 | 1.460E-02 | -7.060E+00 | 1.258E-04 |
| 270 | 3.597E+00 | 2.645E-03 | 1.886E+01 | 1.822E-03 | 4.803E+01 | 1.443E-02 | -6.968E+00 | 8.604E-05 |
| 275 | 4.499E+00 | 4.120E-03 | 1.764E+01 | 1.000E-02 | 5.486E+01 | 3.804E-02 | -6.822E+00 | 1.167E-04 |
| 280 | 5.745E+00 | 1.451E-02 | 1.610E+01 | 2.762E-02 | 6.247E+01 | 9.978E-03 | -6.800E+00 | 1.508E-04 |
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
- J. A. Potoff and J. I. Siepmann, AIChE J., 47, 1676–1682, 2001.
- 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.