Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
SAT-TMMC: Liquid-Vapor coexistence properties - TraPPE Carbon Dioxide (LRC)
SAT-TMMC: Liquid-Vapor coexistence properties - TraPPE Carbon Dioxide
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 | 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 |
+/- |
| 230 | 5.015E-01 | 4.016E-04 | 2.551E+01 | 6.364E-03 | 8.625E+00 | 3.350E-03 | -8.307E+00 | 3.016E-04 |
| 235 | 6.027E-01 | 4.319E-04 | 2.508E+01 | 5.153E-03 | 1.042E+01 | 6.204E-03 | -8.152E+00 | 1.494E-04 |
| 240 | 7.199E-01 | 4.263E-04 | 2.464E+01 | 6.213E-03 | 1.248E+01 | 1.176E-02 | -8.006E+00 | 2.421E-04 |
| 245 | 8.545E-01 | 8.408E-04 | 2.418E+01 | 7.431E-03 | 1.483E+01 | 1.065E-02 | -7.869E+00 | 4.509E-04 |
| 250 | 1.009E+00 | 8.634E-04 | 2.371E+01 | 4.783E-03 | 1.748E+01 | 6.256E-03 | -7.740E+00 | 2.350E-04 |
| 255 | 1.187E+00 | 1.035E-03 | 2.321E+01 | 1.910E-03 | 2.046E+01 | 6.338E-03 | -7.619E+00 | 1.481E-04 |
| 260 | 1.390E+00 | 1.379E-03 | 2.270E+01 | 3.131E-03 | 2.381E+01 | 9.642E-03 | -7.504E+00 | 1.565E-04 |
| 265 | 1.625E+00 | 6.305E-04 | 2.215E+01 | 7.973E-03 | 2.753E+01 | 1.631E-02 | -7.396E+00 | 1.198E-04 |
| 270 | 1.896E+00 | 1.935E-03 | 2.158E+01 | 6.698E-03 | 3.165E+01 | 5.557E-03 | -7.293E+00 | 1.173E-04 |
| 275 | 2.210E+00 | 3.356E-04 | 2.096E+01 | 6.948E-03 | 3.621E+01 | 9.411E-03 | -7.197E+00 | 7.905E-05 |
| 280 | 2.582E+00 | 1.145E-03 | 2.029E+01 | 1.248E-03 | 4.123E+01 | 2.156E-02 | -7.105E+00 | 1.225E-04 |
| 285 | 3.025E+00 | 4.351E-03 | 1.955E+01 | 3.679E-03 | 4.675E+01 | 2.350E-02 | -7.018E+00 | 2.300E-04 |
| 290 | 3.576E+00 | 2.933E-03 | 1.870E+01 | 3.639E-03 | 5.281E+01 | 4.518E-02 | -6.936E+00 | 1.499E-04 |
| 295 | 4.310E+00 | 5.821E-03 | 1.768E+01 | 4.418E-03 | 5.944E+01 | 2.021E-02 | -6.859E+00 | 1.597E-04 |
| 300 | 5.313E+00 | 1.411E-02 | 1.641E+01 | 1.059E-02 | 6.672E+01 | 2.067E-02 | -6.785E+00 | 1.270E-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.