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SAT-TMMC: Liquid-Vapor coexistence properties - TraPPE Carbon Dioxide - 15Å 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 | 15 Å + Linear Force Shift |
| 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 | 6.594E-01 | 4.737E-04 | 2.490E+01 | 7.184E-03 | 1.102E+01 | 6.214E-03 | -8.084E+00 | 2.430E-04 |
| 235 | 7.922E-01 | 5.478E-04 | 2.444E+01 | 5.356E-03 | 1.325E+01 | 4.107E-03 | -7.937E+00 | 1.167E-04 |
| 240 | 9.451E-01 | 4.990E-04 | 2.395E+01 | 4.461E-03 | 1.578E+01 | 6.601E-03 | -7.798E+00 | 3.441E-04 |
| 245 | 1.123E+00 | 1.264E-03 | 2.344E+01 | 3.206E-03 | 1.867E+01 | 1.364E-02 | -7.668E+00 | 1.093E-04 |
| 250 | 1.330E+00 | 9.901E-04 | 2.291E+01 | 4.679E-03 | 2.192E+01 | 1.338E-02 | -7.546E+00 | 1.161E-04 |
| 255 | 1.569E+00 | 1.023E-03 | 2.234E+01 | 7.718E-03 | 2.558E+01 | 1.121E-02 | -7.430E+00 | 1.696E-04 |
| 260 | 1.849E+00 | 1.924E-03 | 2.175E+01 | 3.073E-03 | 2.965E+01 | 6.535E-03 | -7.322E+00 | 1.197E-04 |
| 265 | 2.178E+00 | 1.845E-03 | 2.110E+01 | 7.202E-03 | 3.420E+01 | 1.904E-02 | -7.219E+00 | 7.994E-05 |
| 270 | 2.573E+00 | 3.503E-03 | 2.039E+01 | 6.743E-03 | 3.923E+01 | 2.557E-02 | -7.122E+00 | 7.056E-05 |
| 275 | 3.053E+00 | 4.422E-03 | 1.960E+01 | 6.449E-03 | 4.481E+01 | 3.012E-02 | -7.031E+00 | 1.300E-04 |
| 280 | 3.670E+00 | 9.466E-04 | 1.868E+01 | 6.790E-03 | 5.096E+01 | 3.457E-02 | -6.945E+00 | 1.509E-04 |
| 285 | 4.533E+00 | 4.907E-03 | 1.752E+01 | 6.289E-03 | 5.779E+01 | 2.884E-02 | -6.863E+00 | 1.538E-04 |
| 290 | 5.697E+00 | 2.997E-02 | 1.607E+01 | 2.261E-02 | 6.532E+01 | 5.458E-02 | -6.785E+00 | 1.659E-04 |
| 295 | 6.931E+00 | 4.077E-02 | 1.466E+01 | 2.700E-02 | 7.358E+01 | 3.347E-02 | -6.712E+00 | 8.088E-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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- M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1989).
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- J. R. Errington and A. Z. Panagiotopoulos, J. Chem. Phys., 109, 1093, 1998.
- A. Z. Panagiotopoulos, J. Phys.: Condens. Matter, 12, R25-R52, 2000.
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