Liquid-vapor coexistence properties of n-Butane, modeled by the TraPPE-UA 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, 7-12] |
Fluid | n-Butane |
Model | TraPPE-UA [1] |
V | 91125 Å3 |
TRUNCATION | |
Lennard-Jones | 12 Å + analytic Long-range Corrections |
Prob. of Disp. Move | 0.15 |
Prob. of Rot. Move | 0.15 |
Prob. of Ins/Del Move | 0.6 |
Prob. of Regrowth Move | 0.3 |
Biasing Function Update Frequency | 1.0E5 trial moves |
Simulation Length | 4.0E9 trial moves |
T (K) |
ρvap (kg/m3) |
+/- |
ρliq (kg/m3) |
+/- |
psat (Pa) |
+/- |
lnzsat |
+/- |
260 | 2.6744E+00 | 9.7039E-04 | 6.2214E+02 | 1.1355E-01 | 9.6039E+04 | 4.4275E+01 | -6.6086E+00 | 2.4816E-04 |
270 | 3.7733E+00 | 6.1933E-04 | 6.1120E+02 | 1.5785E-01 | 1.3921E+05 | 3.4763E+01 | -6.2852E+00 | 1.9620E-04 |
280 | 5.1859E+00 | 2.8346E-03 | 6.0021E+02 | 1.6458E-01 | 1.9584E+05 | 1.1170E+02 | -5.9917E+00 | 2.2783E-04 |
290 | 6.9726E+00 | 4.8224E-03 | 5.8850E+02 | 1.6588E-01 | 2.6864E+05 | 1.4197E+02 | -5.7241E+00 | 3.4159E-04 |
300 | 9.1961E+00 | 3.9770E-03 | 5.7660E+02 | 2.1610E-01 | 3.6014E+05 | 8.9835E+01 | -5.4798E+00 | 2.4639E-04 |
310 | 1.1928E+01 | 4.5937E-03 | 5.6426E+02 | 1.2926E-01 | 4.7296E+05 | 7.6236E+01 | -5.2563E+00 | 1.6644E-05 |
320 | 1.5260E+01 | 6.8396E-03 | 5.5140E+02 | 1.0071E-01 | 6.1021E+05 | 1.0262E+02 | -5.0515E+00 | 1.0540E-04 |
330 | 1.9292E+01 | 4.9510E-03 | 5.3792E+02 | 1.1502E-01 | 7.7477E+05 | 2.3778E+02 | -4.8633E+00 | 1.5064E-04 |
340 | 2.4156E+01 | 1.1391E-02 | 5.2384E+02 | 1.4795E-01 | 9.6947E+05 | 2.7508E+02 | -4.6902E+00 | 1.9397E-04 |
350 | 3.0013E+01 | 1.4062E-02 | 5.0883E+02 | 9.2284E-02 | 1.1976E+06 | 3.6212E+02 | -4.5306E+00 | 6.5465E-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.