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 + 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 |
+/- |
60 | 2.209E-02 | 2.053E-05 | 3.090E+01 | 1.778E-02 | 1.093E-01 | 1.007E-04 | -1.124E+01 | 9.142E-04 |
65 | 5.105E-02 | 3.124E-05 | 3.101E+01 | 1.743E-02 | 2.715E-01 | 2.177E-04 | -1.042E+01 | 4.447E-04 |
70 | 1.031E-01 | 7.741E-0 | 2.926E+01 | 5.834E-03 | 5.829E-01 | 6.869E-04 | -9.744E+00 | 5.999E-04 |
75 | 1.880E-01 | 2.428E-04 | 2.840E+01 | 6.531E-03 | 1.119E+00 | 1.754E-03 | -9.177E+00 | 2.677E-04 |
80 | 3.169E-01 | 2.322E-04 | 2.750E+01 | 1.230E-03 | 1.965E+00 | 1.569E-03 | -8.699E+00 | 3.067E-04 |
85 | 5.035E-01 | 5.057E-04 | 2.657E+01 | 1.305E-02 | 3.217E+00 | 1.835E-03 | -8.293E+00 | 1.611E-04 |
90 | 7.634E-01 | 4.938E-04 | 2.558E+01 | 5.156E-03 | 4.972E+00 | 1.624E-03 | -7.944E+00 | 2.169E-04 |
95 | 1.120E-01 | 1.535E-03 | 2.451E+01 | 4.756E-03 | 7.335E+00 | 5.316E-03 | -7.644E+00 | 3.324E-04 |
100 | 1.604E+00 | 2.635E-04 | 2.334E+01 | 5.405E-03 | 1.041E+01 | 1.238E-03 | -7.384E+00 | 9.282E-05 |
105 | 2.271E+00 | 1.783E-03 | 2.200E+01 | 5.937E-03 | 1.432E+01 | 3.218E-03 | -7.156E+00 | 1.773E-04 |
110 | 3.226E+00 | 5.538E-03 | 2.040E+01 | 8.783E-03 | 1.918E+01 | 1.102E-02 | -6.956E+00 | 8.032E-05 |
115 | 4.828E+00 | 3.214E-03 | 1.818E+01 | 6.807E-03 | 2.517E+01 | 6.889E-03 | -6.781E+00 | 1.094E-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
$$ z = \dfrac{\exp\left(\beta \mu\right)}{\lambda^3} $$
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.