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EOS-TMMC: Properties of Binary Mixtures of TraPPE Carbon Dioxide and TraPPE Nitrogen
Properties of constant-composition mixtures of CO2 and N2, modeled by the TraPPE Force Field [1], at 300 K, 350 K, and 400 K, obtained by grand-canonical transition-matrix Monte Carlo and histogram re-weighting. Mean values of the pressure, density, and activity (chemical potentials) for select molar compositions at the two temperatures are reported. The macrostate probability distributions are provided, facilitating the calculation of thermophysical properties at other compositions.
| METHOD | Grand-canonical transition-matrix Monte Carlo and histogram re-weighting [2, 6-10] |
| Fluid | Carbon Dioxide |
| Model | TraPPE [1] |
| V | 27000 Å3 |
| TRUNCATION | |
| Lennard-Jones | 12 Å (cut potential, no tail correction) |
| Electrostatics | 12 Å + Ewald Summation |
| Trial Move Types | ALL: Translation, Pivot rotation Grand-Canonical: Insertion and Deletion Isochoric Semigrand Canonical: Identity-change |
| Biasing Function Update Frequency | 1.0E6 trial moves |
| Simulation Length | 200 sweeps |
Simulations were performed using the open-source FEASST Monte Carlo engine [11], using version 0.21.1 or 0.24.1 [12].
Results:
Set 1: T = 300 K
yCO2 = 0.0004 | yCO2 = 0.1 | yCO2 = 0.5 | yCO2 = 0.9 | |||||
p (bar) | ρ (mol/l) | +/- | ρ (mol/l) | +/- | ρ (mol/l) | +/- | ρ (mol/l) | +/- |
0.01 | 4.009E-04 | 0.000E+00 | 4.009E-04 | 2.425E-15 | 4.009E-04 | 0.000E+00 | 4.009E-04 | 6.782E-16 |
0.02 | 8.018E-04 | 0.000E+00 | 8.018E-04 | 7.152E-15 | 8.018E-04 | 4.681E-14 | 8.019E-04 | 2.068E-15 |
0.03 | 1.203E-03 | 1.633E-14 | 1.203E-03 | 6.471E-15 | 1.203E-03 | 9.452E-14 | 1.203E-03 | 2.830E-15 |
0.04 | 1.604E-03 | 6.868E-15 | 1.604E-03 | 8.281E-15 | 1.604E-03 | 9.945E-14 | 1.604E-03 | 7.926E-16 |
0.05 | 2.005E-03 | 2.935E-16 | 2.005E-03 | 2.932E-16 | 2.005E-03 | 3.859E-15 | 2.005E-03 | 2.540E-16 |
0.06 | 2.406E-03 | 6.759E-15 | 2.406E-03 | 1.268E-14 | 2.406E-03 | 6.022E-14 | 2.406E-03 | 3.362E-15 |
0.07 | 2.806E-03 | 1.361E-14 | 2.807E-03 | 4.795E-14 | 2.807E-03 | 9.116E-14 | 2.807E-03 | 4.396E-15 |
0.08 | 3.207E-03 | 3.346E-15 | 3.207E-03 | 8.434E-15 | 3.208E-03 | 2.381E-13 | 3.208E-03 | 6.120E-16 |
0.09 | 3.608E-03 | 2.540E-16 | 3.608E-03 | 1.381E-14 | 3.609E-03 | 2.935E-16 | 3.609E-03 | 2.383E-15 |
0.1 | 4.009E-03 | 3.194E-14 | 4.009E-03 | 5.865E-16 | 4.010E-03 | 1.178E-13 | 4.011E-03 | 1.351E-15 |
0.2 | 8.019E-03 | 5.623E-14 | 8.019E-03 | 1.026E-14 | 8.022E-03 | 3.644E-14 | 8.025E-03 | 2.503E-15 |
0.3 | 1.203E-02 | 5.981E-15 | 1.203E-02 | 6.991E-15 | 1.203E-02 | 1.060E-13 | 1.204E-02 | 2.938E-15 |
0.4 | 1.604E-02 | 2.595E-15 | 1.604E-02 | 6.327E-15 | 1.605E-02 | 5.251E-16 | 1.606E-02 | 4.698E-15 |
0.5 | 2.005E-02 | 2.543E-15 | 2.005E-02 | 3.924E-15 | 2.007E-02 | 5.881E-16 | 2.009E-02 | 2.556E-15 |
0.6 | 2.406E-02 | 1.241E-15 | 2.406E-02 | 3.658E-15 | 2.408E-02 | 6.624E-15 | 2.411E-02 | 4.997E-16 |
0.7 | 2.807E-02 | 1.651E-15 | 2.808E-02 | 7.250E-15 | 2.810E-02 | 7.355E-16 | 2.814E-02 | 1.182E-14 |
0.8 | 3.208E-02 | 1.381E-14 | 3.209E-02 | 2.645E-14 | 3.212E-02 | 2.692E-14 | 3.218E-02 | 4.188E-15 |
0.9 | 3.609E-02 | 2.656E-15 | 3.610E-02 | 6.578E-15 | 3.615E-02 | 9.993E-16 | 3.621E-02 | 2.050E-15 |
1.0 | 4.011E-02 | 2.098E-15 | 4.012E-02 | 1.320E-14 | 4.017E-02 | 1.034E-14 | 4.025E-02 | 3.707E-15 |
2.0 | 8.023E-02 | 2.675E-15 | 8.027E-02 | 1.924E-15 | 8.049E-02 | 5.770E-16 | 8.082E-02 | 3.626E-15 |
3.0 | 1.203E-01 | 3.510E-15 | 1.204E-01 | 3.870E-15 | 1.209E-01 | 8.080E-14 | 1.217E-01 | 1.999E-15 |
4.0 | 1.605E-01 | 2.159E-15 | 1.606E-01 | 1.612E-14 | 1.615E-01 | 9.412E-14 | 1.629E-01 | 3.783E-15 |
5.0 | 2.006E-01 | 2.159E-15 | 2.009E-01 | 3.053E-15 | 2.023E-01 | 1.434E-14 | 2.044E-01 | 1.390E-14 |
6.0 | 2.407E-01 | 3.997E-15 | 2.411E-01 | 5.161E-15 | 2.431E-01 | 7.868E-14 | 2.462E-01 | 4.080E-15 |
7.0 | 2.809E-01 | 8.281E-15 | 2.814E-01 | 1.437E-14 | 2.842E-01 | 4.761E-14 | 2.884E-01 | 4.896E-15 |
8.0 | 3.210E-01 | 8.160E-15 | 3.216E-01 | 5.996E-15 | 3.253E-01 | 7.344E-15 | 3.309E-01 | 5.996E-15 |
9.0 | 3.611E-01 | 5.161E-15 | 3.619E-01 | 9.792E-15 | 3.666E-01 | 9.516E-15 | 3.738E-01 | 7.113E-15 |
10.0 | 4.012E-01 | 9.516E-15 | 4.022E-01 | 5.412E-15 | 4.080E-01 | 2.464E-14 | 4.169E-01 | 4.318E-15 |
Set 2: T = 350 K
yCO2 = 0.0004 | yCO2 = 0.1 | yCO2 = 0.5 | yCO2 = 0.9 | |||||
p (bar) | ρ (mol/l) | +/- | ρ (mol/l) | +/- | ρ (mol/l) | +/- | ρ (mol/l) | +/- |
0.01 | 3.436E-04 | 3.634E-16 | 3.436E-04 | 5.127E-16 | 3.436E-04 | 3.430E-14 | 3.436E-04 | 3.782E-14 |
0.02 | 6.873E-04 | 1.789E-14 | 6.873E-04 | 2.933E-15 | 6.873E-04 | 1.699E-14 | 6.873E-04 | 1.301E-14 |
0.03 | 1.031E-03 | 0.000E+00 | 1.031E-03 | 2.175E-15 | 1.031E-03 | 2.553E-14 | 1.031E-03 | 3.602E-16 |
0.04 | 1.375E-03 | 1.237E-14 | 1.375E-03 | 9.167E-15 | 1.375E-03 | 3.148E-16 | 1.375E-03 | 1.356E-14 |
0.05 | 1.718E-03 | 1.640E-14 | 1.718E-03 | 1.068E-15 | 1.718E-03 | 3.992E-13 | 1.718E-03 | 1.166E-15 |
0.06 | 2.062E-03 | 6.315E-15 | 2.062E-03 | 3.261E-15 | 2.062E-03 | 8.484E-16 | 2.062E-03 | 1.508E-14 |
0.07 | 2.406E-03 | 1.064E-14 | 2.406E-03 | 8.218E-15 | 2.406E-03 | 5.191E-14 | 2.406E-03 | 2.109E-14 |
0.08 | 2.749E-03 | 7.374E-15 | 2.749E-03 | 4.155E-15 | 2.749E-03 | 3.602E-14 | 2.750E-03 | 9.581E-15 |
0.09 | 3.093E-03 | 4.814E-15 | 3.093E-03 | 1.041E-14 | 3.093E-03 | 1.474E-14 | 3.094E-03 | 1.002E-14 |
0.1 | 3.437E-03 | 8.275E-15 | 3.437E-03 | 5.964E-16 | 3.437E-03 | 9.165E-15 | 3.437E-03 | 1.577E-14 |
0.2 | 6.873E-03 | 4.644E-15 | 6.874E-03 | 1.218E-14 | 6.875E-03 | 1.330E-13 | 6.877E-03 | 3.161E-14 |
0.3 | 1.031E-02 | 6.740E-15 | 1.031E-02 | 1.500E-14 | 1.031E-02 | 1.831E-14 | 1.032E-02 | 1.141E-14 |
0.4 | 1.375E-02 | 4.060E-15 | 1.375E-02 | 4.618E-16 | 1.375E-02 | 5.560E-14 | 1.376E-02 | 3.200E-14 |
0.5 | 1.719E-02 | 1.047E-14 | 1.719E-02 | 4.261E-15 | 1.719E-02 | 6.575E-13 | 1.721E-02 | 1.084E-14 |
0.6 | 2.062E-02 | 9.676E-16 | 2.062E-02 | 2.497E-14 | 2.064E-02 | 3.029E-14 | 2.065E-02 | 1.204E-14 |
0.7 | 2.406E-02 | 9.676E-16 | 2.406E-02 | 8.205E-15 | 2.408E-02 | 8.412E-13 | 2.410E-02 | 2.369E-14 |
0.8 | 2.750E-02 | 7.495E-16 | 2.750E-02 | 4.267E-14 | 2.752E-02 | 1.732E-13 | 2.755E-02 | 1.316E-14 |
0.9 | 3.093E-02 | 6.357E-14 | 3.094E-02 | 7.278E-15 | 3.096E-02 | 2.426E-12 | 3.100E-02 | 2.858E-14 |
1.0 | 3.437E-02 | 6.842E-16 | 3.438E-02 | 1.778E-15 | 3.441E-02 | 2.064E-14 | 3.445E-02 | 9.432E-15 |
2.0 | 6.874E-02 | 1.062E-14 | 6.876E-02 | 9.474E-15 | 6.889E-02 | 3.110E-14 | 6.906E-02 | 1.693E-14 |
3.0 | 1.031E-01 | 2.448E-15 | 1.031E-01 | 6.912E-15 | 1.034E-01 | 1.462E-14 | 1.038E-01 | 8.639E-14 |
4.0 | 1.374E-01 | 7.719E-15 | 1.375E-01 | 6.160E-15 | 1.380E-01 | 1.933E-14 | 1.387E-01 | 5.726E-15 |
5.0 | 1.718E-01 | 4.876E-14 | 1.719E-01 | 7.741E-15 | 1.727E-01 | 5.289E-14 | 1.738E-01 | 2.872E-14 |
6.0 | 2.061E-01 | 2.638E-13 | 2.063E-01 | 1.045E-14 | 2.074E-01 | 5.712E-15 | 2.091E-01 | 1.469E-14 |
7.0 | 2.404E-01 | 4.687E-15 | 2.407E-01 | 9.159E-15 | 2.422E-01 | 6.315E-14 | 2.445E-01 | 7.784E-15 |
8.0 | 2.747E-01 | 4.450E-13 | 2.751E-01 | 9.303E-15 | 2.771E-01 | 3.975E-14 | 2.800E-01 | 2.267E-14 |
9.0 | 3.090E-01 | 4.853E-13 | 3.094E-01 | 7.995E-15 | 3.120E-01 | 1.375E-14 | 3.158E-01 | 1.070E-14 |
10.0 | 3.432E-01 | 2.016E-13 | 3.438E-01 | 1.019E-14 | 3.469E-01 | 1.210E-14 | 3.516E-01 | 5.884E-15 |
Set 3: T = 400 K
yCO2 = 0.0004 | yCO2 = 0.1 | yCO2 = 0.5 | yCO2 = 0.9 | |||||
p (bar) | ρ (mol/l) | +/- | ρ (mol/l) | +/- | ρ (mol/l) | +/- | ρ (mol/l) | +/- |
0.01 | 3.007E-04 | 3.588E-16 | 3.007E-04 | 2.854E-14 | 3.007E-04 | 2.214E-13 | 3.007E-04 | 6.267E-14 |
0.02 | 6.014E-04 | 5.893E-14 | 6.014E-04 | 9.750E-15 | 6.014E-04 | 4.632E-14 | 6.014E-04 | 6.852E-16 |
0.03 | 9.020E-04 | 0.000E+00 | 9.021E-04 | 1.669E-14 | 9.021E-04 | 1.739E-13 | 9.021E-04 | 3.220E-14 |
0.04 | 1.203E-03 | 2.855E-14 | 1.203E-03 | 2.832E-15 | 1.203E-03 | 4.144E-16 | 1.203E-03 | 1.268E-14 |
0.05 | 1.503E-03 | 3.479E-16 | 1.503E-03 | 3.533E-16 | 1.503E-03 | 1.072E-13 | 1.504E-03 | 1.219E-15 |
0.06 | 1.804E-03 | 0.000E+00 | 1.804E-03 | 2.810E-15 | 1.804E-03 | 4.946E-15 | 1.804E-03 | 2.036E-14 |
0.07 | 2.105E-03 | 3.749E-14 | 2.105E-03 | 1.222E-14 | 2.105E-03 | 1.857E-14 | 2.105E-03 | 1.828E-14 |
0.08 | 2.405E-03 | 0.000E+00 | 2.406E-03 | 5.770E-16 | 2.406E-03 | 1.463E-14 | 2.406E-03 | 3.779E-14 |
0.09 | 2.706E-03 | 1.775E-14 | 2.706E-03 | 1.073E-14 | 2.706E-03 | 2.661E-13 | 2.707E-03 | 1.628E-15 |
0.1 | 3.007E-03 | 1.250E-14 | 3.007E-03 | 1.113E-14 | 3.007E-03 | 9.810E-15 | 3.007E-03 | 2.061E-15 |
0.2 | 6.014E-03 | 8.135E-15 | 6.014E-03 | 1.036E-14 | 6.015E-03 | 7.947E-13 | 6.016E-03 | 4.169E-15 |
0.3 | 9.021E-03 | 1.181E-14 | 9.021E-03 | 7.917E-16 | 9.023E-03 | 1.967E-14 | 9.025E-03 | 2.370E-14 |
0.4 | 1.203E-02 | 3.060E-16 | 1.203E-02 | 4.327E-16 | 1.203E-02 | 5.053E-14 | 1.204E-02 | 1.174E-14 |
0.5 | 1.503E-02 | 5.747E-16 | 1.504E-02 | 8.443E-15 | 1.504E-02 | 6.725E-15 | 1.505E-02 | 2.785E-14 |
0.6 | 1.804E-02 | 5.139E-14 | 1.804E-02 | 5.351E-14 | 1.805E-02 | 4.175E-14 | 1.806E-02 | 3.233E-14 |
0.7 | 2.105E-02 | 8.160E-16 | 2.105E-02 | 1.279E-14 | 2.106E-02 | 4.959E-14 | 2.107E-02 | 2.416E-14 |
0.8 | 2.405E-02 | 1.274E-15 | 2.406E-02 | 2.564E-14 | 2.407E-02 | 4.038E-14 | 2.409E-02 | 1.070E-14 |
0.9 | 2.706E-02 | 6.842E-16 | 2.706E-02 | 3.176E-14 | 2.708E-02 | 8.329E-13 | 2.710E-02 | 8.420E-15 |
1.0 | 3.007E-02 | 2.001E-15 | 3.007E-02 | 3.211E-14 | 3.009E-02 | 2.205E-13 | 3.012E-02 | 1.627E-14 |
2.0 | 6.012E-02 | 2.090E-15 | 6.013E-02 | 1.644E-14 | 6.021E-02 | 4.542E-13 | 6.032E-02 | 2.872E-14 |
3.0 | 9.015E-02 | 4.652E-15 | 9.018E-02 | 1.165E-13 | 9.035E-02 | 1.944E-14 | 9.059E-02 | 2.641E-14 |
4.0 | 1.201E-01 | 1.224E-15 | 1.202E-01 | 2.316E-14 | 1.205E-01 | 6.567E-13 | 1.209E-01 | 3.810E-14 |
5.0 | 1.501E-01 | 2.580E-15 | 1.502E-01 | 2.411E-14 | 1.507E-01 | 5.599E-14 | 1.514E-01 | 8.160E-15 |
6.0 | 1.801E-01 | 3.809E-13 | 1.802E-01 | 1.586E-13 | 1.809E-01 | 3.546E-14 | 1.819E-01 | 1.160E-14 |
7.0 | 2.100E-01 | 3.827E-15 | 2.102E-01 | 4.318E-15 | 2.111E-01 | 5.530E-14 | 2.124E-01 | 1.548E-13 |
8.0 | 2.399E-01 | 7.898E-14 | 2.402E-01 | 1.107E-14 | 2.414E-01 | 1.070E-14 | 2.431E-01 | 2.128E-14 |
9.0 | 2.698E-01 | 1.365E-14 | 2.701E-01 | 1.591E-14 | 2.716E-01 | 1.640E-14 | 2.738E-01 | 6.924E-15 |
10.0 | 2.997E-01 | 6.106E-15 | 3.000E-01 | 9.516E-15 | 3.019E-01 | 1.254E-14 | 3.047E-01 | 1.131E-14 |
Data Availability
Various data files used to generate the reported equation-of-state data are available in a Git Repository: https://github.com/dwsideriusNIST/NIST_SRSW_Data/tree/master/BINARY_N2_CO2/L30ANG_CUT12ANG
Files in the repository include:
Particle number probability distributions for the binary N2-CO2 system at the three reported temperatures
Equation-of-state data for the four compositions shown above, with additional decimal figures, and including the activity.
Explanatory metadata
Remarks:
Uncertainties were obtained from four independent simulations and represent 95% confidence limits based on a standard t statistic. Points along the constant-composition curves were identified by adjusting the activity of each species until the target pressure and composition were obtained within specified numerical tolerance (10-15). 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].
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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