| METHOD: | Grand-canonical transition-matrix Monte Carlo [1] and histogram re-weighting [8-12] |
| V/σ3: | 512 |
| TRUNCATION: | Linear Force Shifted at 2.5σ |
| Prob. of Disp. Move: | 0.75 |
| Prob, of Ins/Del. Move: | 0.25 |
| Biasing Function Update
Frequency |
1.0E6 trials |
| Simulation Length: | 8.0E9 trials |
Vapor Phase Properties
| T*=0.65 psat*=6.71090E-03 |
T*=0.70 psat*=1.18932E-02 |
T*=0.75 psat*=1.95405E-02 |
T*=0.80 psat*=3.02538E-02 |
T*=0.85 psat*=4.47539E-02 |
T*=0.90 psat*=6.39698E-02 |
|||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| p/psat | ln z |
ρ* |
ln z |
ρ* |
ln z |
ρ* |
ln z |
ρ* |
ln z |
ρ* |
ln z |
ρ* |
| 0.01 | -9.17926E+00 | 1.03326E-04 | -8.68131E+00 | 1.70091E-04 | -8.25396E+00 | 2.60928E-04 | -7.88206E+00 | 3.78879E-04 | -7.55155E+00 | 5.27784E-04 | -7.25153E+00 | 7.12896E-04 |
| 0.02 | -8.48689E+00 | 2.06814E-04 | -7.98927E+00 | 3.40563E-04 | -7.56230E+00 | 5.22643E-04 | -7.19085E+00 | 7.59242E-04 | -6.86080E+00 | 1.05812E-03 | -6.56135E+00 | 1.43004E-03 |
| 0.03 | -8.08221E+00 | 3.10466E-04 | -7.58492E+00 | 5.11419E-04 | -7.15834E+00 | 7.85157E-04 | -6.78734E+00 | 1.14111E-03 | -6.45774E+00 | 1.59103E-03 | -6.15885E+00 | 2.15142E-03 |
| 0.04 | -7.79532E+00 | 4.14282E-04 | -7.29836E+00 | 6.82664E-04 | -6.87216E+00 | 1.04848E-03 | -6.50161E+00 | 1.52449E-03 | -6.17247E+00 | 2.12654E-03 | -5.87412E+00 | 2.87705E-03 |
| 0.05 | -7.57296E+00 | 5.18263E-04 | -7.07633E+00 | 8.54300E-04 | -6.65053E+00 | 1.31262E-03 | -6.28042E+00 | 1.90940E-03 | -5.95173E+00 | 2.66468E-03 | -5.65393E+00 | 3.60697E-03 |
| 0.06 | -7.39143E+00 | 6.22410E-04 | -6.89513E+00 | 1.02633E-03 | -6.46972E+00 | 1.57758E-03 | -6.10005E+00 | 2.29585E-03 | -5.77182E+00 | 3.20548E-03 | -5.47455E+00 | 4.34125E-03 |
| 0.07 | -7.23807E+00 | 7.26724E-04 | -6.74211E+00 | 1.19876E-03 | -6.31709E+00 | 1.84338E-03 | -5.94786E+00 | 2.68385E-03 | -5.62008E+00 | 3.74899E-03 | -5.32334E+00 | 5.07998E-03 |
| 0.08 | -7.10532E+00 | 8.31205E-04 | -6.60970E+00 | 1.37159E-03 | -6.18508E+00 | 2.11001E-03 | -5.81629E+00 | 3.07342E-03 | -5.48897E+00 | 4.29524E-03 | -5.19274E+00 | 5.82325E-03 |
| 0.09 | -6.98833E+00 | 9.35854E-04 | -6.49305E+00 | 1.54483E-03 | -6.06882E+00 | 2.37749E-03 | -5.70047E+00 | 3.46457E-03 | -5.37360E+00 | 4.84428E-03 | -5.07791E+00 | 6.57115E-03 |
| 0.10 | -6.88376E+00 | 1.04067E-03 | -6.38882E+00 | 1.71847E-03 | -5.96498E+00 | 2.64583E-03 | -5.59708E+00 | 3.85731E-03 | -5.27067E+00 | 5.39616E-03 | -4.97549E+00 | 7.32379E-03 |
| 0.11 | -6.78924E+00 | 1.14566E-03 | -6.29464E+00 | 1.89252E-03 | -5.87120E+00 | 2.91502E-03 | -5.50373E+00 | 4.25167E-03 | -5.17779E+00 | 5.95092E-03 | -4.88313E+00 | 8.08123E-03 |
| 0.12 | -6.70302E+00 | 1.25082E-03 | -6.20876E+00 | 2.06698E-03 | -5.78572E+00 | 3.18509E-03 | -5.41869E+00 | 4.64765E-03 | -5.09321E+00 | 6.50860E-03 | -4.79908E+00 | 8.84357E-03 |
| 0.13 | -6.62377E+00 | 1.35615E-03 | -6.12985E+00 | 2.24186E-03 | -5.70722E+00 | 3.45603E-03 | -5.34062E+00 | 5.04529E-03 | -5.01561E+00 | 7.06926E-03 | -4.72200E+00 | 9.61088E-03 |
| 0.14 | -6.55045E+00 | 1.46166E-03 | -6.05688E+00 | 2.41715E-03 | -5.63465E+00 | 3.72786E-03 | -5.26849E+00 | 5.44459E-03 | -4.94395E+00 | 7.63293E-03 | -4.65087E+00 | 1.03832E-02 |
| 0.15 | -6.48226E+00 | 1.56734E-03 | -5.98903E+00 | 2.59286E-03 | -5.56719E+00 | 4.00058E-03 | -5.20147E+00 | 5.84559E-03 | -4.87741E+00 | 8.19967E-03 | -4.58485E+00 | 1.11607E-02 |
| 0.16 | -6.41851E+00 | 1.67319E-03 | -5.92563E+00 | 2.76900E-03 | -5.50420E+00 | 4.27421E-03 | -5.13891E+00 | 6.24830E-03 | -4.81533E+00 | 8.76952E-03 | -4.52330E+00 | 1.19435E-02 |
| 0.17 | -6.35868E+00 | 1.77922E-03 | -5.86615E+00 | 2.94556E-03 | -5.44512E+00 | 4.54875E-03 | -5.08027E+00 | 6.65275E-03 | -4.75717E+00 | 9.34252E-03 | -4.46566E+00 | 1.27315E-02 |
| 0.18 | -6.30232E+00 | 1.88542E-03 | -5.81013E+00 | 3.12256E-03 | -5.38951E+00 | 4.82420E-03 | -5.02510E+00 | 7.05896E-03 | -4.70248E+00 | 9.91871E-03 | -4.41150E+00 | 1.35249E-02 |
| 0.19 | -6.24905E+00 | 1.99180E-03 | -5.75721E+00 | 3.29998E-03 | -5.33699E+00 | 5.10059E-03 | -4.97302E+00 | 7.46695E-03 | -4.65089E+00 | 1.04981E-02 | -4.36044E+00 | 1.43238E-02 |
| 0.20 | -6.19855E+00 | 2.09836E-03 | -5.70706E+00 | 3.47784E-03 | -5.28725E+00 | 5.37791E-03 | -4.92371E+00 | 7.87677E-03 | -4.60207E+00 | 1.10809E-02 | -4.31216E+00 | 1.51284E-02 |
| 0.21 | -6.15056E+00 | 2.20510E-03 | -5.65942E+00 | 3.65613E-03 | -5.24001E+00 | 5.65618E-03 | -4.87692E+00 | 8.28842E-03 | -4.55577E+00 | 1.16669E-02 | -4.26639E+00 | 1.59386E-02 |
| 0.22 | -6.10484E+00 | 2.31202E-03 | -5.61405E+00 | 3.83487E-03 | -5.19505E+00 | 5.93540E-03 | -4.83240E+00 | 8.70193E-03 | -4.51174E+00 | 1.22564E-02 | -4.22290E+00 | 1.67547E-02 |
| 0.23 | -6.06119E+00 | 2.41912E-03 | -5.57075E+00 | 4.01405E-03 | -5.15216E+00 | 6.21559E-03 | -4.78994E+00 | 9.11735E-03 | -4.46979E+00 | 1.28493E-02 | -4.18149E+00 | 1.75768E-02 |
| 0.24 | -6.01943E+00 | 2.52640E-03 | -5.52934E+00 | 4.19368E-03 | -5.11116E+00 | 6.49676E-03 | -4.74939E+00 | 9.53468E-03 | -4.42974E+00 | 1.34457E-02 | -4.14197E+00 | 1.84049E-02 |
| 0.25 | -5.97940E+00 | 2.63387E-03 | -5.48967E+00 | 4.37375E-03 | -5.07190E+00 | 6.77891E-03 | -4.71058E+00 | 9.95396E-03 | -4.39142E+00 | 1.40456E-02 | -4.10420E+00 | 1.92393E-02 |
| 0.26 | -5.94099E+00 | 2.74152E-03 | -5.45161E+00 | 4.55428E-03 | -5.03425E+00 | 7.06206E-03 | -4.67337E+00 | 1.03752E-02 | -4.35472E+00 | 1.46491E-02 | -4.06804E+00 | 2.00800E-02 |
| 0.27 | -5.90405E+00 | 2.84936E-03 | -5.41502E+00 | 4.73527E-03 | -4.99808E+00 | 7.34621E-03 | -4.63764E+00 | 1.07985E-02 | -4.31950E+00 | 1.52563E-02 | -4.03337E+00 | 2.09271E-02 |
| 0.28 | -5.86848E+00 | 2.95738E-03 | -5.37981E+00 | 4.91672E-03 | -4.96329E+00 | 7.63138E-03 | -4.60330E+00 | 1.12238E-02 | -4.28566E+00 | 1.58673E-02 | -4.00008E+00 | 2.17809E-02 |
| 0.29 | -5.83420E+00 | 3.06558E-03 | -5.34588E+00 | 5.09864E-03 | -4.92977E+00 | 7.91757E-03 | -4.57023E+00 | 1.16511E-02 | -4.25311E+00 | 1.64820E-02 | -3.96807E+00 | 2.26415E-02 |
| 0.30 | -5.80110E+00 | 3.17398E-03 | -5.31314E+00 | 5.28102E-03 | -4.89745E+00 | 8.20481E-03 | -4.53836E+00 | 1.20806E-02 | -4.22175E+00 | 1.71006E-02 | -3.93726E+00 | 2.35090E-02 |
| 0.31 | -5.76911E+00 | 3.28257E-03 | -5.28151E+00 | 5.46388E-03 | -4.86624E+00 | 8.49309E-03 | -4.50760E+00 | 1.25121E-02 | -4.19150E+00 | 1.77231E-02 | -3.90758E+00 | 2.43835E-02 |
| 0.32 | -5.73817E+00 | 3.39134E-03 | -5.25093E+00 | 5.64721E-03 | -4.83607E+00 | 8.78243E-03 | -4.47789E+00 | 1.29459E-02 | -4.16231E+00 | 1.83497E-02 | -3.87894E+00 | 2.52652E-02 |
| 0.33 | -5.70821E+00 | 3.50031E-03 | -5.22132E+00 | 5.83102E-03 | -4.80688E+00 | 9.07284E-03 | -4.44916E+00 | 1.33818E-02 | -4.13410E+00 | 1.89803E-02 | -3.85129E+00 | 2.61543E-02 |
| 0.34 | -5.67916E+00 | 3.60947E-03 | -5.19263E+00 | 6.01531E-03 | -4.77862E+00 | 9.36433E-03 | -4.42136E+00 | 1.38199E-02 | -4.10681E+00 | 1.96151E-02 | -3.82457E+00 | 2.70509E-02 |
| 0.35 | -5.65098E+00 | 3.71882E-03 | -5.16481E+00 | 6.20009E-03 | -4.75122E+00 | 9.65692E-03 | -4.39442E+00 | 1.42602E-02 | -4.08040E+00 | 2.02541E-02 | -3.79873E+00 | 2.79551E-02 |
| 0.36 | -5.62362E+00 | 3.82837E-03 | -5.13781E+00 | 6.38537E-03 | -4.72464E+00 | 9.95061E-03 | -4.36831E+00 | 1.47029E-02 | -4.05480E+00 | 2.08975E-02 | -3.77371E+00 | 2.88673E-02 |
| 0.37 | -5.59703E+00 | 3.93811E-03 | -5.11158E+00 | 6.57114E-03 | -4.69884E+00 | 1.02454E-02 | -4.34297E+00 | 1.51478E-02 | -4.02999E+00 | 2.15453E-02 | -3.74947E+00 | 2.97874E-02 |
| 0.38 | -5.57117E+00 | 4.04805E-03 | -5.08609E+00 | 6.75741E-03 | -4.67377E+00 | 1.05414E-02 | -4.31837E+00 | 1.55951E-02 | -4.00592E+00 | 2.21976E-02 | -3.72597E+00 | 3.07158E-02 |
| 0.39 | -5.54601E+00 | 4.15818E-03 | -5.06128E+00 | 6.94418E-03 | -4.64940E+00 | 1.08385E-02 | -4.29446E+00 | 1.60448E-02 | -3.98254E+00 | 2.28544E-02 | -3.70317E+00 | 3.16525E-02 |
| 0.40 | -5.52150E+00 | 4.26852E-03 | -5.03714E+00 | 7.13147E-03 | -4.62568E+00 | 1.11367E-02 | -4.27122E+00 | 1.64968E-02 | -3.95983E+00 | 2.35160E-02 | -3.68105E+00 | 3.25979E-02 |
| 0.41 | -5.49762E+00 | 4.37905E-03 | -5.01362E+00 | 7.31927E-03 | -4.60260E+00 | 1.14361E-02 | -4.24861E+00 | 1.69513E-02 | -3.93775E+00 | 2.41823E-02 | -3.65955E+00 | 3.35522E-02 |
| 0.42 | -5.47434E+00 | 4.48979E-03 | -4.99070E+00 | 7.50758E-03 | -4.58011E+00 | 1.17367E-02 | -4.22659E+00 | 1.74083E-02 | -3.91627E+00 | 2.48536E-02 | -3.63867E+00 | 3.45154E-02 |
| 0.43 | -5.45162E+00 | 4.60072E-03 | -4.96835E+00 | 7.69642E-03 | -4.55819E+00 | 1.20385E-02 | -4.20515E+00 | 1.78679E-02 | -3.89537E+00 | 2.55298E-02 | -3.61836E+00 | 3.54880E-02 |
| 0.44 | -5.42945E+00 | 4.71186E-03 | -4.94655E+00 | 7.88579E-03 | -4.53682E+00 | 1.23415E-02 | -4.18426E+00 | 1.83300E-02 | -3.87502E+00 | 2.62111E-02 | -3.59860E+00 | 3.64701E-02 |
| 0.45 | -5.40779E+00 | 4.82321E-03 | -4.92526E+00 | 8.07568E-03 | -4.51596E+00 | 1.26457E-02 | -4.16389E+00 | 1.87947E-02 | -3.85519E+00 | 2.68975E-02 | -3.57937E+00 | 3.74621E-02 |
| 0.46 | -5.38663E+00 | 4.93476E-03 | -4.90446E+00 | 8.26612E-03 | -4.49560E+00 | 1.29512E-02 | -4.14401E+00 | 1.92620E-02 | -3.83586E+00 | 2.75893E-02 | -3.56065E+00 | 3.84641E-02 |
| 0.47 | -5.36594E+00 | 5.04652E-03 | -4.88414E+00 | 8.45709E-03 | -4.47572E+00 | 1.32579E-02 | -4.12462E+00 | 1.97320E-02 | -3.81701E+00 | 2.82865E-02 | -3.54241E+00 | 3.94765E-02 |
| 0.48 | -5.34571E+00 | 5.15848E-03 | -4.86427E+00 | 8.64861E-03 | -4.45629E+00 | 1.35659E-02 | -4.10568E+00 | 2.02048E-02 | -3.79863E+00 | 2.89893E-02 | -3.52463E+00 | 4.04996E-02 |
| 0.49 | -5.32591E+00 | 5.27066E-03 | -4.84484E+00 | 8.84068E-03 | -4.43730E+00 | 1.38752E-02 | -4.08718E+00 | 2.06804E-02 | -3.78068E+00 | 2.96977E-02 | -3.50730E+00 | 4.15336E-02 |
| 0.50 | -5.30652E+00 | 5.38304E-03 | -4.82583E+00 | 9.03331E-03 | -4.41873E+00 | 1.41858E-02 | -4.06910E+00 | 2.11587E-02 | -3.76316E+00 | 3.04119E-02 | -3.49040E+00 | 4.25790E-02 |
| 0.51 | -5.28754E+00 | 5.49564E-03 | -4.80722E+00 | 9.22650E-03 | -4.40057E+00 | 1.44977E-02 | -4.05143E+00 | 2.16400E-02 | -3.74605E+00 | 3.11321E-02 | -3.47391E+00 | 4.36361E-02 |
| 0.52 | -5.26895E+00 | 5.60845E-03 | -4.78900E+00 | 9.42025E-03 | -4.38279E+00 | 1.48109E-02 | -4.03415E+00 | 2.21242E-02 | -3.72933E+00 | 3.18583E-02 | -3.45782E+00 | 4.47052E-02 |
| 0.53 | -5.25072E+00 | 5.72148E-03 | -4.77115E+00 | 9.61458E-03 | -4.36538E+00 | 1.51255E-02 | -4.01724E+00 | 2.26113E-02 | -3.71299E+00 | 3.25907E-02 | -3.44211E+00 | 4.57867E-02 |
| 0.54 | -5.23285E+00 | 5.83472E-03 | -4.75365E+00 | 9.80948E-03 | -4.34833E+00 | 1.54415E-02 | -4.00070E+00 | 2.31015E-02 | -3.69702E+00 | 3.33295E-02 | -3.42677E+00 | 4.68811E-02 |
| 0.55 | -5.21533E+00 | 5.94817E-03 | -4.73650E+00 | 1.00050E-02 | -4.33163E+00 | 1.57589E-02 | -3.98450E+00 | 2.35948E-02 | -3.68139E+00 | 3.40747E-02 | -3.41178E+00 | 4.79886E-02 |
| 0.56 | -5.19813E+00 | 6.06185E-03 | -4.71968E+00 | 1.02010E-02 | -4.31526E+00 | 1.60776E-02 | -3.96864E+00 | 2.40913E-02 | -3.66611E+00 | 3.48267E-02 | -3.39714E+00 | 4.91098E-02 |
| 0.57 | -5.18126E+00 | 6.17574E-03 | -4.70319E+00 | 1.03977E-02 | -4.29922E+00 | 1.63978E-02 | -3.95310E+00 | 2.45909E-02 | -3.65115E+00 | 3.55854E-02 | -3.38283E+00 | 5.02452E-02 |
| 0.58 | -5.16469E+00 | 6.28986E-03 | -4.68700E+00 | 1.05950E-02 | -4.28348E+00 | 1.67194E-02 | -3.93788E+00 | 2.50938E-02 | -3.63652E+00 | 3.63512E-02 | -3.36884E+00 | 5.13951E-02 |
| 0.59 | -5.14843E+00 | 6.40419E-03 | -4.67111E+00 | 1.07928E-02 | -4.26805E+00 | 1.70425E-02 | -3.92296E+00 | 2.56001E-02 | -3.62218E+00 | 3.71242E-02 | -3.35517E+00 | 5.25601E-02 |
| 0.60 | -5.13245E+00 | 6.51876E-03 | -4.65551E+00 | 1.09913E-02 | -4.25290E+00 | 1.73671E-02 | -3.90833E+00 | 2.61097E-02 | -3.60815E+00 | 3.79045E-02 | -3.34179E+00 | 5.37407E-02 |
| 0.61 | -5.11675E+00 | 6.63354E-03 | -4.64019E+00 | 1.11904E-02 | -4.23804E+00 | 1.76931E-02 | -3.89399E+00 | 2.66228E-02 | -3.59440E+00 | 3.86924E-02 | -3.32871E+00 | 5.49375E-02 |
| 0.62 | -5.10132E+00 | 6.74856E-03 | -4.62514E+00 | 1.13901E-02 | -4.22345E+00 | 1.80207E-02 | -3.87992E+00 | 2.71395E-02 | -3.58093E+00 | 3.94881E-02 | -3.31592E+00 | 5.61510E-02 |
| 0.63 | -5.08615E+00 | 6.86380E-03 | -4.61035E+00 | 1.15904E-02 | -4.20912E+00 | 1.83499E-02 | -3.86612E+00 | 2.76597E-02 | -3.56773E+00 | 4.02918E-02 | -3.30339E+00 | 5.73819E-02 |
| 0.64 | -5.07123E+00 | 6.97927E-03 | -4.59582E+00 | 1.17914E-02 | -4.19505E+00 | 1.86806E-02 | -3.85258E+00 | 2.81836E-02 | -3.55479E+00 | 4.11037E-02 | -3.29114E+00 | 5.86308E-02 |
| 0.65 | -5.05656E+00 | 7.09497E-03 | -4.58153E+00 | 1.19930E-02 | -4.18122E+00 | 1.90129E-02 | -3.83929E+00 | 2.87113E-02 | -3.54211E+00 | 4.19240E-02 | -3.27915E+00 | 5.98984E-02 |
| 0.66 | -5.04212E+00 | 7.21090E-03 | -4.56749E+00 | 1.21953E-02 | -4.16764E+00 | 1.93468E-02 | -3.82624E+00 | 2.92428E-02 | -3.52967E+00 | 4.27531E-02 | -3.26740E+00 | 6.11855E-02 |
| 0.67 | -5.02792E+00 | 7.32707E-03 | -4.55367E+00 | 1.23982E-02 | -4.15429E+00 | 1.96823E-02 | -3.81342E+00 | 2.97782E-02 | -3.51747E+00 | 4.35911E-02 | -3.25591E+00 | 6.24929E-02 |
| 0.68 | -5.01394E+00 | 7.44347E-03 | -4.54008E+00 | 1.26017E-02 | -4.14116E+00 | 2.00195E-02 | -3.80084E+00 | 3.03176E-02 | -3.50551E+00 | 4.44383E-02 | -3.24466E+00 | 6.38214E-02 |
| 0.69 | -5.00018E+00 | 7.56012E-03 | -4.52670E+00 | 1.28060E-02 | -4.12826E+00 | 2.03584E-02 | -3.78847E+00 | 3.08611E-02 | -3.49378E+00 | 4.52951E-02 | -3.23363E+00 | 6.51719E-02 |
| 0.70 | -4.98662E+00 | 7.67699E-03 | -4.51354E+00 | 1.30109E-02 | -4.11557E+00 | 2.06991E-02 | -3.77633E+00 | 3.14088E-02 | -3.48226E+00 | 4.61617E-02 | -3.22284E+00 | 6.65454E-02 |
| 0.71 | -4.97328E+00 | 7.79411E-03 | -4.50058E+00 | 1.32164E-02 | -4.10308E+00 | 2.10414E-02 | -3.76439E+00 | 3.19607E-02 | -3.47096E+00 | 4.70384E-02 | -3.21227E+00 | 6.79431E-02 |
| 0.72 | -4.96013E+00 | 7.91148E-03 | -4.48783E+00 | 1.34227E-02 | -4.09080E+00 | 2.13855E-02 | -3.75266E+00 | 3.25171E-02 | -3.45987E+00 | 4.79256E-02 | -3.20192E+00 | 6.93660E-02 |
| 0.73 | -4.94718E+00 | 8.02908E-03 | -4.47526E+00 | 1.36297E-02 | -4.07871E+00 | 2.17315E-02 | -3.74113E+00 | 3.30778E-02 | -3.44899E+00 | 4.88236E-02 | -3.19178E+00 | 7.08155E-02 |
| 0.74 | -4.93441E+00 | 8.14693E-03 | -4.46289E+00 | 1.38373E-02 | -4.06682E+00 | 2.20792E-02 | -3.72980E+00 | 3.36432E-02 | -3.43830E+00 | 4.97328E-02 | -3.18184E+00 | 7.22928E-02 |
| 0.75 | -4.92183E+00 | 8.26503E-03 | -4.45071E+00 | 1.40457E-02 | -4.05511E+00 | 2.24288E-02 | -3.71865E+00 | 3.42132E-02 | -3.42781E+00 | 5.06536E-02 | -3.17211E+00 | 7.37995E-02 |
| 0.76 | -4.90943E+00 | 8.38337E-03 | -4.43870E+00 | 1.42548E-02 | -4.04359E+00 | 2.27803E-02 | -3.70769E+00 | 3.47880E-02 | -3.41751E+00 | 5.15864E-02 | -3.16258E+00 | 7.53372E-02 |
| 0.77 | -4.89720E+00 | 8.50197E-03 | -4.42687E+00 | 1.44646E-02 | -4.03224E+00 | 2.31337E-02 | -3.69691E+00 | 3.53678E-02 | -3.40740E+00 | 5.25317E-02 | -3.15324E+00 | 7.69077E-02 |
| 0.78 | -4.88514E+00 | 8.62081E-03 | -4.41520E+00 | 1.46751E-02 | -4.02106E+00 | 2.34890E-02 | -3.68631E+00 | 3.59525E-02 | -3.39747E+00 | 5.34900E-02 | -3.14409E+00 | 7.85129E-02 |
| 0.79 | -4.87324E+00 | 8.73992E-03 | -4.40371E+00 | 1.48864E-02 | -4.01005E+00 | 2.38463E-02 | -3.67587E+00 | 3.65425E-02 | -3.38771E+00 | 5.44617E-02 | -3.13513E+00 | 8.01550E-02 |
| 0.80 | -4.86151E+00 | 8.85927E-03 | -4.39238E+00 | 1.50984E-02 | -3.99921E+00 | 2.42057E-02 | -3.66561E+00 | 3.71377E-02 | -3.37813E+00 | 5.54474E-02 | -3.12636E+00 | 8.18364E-02 |
| 0.81 | -4.84993E+00 | 8.97889E-03 | -4.38120E+00 | 1.53111E-02 | -3.98852E+00 | 2.45671E-02 | -3.65551E+00 | 3.77383E-02 | -3.36872E+00 | 5.64477E-02 | -3.11776E+00 | 8.35596E-02 |
| 0.82 | -4.83851E+00 | 9.09876E-03 | -4.37018E+00 | 1.55247E-02 | -3.97799E+00 | 2.49306E-02 | -3.64557E+00 | 3.83446E-02 | -3.35947E+00 | 5.74633E-02 | -3.10934E+00 | 8.53278E-02 |
| 0.83 | -4.82724E+00 | 9.21889E-03 | -4.35931E+00 | 1.57390E-02 | -3.96762E+00 | 2.52962E-02 | -3.63578E+00 | 3.89566E-02 | -3.35039E+00 | 5.84947E-02 | -3.10110E+00 | 8.71442E-02 |
| 0.84 | -4.81611E+00 | 9.33929E-03 | -4.34859E+00 | 1.59541E-02 | -3.95739E+00 | 2.56640E-02 | -3.62615E+00 | 3.95744E-02 | -3.34147E+00 | 5.95427E-02 | -3.09303E+00 | 8.90126E-02 |
| 0.85 | -4.80513E+00 | 9.45995E-03 | -4.33801E+00 | 1.61699E-02 | -3.94731E+00 | 2.60339E-02 | -3.61667E+00 | 4.01984E-02 | -3.33271E+00 | 6.06081E-02 | -3.08513E+00 | 9.09374E-02 |
| 0.86 | -4.79428E+00 | 9.58088E-03 | -4.32758E+00 | 1.63866E-02 | -3.93738E+00 | 2.64062E-02 | -3.60734E+00 | 4.08286E-02 | -3.32409E+00 | 6.16917E-02 | -3.07740E+00 | 9.29236E-02 |
| 0.87 | -4.78357E+00 | 9.70208E-03 | -4.31728E+00 | 1.66041E-02 | -3.92758E+00 | 2.67807E-02 | -3.59815E+00 | 4.14652E-02 | -3.31563E+00 | 6.27945E-02 | -3.06983E+00 | 9.49770E-02 |
| 0.88 | -4.77300E+00 | 9.82355E-03 | -4.30711E+00 | 1.68224E-02 | -3.91792E+00 | 2.71575E-02 | -3.58910E+00 | 4.21084E-02 | -3.30732E+00 | 6.39175E-02 | -3.06243E+00 | 9.71047E-02 |
| 0.89 | -4.76255E+00 | 9.94529E-03 | -4.29707E+00 | 1.70415E-02 | -3.90839E+00 | 2.75368E-02 | -3.58018E+00 | 4.27585E-02 | -3.29916E+00 | 6.50617E-02 | -3.05519E+00 | 9.93154E-02 |
| 0.90 | -4.75224E+00 | 1.00673E-02 | -4.28717E+00 | 1.72614E-02 | -3.89900E+00 | 2.79184E-02 | -3.57141E+00 | 4.34156E-02 | -3.29114E+00 | 6.62284E-02 | -3.04811E+00 | 1.01620E-01 |
| 0.91 | -4.74204E+00 | 1.01896E-02 | -4.27739E+00 | 1.74822E-02 | -3.88973E+00 | 2.83025E-02 | -3.56276E+00 | 4.40800E-02 | -3.28326E+00 | 6.74189E-02 | -3.04120E+00 | 1.04037E-01 |
| 0.92 | -4.73197E+00 | 1.03122E-02 | -4.26773E+00 | 1.77039E-02 | -3.88058E+00 | 2.86892E-02 | -3.55425E+00 | 4.47519E-02 | -3.27552E+00 | 6.86347E-02 | -3.03445E+00 | 1.06592E-01 |
| 0.93 | -4.72202E+00 | 1.04350E-02 | -4.25819E+00 | 1.79264E-02 | -3.87156E+00 | 2.90784E-02 | -3.54586E+00 | 4.54317E-02 | -3.26792E+00 | 6.98773E-02 | -3.02787E+00 | 1.09349E-01 |
| 0.94 | -4.71218E+00 | 1.05582E-02 | -4.24877E+00 | 1.81498E-02 | -3.86266E+00 | 2.94703E-02 | -3.53760E+00 | 4.61194E-02 | -3.26045E+00 | 7.11488E-02 | -3.02146E+00 | 1.12469E-01 |
| 0.95 | -4.70246E+00 | 1.06816E-02 | -4.23947E+00 | 1.83742E-02 | -3.85388E+00 | 2.98648E-02 | -3.52946E+00 | 4.68156E-02 | -3.25311E+00 | 7.24511E-02 | -3.01518E+00 | 1.15211E-01 |
| 0.96 | -4.69285E+00 | 1.08053E-02 | -4.23028E+00 | 1.85993E-02 | -3.84521E+00 | 3.02621E-02 | -3.52145E+00 | 4.75204E-02 | -3.24591E+00 | 7.37866E-02 | -3.00910E+00 | 1.18580E-01 |
| 0.97 | -4.68335E+00 | 1.09293E-02 | -4.22120E+00 | 1.88254E-02 | -3.83666E+00 | 3.06622E-02 | -3.51355E+00 | 4.82342E-02 | -3.23884E+00 | 7.51583E-02 | -3.00318E+00 | 1.22175E-01 |
| 0.98 | -4.67395E+00 | 1.10536E-02 | -4.21223E+00 | 1.90524E-02 | -3.82822E+00 | 3.10652E-02 | -3.50577E+00 | 4.89573E-02 | -3.23190E+00 | 7.65692E-02 | -2.99745E+00 | 1.26147E-01 |
| 0.99 | -4.66467E+00 | 1.11781E-02 | -4.20336E+00 | 1.92804E-02 | -3.81989E+00 | 3.14711E-02 | -3.49810E+00 | 4.96902E-02 | -3.22509E+00 | 7.80234E-02 | -2.99189E+00 | 1.30394E-01 |
| 1.00 | -4.65548E+00 | 1.13030E-02 | -4.19460E+00 | 1.95093E-02 | -3.81166E+00 | 3.18800E-02 | -3.49055E+00 | 5.04332E-02 | -3.21841E+00 | 7.95256E-02 | -2.98651E+00 | 1.35122E-01 |
Remarks:
Uncertainties were obtained
from 5 independent simulations and represent 67% confidence limits (one
standard deviation).
Liquid-vapor coexistence was determined by adjusting the activity such
that the pressures of the liquid and vapor phases were
equal. Following, identification of state points below the coexistence pressure was accomplished by adjusting the activity until the pressure of the vapor phase was equal to the desired fraction of psat[6]. Here, the pressure is not the conventional virial pressure [2,
3] but is the actual thermodynamic pressure, based on the
fact that the absolute free energies can be obtained from the
distributions determined from simulation [4]. 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. 5.
As introduced in Refs. 2 and 3, 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.
Phase-coexistence energies were obtained by determining the
mean potential energy at a given value of N for an additional 8 billion
MC trials. Combining this information with the particle number
probability distribution, the mean potential energy of the coexisting
phases can be calculated [6].
For the Lennard-Jones fluid, linear force shifted at 2.5σ, the critical properties are Tc*=0.937, ρc*=0.320, and pc*=0.0820 [7].
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9915 (2003).
[2] M. P. Allen and D. J. Tildesley, Computer
Simulation of Liquids
(Oxford University Press, New York, 1989).
[3] D. Frenkel and B. Smit, Understanding
Molecular Simulation, 2nd ed.
(Academic, San Diego, 2002).
[4] J. R. Errington and A. Z. Panagiotopoulos,
J. Chem. Phys. 109, 1093
(1998).
[5] A. Z. Panagiotopoulos, J. Phys.: Condens.
Matter 12, 25 (2000).
[6] J. R. Errington and V. K. Shen, J. Chem. Phys. 123, 164103 (2005).
[7] J. R. Errington P. G. Debenedetti, and S. Torquato, J. Chem. Phys. 118, 2256 (2003).
[8] V. K. Shen and D. W. Siderius, J. Chem. Phys., 140, 244106, (2014).
[9] V. K. Shen and J. R. Errington, J. Phys. Chem. B 108, 19595, (2004).
[10] V. K. Shen and J. R. Errington, J. Chem. Phys. 122, 064508, (2005).
[11] V. K. Shen, R. D. Mountain, and J. R. Errington, J. Phys. Chem. B 111, 6198, (2007).
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