3D. SAT-TMMC: Liquid-Vapor coexistence properties - Linear Force Shifted Potential at r=3.5σ
Liquid-vapor coexistence properties obtained by grand-canonical transition-matrix Monte Carlo and histogram re-weighting over the reduced temperature range 0.70 to 1.15 at increments of 0.05. Mean values of the saturation pressure, density, potential energy per molecule, and activity (chemical potential- see below) for each phase are reported.
Uncertainties were obtained from five 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 [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 . 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.
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. (NOTE: The reported activity is dimensionless, having been scaled by the LJ length cubed.)
Phase-coexistence energies were obtained by determining the mean potential energy at a given value of N for an additional 40 billion MC trials. Combining this information with the particle number probability distribution, the mean potential energy of the coexisting phases can be calculated .
For the Lennard-Jones fluid, linear force shifted at 3.0σ, the critical properties were estimated to be Tc*=1.162, ρc*=0.320, and pc*=0.107. Estimates were found via rectilinear diameter analysis of TMMC data computed with V*=512 close to the critical point . (Finite-size scaling analysis has not been completed, so these critical properties should be taken simply as estimates.)
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