Calculating the high-temperature vapour line by Monte Carlo

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Abstract
The 6:12 Lennard-Jones potential fluid has been studied by grand canonical ensemble Monte Carlo. Two series of calculations have been made with reduced volumes of 300 and 18 000 at reduced temperatures of 1·15, 1·25, 1·30 and 1·35. It is found that the smaller volume results for density as a function of chemical potential are sufficient to approximately locate the phase transition but that the pressure results were too low and showed van der Waals type loops in the transition region. The large volume results were used to calculate the properties of the coexistence curve. The results at = 1·15 and 1·25 were combined with published results at lower temperatures to extrapolate to the critical point using critical exponent equations. The estimated location of the critical point of the Lennard-Jones fluid is c = 1·30 ± 0·02, c = 0·33 ± 0·03 and c = 0·13 ± 0·02.