We apply the fluctuating cell model to the calculation of free energies and pressures of high density phases of two-dimensional hard-dumbbells using the Metropolis algorithm to generate configurations in the NVT ensemble. The natural logarithm of the average free volume is found to yield a better approximation of the free energy of the system than the value obtained from simple cell theory for all reduced bond lengths except very near the previously-calculated hard disk limit. The proposed approximation for the free energy, when used in combination with a semi-analytic algorithm to calculate free volumes, is found to be more computationally efficient than the lattice-coupling method of Frenkel and Ladd. Unlike the simple cell model, the fluctuating cell model is applicable to molecules that freeze into plastic crystals as well as orientationally-ordered crystals. We find a simple linear relationship to exist between the compressibility and the average of the ratio of the surface area and volume of the angle-averaged free volumes of the dumbbells.

• Contact: Jim Rainwater