Two-dimensional hard dumbbells. I. Fluctuating cell model

Abstract

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 semianalytic algorithm to calculate free volumes, is found to be of comparable efficiency to 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 also calculate the distribution of free volumes in the solid phase. The nature of the distribution of free volumes changes abruptly near the hard-disk limit, similarly to the sudden change in validity of the fluctuating cell theory approximation.