EXACT HARD-DISK FREE VOLUMES

Properties of exact hard-disk free volumes are determined by a combination of analytical and numerical techniques. Both the high-density fluid phase and the lower-density fluid phase are treated. These one-particle free volumes are used to verify known thermodynamic information for hard disks and to calculate the shear modulus for the hard-disk solid phase. The free volumes are also compared to approximate free-volume estimates made from the known hard-disk entropy. The statistical distributions of free volume and free surface (perimeter of the free volume) are studied. The percolation transition, at which the free-volume changes from extensive to intensive, is found to occur at about one-third of the freezing density. © 1979 American Institute of Physics.