Maximally random jamming of one-component and binary hard-disk fluids in two dimensions

Abstract

We report calculations of the density of maximally random jamming of one-component and binary hard-disk fluids. The theoretical structure used provides a common framework for description of the hard-disk liquid-to-hexatic, the liquid-to-hexagonal crystal, and the liquid to maximally random jammed state transitions. Our analysis is based on locating a particular bifurcation of the solutions of the integral equation for the inhomogeneous single-particle density at the transition between different spatial structures. The bifurcation of solutions we study is initiated from the dense metastable fluid, and we associate it with the limit of stability of the fluid, which we identify with the transition from the metastable fluid to a maximally random jammed state. For the one-component hard-disk fluid the predicted packing fraction at which the metastable fluid to maximally random jammed state transition occurs is 0.84, in excellent agreement with the experimental value 0.84 ± 0.02. The corresponding analysis of the limit of stability of a binary hard-disk fluid with specified disk-diameter ratio and disk composition requires extra approximations in the representations of the direct correlation function, the equation of state, and the number of order parameters accounted for. Keeping only the order parameter identified with the largest peak in the structure factor of the highest-density regular lattice with the same disk- diameter ratio and disk composition as the binary fluid, the predicted density of maximally random jamming is found to be 0.84-0.87, depending on the equation of state used, and very weakly dependent on the ratio of disk diameters and the fluid composition, in agreement with both experimental data and computer simulation data.