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We report calculations of the density of maximally random jamming (aka randomclose packing) of one-component and binary hard disc fluids. The theoreticalstructure used provides a common framework for description of the hard discliquid to hexatic, the liquid to hexagonal crystal and the liquid-to-maximallyrandom jammed state transitions. Our analysis is based on locating a particularbifurcation of the solutions of the integral equation for the inhomogeneoussingle particle density at the transition between different spatial structures.The bifurcation of solutions we study is initiated from the dense metastablefluid, and we associate it with the limit of stability of the fluid, which weidentify with the transition from the metastable fluid to a maximally randomjammed state. For the one-component hard disc fluid the predicted packingfraction at which the metastable fluid to maximally random jammed statetransition occurs is 0.84, in excellent agreement with the experimental value0.84 \pm 0.02. The corresponding analysis of the limit of stability of a binaryhard disc fluid with specified disc diameter ratio and disc compositionrequires extra approximations in the representations of the direct correlationfunction, the equation of state, and the number of order parameters accountedfor. Keeping only the order parameter identified with the largest peak in thestructure factor of the highest density regular lattice with the same discdiameter ratio and disc composition as the binary fluid, the predicted densityof maximally random jamming is found to be 0.84 to 0.87, depending on theequation of state used, and very weakly dependent on the ratio of discdiameters and the fluid composition, in agreement with both experimental dataand computer simulation data.

Maximally Random Jamming of Two-Dimensional One-Component and Binary Hard Disc Fluids