Dense disordered jammed packings of hard very elongate particles: A new derivation of the random contact equation

This work describes a derivation of the random contact equation that predicts the packing fraction phi MRJ hr of a dense disordered (maximally random) jammed state of hard, very elongate particles. This derivation is based on (I) the compressibility equation connecting the compressibility of a uniform system with its pair-correlation function: it is assumed equal to zero at jamming; (II) the pair-correlation function of the interparticle distance scaled with respect to the orientationally dependent contact distance: it is assumed equal to the sum of a delta function and a unit-step function at jamming, where the former function accounts for the interparticle contacts, while the latter function accounts for the background. On assuming that the hard, very elongate particles are cylindrically symmetric with a length L and a diameter D and isostaticity occurs at jamming, the prediction, in particular that, in the limit of L/D -> +infinity, phi L-MRJ hr/D = (10 + 1)/2, is compared to the available experimental data. Published under an exclusive license by AIP Publishing.

Automated summary

This work describes the derivation of a random contact equation to predict the packing fraction of a dense disordered state of elongate particles. The derivation is based on the compressibility equation and the pair-correlation function, and the predicted results are compared to experimental data.