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Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

2014; American Physical Society; Volume: 89; Issue: 4 Linguagem: Inglês

10.1103/physreve.89.040302

1550-2376

Andrés Santos, S. B. Yuste, M. López de Haro, Gerardo Odriozola, Vitaliy Ogarko,

Theoretical and Computational Physics

A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction ${\ensuremath{\phi}}_{\mathrm{J}}$ of the polydisperse system as a simple function of ${M}_{1}{M}_{3}/{M}_{2}^{2}$, where ${M}_{k}$ is the $k$th moment of the size distribution. An analysis of experimental and simulation data of ${\ensuremath{\phi}}_{\mathrm{J}}$ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the high-density region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures.