Disordered Bimodal Sphere Packings Achieve Higher Packing Fractions Than Their Binary and Monomodal Counterparts

Studies of dense, disordered, polydisperse sphere packings are typically limited to discrete or monomodal particle-size distributions (PSD) or bimodal PSD with a very limited range of the polydispersity δ, which is the ratio of the mean and standard deviation of the PSD. Here, we use the Torquato-Jiao linear-programming packing algorithm [1] to produce strictly jammed isostatic disordered sphere packings with radius distributions given by the combination of two truncated Gaussian distributions with mean ratios α between 0.45 and 0.125 and individual-mode δ up to 0.7. We show that such bimodal packings can fill space more efficiently than their binary counterparts and equivalently polydisperse monomodal packings. Any putatively monodisperse set of particles will, in practice, exhibit a positive δ, even if small. Thus, these findings more accurately describe the packing fraction φ for practical binary (i.e., bimodal) packings and can inform the choice of PSD for tuning the density of polydisperse systems such as additive manufacturing particle beds or understanding the jamming transitions in glassy colloidal systems. Moreover, given α, one can use these results to determine which δ and relative number fraction of small spheres mimics φ of an idealized binary packing.

1. S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2001).