Subjamming transition in binary sphere mixtures

Abstract

We study the influence of particle-size asymmetry on structural evolution of randomly jammed binary sphere mixtures with varying large-sphere and small-sphere composition. Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures. For weakly asymmetric particle sizes, packing properties evolve smoothly, but not monotonically, with increasing small-sphere composition, $f$. Our simulations reveal that at high values of ratio $\ensuremath{\alpha}$ of large- to small-sphere radii ($\ensuremath{\alpha}\ensuremath{\ge}{\ensuremath{\alpha}}_{c}\ensuremath{\approx}5.75$), evolution of structural properties, such as packing density, fraction of jammed spheres, and contact statistics with $f$, exhibit features that suggest a sharp transition, either through discontinuities in structural measures or their derivatives. We argue that this behavior is related to the singular, composition dependence of close-packing fraction predicted in infinite aspect ratio mixtures $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$ by the Furnas model, but occurring for finite valued range of $\ensuremath{\alpha}$ above a critical value, ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}5.75$. The existence of a sharp transition from small- to large-$f$ values for $\ensuremath{\alpha}\ensuremath{\ge}{\ensuremath{\alpha}}_{c}$ can be attributed to the existence of a subjamming transition of small spheres within the interstices of jammed large spheres along the line of compositions ${f}_{\text{sub}}(\ensuremath{\alpha})$. We argue that the critical value of finite-size asymmetry ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}5.75$ is consistent with the geometric criterion for the transmission of small-sphere contacts between neighboring tetrahedrally close-packed interstices of large spheres, facilitating a cooperative subjamming transition of small spheres confined within the disjoint volumes.