Subjamming transition in binary sphere mixtures

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 α of large- to small-sphere radii (α ≥α_c≈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 α →∞ by the Furnas model, but occurring for finite valued range of α above a critical value, α_c≈5.75 . The existence of a sharp transition from small- to large-f values for α ≥α_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_sub(α ) . We argue that the critical value of finite-size asymmetry α_c≃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.