Sub-Jamming Transition in Jammed Binary Sphere Mixtures

We study influence of bi-dispersity on structural evolution of jammed binary sphere mixtures with increasing small-sphere composition, $f_s$. In binary spheres, maximally dense, random packing is achieved at infinite size ratio and unique composition ($f_s=0.2659$) where small spheres jam within interstitial volume of jammed large spheres, leading to a kink in total volume fraction, $\phi$, vs. $f_s$. Using simulations of athermally jammed packings, we explore how this critical feature influences the evolution of random binary sphere packings at finite size ratio, $\alpha$, ranging from 1 to 10. We report a clear distinction between large and small $\alpha$ behavior, separated by a critical value of $\alpha_c = 5.8$. For $\alpha < \alpha_c$ structural properties --such as total volume fraction, rattler fraction and contact statistics-- are found to crossover smoothly from small to large $f_s$, while above a critical size asymmetry these properties indicate an abrupt, first-order like transition. We correlate this sharp transition with a ``sub-jamming'' transition of small-spheres occurring at finite values of $f_s$, which becomes cooperative only for sufficiently asymmetric mixtures. We propose a heuristic geometric and mechanical argument to understand what determines $\alpha_c$.