  We study the influence of particle size asymmetry on structural evolution of
randomly jammed binary sphere mixtures with varying large-sphere/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 $\alpha$ of large to small sphere radii,
($\alpha\geq \alpha_c \approx 5.75$) 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 $\alpha\rightarrow\infty$
by the Furnas model, but occurring for finite values range of $\alpha$ above a
critical value, $\alpha_c \approx 5.75$. The existence of a sharp transition
from small- to large-$f$ values for $\alpha\geq \alpha_c$ can be attributed to
the existence of a {\it sub-jamming transition} of small spheres in the
interstices of jammed large spheres along the line of compositions
$f_{sub}(\alpha)$. We argue that the critical value of finite size asymmetry
$\alpha_c \simeq 5.75$ 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 sub-jamming
transition of small spheres confined within the disjoint volumes.
