Mechanically-ultrastable jammed sphere packings with a wide range of polydispersities

We show that for a standard continuously-polydisperse model with particle-diameter distribution P(σ) ~ σ⁻³ and polydispersity index Δ, employing a combination of standard SWAP moves and transient degree of freedom (TDOF) moves during a Lubachevsky-Stillinger-like particle-growth process significantly increases the jamming densities φ_J(Δ) and coordination numbers Z_J(Δ) while dramatically decreasing the rattler fractions f_ratt(Δ) for all 0 < Δ ≤ 0.5. The resulting enhancements to the jammed packings' mechanical properties are substantial, and increase monotonically with Δ. For example, packings prepared with these moves have bulk (shear) moduli that are at least 2 (3) times larger than packings prepared without these moves for all Δ > 0.45, despite lacking any clearly-noticeable local crystalline order or fractionation for Δ > 0.1. We argue that the rattler-fraction reductions enabled by employing TDOF moves at the end of the particle-growth process are a key to achieving these large enhancements.