Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic

We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates $r$ and initial packing fractions followed by compression and decompression in small steps to reach packing fractions $ϕ_J$ at jamming onset. For the second, we seed the system with initial configurations that promote micro- and macrophase-separated packings followed by compression and decompression to $ϕ_J$. We find that amorphous, isostatic packings exist over a finite range of packing fractions from $ϕ_{\rm min} \le ϕ_J \le ϕ_{\rm max}$ in the large-system limit, with $ϕ_{\rm max} \approx 0.853$. In agreement with previous calculations, we obtain $ϕ_{\rm min} \approx 0.84$ for $r > r^*$, where $r^*$ is the rate above which $ϕ_J$ is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, bond orientational order, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered, whereas bond-orientational and compositional order increase with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies of the static packings to understand the extent to which the mechanical properties of amorphous, isostatic packings are different from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.

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