Compression Driven Jamming of Athermal Frictionless Spherocylinders in Two Dimensions

Abstract

We simulate numerically the compression driven jamming of athermal, frictionless, soft-core spherocylinders in two dimensions, for a range of particle aspect ratios $\alpha$. We find the critical packing fraction $\phi_J(\alpha)$ for the jamming transition, and the average number of contacts per particle $z_J(\alpha)$ at jamming. We find that both are nonmonotonic, with a peak at $\alpha\approx 1$. We find that configurations at the compression driven jamming point are always hypostatic for all $\alpha$, with $z_J<z_\mathrm{iso}=2d_f=6$ the isostatic value. We show that, for moderately elongated spherocylinders, there is no orientational ordering upon athermal compression through jamming. We analyze in detail the eigenmodes of the dynamical matrix close to the jamming point for a few different values of the aspect ratio, from nearly circular to moderately elongated. We find that there are low frequency bands containing $N(z_\mathrm{iso}-z_J)/2$ modes, such that the frequency of these modes vanish as $\phi\to\phi_J$. We consider the extended vs localized nature of these low frequency modes, and the extent to which they involve translational or rotational motion, and find many low frequency sliding modes where particles can move with little rotation. We highlight the importance of treating side-to-side contacts, along flat sides of the spherocylinder, properly for the correct determination of $z_J$. We note the singular nature of taking the $\alpha\to 0$ limit. We discuss the similarities and differences with previous work on jammed ellipses and ellipsoids, to illustrate the effects that different particle shape have on configurations at jamming.