Structure of ellipses and ellipsoids at their RSA densities

Motivated by the recent observation of liquid glass in suspensions of ellipsoidal colloids [J. Roller et al, Proc. Nat. Acad. Sci. 118, e2018072118 (2018)], we examine the structure of ellipses and prolate ellipsoids at their random sequential addition densities φ_s(α,d), where α is particle aspect ratio and d is spatial dimension.  φ_s(α,d) is the maximum density at which these systems can be prepared with no correlation of particles’ positions or orientations save that required by 2-body impenetrability constraints.  The differences φ_g(α,d) -  φ_s(α,d) and φ_MRJ(α,d) - φ_s(α,d) are of particular interest because they indicate how much packing efficiency can be gained (before glass formation and jamming, respectively) by allowing particles to translate and rotate freely while remaining positionally and orientationally disordered.  We determine φ_s(α,d) for a wider range of α (and to considerably higher precision for all α) than had been previously reported, explore in detail how these maximally dense and random states’ structure varies with α and d, and attempt to connect our findings to α- and d-dependent trends in these systems’ jamming behavior.