Generation, Characterization, and Physical Properties of Particle Packings Across Dimensions

Abstract

Hard-particle packings in d-dimensional Euclidean space have been used as simple models of physical systems across scientific disciplines. Particular focus is placed on maximally random jammed (MRJ) packings, which are the most random (disordered) configurations of strictly jammed (mechanically rigid) particles and are known to be hyperuniform. More precisely, their structure factors S(k) tend to 0 as the wavenumber |k| tends to 0. The hyperuniformity scaling exponent α > 0 is defined as the power-law scaling of S(k) in the vicinity of the origin, i.e., S(k) ∼ |k|^α as |k| → 0. This dissertation presents studies on the generation of hard-particle packings and their characterization via statistical mechanics. In Chapter2, we examine how compression rate and particle shape induce kinetic frustration and affect translational and orientational order in jammed packings of two-dimensional noncircular particles. In Chapter 3, we characterize the structure of MRJ packings of three-dimensional superballs, which are cubic or octahedral deformations of the sphere, and show they are hyperuniform. We then estimate their transport characteristics using pore-space statistics and excess spreadability, a time-dependent diffusion characteristic. In Chapter 4, we demonstrate that achieving strict jamming is critical to ensuring the hyperuniformity of and extracting precise values of α from MRJ hypersphere packings for 3 ≤ d ≤ 5 and show that α for these packings increases as d increases. In Chapter 5, we show the family of disordered strictly jammed equimolar binary disk packings with large to small disk diameter ratios between 1.2 and 1.8 are MRJ-like according to several criteria and, to within numerical error, have a universal value α ≈ 0.45. In Chapter 6, we demonstrate the excess spreadability accurately extracts α from the scattering information of self-similar quasiperiodic packings of identical rods and disks for d = 1 and 2. In Chapter 7, we show the local number variance σ_2^N(R) (associated with a spherical sampling window of radius R) sensitively characterizes the order/disorder of hyperuniform and nonhyperuniform point patterns for d = 1, 2 and 3 across length scales using only pair statistics.