Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function

Dynamical signatures are known to precede jamming in hard-particle systems, but static structural signatures have proven more elusive. The observation that compressing hard-particle packings towards jamming causes growing hyperuniformity has paved the way for the analysis of jamming as an "inverted critical point" in which the direct correlation function $c(r)$ diverges. We establish quantitative relationships between various singularities in $c(r)$ and the total correlation function $h(r)$ that provide a concrete means of identifying features that must be expressed in $c(r)$ if one hopes to reproduce details in the pair correlation function accurately. We also analyze systems of three-dimensional monodisperse hard-spheres of diameter $D$ as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) and Torquato-Jiao (TJ) packing algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling $c(r) \propto -1/r$ as $r \rightarrow 0$ and show that this, along with the developing delta function at $c(D)$, is a consequence of the growing long-rangedness in $c(r)$. Near the freezing density, we identify qualitative differences in the structure factor $S(k)$ as well as $c(r)$ between TJ- and LS-generated configurations and link them to differences in the protocols' packing dynamics. Configurations from both algorithms have structure factors that approach zero in the low-wavenumber limit as jamming is approached and are shown to exhibit a corresponding power-law decay in $c(r)$ for large $r$ as a consequence. Our work advances the notion that static signatures are exhibited by hard-particle packings as they approach jamming and underscores the utility of the direct correlation function as a means of monitoring for an incipient rigid network

Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations

Systems of particles interacting with "stealthy" pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical ensemble (in the zero-temperature limit). In this paper, we provide details and justifications of the simulation procedure, which involves performing molecular dynamics simulations at sufficiently low temperatures and minimizing the energy of the snapshots for both the high-density disordered regime, where the theory applies, as well as lower densities. We also use numerical simulations to extend our study to the lower-density regime. We report results for the pair correlation functions, structure factors, and Voronoi cell statistics. In the high-density regime, we verify the theoretical ansatz that stealthy disordered ground states behave like "pseudo" disordered equilibrium hard-sphere systems in Fourier space. These results show that as the density decreases from the high-density limit, the disordered ground states in the canonical ensemble are characterized by an increasing degree of short-range order and eventually the system undergoes a phase transition to crystalline ground states. We also provide numerical evidence suggesting that different forms of stealthy pair potentials produce the same ground-state ensemble in the zero-temperature limit. Our techniques may be applied to sample this limit of the canonical ensemble of other potentials with highly degenerate ground states

Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases

Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in d-dimensional Euclidean space R^d. In the previous paper in this series, we numerically studied the entropically favored ground states in the canonical ensemble in the zero-temperature limit across the first three Euclidean space dimensions. In this paper, we investigate using both numerical and theoretical techniques metastable stacked-slider phases, which are part of the ground-state manifold of stealthy potentials at densities in which crystal ground states are favored entropically. Our numerical results enable us to devise analytical models of this phase in two, three, and higher dimensions. Utilizing this model, we estimated the size of the feasible region in configuration space of the stacked-slider phase, finding it to be smaller than that of crystal structures in the infinite-system-size limit, which is consistent with our recent previous work. In two dimensions, we also determine exact expressions for the pair correlation function and structure factor of the analytical model of stacked-slider phases and analyze the connectedness of the ground-state manifold of stealthy potentials in this density regime. We demonstrate that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus. We outline some possible future avenues of research to elucidate our understanding of this unusual phase of matter

Negative thermal expansion in single-component systems with isotropic interactions

We have devised an isotropic interaction potential that gives rise to negative thermal expansion (NTE) behavior in equilibrium many-particle systems in both two and three dimensions over a wide temperature and pressure range (including zero pressure). An optimization procedure is used in order to find a potential that yields a strong NTE effect. A key feature of the potential that gives rise to this behavior is the softened interior of its basin of attraction. Although such anomalous behavior is well known in material systems with directional interactions (e.g., zirconium tungstate), to our knowledge this is the first time that NTE behavior has been established to occur in single-component many-particle systems for isotropic interactions. Using constant-pressure Monte Carlo simulations, we show that as the temperature is increased, the system exhibits negative, zero and then positive thermal expansion before melting (for both two- and three-dimensional systems). The behavior is explicitly compared to that of a Lennard-Jones system, which exhibits typical expansion upon heating for all temperatures and pressures.Comment: 21 pages, 13 figure

Scaled Particle Theory for Hard Sphere Pairs. II. Numerical Analysis

We use the extension of scaled particle theory (ESPT) presented in the accompanying paper [Stillinger et al. J. Chem. Phys. xxx, xxx (2007)] to calculate numerically pair correlation function of the hard sphere fluid over the density range $0\leq \rho\sigma^3\leq 0.96$. Comparison with computer simulation results reveals that the new theory is able to capture accurately the fluid's structure across the entire density range examined. The pressure predicted via the virial route is systematically lower than simulation results, while that obtained using the compressibility route is lower than simulation predictions for $\rho\sigma^3\leq 0.67$ and higher than simulation predictions for $\rho\sigma^3\geq 0.67$. Numerical predictions are also presented for the surface tension and Tolman length of the hard sphere fluid