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Frank H. Stillinger

Publications and source records attributed to Frank H. Stillinger.

46 records · Page 3Linked to original sources
arXiv2006

Self-assembly of the simple cubic lattice with an isotropic potential

Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures (Phys. Rev. Lett. 95, 228301 (2005), Phys. Rev. E 73, 011406 (2006)), we present an isotropic pair potential $V(r)$ for a three-dimensional many-particle system whose classical ground state is the low-coordinated simple cubic (SC) lattice. This result is part of an ongoing pursuit by the authors to develop analytical and computational tools to solve statistical-mechanical inverse problems for the purpose of achieving targeted self-assembly. The purpose of these methods is to design interparticle interactions that cause self-assembly of technologically important target structures for applications in photonics, catalysis, separation, sensors and electronics. We also show that standard approximate integral-equation theories of the liquid state that utilize pair correlation function information cannot be used in the reverse mode to predict the correct simple cubic potential. We report in passing optimized isotropic potentials that yield the body-centered cubic and simple hexagonal lattices, which provide other examples of non-close-packed structures that can be assembled using isotropic pair interactions.

cond-mat.soft↗
arXiv2006

Designed Interaction Potentials via Inverse Methods for Self-Assembly

We formulate statistical-mechanical inverse methods in order to determine optimized interparticle interactions that spontaneously produce target many-particle configurations. Motivated by advances that give experimentalists greater and greater control over colloidal interaction potentials, we propose and discuss two computational algorithms that search for optimal potentials for self-assembly of a given target configuration. The first optimizes the potential near the ground state and the second near the melting point. We begin by applying these techniques to assembling open structures in two dimensions (square and honeycomb lattices) using only circularly symmetric pair interaction potentials ; we demonstrate that the algorithms do indeed cause self-assembly of the target lattice. Our approach is distinguished from previous work in that we consider (i) lattice sums, (ii) mechanical stability (phonon spectra), and (iii) annealed Monte Carlo simulations. We also devise circularly symmetric potentials that yield chain-like structures as well as systems of clusters.

cond-mat.soft↗
arXiv2005

Dynamic heterogeneity and non-Gaussian behavior in a model supercooled liquid

We use a recently-derived reformulation of the diffusion constant [Stillinger F H and Debenedetti P G 2005 J. Phys. Chem. B 109 6604] to investigate heterogeneous dynamics and non-Gaussian diffusion in a binary Lennard-Jones mixture. Our work focuses on the joint probability distribution of particles with velocity v_0 at time t=0 and eventual displacement Delta x at time t=Delta t. We show that this distribution attains a distinctive shape at the time of maximum non-Gaussian behavior in the supercooled liquid. By performing a two-Gaussian fit of the displacement data, we obtain, in a non-arbitrary manner, two diffusive length scales inherent to the supercooled liquid and use them to identify spatially separated regions of mobile and immobile particles.

cond-mat.soft↗
arXiv2004

Epitaxial Frustration in Deposited Packings of Rigid Disks and Spheres

We use numerical simulation to investigate and analyze the way that rigid disks and spheres arrange themselves when compressed next to incommensurate substrates. For disks, a movable set is pressed into a jammed state against an ordered fixed line of larger disks, where the diameter ratio of movable to fixed disks is 0.8. The corresponding diameter ratio for the sphere simulations is 0.7, where the fixed substrate has the structure of a (001) plane of a face-centered cubic array. Results obtained for both disks and spheres exhibit various forms of density-reducing packing frustration next to the incommensurate substrate, including some cases displaying disorder that extends far from the substrate. The disk system calculations strongly suggest that the most efficient (highest density) packings involve configurations that are periodic in the lateral direction parallel to the substrate, with substantial geometric disruption only occurring near the substrate. Some evidence has also emerged suggesting that for the sphere systems a corresponding structure doubly periodic in the lateral directions would yield the highest packing density; however all of the sphere simulations completed thus far produced some residual "bulk" disorder not obviously resulting from substrate mismatch. In view of the fact that the cases studied here represent only a small subset of all that eventually deserve attention, we end with discussion of the directions in which first extensions of the present simulations might profitably be pursued.

cond-mat.mtrl-sci↗
arXiv2004

Neighbor List Collision-Driven Molecular Dynamics Simulation for Nonspherical Particles. I. Algorithmic Details II. Applications to Ellipses and Ellipsoids

In the first part of a series of two papers, we present in considerable detail a collision-driven molecular dynamics algorithm for a system of nonspherical particles, within a parallelepiped simulation domain, under both periodic or hard-wall boundary conditions. The algorithm extends previous event-driven molecular dynamics algorithms for spheres. We present a novel partial-update near-neighbor list (NNL) algorithm that is superior to previous algorithms at high densities, without compromising the correctness of the algorithm. This efficiency of the algorithm is further increased for systems of very aspherical particles by using bounding sphere complexes (BSC). In the second part of this series of papers we apply the algorithm presented in the first part of this series of papers to systems of hard ellipses and ellipsoids. The theoretical machinery needed to treat such particles, including the overlap potentials, is developed in full detail. We describe an algorithm for predicting the time of collision for two moving ellipses or ellipsoids. We present performance results for our implementation of the algorithm. The practical utility of the algorithm is demonstrated by presenting several interesting physical applications, including the generation of jammed packings inside spherical containers, the study of contact force chains in jammed packings, and melting the densest-known equilibrium crystals of prolate spheroids.

physics.comp-ph↗
arXiv2004

Superdense Crystal Packings of Ellipsoids

Particle packing problems have fascinated people since the dawn of civilization, and continue to intrigue mathematicians and scientists. Resurgent interest has been spurred by the recent proof of Kepler's conjecture: the face-centered cubic lattice provides the densest packing of equal spheres with a packing fraction $ϕ\approx0.7405$ \cite{Kepler_Hales}. Here we report on the densest known packings of congruent ellipsoids. The family of new packings are crystal (periodic) arrangements of nearly spherically-shaped ellipsoids, and always surpass the densest lattice packing. A remarkable maximum density of $ϕ\approx0.7707$ is achieved for both prolate and oblate ellipsoids with aspect ratios of $\sqrt{3}$ and $1/\sqrt{3}$, respectively, and each ellipsoid has 14 touching neighbors. Present results do not exclude the possibility that even denser crystal packings of ellipsoids could be found, and that a corresponding Kepler-like conjecture could be formulated for ellipsoids.

cond-mat.stat-mech↗
arXiv2003

Local Density Fluctuations, Hyperuniformity, and Order Metrics

We study the variance in the number of points contained within a window $Ω$ of arbitrary size, and to further illuminate our understanding of {\it hyperuniform} systems, i.e., point patterns that do not possess long-wavelength fluctuations. For large windows, hyperuniform systems are characterized by a local variance that grows only as the surface area (rather than the volume) of the window. We show that a homogeneous point pattern in a hyperuniform state is at a ``critical-point'' of a type with appropriate scaling laws and critical exponents, but one in which the {\it direct correlation function} (rather than the pair correlation function) is long-ranged.variance.We prove that the simple periodic linear array yields the global minimum value of the average variance among all infinite one-dimensional hyperuniform patterns. We also evaluate the variance for common infinite periodic lattices as well as certain nonperiodic point patterns in one, two, and three dimensions for spherical windows.Our results suggest that the local variance may serve as a useful order metric for general point patterns. Contrary to the conjecture that the lattices associated with the densest packing of congruent spheres have the smallest variance regardless of the space dimension, we show that for $d=3$, the body-centered cubic lattice has a smaller variance than the face-centered cubic lattice. Finally, for certain hyperuniform disordered point patterns, we evaluate the direct correlation function, structure factor, and associated critical exponents exactly.

cond-mat.stat-mech↗
arXiv2002

A Linear Programming Algorithm to Test for Jamming in Hard-Sphere Packings

Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B, 105 (2001)], a classification scheme of jammed packings into hierarchical categories of locally, collectively and strictly jammed configurations has been proposed. They suggest that these jamming categories can be tested using numerical algorithms that analyze an equivalent contact network of the packing under applied displacements, but leave the design of such algorithms as a future task. In this work we present a rigorous and efficient algorithm to assess whether a hard-sphere packing is jammed according to the afformentioned categories. The algorithm is based on linear programming and is applicable to regular as well as random packings of finite size with hard-wall and periodic boundary conditions. If the packing is not jammed, the algorithm yields representative multi-particle unjamming motions. We have implemented this algorithm and applied it to ordered lattices as well as random packings of disks and spheres under periodic boundary conditions. Some representative results for ordered and disordered packings are given, but more applications are anticipated for the future. One important and interesting result is that the random packings that we tested were strictly jammed in three dimensions, but not in two dimensions. Numerous interactive visualization models are provided on the authors' webpage.

cond-mat.mtrl-sci↗
arXiv1999

Triangle Distribution and Equation of State for Classical Rigid Disks

The triangle distribution function f^(3) for three mutual nearest neighbors in the plane describes basic aspects of short-range order and statistical thermodynamics in two-dimensional many-particle systems. This paper examines prospects for constructing a self-consistent calculation for the rigid-disk system f^(3). We present several identities obeyed by f^(3). A rudimentary closure suggested by scaled-particle theory is introduced. In conjunction with three of the basic identities, this closure leads to a unique f^(3) over the entire density range. The pressure equation of state exhibits qualitatively correct behavior in both the low density and the close-packed limits, but no intervening phase transition appears. We discuss extensions to improved disk closures, and to the three-dimensional rigid sphere system.

cond-mat.stat-mech↗