Moving beyond the constraints of chemistry via crystal structure discovery with isotropic multiwell pair potentials.

The rigid constraints of chemistry-dictated by quantum mechanics and the discrete nature of the atom-limit the set of observable atomic crystal structures. What structures are possible in the absence of these constraints? Here, we systematically crystallize one-component systems of particles interacting with isotropic multiwell pair potentials. We investigate two tunable families of pairwise interaction potentials. Our simulations self-assemble a multitude of crystal structures ranging from basic lattices to complex networks. Sixteen of the structures have natural analogs spanning all coordination numbers found in inorganic chemistry. Fifteen more are hitherto unknown and occupy the space between covalent and metallic coordination environments. The discovered crystal structures constitute targets for self-assembly and expand our understanding of what a crystal structure can look like.

Nonlinear machine learning and design of reconfigurable digital colloids.

Digital colloids, a cluster of freely rotating "halo" particles tethered to the surface of a central particle, were recently proposed as ultra-high density memory elements for information storage. Rational design of these digital colloids for memory storage applications requires a quantitative understanding of the thermodynamic and kinetic stability of the configurational states within which information is stored. We apply nonlinear machine learning to Brownian dynamics simulations of these digital colloids to extract the low-dimensional intrinsic manifold governing digital colloid morphology, thermodynamics, and kinetics. By modulating the relative size ratio between halo particles and central particles, we investigate the size-dependent configurational stability and transition kinetics for the 2-state tetrahedral (N = 4) and 30-state octahedral (N = 6) digital colloids. We demonstrate the use of this framework to guide the rational design of a memory storage element to hold a block of text that trades off the competing design criteria of memory addressability and volatility.

Tracking vortices in superconductors: Extracting singularities from a discretized complex scalar field evolving in time.

In type-II superconductors, the dynamics of magnetic flux vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter field. Earlier, in Phillips et al. [Phys. Rev. E 91, 023311 (2015)], we introduced a method for extracting vortices from the discretized complex order parameter field generated by a large-scale simulation of vortex matter. With this method, at a fixed time step, each vortex [simplistically, a one-dimensional (1D) curve in 3D space] can be represented as a connected graph extracted from the discretized field. Here we extend this method as a function of time as well. A vortex now corresponds to a 2D space-time sheet embedded in 4D space time that can be represented as a connected graph extracted from the discretized field over both space and time. Vortices that interact by merging or splitting correspond to disappearance and appearance of holes in the connected graph in the time direction. This method of tracking vortices, which makes no assumptions about the scale or behavior of the vortices, can track the vortices with a resolution as good as the discretization of the temporally evolving complex scalar field. Additionally, even details of the trajectory between time steps can be reconstructed from the connected graph. With this form of vortex tracking, the details of vortex dynamics in a model of a superconducting materials can be understood in greater detail than previously possible.

Extracting, Tracking, and Visualizing Magnetic Flux Vortices in 3D Complex-Valued Superconductor Simulation Data.

We propose a method for the vortex extraction and tracking of superconducting magnetic flux vortices for both structured and unstructured mesh data. In the Ginzburg-Landau theory, magnetic flux vortices are well-defined features in a complex-valued order parameter field, and their dynamics determine electromagnetic properties in type-II superconductors. Our method represents each vortex line (a 1D curve embedded in 3D space) as a connected graph extracted from the discretized field in both space and time. For a time-varying discrete dataset, our vortex extraction and tracking method is as accurate as the data discretization. We then apply 3D visualization and 2D event diagrams to the extraction and tracking results to help scientists understand vortex dynamics and macroscale superconductor behavior in greater detail than previously possible.

Detecting vortices in superconductors: extracting one-dimensional topological singularities from a discretized complex scalar field.

In type II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise positions and motion from discretized numerical simulation data is an important, but challenging, task. In the past, vortices have mostly been detected by analyzing the magnitude of the complex scalar field representing the order parameter and visualized by corresponding contour plots and isosurfaces. However, these methods, primarily used for small-scale simulations, blur the fine details of the vortices, scale poorly to large-scale simulations, and do not easily enable isolating and tracking individual vortices. Here we present a method for exactly finding the vortex core lines from a complex order parameter field. With this method, vortices can be easily described at a resolution even finer than the mesh itself. The precise determination of the vortex cores allows the interplay of the vortices inside a model superconductor to be visualized in higher resolution than has previously been possible. By representing the field as the set of vortices, this method also massively reduces the data footprint of the simulations and provides the data structures for further analysis and feature tracking.

Computational self-assembly of a one-component icosahedral quasicrystal.

Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems.

Digital colloids: reconfigurable clusters as high information density elements.

Through the design and manipulation of discrete, nanoscale systems capable of encoding massive amounts of information, the basic components of computation are open to reinvention. These components will enable tagging, memory storage, and sensing in unusual environments - elementary functions crucial for soft robotics and "wet computing". Here we show how reconfigurable clusters made of N colloidal particles bound flexibly to a central colloidal sphere have the capacity to store an amount of information that increases as O(N ln(N)). Using Brownian dynamics simulations, we predict dynamical regimes that allow for information to be written, saved, and erased. We experimentally assemble an N = 4 reconfigurable cluster from chemically synthesized colloidal building blocks, and monitor its equilibrium dynamics. We observe state switching in agreement with simulations. This cluster can store one bit of information, and represents the simplest digital colloid.

Phase behavior and complex crystal structures of self-assembled tethered nanoparticle telechelics.

Motivated by growing interest in the self-assembly of nanoparticles for applications such as photonics, organic photovoltaics, and DNA-assisted designer crystals, we explore the phase behavior of tethered spherical nanoparticles. Here, a polymer tether is used to geometrically constrain a pair of nanoparticles creating a tethered nanoparticle "telechelic". Using simulation, we examine how varying architectural features, such as the size ratio of the two end-group nanospheres and the length of the flexible tether, affects the self-assembled morphologies. We demonstrate not only that this hybrid building block maintains the same phase diversity as linear triblock copolymers, allowing for a variety of nanoparticle materials to replace polymer blocks, but also that new structures not previously reported are accessible. Our findings imply a robust underlying ordering mechanism is common among these systems, thus allowing flexibility in synthesis approaches to achieve a target morphology.

Self-assembled clusters of spheres related to spherical codes.

We consider the thermodynamically driven self-assembly of spheres onto the surface of a central sphere. This assembly process forms self-limiting, or terminal, anisotropic clusters (N-clusters) with well-defined structures. We use Brownian dynamics to model the assembly of N-clusters varying in size from two to twelve outer spheres and free energy calculations to predict the expected cluster sizes and shapes as a function of temperature and inner particle diameter. We show that the arrangements of outer spheres at finite temperatures are related to spherical codes, an ideal mathematical sequence of points corresponding to the densest possible sphere packings. We demonstrate that temperature and the ratio of the diameters of the inner and outer spheres dictate cluster morphology. We present a surprising result for the equilibrium structure of a 5-cluster, for which the square pyramid arrangement is preferred over a more symmetric structure. We show this result using Brownian dynamics, a Monte Carlo simulation, and a free energy approximation. Our results suggest a promising way to assemble anisotropic building blocks from constituent colloidal spheres.

Effect of nanoparticle polydispersity on the self-assembly of polymer tethered nanospheres.

Recent simulations predict that aggregating nanospheres functionalized with polymer "tethers" can self-assemble to form a cylinder, perforated lamellae, lamellae, and even the double gyroid phase, which are phases also seen in block copolymer and surfactant systems. Nanoparticle size polydispersity is likely to be a characteristic of these systems. If too high, polydispersity may destabilize a phase. Using multiple thermodynamic paths to explore the phase diagram as a function of temperature and polydispersity, we explore the effect of nanosphere size polydispersity on the phase diagram. We show that in the portions of the phase diagram characterized by an icosahedral local nanoparticle packing motif, a low amount of polydispersity lowers the energy and a large amount of polydispersity raises the energy of the system by disrupting the icosahedral packing. In general, regions of the phase diagram characterized by liquid-like icosahedral packing have high terminal polydispersities from 15% to more than 30%. In the regions of the phase diagram characterized by crystalline local packing, polydispersity raises the energy of the system and induces a phase transition from crystalline to liquid-like ordering within the nanosphere rich regions of the microphase. We find the bilayer crystalline lamellae phase has a terminal polydispersity of 6%, but may still be partially crystalline up to 12%.

Optimal filling of shapes.

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal disks. We consider the properties of ideal distributions of N disks as N→∞. We note an analogy with energy landscapes.

A two-temperature model of radiation damage in α-quartz.

Two-temperature models are used to represent the physics of the interaction between atoms and electrons during thermal transients such as radiation damage, laser heating, and cascade simulations. We introduce a two-temperature model applied to an insulator, α-quartz, to model heat deposition in a SiO(2) lattice. Our model of the SiO(2) electronic subsystem is based on quantum simulations of the electronic response in a SiO(2) repeat cell. We observe how the parametrization of the electronic subsystem impacts the degree of permanent amorphization of the lattice, especially compared to a metallic electronic subsystem. The parametrization of the insulator electronic subsystem has a significant effect on the amount of residual defects in the crystal after 10 ps. While recognizing that more development in the application of two-temperature models to insulators is needed, we argue that the inclusion of a simple electronic subsystem substantially improves the realism of such radiation damage simulations.

An energy-conserving two-temperature model of radiation damage in single-component and binary Lennard-Jones crystals.

Two-temperature models are used to represent the interaction between atoms and free electrons during thermal transients such as radiation damage, laser heating, and cascade simulations. In this paper, we introduce an energy-conserving version of an inhomogeneous finite reservoir two-temperature model using a Langevin thermostat to communicate energy between the electronic and atomic subsystems. This energy-conserving modification allows the inhomogeneous two-temperature model to be used for longer and larger simulations and simulations of small energy phenomena, without introducing nonphysical energy fluctuations that may affect simulation results. We test this model on the annealing of Frenkel defects. We find that Frenkel defect annealing is largely indifferent to the electronic subsystem, unless the electronic subsystem is very tightly coupled to the atomic subsystem. We also consider radiation damage due to local deposition of heat in two idealized systems. We first consider radiation damage in a large face-centered-cubic Lennard-Jones (LJ) single-component crystal that readily recrystallizes. Second, we consider radiation damage in a large binary glass-forming LJ crystal that retains permanent damage. We find that the electronic subsystem parameters can influence the way heat is transported through the system and have a significant impact on the number of defects after the heat deposition event. We also find that the two idealized systems have different responses to the electronic subsystem. The single-component LJ system anneals most rapidly with an intermediate electron-ion coupling and a high electronic thermal conductivity. If sufficiently damaged, the binary glass-forming LJ system retains the least permanent damage with both a high electron-ion coupling and a high electronic thermal conductivity. In general, we find that the presence of an electronic gas can affect short and long term material annealing.