Isotropic Pair Research Articles

Anisotropic remixing of a phase separated binary colloidal system with particles of different sizes in an external modulation.

We explore the phase behavior of a binary colloidal system under external spatially periodic modulation. We perform Monte Carlo simulations on a binary mixture of big and small repulsive Lennard-Jones particles with a diameter ratio of 2:1. We characterize structure by isotropic and anisotropic pair correlation functions, cluster size distribution, bond angle distribution, order parameter, and specific heat. We observe the demixing of the species in the absence of external modulation. However, the mixing of the species gets enhanced with increasing potential strength along with the alignment of the particles transverse to the modulation. The de-mixing order parameter shows discontinuity with increasing modulation strength, characterizing a first order phase transition. The peak in specific heat increases linearly with the size of the system. We also look into the dynamical behavior of the system via computing Mean Square Displacement (MSD) along both parallel and perpendicular directions to the modulation. We observe a decrease in the diffusion coefficient for both types of particles as we increase the strength of the modulation.

Local Structural Features Elucidate Crystallization of Complex Structures.

Complex crystal structures are composed of multiple local environments, and how this type of order emerges spontaneously during crystal growth has yet to be fully understood. We study crystal growth across various structures and along different crystallization pathways, using self-assembly simulations of identical particles that interact via multiwell isotropic pair potentials. We apply an unsupervised machine learning method to features from bond-orientational order metrics to identify different local motifs present during a given structure's crystallization process. In this manner, we distinguish different crystallographic sites in highly complex structures. Tailoring this order parameter to structures of varying complexity and coordination number, we study the emergence of local order along a multistep crystal growth pathway─from a low-density fluid to a high-density, supercooled amorphous liquid droplet and to a bulk crystal. We find a consistent under-coordination of the liquid relative to the average coordination number in the bulk crystal. We use our order parameter to analyze the geometrically frustrated growth of a Frank-Kasper phase and discover how structural defects compete with the formation of crystallographic sites that are more high-coordinated than the liquid environments. The method presented here for classifying order on a particle-by-particle level has broad applicability to future studies of structural self-assembly and crystal growth, and they can aid in the design of building blocks and for targeting pathways of formation of soft-matter structures.

Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions

Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions

Mean-field model for a mixture of biaxial nematogens and dipolar nanoparticles.

We analyze a mean-field model for mixtures involving biaxial nematogens and dipolar nanoparticles, taking into account not only orientational and isotropic pair interactions between nematogens but also orientational nematogen-nanoparticle interactions. We determine bulk equilibrium phase diagrams for a wide range of interaction strengths, identifying in each case the effect of the nanoparticles on the stability of nematic phases and on the appearance of multicritical points. Special attention is given to the limit of a low concentration of nanoparticles, in which their effect on the temperatures of both the first-order uniaxial-isotropic and the continuous biaxial-uniaxial transitions is investigated in detail.

Observation of long-range anisotropy in a vapor-deposited metallic glass

The mesoscopic structure of amorphous materials remains to be understood. Although amorphous systems are often thought to be randomly structured beyond short-range ordering, a number of studies reveal the importance of medium-range ordering up to a few nanometers. Here, using a newly available high-flux nano-focused X-ray beam, we observe anisotropy in a vapor-deposited PdCuSi metallic glass even in a large probed volume of around 60 nm × 60 nm × 5 μm. With annealing, the anisotropy disappears without crystallization. The observations allow us to exclude alternative explanations including geometric and strain effects, leading to the conclusion that the anisotropy must arise from structural correlations. Our results suggest that anisotropy may persist even to macroscopic scales in amorphous materials, pointing out the need for structural descriptions of glasses beyond isotropic pair correlation functions as well as the possibility to realize glassy structures with long-range correlations.

Many-Body Neural Network-Based Force Field for Structure-Based Coarse-Graining of Water.

High-fidelity results from atomistic simulations can only be obtained by using accurate force-field (FF) parameters. Although empirical FFs are commonly used in the modeling of atomistic systems due to their simplicity, they have many limitations inherent in the crude approximations associated with their analytical form. Recent advances in neural network-based FFs have led to more accurate FFs by using symmetry functions or full many-body expansions. However, this approach leads to several issues including the arbitrariness of the symmetry functions, and the intangible and uninterpretable interactions which are only known once the positions of all atoms are set. More importantly, training is another bottleneck, as high-quality force and energy information is required, which is usually not accessible from experimental data. To solve these issues within the context of structure-based coarse-graining methods, we switch in this work to a local-search method to target the reference structure instead of using conventional backpropagation algorithms used to target the forces and energies of the reference structure. Our FF is decomposed into two-, three-, and higher-order terms, where each term is modeled with a separate neural network. To show the versatility of our method, we study four different systems, namely, Stillinger-Weber particles as an atomistic case and three water models, namely SPC/E, MB-pol, and ab initio, as coarse-graining cases. We show the successful application of our approach, by reproducing structural properties of different water models, followed by providing insight into the role of two-and three-body interactions. The results of all models indicate that the double-well isotropic pair potential, the signature of water-like behavior in an isotropic system, vanishes upon inclusion of the three-body interaction, showing dominance of the three-body interaction over the two-body interaction in water-like behavior with the single-well isotropic pair potential.

Inverse design of isotropic pair potentials using digital alchemy with a generalized Fourier potential

Inverse design of isotropic pair potentials using digital alchemy with a generalized Fourier potential

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.

BoltzmaNN: Predicting effective pair potentials and equations of state using neural networks.

Neural networks (NNs) are employed to predict equations of state from a given isotropic pair potential using the virial expansion of the pressure. The NNs are trained with data from molecular dynamics simulations of monoatomic gases and liquids, sampled in the NVT ensemble at various densities. We find that the NNs provide much more accurate results compared to the analytic low-density limit estimate of the second virial coefficient and the Carnahan-Starling equation of state for hard sphere liquids. Furthermore, we design and train NNs for computing (effective) pair potentials from radial pair distribution functions, g(r), a task that is often performed for inverse design and coarse-graining. Providing the NNs with additional information on the forces greatly improves the accuracy of the predictions since more correlations are taken into account; the predicted potentials become smoother, are significantly closer to the target potentials, and are more transferable as a result.

A mean-field approach to simulating anisotropic particles.

We introduce a mean-field theoretical framework for generalizing isotropic pair potentials to anisotropic shapes. This method is suitable for generating pair potentials that can be used in both Monte Carlo and molecular dynamics simulations. We demonstrate the application of this theory by deriving a Lennard-Jones (LJ)-like potential for arbitrary geometries along with a Weeks-Chandler-Anderson-like repulsive variant, showing that the resulting potentials behave very similarly to standard LJ potentials while also providing a nearly conformal mapping of the underlying shape. We then describe an implementation of this potential in the simulation engine HOOMD-blue and discuss the challenges that must be overcome to achieve a sufficiently robust and performant implementation. The resulting potential can be applied to smooth geometries like ellipsoids and to convex polytopes. We contextualize these applications with reference to the existing methods for simulating such particles. The pair potential is validated using standard criteria, and its performance is compared to existing methods for comparable simulations. Finally, we show the results of self-assembly simulations, demonstrating that this method can be used to study the assembly of anisotropic particles into crystal structures.

Continuum Electrostatic Behavior of a 3D-RISM Theory.

The electrostatic response underlying the 3D-RISM theory and its general relationship to models in which the solvent is represented in terms of a dielectric continuum are examined. It is found that the theory provides a coherent picture of solvation, although its behavior is not entirely consistent with the trends that are expected in the limit of a large solute. The electrostatic discrepancy is due to the nature of the isotropic pair additive site-site correlation function associated with the susceptibility response of the uniform fluid. The influence of the discrepancy in the magnitude of the solvation free energy is negligible for a solvent with a large dielectric constant.

Integral-equation theories of fluid phase equilibria in simple fluids

We briefly review the application of integral equation theories (IETs) of the fluid state in order to predict fluid phase equilibria of simple fluids. In spite of the relatively simple picture emerging from an isotropic pair potential, IETs have been instrumental in the last few decades to show a quite complex phase behaviour, where multiple critical points are observed in the phase diagram. The application of thermodynamic self-consistency within the theory is shown to dramatically improve the reliability of IETs, allowing them to become a valid and computationally cheap tool, in comparison to computer simulation, to investigate the limits of stability of the fluid phase.

Nonparametric estimation of the pair correlation function of replicated inhomogeneous point processes

We consider the nonparametric estimation of the isotropic pair correlation function (PCF) of inhomogeneous point processes when replicates are available. Based on carefully designed estimating equations, two types of nonparametric estimators, i.e., the local polynomial estimator and the orthogonal series estimator, are proposed and studied. The proposed estimators circumvent the problems caused by the need for estimating the unknown intensity function for kernel smoothed PCF estimators and they are free of edge correction terms. Asymptotic properties are investigated for both estimators and valid point-wise confidence bands are derived. Finite sample performances of the proposed estimators are demonstrated by simulation as well as an application to the Sina Weibo posting data.

Analysis of Self-Assembly Pathways with Unsupervised Machine Learning Algorithms.

Colloidal and nanoparticle systems display a rich and exciting phase behavior including the self-assembly of highly complex crystal structures. Nucleation and growth pathways toward crystallization have been studied both computationally and experimentally, but the mechanisms for the formation of the precritical nucleus and consequent crystal growth are yet to be fully understood. Recent advances in the application of machine learning algorithms applied to many-particle systems have led to significant breakthroughs in the ability for high-throughput analysis of phase transitions and the identification of crystal structures. We build upon these techniques to identify and analyze pathways for nucleation and growth in supercooled liquids of colloidal systems modeled with isotropic pair potentials. Our study involves the development of unsupervised machine learning models trained on spherical-harmonics-based descriptors. These models allow us to determine clusters of local environments that are present prior to and during crystallization. We analyze these environments to identify prevalent motifs and local order within the supercooled liquid prior to formation of the critical nucleus.

On algebraic properties of the sub-block of zero field hyperfine Hamiltonian with penultimate total spin projection for arbitrary hyperfine structure, and field dependence of radical pair recombination probability in the vicinity of zero field.

Basic algebraic arguments demonstrate that the probability of radical pair recombination in low field for an arbitrary pair with Hamiltonian confined to Zeeman and isotropic hyperfine interactions contains two additive contributions linear with applied field with equal, but opposite in sign, proportionality factors. Their weights are determined by the probability of having all nuclear spins along the field in the initial electron-singlet state of the pair, and in the case of equilibrium with respect to nuclear spins, the two contributions completely compensate the field dependences of each other, producing an additive term in the singlet yield with zero derivative. However, if the nuclear set is polarized, a linear skew proportional to polarization appears, introducing anisotropy in the intrinsically spherically symmetric system. The key element in this derivation is guaranteed nondegeneracy of the eigenvalues of the "penultimate" (Mmax - 1) block of the Hamiltonian for a radical with any number of distinct spin-1/2 nuclei in zero field, which leads to guaranteed applicability of the first-order nondegenerate perturbation theory with nonvanishing linear in field admixture of states, persisting all the way into the final expression for singlet yield for a pair with an arbitrary isotropic hyperfine structure. We argue that this behavior of the field dependence of recombination yield is representative of a radical pair of an arbitrarily complex hyperfine structure; this may be a possible mechanism for anisotropic response ("chemical compass") for an isotropic radical pair based system with isotropic-only internal interactions and anisotropy introduced via the initial state of nuclei, while such an approach may complement the usually needed numerical simulations.

Event-chain Monte Carlo simulations of the liquid to solid transition of two-dimensional decagonal colloidal quasicrystals

In event-chain Monte Carlo simulations, we model colloidal particles in two dimensions that interact according to an isotropic short-ranged pair potential which supports the two typical length scales present in decagonal quasicrystals. We investigate the assembled structures as we vary the density and temperature. Our special interest is related to the transition from quasicrystal to liquid. In contrast to the KTHNY melting theory for quasicrystals which predicts an intermediate pentahedratic phase, we find a one-step first-order melting transition. However, we discover that the slow relaxation of phasonic flips, i.e. rearrangements of the particles due to additional degrees of freedom in quasicrystals, changes the positional correlation functions, to the extent that structures with long-range orientational correlations, but exponentially decaying positional correlations, are observed.

Stabilizing quasicrystals composed of patchy colloids by narrowing the patch width

We explore the behavior of two-dimensional patchy colloidal particles with 8 or 10 symmetrically arranged patches by employing Monte Carlo simulations. The particles interact according to an isotropic pair potential that possesses only one typical length. The patches lead to additional attractions that are anisotropic and depend on the relative orientation of two neighboring particles. We investigate the assembled structures with a special interest in quasicrystals. We found that the patch width is of great importance: Only in the case of narrow patch widths we are able to observe metastable octagonal and decagonal quasicrystals, while dodecagonal quasicrystals can also occur for broad patches. These results are important to understand the role of interactions with preferred binding angles in order to obtain quasicrystals. Our findings suggest that in the case of sharp binding angles, as they occur in metallic alloys, octagonal and decagonal symmetries might be observed more often than in systems with less sharp binding angles as it is the case in soft-matter systems where dodecagonal quasicrystals dominate.

Assembly of particle strings via isotropic potentials.

Assembly of spherical colloidal particles into extended structures, including linear strings, in the absence of directional interparticle bonding interactions or external perturbation could facilitate the design of new functional materials. Here, we use methods of inverse design to discover isotropic pair potentials that promote the formation of single-stranded, polydisperse strings of colloids "colloidomers" as well as size-specific, compact colloidal clusters. Based on the designed potentials, a simple model pair interaction with a short-range attraction and a longer-range repulsion is proposed which stabilizes a variety of different particle morphologies including (i) dispersed fluid of monomers, (ii) ergodic short particle chains as well as porous networks of percolated strings, (iii) compact clusters, and (iv) thick cylindrical structures including trihelical Bernal spirals.

Revealing a Vacancy Analog of the Crowdion Interstitial in Simple Cubic Crystals.

Vacancies in simple cubic crystals of hard cubes are known to delocalize over one-dimensional chains of several lattice sites. Here, we use computer simulations to examine the structure and dynamics of vacancies in simple cubic crystals formed by hard cubes, right rhombic prisms (slanted cubes), truncated cubes, and particles interacting via a soft isotropic pair potential. We show that these vacancies form a vacancy analog of the crowdion interstitial, generating a strain field which follows a soliton solution of the sine-Gordon equation, and diffusing via a persistent random walk. Surprisingly, we find that the structure of these "voidions" is not significantly affected by changes in density, vacancy concentration, and even particle interaction. We explain this structure quantitatively using a one-dimensional model that includes the free-energy barrier particles have to overcome to slide between lattice sites and the effective pair interaction along this line. We argue that voidions are a robust phenomenon in systems of repulsive particles forming simple cubic crystals.

Inverse design of simple pair potentials for the self-assembly of complex structures.

The synthesis of complex materials through the self-assembly of particles at the nanoscale provides opportunities for the realization of novel material properties. However, the inverse design process to create experimentally feasible interparticle interaction strategies is uniquely challenging. Standard methods for the optimization of isotropic pair potentials tend toward overfitting, resulting in solutions with too many features and length scales that are challenging to map to mechanistic models. Here we introduce a method for the optimization of simple pair potentials that minimizes the relative entropy of the complex target structure while directly considering only those length scales most relevant for self-assembly. Our approach maximizes the relative information of a target pair distribution function with respect to an ansatz distribution function via an iterative update process. During this process, we filter high frequencies from the Fourier spectrum of the pair potential, resulting in interaction potentials that are smoother and simpler in real space and therefore likely easier to make. We show that pair potentials obtained by this method assemble their target structure more robustly with respect to optimization method parameters than potentials optimized without filtering.