Treating random sequential addition via the replica method.

While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition.

First principles reactive simulation for equation of state prediction.

The high cost of density functional theory (DFT) has hitherto limited the ab initio prediction of the equation of state (EOS). In this article, we employ a combination of large scale computing, advanced simulation techniques, and smart data science strategies to provide an unprecedented ab initio performance analysis of the high explosive pentaerythritol tetranitrate (PETN). Comparison to both experiment and thermochemical predictions reveals important quantitative limitations of DFT for EOS prediction and thus the assessment of high explosives. In particular, we find that DFT predicts the energy of PETN detonation products to be systematically too high relative to the unreacted neat crystalline material, resulting in an underprediction of the detonation velocity, pressure, and temperature at the Chapman-Jouguet state. The energetic bias can be partially accounted for by high-level electronic structure calculations of the product molecules. We also demonstrate a modeling strategy for mapping chemical composition across a wide parameter space with limited numerical data, the results of which suggest additional molecular species to consider in thermochemical modeling.

Gelation of plasmonic metal oxide nanocrystals by polymer-induced depletion attractions.

Gelation of colloidal nanocrystals emerged as a strategy to preserve inherent nanoscale properties in multiscale architectures. However, available gelation methods to directly form self-supported nanocrystal networks struggle to reliably control nanoscale optical phenomena such as photoluminescence and localized surface plasmon resonance (LSPR) across nanocrystal systems due to processing variabilities. Here, we report on an alternative gelation method based on physical internanocrystal interactions: short-range depletion attractions balanced by long-range electrostatic repulsions. The latter are established by removing the native organic ligands that passivate tin-doped indium oxide (ITO) nanocrystals while the former are introduced by mixing with small PEG chains. As we incorporate increasing concentrations of PEG, we observe a reentrant phase behavior featuring two favorable gelation windows; the first arises from bridging effects while the second is attributed to depletion attractions according to phase behavior predicted by our unified theoretical model. Our assembled nanocrystals remain discrete within the gel network, based on X-ray scattering and high-resolution transmission electron microscopy. The infrared optical response of the gels is reflective of both the nanocrystal building blocks and the network architecture, being characteristic of ITO nanocrystals' LSPR with coupling interactions between neighboring nanocrystals.

Inverse methods for design of soft materials.

Functional soft materials, comprising colloidal and molecular building blocks that self-organize into complex structures as a result of their tunable interactions, enable a wide array of technological applications. Inverse methods provide a systematic means for navigating their inherently high-dimensional design spaces to create materials with targeted properties. While multiple physically motivated inverse strategies have been successfully implemented in silico, their translation to guiding experimental materials discovery has thus far been limited to a handful of proof-of-concept studies. In this perspective, we discuss recent advances in inverse methods for design of soft materials that address two challenges: (1) methodological limitations that prevent such approaches from satisfying design constraints and (2) computational challenges that limit the size and complexity of systems that can be addressed. Strategies that leverage machine learning have proven particularly effective, including methods to discover order parameters that characterize complex structural motifs and schemes to efficiently compute macroscopic properties from the underlying structure. We also highlight promising opportunities to improve the experimental realizability of materials designed computationally, including discovery of materials with functionality at multiple thermodynamic states, design of externally directed assembly protocols that are simple to implement in experiments, and strategies to improve the accuracy and computational efficiency of experimentally relevant models.

The role of pressure in inverse design for assembly.

Isotropic pairwise interactions that promote the self-assembly of complex particle morphologies have been discovered by inverse design strategies derived from the molecular coarse-graining literature. While such approaches provide an avenue to reproduce structural correlations, thermodynamic quantities such as the pressure have typically not been considered in self-assembly applications. In this work, we demonstrate that relative entropy optimization can be used to discover potentials that self-assemble into targeted cluster morphologies with a prescribed pressure when the iterative simulations are performed in the isothermal-isobaric ensemble. The benefits of this approach are twofold. First, the structure and the thermodynamics associated with the optimized interaction can be controlled simultaneously. Second, by varying the pressure in the optimization, a family of interparticle potentials that all self-assemble the same structure can be systematically discovered, allowing for a deeper understanding of self-assembly of a given target structure and providing multiple assembly routes for its realization. Selecting an appropriate simulation ensemble to control the thermodynamic properties of interest is a general design strategy that could also be used to discover interaction potentials that self-assemble structures having, for example, a specified chemical potential.

Structure and phase behavior of polymer-linked colloidal gels.

Low-density "equilibrium" gels that consist of a percolated, kinetically arrested network of colloidal particles and are resilient to aging can be fabricated by restricting the number of effective bonds that form between the colloids. Valence-restricted patchy particles have long served as one archetypal example of such materials, but equilibrium gels can also be realized through a synthetically simpler and scalable strategy that introduces a secondary linker, such as a small ditopic molecule, to mediate the bonds between the colloids. Here, we consider the case where the ditopic linker molecules are low-molecular-weight polymers and demonstrate using a model colloid-polymer mixture how macroscopic properties such as the phase behavior as well as the microstructure of the gel can be designed through the polymer molecular weight and concentration. The low-density window for equilibrium gel formation is favorably expanded using longer linkers while necessarily increasing the spacing between all colloids. However, we show that blends of linkers with different sizes enable wider variation in microstructure for a given target phase behavior. Our computational study suggests a robust and tunable strategy for the experimental realization of equilibrium colloidal gels.

Communication: From close-packed to topologically close-packed: Formation of Laves phases in moderately polydisperse hard-sphere mixtures.

Particle size polydispersity can help to inhibit crystallization of the hard-sphere fluid into close-packed structures at high packing fractions and thus is often employed to create model glass-forming systems. Nonetheless, it is known that hard-sphere mixtures with modest polydispersity still have ordered ground states. Here, we demonstrate by computer simulation that hard-sphere mixtures with increased polydispersity fractionate on the basis of particle size and a bimodal subpopulation favors the formation of topologically close-packed C14 and C15 Laves phases in coexistence with a disordered phase. The generality of this result is supported by simulations of hard-sphere mixtures with particle-size distributions of four different forms.

Inverse design of multicomponent assemblies.

Inverse design can be a useful strategy for discovering interactions that drive particles to spontaneously self-assemble into a desired structure. Here, we extend an inverse design methodology-relative entropy optimization-to determine isotropic interactions that promote assembly of targeted multicomponent phases, and we apply this extension to design interactions for a variety of binary crystals ranging from compact triangular and square architectures to highly open structures with dodecagonal and octadecagonal motifs. We compare the resulting optimized (self- and cross) interactions for the binary assemblies to those obtained from optimization of analogous single-component systems. This comparison reveals that self-interactions act as a "primer" to position particles at approximately correct coordination shell distances, while cross interactions act as the "binder" that refines and locks the system into the desired configuration. For simpler binary targets, it is possible to successfully design self-assembling systems while restricting one of these interaction types to be a hard-core-like potential. However, optimization of both self- and cross interaction types appears necessary to design for assembly of more complex or open structures.

Interactions and design rules for assembly of porous colloidal mesophases.

Porous mesophases, where well-defined particle-depleted 'void' spaces are present within a particle-rich background fluid, can be self-assembled from colloidal particles interacting via isotropic pair interactions with competing attractions and repulsions. While such structures could be of wide interest for technological applications (e.g., filtration, catalysis, absorption, etc.), relatively few studies have investigated the interactions that lead to these morphologies and how they compare to those that produce other micro-phase-separated structures, such as clusters. In this work, we use inverse methods of statistical mechanics to design model isotropic pair potentials that form porous mesophases. We characterize the resulting porous structures, correlating features of the pair potential with the targeted pore size and the particle packing fraction. The former is primarily encoded by the amplitude and range of the repulsive barrier of the designed pair potential and the latter by the attractive well depth. We observe a trade-off with respect to the packing fraction of the targeted morphology: greater values support more spherical and monodisperse pores that themselves organize into periodic structures, while lower values yield more mobile pores that do not assemble into ordered structures but remain stable over a larger range of packing fraction. We conclude by commenting on the limitations of targeting a specific pore diameter within the present inverse design approach as well as by describing future directions to overcome these limitations.

Assembly of nothing: equilibrium fluids with designed structured porosity.

Controlled micro- to meso-scale porosity is a common materials design goal with possible applications ranging from molecular gas adsorption to particle size selective permeability or solubility. Here, we use inverse methods of statistical mechanics to design an isotropic pair interaction that, in the absence of an external field, assembles particles into an inhomogeneous fluid matrix surrounding pores of prescribed size ordered in a lattice morphology. The pore size can be tuned via modification of temperature or particle concentration. Moreover, modulating density reveals a rich series of microphase-separated morphologies including pore- or particle-based lattices, pore- or particle-based columns, and bicontinuous or lamellar structures. Sensitivity of pore assembly to the form of the designed interaction potential is explored.

Linking Semiconductor Nanocrystals into Gel Networks through All-Inorganic Bridges.

For colloidal semiconductor nanocrystals (NCs), replacement of insulating organic capping ligands with chemically diverse inorganic clusters enables the development of functional solids in which adjacent NCs are strongly coupled. Yet controlled assembly methods are lacking to direct the arrangement of charged, inorganic cluster-capped NCs into open networks. Herein, we introduce coordination bonds between the clusters capping the NCs thus linking the NCs into highly open gel networks. As linking cations (Pt(2+)) are added to dilute (under 1 vol %) chalcogenidometallate-capped CdSe NC dispersions, the NCs first form clusters, then gels with viscoelastic properties. The phase behavior of the gels for variable [Pt(2+)] suggests they may represent nanoscale analogues of bridged particle gels, which have been observed to form in certain polymer colloidal suspensions.

Directing colloidal assembly and a metal-insulator transition using a quench-disordered porous rod template.

Replica and effective-medium theory methods are employed to elucidate how to massively reconfigure a colloidal assembly to achieve globally homogeneous, strongly clustered, and percolated equilibrium states of high electrical conductivity at low physical volume fractions. A key idea is to employ a quench-disordered, large-mesh rigid-rod network as a templating internal field. By exploiting bulk phase separation frustration and the tunable competing processes of colloid adsorption on the low-dimensional network and fluctuation-driven colloid clustering in the pore spaces, two distinct spatial organizations of greatly enhanced particle contacts can be achieved. As a result, a continuous, but very abrupt, transition from an insulating to metallic-like state can be realized via a small change of either the colloid-template or colloid-colloid attraction strength. The approach is generalizable to more complicated template or colloidal architectures.

Machine Learning Potentials with the Iterative Boltzmann Inversion: Training to Experiment.

Methodologies for training machine learning potentials (MLPs) with quantum-mechanical simulation data have recently seen tremendous progress. Experimental data have a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on iterative Boltzmann inversion that produces a pair potential correction to an existing MLP using equilibrium radial distribution function data. By applying these corrections to an MLP for pure aluminum based on density functional theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require autodifferentiating through a molecular dynamics solver and does not make assumptions about the MLP architecture. Our results suggest a practical framework for incorporating experimental data into machine learning models to improve the accuracy of molecular dynamics simulations.

Exploring the frontiers of condensed-phase chemistry with a general reactive machine learning potential.

Atomistic simulation has a broad range of applications from drug design to materials discovery. Machine learning interatomic potentials (MLIPs) have become an efficient alternative to computationally expensive ab initio simulations. For this reason, chemistry and materials science would greatly benefit from a general reactive MLIP, that is, an MLIP that is applicable to a broad range of reactive chemistry without the need for refitting. Here we develop a general reactive MLIP (ANI-1xnr) through automated sampling of condensed-phase reactions. ANI-1xnr is then applied to study five distinct systems: carbon solid-phase nucleation, graphene ring formation from acetylene, biofuel additives, combustion of methane and the spontaneous formation of glycine from early earth small molecules. In all studies, ANI-1xnr closely matches experiment (when available) and/or previous studies using traditional model chemistry methods. As such, ANI-1xnr proves to be a highly general reactive MLIP for C, H, N and O elements in the condensed phase, enabling high-throughput in silico reactive chemistry experimentation.

First-Principles Simulations of CuCl in High-Temperature Water Vapor.

Experimental data suggest that the solubility of copper in high-temperature water vapor is controlled by the formation of hydrated clusters of the form CuCl(H2O)n, where the average number of water molecules in the cluster generally increases with increasing density [Migdisov, A. A.; et al. Geochim. Cosmochim. Acta 2014, 129, 33-53]. However, the precise nature of these clusters is difficult to probe experimentally. Moreover, there are some discrepancies between experimental estimates of average cluster size and prior simulation work [Mei, Y. Geofluids 2018, 2018, 4279124]. We have performed first-principles Monte Carlo (MC) and molecular dynamics (MD) simulations to explore these clusters in finer detail. We find that molecular dynamics is not the most appropriate technique for studying aggregation in vapor phases, even at relatively high temperatures. Specifically, our MD simulations exhibit substantial problems in adequately sampling the equilibrium cluster size distribution. In contrast, MC simulations with specialized cluster moves are able to accurately sample the phase space of hydrogen-bonding vapors. At all densities, we find a stable, slightly distorted linear H2O-Cu-Cl structure, which is in agreement with the earlier simulations, surrounded by a variable number of water molecules. The surrounding water molecules do not form a well-defined second solvation shell but rather a loose network of hydrogen-bonded water with molecular CuCl on the outside edge of the water cluster. We also find a broad distribution of hydration numbers, especially at higher densities. In contrast to previous simulation work but in agreement with experimental data, we find that the average hydration number substantially increases with increasing density. Moreover, the value of the hydration number depends on the choice of cluster definition.

Accelerating Ab Initio Simulation via Nested Monte Carlo and Machine Learned Reference Potentials.

As a corollary of the rapid advances in computing, ab initio simulation is playing an increasingly important role in modeling materials at the atomic scale. Two strategies are possible, ab initio Monte Carlo (AIMC) and molecular dynamics (AIMD) simulation. The former benefits from exact sampling from the correct thermodynamic distribution, while the latter is typically more efficient with its collective all-atom coordinate updates. Here, using a relatively simple test model comprised of helium and argon, we show that AIMC can be brought up to, and even above, the performance levels of AIMD via a hybrid nested sampling/machine learning (ML) strategy. Here, ML provides an accurate classical reference potential (up to three-body explicit interactions) that can pilot long collective Monte Carlo moves that are accepted or rejected in toto à la nested Monte Carlo (NMC); this is in contrast to the single move nature of a naive implementation. Our proposed method only requires a small up front expense from evaluating the ab initio energies and forces of [Formula: see text](100) random configurations for training. Importantly, our method does not totally rely on the trained, assuredly imperfect, interaction. We show that high performance and exact sampling at the desired level of theory can be realized even when the trained interaction has appreciable differences from the ab initio potential. Remarkably, at the highest levels of performance realized via our approach, a pair of statistically uncorrelated atomic configurations can be generated with [Formula: see text](1) ab initio calculations.

Inverse Design of Self-Assembling Frank-Kasper Phases and Insights Into Emergent Quasicrystals.

We discuss how a machine learning approach based on relative entropy optimization can be used as an inverse design strategy to discover isotropic pair interactions that self-assemble single- or multicomponent particle systems into Frank-Kasper phases. In doing so, we also gain insights into the self-assembly of quasicrystals.

Origin and detection of microstructural clustering in fluids with spatial-range competitive interactions.

Fluids with competing short-range attractions and long-range repulsions mimic dispersions of charge-stabilized colloids that can display equilibrium structures with intermediate-range order (IRO), including particle clusters. Using simulations and analytical theory, we demonstrate how to detect cluster formation in such systems from the static structure factor and elucidate links to macrophase separation in purely attractive reference fluids. We find that clusters emerge when the thermal correlation length encoded in the IRO peak of the structure factor exceeds the characteristic length scale of interparticle repulsions. We also identify qualitative differences between the dynamics of systems that form amorphous versus microcrystalline clusters.