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relentless is an open-source Python package that enables the optimization of objective functions computed using molecular dynamics simulations. It has a high-level, extensible interface for model parameterization; setting up, running, and analyzing simulations natively in established software packages; and gradient-based optimization. We describe the design and implementation of relentless in the context of relative entropy minimization, and we demonstrate its abilities to design pairwise interactions between particles that form targeted structures. relentless aims to streamline the development of computational materials design methodologies and promote the transparency and reproducibility of complex workflows integrating molecular dynamics simulations., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Understanding how colloidal soft materials interact with light is crucial to the rational design of optical metamaterials. Electromagnetic simulations are computationally expensive and have primarily been limited to model systems described by a small number of particles-dimers, small clusters, and small periodic unit cells of superlattices. In this work we study the optical properties of bulk, disordered materials comprising a large number of plasmonic colloidal nanoparticles using Brownian dynamics simulations and the mutual polarization method. We investigate the far-field and near-field optical properties of both colloidal fluids and gels, which require thousands of nanoparticles to describe statistically. We show that these disordered materials exhibit a distribution of particle-level plasmonic resonance frequencies that determines their ensemble optical response. Nanoparticles with similar resonant frequencies form anisotropic and oriented clusters embedded within the otherwise isotropic and disordered microstructures. These collectively resonating morphologies can be tuned with the frequency and polarization of incident light. Knowledge of particle resonant distributions may help to interpret and compare the optical responses of different colloidal structures, correlate and predict optical properties, and rationally design soft materials for applications harnessing light.

The optical properties of disordered plasmonic nanoparticle assemblies can be continuously tuned through the structural organization and composition of their colloidal building blocks. However, progress in the design and experimental realization of these materials has been limited by challenges associated with controlling and characterizing disordered assemblies and predicting their optical properties. This Perspective discusses integrated studies of experimental assembly of disordered optical materials, such as doped metal oxide nanocrystal gels and metasurfaces, with electromagnetic computations on large-scale simulated structures. The simulations prove vital for connecting experimental parameters to disordered structural motifs and optical properties, revealing structure-property relations that inform design choices. Opportunities are identified for optimizing optical property designs for disordered materials using computational inverse methods and tools from machine learning.

Nanocrystal gels exhibit collective optical phenomena based on interactions among their constituent building blocks. However, their inherently disordered structures have made it challenging to understand, predict, or design properties such as optical absorption spectra that are sensitive to the coupling between the plasmon resonances of the individual nanocrystals. Here, we bring indium tin oxide nanocrystal gels under chemical control and show that their infrared absorption can be predicted and systematically tuned by selecting the nanocrystal sizes and compositions and molecular structures of the link-mediating surface ligands. Thermoreversible assemblies with metal-terpyridine links form reproducible gel architectures, enabling us to derive a plasmon ruler that governs the spectral shifts upon gelation, predicated on the nanocrystal and ligand compositions. This empirical guide is validated using large-scale, many-bodied simulations to compute the optical spectra of gels with varied structural parameters. Based on the derived plasmon ruler, we design and demonstrate a nanocrystal mixture whose spectrum exhibits distinctive line narrowing upon assembly.

Assembling plasmonic nanocrystals in regular superlattices can produce effective optical properties not found in homogeneous materials. However, the range of these metamaterial properties is limited when a single nanocrystal composition is selected for the constituent meta-atoms. Here, we show how continuously varying doping at two length scales, the atomic and nanocrystal scales, enables tuning of both the frequency and bandwidth of the collective plasmon resonance in nanocrystal-based metasurfaces, while these features are inextricably linked in single-component superlattices. Varying the mixing ratio of indium tin oxide nanocrystals with different dopant concentrations, we use large-scale simulations to predict the emergence of a broad infrared spectral region with near-zero permittivity. Experimentally, tunable reflectance and absorption bands are observed, owing to in- and out-of-plane collective resonances. These spectral features and the predicted strong near-field enhancement establish this multiscale doping strategy as a powerful new approach to designing metamaterials for optical applications.

Colloidal suspensions are an ideal model for studying crystallization, nucleation, and glass transition mechanisms, due to the precise control of interparticle interactions by changing the shape, charge, or volume fraction of particles. However, these tuning parameters offer insufficient active control over interparticle interactions and reconfigurability of assembled structures. Dynamic control over the interparticle interactions can be obtained through the application of external magnetic fields that are contactless and chemically inert. In this work, we demonstrate the dual nature of magnetic nanoparticle dispersions to program interactions between suspended nonmagnetic microspheres using an external magnetic field. The nanoparticle dispersion simultaneously behaves as a continuous magnetic medium at the microscale and a discrete medium composed of individual particles at the nanoscale. This enables control over a depletion attractive potential and the introduction of a magnetic repulsive potential, allowing a reversible transition of colloidal structures within a rich phase diagram by applying an external magnetic field. Active control over competing interactions allows us to create a model system encompassing a range of states, from large fractal clusters to low-density Wigner glass states. Monitoring the dynamics of colloidal particles reveals dynamic heterogeneity and a marked slowdown associated with approaching the Wigner glass state.

Optical properties of nanoparticle assemblies reflect distinctive characteristics of their building blocks and spatial organization, giving rise to emergent phenomena. Integrated experimental and computational studies have established design principles connecting the structure to properties for assembled clusters and superlattices. However, conventional electromagnetic simulations are too computationally expensive to treat more complex assemblies. Here we establish a fast, materials agnostic method to simulate the optical response of large nanoparticle assemblies incorporating both structural and compositional complexity. This many-bodied, mutual polarization method resolves limitations of established approaches, achieving rapid, accurate convergence for configurations including thousands of nanoparticles, with some overlapping. We demonstrate these capabilities by reproducing experimental trends and uncovering far- and near-field mechanisms governing the optical response of plasmonic semiconductor nanocrystal assemblies including structurally complex gel networks and compositionally complex mixed binary superlattices. This broadly applicable framework will facilitate the design of complex, hierarchically structured, and dynamic assemblies for desired optical characteristics.

Gelation offers a powerful strategy to assemble plasmonic nanocrystal networks incorporating both the distinctive optical properties of constituent building blocks and customizable collective properties. Beyond what a single-component assembly can offer, the characteristics of nanocrystal networks can be tuned in a broader range when two or more components are intimately combined. Here, we demonstrate mixed nanocrystal gel networks using thermoresponsive metal-terpyridine links that enable rapid gel assembly and disassembly with thermal cycling. Plasmonic indium oxide nanocrystals with different sizes, doping concentrations, and shapes are reliably intermixed in linked gel assemblies, exhibiting collective infrared absorption that reflects the contributions of each component while also deviating systematically from a linear combination of the spectra for single-component gels. We extend a many-bodied, mutual polarization method to simulate the optical response of mixed nanocrystal gels, reproducing the experimental trends with no free parameters and revealing that spectral deviations originate from cross-coupling between nanocrystals with distinct plasmonic properties. Our thermoreversible linking strategy directs the assembly of mixed nanocrystal gels with continuously tunable far- and near-field optical properties that are distinct from those of the building blocks or mixed close-packed structures.

Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical, inverse methods that frame design as a constrained optimization problem present an attractive alternative. However, even efficient algorithms require time- and resource-intensive characterization of material properties many times during optimization, imposing a design bottleneck. Approaches that incorporate machine learning can help address this limitation and accelerate the discovery of materials with targeted properties. In this article, we review how to leverage machine learning to reduce dimensionality in order to effectively explore design space, accelerate property evaluation, and generate unconventional material structures with optimal properties. We also discuss promising future directions, including integration of machine learning into multiple stages of a design algorithm and interpretation of machine learning models to understand how design parameters relate to material properties.

Nanocrystal gels can be responsive, tunable materials, but designing their structure and properties is challenging. By using reversibly bonded molecular linkers, gelation can be realized under conditions predicted by thermodynamics. However, simulations have offered the only microscopic insights, with no experimental means to monitor linking leading to gelation. We introduce a metal coordination linkage with a distinct optical signature allowing us to quantify linking in situ and establish structural and thermodynamic bases for assembly. Because of coupling between linked indium tin oxide nanocrystals, their infrared absorption shifts abruptly at a chemically tunable gelation temperature. We quantify bonding spectroscopically and use molecular simulation to understand temperature-dependent bonding motifs, revealing that gel formation is governed by reaching a critical number of effective links that extend the nanocrystal network. Microscopic insights from our colorimetric linking chemistry enable switchable gels based on thermodynamic principles, opening the door to rational design of programmable nanocrystal networks.

Colloidal nanocrystal gels can be assembled using a difunctional "linker" molecule to mediate bonding between nanocrystals. The conditions for gelation and the structure of the gel are controlled macroscopically by the linker concentration and microscopically by the linker's molecular characteristics. Here, we demonstrate using a toy model for a colloid-linker mixture that linker flexibility plays a key role in determining both phase behavior and the structure of the mixture. We fix the linker length and systematically vary its bending stiffness to span the flexible, semiflexible, and rigid regimes. At fixed linker concentration, flexible-linker and rigid-linker mixtures phase separate at low colloid volume fractions, in agreement with predictions of first-order thermodynamic perturbation theory, but the semiflexible-linker mixtures do not. We correlate and attribute this qualitatively different behavior to undesirable "loop" linking motifs that are predicted to be more prevalent for linkers with end-to-end distances commensurate with the locations of chemical bonding sites on the colloids. Linker flexibility also influences the spacing between linked colloids, suggesting strategies to design gels with desired phase behavior, structure, and, by extension, structure-dependent properties.

Gels assembled from solvent-dispersed nanocrystals are of interest for functional materials because they promise the opportunity to retain distinctive properties of individual nanocrystals combined with tunable, structure-dependent collective behavior. By incorporating stimuli-responsive components, these materials could also be dynamically reconfigured between structurally distinct states. However, nanocrystal gels have so far been formed mostly through irreversible aggregation, which has limited the realization of these possibilities. Meanwhile, gelation strategies for larger colloidal microparticles have been developed using reversible physical or chemical interactions. These approaches have enabled the experimental navigation of theoretically predicted phase diagrams, helping to establish an understanding of how thermodynamic behavior can guide gel formation in these materials. However, the translation of these principles to the nanoscale poses both practical and fundamental challenges. The molecules guiding assembly can no longer be safely assumed to be vanishingly small compared to the particles nor large compared to the solvent.In this Account, we discuss recent progress toward the assembly of tunable nanocrystal gels using two strategies guided by equilibrium considerations: (1) reversible chemical bonding between functionalized nanocrystals and difunctional linker molecules and (2) nonspecific, polymer-induced depletion attractions. The effective nanocrystal attractions, mediated in both approaches by a secondary molecule, compete against stabilizing repulsions to promote reversible assembly. The structure and properties of the nanocrystal gels are controlled microscopically by the design of the secondary molecule and macroscopically by its concentration. This mode of control is compelling because it largely decouples nanocrystal synthesis and functionalization from the design of interactions that drive assembly. Statistical thermodynamic theory and computer simulation have been applied to simple models that describe the bonding motifs in these assembling systems, furnish predictions for conditions under which gelation is likely to occur, and suggest strategies for tuning and disassembling the gel networks. Insights from these models have guided experimental realizations of reversible gels with optical properties in the infrared range that are sensitive to the gel structure. This process avoids time-consuming and costly trial-and-error experimental investigations to accelerate the development of nanocrystal gel assemblies.These advances highlight the need to better understand interactions between nanocrystals, how interactions give rise to gel structure, and properties that emerge. Such an understanding could suggest new approaches for creating stimuli-responsive and dissipative assembled materials whose properties are tunable on demand through directed reconfiguration of the underlying gel microstructure. It may also make nanocrystal gels amenable to computationally guided design using inverse methods to rapidly optimize experimental parameters for targeted functionalities.

We extend Wertheim's thermodynamic perturbation theory to derive the association free energy of a multicomponent mixture for which double bonds can form between any two pairs of the molecules' arbitrary number of bonding sites. This generalization reduces in limiting cases to prior theories that restrict double bonding to at most one pair of sites per molecule. We apply the new theory to an associating mixture of colloidal particles ("colloids") and flexible chain molecules ("linkers"). The linkers have two functional end groups, each of which may bond to one of several sites on the colloids. Due to their flexibility, a significant fraction of linkers can "loop" with both ends bonding to sites on the same colloid instead of bridging sites on different colloids. We use the theory to show that the fraction of linkers in loops depends sensitively on the linker end-to-end distance relative to the colloid bonding-site distance, which suggests strategies for mitigating the loop formation that may otherwise hinder linker-mediated colloidal assembly.

Colloids dispersed in electrolytes and exposed to an electric field produce a locally polarized cloud of ions around them. Above a critical electric field strength, an instability occurs causing these ion clouds to break symmetry leading to spontaneous rotation of particles about an axis orthogonal to the applied field, a phenomenon named Quincke rotation. In this Letter, we characterize a new mode of electrokinetic transport. If the colloids have a net charge, Quincke rotation couples with electrophoretic motion and propels particles in a direction orthogonal to both the applied field and the axis of rotation. This motion is a spontaneous, electrokinetic analogue to the well-known Magnus effect. Typically, motion orthogonal to a field requires anisotropy in particle shape, dielectric properties, or boundary geometry. Here, the electrokinetic Magnus (EKM) effect occurs for spheres with isotropic properties in an unbounded environment, with the Quincke rotation instability providing the broken symmetry needed to drive orthogonal motion. We study the EKM effect using explicit ion, Brownian dynamics simulations and develop a simple, continuum, analytic electrokinetic theory, which are in agreement. We also explain how nonlinearities in the theoretical description of the ions affect Quincke rotation and the EKM effect.

Nanocrystal gelation provides a powerful framework to translate nanoscale properties into bulk materials and to engineer emergent properties through the assembled microstructure. However, many established gelation strategies rely on chemical reactions and specific interactions, e.g., stabilizing ligands or ions on the nanocrystals' surfaces, and are therefore not easily transferable. Here, we report a general gelation strategy via nonspecific and purely entropic depletion attractions applied to three types of metal oxide nanocrystals. The gelation thresholds of two compositionally distinct spherical nanocrystals agree quantitatively, demonstrating the adaptability of the approach for different chemistries. Consistent with theoretical phase behavior predictions, nanocrystal cubes form gels at a lower polymer concentration than nanocrystal spheres, allowing shape to serve as a handle to control gelation. These results suggest that the fundamental underpinnings of depletion-driven assembly, traditionally associated with larger colloidal particles, are also applicable at the nanoscale.

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.

Dispersions of paramagnetic colloids can be manipulated with external magnetic fields to assemble structures via dipolar assembly and control transport via magnetophoresis. For fields held steady in time, the dispersion structure and dynamic properties are coupled. This coupling can be problematic when designing processes involving field-induced forces, as particle aggregation competes against and hinders particle transport. Time-varying fields drive dispersions out-of-equilibrium, allowing the structure and dynamics to be tuned independently. Rotating the magnetic field direction using two biaxial fields is a particularly effective mode of time-variation and has been used experimentally to enhance particle transport. Fundamental transport properties, like the diffusivity and magnetophoretic mobility, dictate dispersions' out-of-equilibrium responses to such time-varying fields, and are therefore crucial to understand to effectively design processes utilizing rotating fields. However, a systematic study of these dynamic quantities in rotating fields has not been performed. Here, we investigate the transport properties of dispersions of paramagnetic colloids in rotating magnetic fields using dynamic simulations. We find that self-diffusion of particles is enhanced in rotating fields compared to steady fields, and that the self-diffusivity in the plane of rotation reaches a maximum value at intermediate rotation frequencies that is larger than the Stokes-Einstein diffusivity of an isolated particle. We also show that, while the magnetophoretic velocity of particles through the bulk in a field gradient decreases with increasing rotation frequency, the enhanced in-plane diffusion allows for faster magnetophoretic transport through porous materials in rotating fields. We examine the effect of porous confinement on the transport properties in rotating fields and find enhanced diffusion at all pore sizes. The confined and bulk values of the transport properties are leveraged in simple models of magnetophoresis through tortuous porous media.

Colloidal systems that undergo gelation attract much attention in both fundamental studies and practical applications. Rational tuning of interparticle interactions allows researchers to precisely engineer colloidal material properties and microstructures. Here, contrary to the traditional approaches where modulating attractive interactions is the major focus, we present a platform wherein colloidal gelation is controlled by tuning repulsive interactions. By including amphiphilic oligomers in colloidal suspensions, the ionic surfactants on the colloids are replaced by the nonionic oligomer surfactants at elevated temperatures, leading to a decrease in electrostatic repulsion. The mechanism is examined by carefully characterizing the colloids, and subsequently allowing the construction of interparticle potentials to capture the material behaviors. With the thermally triggered surfactant displacement, the dispersion assembles into a macroporous viscoelastic network and the gelling mechanism is robust over a wide range of compositions, colloid sizes, and component chemistries. This stimulus-responsive gelation platform is general and offers new strategies to engineer complex viscoelastic soft materials.

A diverse set of functional materials can be fabricated by assembling dispersions of colloids and nanoparticles. Two principal engineering challenges prevent efficient production of these materials: first, scalable synthesis of particles with carefully tailored interactions required to generate complex structures, and second, the propensity of such materials to arrest in undesirable metastable states. Active assembly processes, such as dynamic, directed self-assembly in which the interactions among particles are externally controlled and vary over time, offer a promising method to address these challenges. For dispersions of polarizable dielectric or paramagnetic nanoparticles, an effective mode of active assembly can be achieved by toggling an external electric or magnetic field, which induces attractive particle interactions, on and off cyclically over time. Here, we develop computational and theoretical models for such active assembly processes and find that cyclically toggling the external field leads to growth of colloidal crystals at significantly faster rates and with many fewer defects than for assembly in a steady field. The active process stabilizes phases that are only metastable in steady fields, including a dense fluid phase and body-centered orthorhombic crystals. The growth mechanism and terminal structure of the dispersion are easily controlled by the toggling protocol, and the toggle parameters can be used to continuously transmute between crystal structures with different lattice parameters. Finally, we show how results from linear irreversible thermodynamics can be used to predict the dissipative terminal states of the active assembly process in terms of parameters of the toggling protocol.

Directed assembly of dielectric and paramagnetic nanoparticles can be used to synthesize diverse functional materials that polarize in response to an externally applied electric or magnetic field. However, theories capable of predicting the self-assembled states are lacking. In the proposed work, we develop a complete thermodynamic description of such assemblies for spherical nanoparticles. We show how an important physical feature of these types of particles, mutual polarization, sculpts the free energy landscape and has a remarkably strong influence on the nature of the self-assembled states. Modeling the mutual polarization among nanoparticles requires solving a many-bodied problem for the particle dipole moments. Typically, this computationally expensive task is avoided by neglecting mutual polarization and assuming that each particle in a concentrated dispersion acquires the same dipole moment as a single, isolated particle. Although valid in the limit of small dielectric or permeability contrasts between particles and solvent, this constant dipole assumption leads to qualitatively incorrect predictions for coexisting phases in equilibrium at large dielectric or permeability contrasts. Correctly accounting for mutual polarization enables a thermodynamic theory that describes the equilibrium phase diagram of polarizable dispersions in terms of experimentally controllable variables. Our theoretical predictions agree with the phase behavior we observe in dynamic simulations of these dispersions as well as that in experiments of field-directed structural transitions. In contrast to predictions of a constant dipole model, we find that dispersions of particles with different dielectric constants or magnetic permeabilities exhibit qualitatively different phase behavior. This new model also predicts the existence of a eutectic point at which two crystalline phases and a disordered phase of nanoparticles all simultaneously coexist.

Ordered materials passively self-assembled from dispersions of nanoparticles with steady interactions are subject to thermodynamic constraints on their phase separation kinetics forcing a trade-off between throughput and quality. Dynamically self-assembling dispersions whose interactions vary in a controlled way with time do not have these constraints and can rapidly form ordered structures while avoiding kinetic arrest. These out-of-equilibrium processes cannot be understood in terms of equilibrium thermodynamics or kinetic models derived from equilibrium thermodynamics, so new theories must be developed before dynamic self-assembly can be used to reliably fabricate nanomaterials. Here, we use dynamic simulation and theory to study the self-assembly kinetics of a monodisperse suspension of spherical nanoparticles interacting with a short-ranged, isotropic attraction that is toggled on and off cyclically in time. The rate of phase separation, local and global quality of the self-assembled structures, and range of tunable parameters leading to acceptable self-assembly are all enhanced with toggled attractions compared to steady attractions. The kinetic mechanism and rate of assembly can be easily controlled with the temporal toggling parameters. We develop simple phenomenological expressions to describe and predict the self-assembly rates for two predominant kinetic mechanisms. The first model describes the coarsening of percolated, gel-like networks, and the second describes the nucleation and growth of dense phases.

Crystals self-assembled from nanoparticles have useful properties such as optical activity and sensing capability. During fabrication, however, gelation and glassification often leave these materials arrested in defective or disordered metastable states. This is a key difficulty preventing adoption of self-assembled nanoparticle materials at scale. Processes which suppress kinetic arrest and defect formation while accelerating growth of ordered materials are essential for bottom-up approaches to creating nanomaterials. Dynamic, directed self-assembly processes in which the interactions between self-assembling components are actuated temporally offer one promising methodology for accelerating and controlling bottom-up growth of nanostructures. In this article, we show through simulation and theory how time-dependent, periodically toggled interparticle attractions can avoid kinetic barriers and yield well-ordered crystalline domains for a dispersion of nanoparticles interacting via a short-ranged, isotropic potential. The growth mechanism and terminal structure of the dispersion are controlled by parameters of the toggling protocol. This control allows for selection of processes that yield rapid self-assembled, low defect crystals. Although self-assembly via periodically toggled attractions is inherently unsteady and out-of-equilibrium, its outcome is predicted by a first-principles theory of nonequilibrium thermodynamics. The theory necessitates equality of the time average of pressure and chemical potential in coexisting phases of the dispersion. These quantities are evaluated using well known equations of state. The phase behavior predicted by this theory agrees well with measurements made in Brownian dynamics simulations of sedimentation equilibrium and homogeneous nucleation. The theory can easily be extended to model dynamic self-assembly directed by other toggled conservative force fields.

Objective: Prompted by anecdotal evidence of a higher rate of type 2 diabetes, we set out to investigate the prevalence of diabetes, its risk factors, and co-morbidities among immigrant Guyanese patients being treated in a family medicine health center in Schenectady, New York., Methods: Patients were ascertained from a registration database of all patients aged > or = 30 years who were treated from 2004 to 2006. We then conducted a detailed retrospective chart review of all Guyanese, Caucasian, African American, and Hispanic patients with diabetes and randomly selected non-diabetic controls., Results: Of 222 Guyanese patients, 67 (30.2%) had a diagnosis of diabetes, compared with 47/219 (21.5%) of Hispanics, 132/777 (17.0%) of African Americans, and 442/2834 (15.6%) of Caucasians (P<.0001). Compared with the other racial and ethnic groups, the Guyanese diabetic patients were significantly leaner and more likely to be male., Conclusion: We found a very high prevalence of type 2 diabetes among the Guyanese patient population studied and found unique characteristics when compared with other ethnic and racial groups. These findings have alerted local clinicians to intensify diabetes screening among Guyanese patients. Furthermore, in response to these findings, a broad coalition including public health, clinical, and community groups has been established with the goal of developing culturally appropriate strategies to prevent and control diabetes among Guyanese residents.