Designing DNA-grafted particles that self-assemble into desired crystalline structures using the genetic algorithm

Computation-aided Design of Rod-Shaped Janus Base Nanopieces for Improved Tissue Penetration and Therapeutics Delivery

Despite the development of various drug delivery technologies, there remains a significant need for vehicles that can improve targeting and biodistribution in "hard-to-penetrate" tissues. Some solid tumors, for example, are particularly challenging to penetrate due to their dense extracellular matrix (ECM). In this study, we have formulated a new family of rod-shaped delivery vehicles named Janus base nanopieces (Rod JBNps), which are more slender than conventional spherical nanoparticles, such as lipid nanoparticles (LNPs). These JBNp nanorods are formed by bundles of DNA-inspired Janus base nanotubes (JBNts) with intercalated delivery cargoes. To develop this novel family of delivery vehicles, we employed a computation-aided design (CAD) methodology that includes molecular dynamics and response surface methodology. This approach precisely and efficiently guides experimental designs. Using an ovarian cancer model, we demonstrated that JBNps markedly improve penetration into the dense ECM of solid tumors, leading to better treatment outcomes compared to FDA-approved spherical LNP delivery. This study not only successfully developed a rod-shaped delivery vehicle for improved tissue penetration but also established a CAD methodology to effectively guide material design.

Regulating phase behavior of nanoparticle assemblies through engineering of DNA-mediated isotropic interactions

Self-assembly of isotropically interacting particles into desired crystal structures could allow for creating designed functional materials via simple synthetic means. However, the ability to use isotropic particles to assemble different crystal types remains challenging, especially for generating low-coordinated crystal structures. Here, we demonstrate that isotropic pairwise interparticle interactions can be rationally tuned through the design of DNA shells in a range that allows transition from common, high-coordinated FCC-CuAu and BCC-CsCl lattices, to more exotic symmetries for spherical particles such as the SC-NaCl lattice and to low-coordinated crystal structures (i.e., cubic diamond, open honeycomb). The combination of computational and experimental approaches reveals such a design strategy using DNA-functionalized nanoparticles and successfully demonstrates the realization of BCC-CsCl, SC-NaCl, and a weakly ordered cubic diamond phase. The study reveals the phase behavior of isotropic nanoparticles for DNA-shell tunable interaction, which, due to the ease of synthesis is promising for the practical realization of non-close-packed lattices.

Engineering Azeotropy to Optimize the Self-Assembly of Colloidal Mixtures

The goal of inverse self-assembly is to design interparticle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new component increasing the thermodynamic degrees of freedom and, hence, the complexity of the self-assembly pathway. In this work we explore the possibility to use azeotropy, i.e., a special thermodynamic condition where the system behaves effectively as a one-component system, as a way to control the self-assembly of an arbitrary number of components. Exploiting the mass-balance equations, we show how to select patchy particle systems that exhibit azeotropic points along the desired self-assembly pathway. As an example we map the phase diagram of a binary mixture that, by design, fully assembles into cubic (and only cubic) diamond crystal via an azeotropic point. The ability to explicitly include azeotropic points in artificial designs reveals effective pathways for the self-assembly of complex structures.

Crystal Prediction via Genetic Algorithms in a Model Chiral System

Chiral crystals and their constituent molecules play a prominent role in theories about the origin of biological homochirality and in drug discovery, design, and stability. Although the prediction and identification of stable chiral crystal structures is crucial for numerous technologies, including separation processes and polymorph selection and control, predictive ability is often complicated by a combination of many-body interactions and molecular complexity and handedness. In this work, we address these challenges by applying genetic algorithms to predict the ground-state crystal lattices formed by a chiral tetramer molecular model, which we have previously shown to exhibit complex fluid-phase behavior. Using this approach, we explore the relative stability and structures of the model's conglomerate and racemic crystals, and present a structural phase diagram for the stable Bravais crystal types in the zero-temperature limit.

Artificial Intelligence (AI) and Internet of Medical Things (IoMT) Assisted Biomedical Systems for Intelligent Healthcare

Artificial intelligence (AI) is a modern approach based on computer science that develops programs and algorithms to make devices intelligent and efficient for performing tasks that usually require skilled human intelligence. AI involves various subsets, including machine learning (ML), deep learning (DL), conventional neural networks, fuzzy logic, and speech recognition, with unique capabilities and functionalities that can improve the performances of modern medical sciences. Such intelligent systems simplify human intervention in clinical diagnosis, medical imaging, and decision-making ability. In the same era, the Internet of Medical Things (IoMT) emerges as a next-generation bio-analytical tool that combines network-linked biomedical devices with a software application for advancing human health. In this review, we discuss the importance of AI in improving the capabilities of IoMT and point-of-care (POC) devices used in advanced healthcare sectors such as cardiac measurement, cancer diagnosis, and diabetes management. The role of AI in supporting advanced robotic surgeries developed for advanced biomedical applications is also discussed in this article. The position and importance of AI in improving the functionality, detection accuracy, decision-making ability of IoMT devices, and evaluation of associated risks assessment is discussed carefully and critically in this review. This review also encompasses the technological and engineering challenges and prospects for AI-based cloud-integrated personalized IoMT devices for designing efficient POC biomedical systems suitable for next-generation intelligent healthcare.

Two-Stage Assembly of Nanoparticle Superlattices with Multiscale Organization

Self-assembly processes, while promising for enabling the fabrication of complexly organized nanomaterials from nanoparticles, are often limited in creating structures with multiscale order. These limitations are due to difficulties in practically realizing the assembly processes required to achieve such complex organizations. For a long time, a hierarchical assembly attracted interest as a potentially powerful approach. However, due to the experimental limitations, intermediate-level structures are often heterogeneous in composition and structure, which significantly impacts the formation of large-scale organizations. Here, we introduce a two-stage assembly strategy: DNA origami frames scaffold a coordination of nanoparticles into designed 3D nanoclusters, and then these clusters are assembled into ordered lattices whose types are determined by the clusters' valence. Through modulating the nanocluster architectures and intercluster bindings, we demonstrate the successful formation of complexly organized nanoparticle crystals. The presented two-stage assembly method provides a powerful fabrication strategy for creating nanoparticle superlattices with prescribed unit cells.

Data-driven algorithms for inverse design of polymers

The ever-increasing demand for novel polymers with superior properties requires a deeper understanding and exploration of the chemical space. Recently, data-driven approaches to explore the chemical space for polymer design have emerged. Among them, inverse design strategies for designing polymers with specific properties have evolved to be a significant materials informatics platform by learning hidden knowledge from materials data as well as smartly navigating the chemical space in an optimized way. In this review, we first summarize the progress in the representation of polymers, a prerequisite step for the inverse design of polymers. Then, we systematically introduce three data-driven strategies implemented for the inverse design of polymers, i.e., high-throughput virtual screening, global optimization, and generative models. Finally, we discuss the challenges and opportunities of the data-driven strategies as well as optimization algorithms employed in the inverse design of polymers.

Designer Nanomaterials through Programmable Assembly

Nanoparticles have long been recognized for their unique properties, leading to exciting potential applications across optics, electronics, magnetism, and catalysis. These specific functions often require a designed organization of particles, which includes the type of order as well as placement and relative orientation of particles of the same or different kinds. DNA nanotechnology offers the ability to introduce highly addressable bonds, tailor particle interactions, and control the geometry of bindings motifs. Here, we discuss how developments in structural DNA nanotechnology have enabled greater control over 1D, 2D, and 3D particle organizations through programmable assembly. This Review focuses on how the use of DNA binding between nanocomponents and DNA structural motifs has progressively allowed the rational formation of prescribed particle organizations. We offer insight into how DNA-based motifs and elements can be further developed to control particle organizations and how particles and DNA can be integrated into nanoscale building blocks, so-called "material voxels", to realize designer nanomaterials with desired functions.

Exploring the Design Rules for Efficient Membrane-Reshaping Nanostructures

In this study, we investigate the role of the surface patterning of nanostructures for cell membrane reshaping. To accomplish this, we combine an evolutionary algorithm with coarse-grained molecular dynamics simulations and explore the solution space of ligand patterns on a nanoparticle that promote efficient and reliable cell uptake. Surprisingly, we find that in the regime of low ligand number the best-performing structures are characterized by ligands arranged into long one-dimensional chains that pattern the surface of the particle. We show that these chains of ligands provide particles with high rotational freedom and they lower the free energy barrier for membrane crossing. Our approach reveals a set of nonintuitive design rules that can be used to inform artificial nanoparticle construction and the search for inhibitors of viral entry.

The Phase Behavior of Nanoparticle Superlattices in the Presence of a Solvent

Superlattices of nanoparticles coated by alkyl-chain ligands are usually prepared from a stable solution by evaporation, therefore the pathway of superlattice self-assembly critically depends on the amount of solvent present within it. This work addresses the role of the solvent on the structure and the relative stability of the different supercrystalline phases of single-component superlattices (simple cubic, body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed). The study is performed with a molecular theory for nanoparticle superlattices introduced in this work, which predicts the structure and thermodynamics of the supercrystals explicitly treating the presence and molecular details of the solvent and the ligands. The theory predicts a FCC-BCC transition with decreasing solvent content due to the competition between the translational entropy of the solvent and the entropy and internal energy of the ligands. This result provides an explanation for recent experimental observations by in situ X-ray scattering, which reported a FCC-BCC transition during solvent evaporation. The theory also predicts the effects of the length and surface coverage of the ligands and the radius of the core on the phase behavior in agreement with experimental evidence and previous molecular dynamics simulations. These results validate the use of the dimensionless softness parameter λ (ratio of ligand length to core radius) to predict the phase behavior of wet superlattices. Our results stress the importance of explicitly considering the presence of the solvent in order to reach a complete picture of the mechanisms that mediate the self-assembly of nanoparticle superlattices.

First-order 'hyper-selective' binding transition of multivalent particles under force

Multivalent particles bind to targets via many independent ligand-receptor bonding interactions. This microscopic design spans length scales in both synthetic and biological systems. Classic examples include interactions between cells, virus binding, synthetic ligand-coated micrometer-scale vesicles or smaller nano-particles, functionalised polymers, and toxins. Equilibrium multivalent binding is a continuous yet super-selective transition with respect to the number of ligands and receptors involved in the interaction. Increasing the ligand or receptor density on the two particles leads to sharp growth in the number of bound particles at equilibrium. Here we present a theory and Monte Carlo simulations to show that applying mechanical force to multivalent particles causes their adsorption/desorption isotherm on a surface to become sharper and more selective, with respect to variation in the number of ligands and receptors on the two objects. When the force is only applied to particles bound to the surface by one or more ligands, then the transition can become infinitely sharp and first-order-a new binding regime which we term 'hyper-selective'. Force may be imposed by, e.g. flow of solvent around the particles, a magnetic field, chemical gradients, or triggered uncoiling of inert oligomers/polymers tethered to the particles to provide a steric repulsion to the surface. This physical principle is a step towards 'all or nothing' binding selectivity in the design of multivalent constructs.

Dendrimer Ligand Directed Nanoplate Assembly

Many studies on nanocrystal (NC) self-assembly into ordered superlattices have focused mainly on attractive forces between the NCs, whereas the role of organic ligands on anisotropic NCs is only in its infancy. Herein, we report the use of a series of dendrimer ligands to direct the assembly of nanoplates into 2D and 3D geometries. It was found that the dendrimer-nanoplates consistently form a directionally offset architecture in 3D films. We present a theory to predict ligand surface distribution and Monte Carlo simulation results that characterize the ligand shell around the nanoplates. Bulky dendrimer ligands create a nontrivial corona around the plates that changes with ligand architecture. When this organic-inorganic effective shape is used in conjunction with thermodynamic perturbation theory to predict both lattice morphology and equilibrium relative orientations between NCs, a lock-and-key type of mechanism is found for the 3D assembly. We observe excellent agreement between our experimental results and theoretical model for 2D and 3D geometries, including the percent of offset between the layers of NCs. Such level of theoretical understanding and modeling will help guide future design frameworks to achieve targeted assemblies of NCs.

Optical Processing of DNA-Programmed Nanoparticle Superlattices

Hierarchical structural control across multiple size regimes requires careful consideration of the complex energy- and time-scales which govern the system's morphology at each of these different size ranges. At the nanoscale, synthetic chemistry techniques have been developed to create nanoparticles of well-controlled size and composition. At the macroscale, it is feasible to directly impose material structure via physical manipulation. However, in between these two size regimes at the mesoscale, structural control is more challenging as the physical forces that govern material assembly at larger and smaller scales begin to interfere with one another. In this work, the interplay of structure-directing forces at multiple length-scales is investigated by utilizing optical processing to influence both nanoscale and microscale features of self-assembled, DNA-grafted nanoparticle films. Optical processing is used to generate heat, which causes the self-assembled particles to rearrange from a kinetically trapped, amorphous state into a thermodynamically preferred superlattice structure. The gradient in the heat profile, however, also induces thermophoretic motion within the nanoparticle film, resulting in microscale movement at a comparable time-scale. By utilizing precise exposure times enabled by optical processing, crystallization and thermophoresis occur concurrently in the self-assembling nanoparticle system, enabling a dynamic growth mechanism whereby nucleation and growth occur in separate regions of the material. Furthermore, utilizing sufficiently short processing times allows for the formation of a fluidlike state of the DNA-functionalized nanoparticle materials that is inaccessible via typical thermal processing setups. This unique phase of the material allows for both pathway-dependent and pathway-independent growth phenomena, as appropriately tuning the experimental conditions enables the formation of morphologically equivalent nanoparticle lattices that are generated through different intermediate states (pathway-independent structures), or kinetically preprocessing a material to yield unique thermodynamic arrangements of particles once fully annealed (pathway-dependent structures).

Investigation of Geometric Landscape and Structure-Property Relations for Colloidal Superstructures Using Genetic Algorithm

Over the past two decades, colloidal particles with a variety of shapes, sizes, and compositions have been synthesized and characterized successfully. One of the most important applications for colloidal building blocks is to engineer functional structures as mechanical, electrical, and optical metamaterials. However, complex interaction dynamics between the building blocks as well as sophisticated structure-property relationships make it challenging to design structures with predictable target properties. In this paper, we implement an inverse material design framework using Genetic Algorithm (GA)-based techniques to streamline the design of colloidal structures based on target properties. We investigate spherical particles as well as colloidal molecules of different sizes and shapes and evaluate a Geometric Landscape Accessibility parameter that identifies the size of feasible domains within the geometric phase space of each structure. Considering target photonic properties, our GA-assisted framework is further utilized to identify sets of building blocks and structures that lead to various target values for the size of the photonic band gaps. The proposed framework in this study will provide new insight for predictive computational material design approaches and help establish more efficient ways of understanding structure-property relations in sub-micrometer-scale materials.

Engineering entropy for the inverse design of colloidal crystals from hard shapes

Throughout the physical sciences, entropy stands out as a pivotal but enigmatic concept that, in materials design, typically takes a backseat to energy. Here, we demonstrate how to precisely engineer entropy to achieve desired colloidal crystals via particle shapes that, importantly, can be made in the laboratory. We demonstrate the inverse design of symmetric hard particles that assemble six different target colloidal crystals due solely to entropy maximization. Our approach efficiently samples 10⁸ particle shapes from 92- and 188-dimensional design spaces to discover thermodynamically optimal shapes. We design particle shapes that self-assemble into known crystals with optimized symmetry and thermodynamic stability, as well as new crystal structures with no known atomic or other equivalent.

Programmable Atom Equivalents: Atomic Crystallization as a Framework for Synthesizing Nanoparticle Superlattices

Decades of research efforts into atomic crystallization phenomenon have led to a comprehensive understanding of the pathways through which atoms form different crystal structures. With the onset of nanotechnology, methods that use colloidal nanoparticles (NPs) as nanoscale "artificial atoms" to generate hierarchically ordered materials are being developed as an alternative strategy for materials synthesis. However, the assembly mechanisms of NP-based crystals are not always as well-understood as their atomic counterparts. The creation of a tunable nanoscale synthon whose assembly can be explained using the context of extensively examined atomic crystallization will therefore provide significant advancement in nanomaterials synthesis. DNA-grafted NPs have emerged as a strong candidate for such a "programmable atom equivalent" (PAE), because the predictable nature of DNA base-pairing allows for complex yet easily controlled assembly. This Review highlights the characteristics of these PAEs that enable controlled assembly behaviors analogous to atomic phenomena, which allows for rational material design well beyond what can be achieved with other crystallization techniques.

Using symmetry to elucidate the importance of stoichiometry in colloidal crystal assembly

We demonstrate a method based on symmetry to predict the structure of self-assembling, multicomponent colloidal mixtures. This method allows us to feasibly enumerate candidate structures from all symmetry groups and is many orders of magnitude more computationally efficient than combinatorial enumeration of these candidates. In turn, this permits us to compute ground-state phase diagrams for multicomponent systems. While tuning the interparticle potentials to produce potentially complex interactions represents the conventional route to designing exotic lattices, we use this scheme to demonstrate that simple potentials can also give rise to such structures which are thermodynamically stable at moderate to low temperatures. Furthermore, for a model two-dimensional colloidal system, we illustrate that lattices forming a complete set of 2-, 3-, 4-, and 6-fold rotational symmetries can be rationally designed from certain systems by tuning the mixture composition alone, demonstrating that stoichiometric control can be a tool as powerful as directly tuning the interparticle potentials themselves.

Assembly of three-dimensional binary superlattices from multi-flavored particles

Binary superlattices constructed from nano- or micron-sized colloidal particles have a wide variety of applications, including the design of advanced materials. Self-assembly of such crystals from their constituent colloids can be achieved in practice by, among other means, the functionalization of colloid surfaces with single-stranded DNA sequences. However, when driven by DNA, this assembly is traditionally premised on the pairwise interaction between a single DNA sequence and its complement, and often relies on particle size asymmetry to entropically control the crystalline arrangement of its constituents. The recently proposed "multi-flavoring" motif for DNA functionalization, wherein multiple distinct strands of DNA are grafted in different ratios to different colloids, can be used to experimentally realize a binary mixture in which all pairwise interactions are independently controllable. In this work, we use various computational methods, including molecular dynamics and Wang-Landau Monte Carlo simulations, to study a multi-flavored binary system of micron-sized DNA-functionalized particles modeled implicitly by Fermi-Jagla pairwise interactions. We show how self-assembly of such systems can be controlled in a purely enthalpic manner, and by tuning only the interactions between like particles, demonstrate assembly into various morphologies. Although polymorphism is present over a wide range of pairwise interaction strengths, we show that careful selection of interactions can lead to the generation of pure compositionally ordered crystals. Additionally, we show how the crystal composition changes with the like-pair interaction strengths, and how the solution stoichiometry affects the assembled structures.

Re-inspiring the genetic algorithm with multi-level selection theory: multi-level selection genetic algorithm

Genetic algorithms are integral to a range of applications. They utilise Darwin's theory of evolution to find optimal solutions in large complex spaces such as engineering, to visualise the design space, artificial intelligence, for pattern classification, and financial modelling, improving predictions. Since the original genetic algorithm was developed, new theories have been proposed which are believed to be integral to the evolution of biological systems. However, genetic algorithm development has focused on mathematical or computational methods as the basis for improvements to the mechanisms, moving it away from its original evolutionary inspiration. There is a possibility that the new evolutionary mechanisms are vital to explain how biological systems developed but they are not being incorporated into the genetic algorithm; it is proposed that their inclusion may provide improved performance or interesting feedback to evolutionary theory. Multi-level selection is one example of an evolutionary theory that has not been successfully implemented into the genetic algorithm and these mechanisms are explored in this paper. The resulting multi-level selection genetic algorithm (MLSGA) is unique in that it has different reproduction mechanisms at each level and splits the fitness function between these mechanisms. There are two variants of this theory and these are compared with each other alongside a unified approach. This paper documents the behaviour of the two variants, which show a difference in behaviour especially in terms of the diversity of the population found between each generation. The multi-level selection 1 variant moves rapidly towards the optimal front but with a low diversity amongst its children. The multi-level selection 2 variant shows a slightly slower evolution speed but with a greater diversity of children. The unified selection exhibits a mixed behaviour between the original variants. The different performance of these variants can be utilised to provide specific solvers for different problem types when using the MLSGA methodology.

Modeling antigen-antibody nanoparticle bioconjugates and their polymorphs

The integration of nanomaterials with biomolecules has recently led to the development of new ways of designing biosensors, and through their assembly, to new hybrid structures for novel and exciting applications. In this work, we develop a coarse-grained model for nanoparticles grafted with antibody molecules and their binding with antigens. In particular, we isolate two possible states for antigen-antibody pairs during the binding process, termed as recognition and anchoring states. Using molecular simulation, we calculate the thermodynamic and structural features of three possible crystal structures or polymorphs, the body-centered cubic, simple cubic, and face-centered cubic phases, and of the melt. This leads us to determine the domain of stability of the three solid phases. In particular, the role played by the switching process between anchoring and recognition states during melting is identified, shedding light on the complex microscopic mechanisms in these systems.

Optimising minimal building blocks for addressable self-assembly

Addressable structures are characterised by the set of unique components from which they are built and by the specific location that each component occupies. For an addressable structure to self-assemble, its constituent building blocks must be encoded with sufficient information to define their positions with respect to each other and to enable them to navigate to those positions. DNA, with its vast scope for encoding specific interactions, has been successfully used to synthesise addressable systems of several hundred components. In this work we examine the complementary question of the minimal requirements for building blocks to undergo addressable self-assembly driven by a controlled temperature quench. Our testbed is an idealised model of cubic particles patterned with attractive interactions. We introduce a scheme for optimising the interactions using a variant of basin-hopping and a negative design principle. The designed building blocks are tested dynamically in simple target structures to establish how their complexity affects the limits of reliable self-assembly.

Self-assembly with colloidal clusters: facile crystal design using connectivity landscape analysis

Recent experimental and theoretical studies demonstrate that prefabricated micron-scale colloidal clusters functionalized with DNA oligomers offer a practical way for introducing anisotropic interactions, significantly extending the scope of DNA-mediated colloidal assembly, and enabling the formation of interesting crystalline superstructures that are otherwise inaccessible with short-ranged, spherically symmetric interactions. However, it is apparent that the high-dimensional parameter space that defines the geometric and interaction properties of such systems poses an obstacle to assembly design and optimization. Here, we present a geometrical analysis that generates connectivity landscapes for target superstructures, greatly reducing the space over which subsequent experimental trials must search. We focus on several superstructures that are assembled from binary systems comprised of 'merged' or 'sintered' tetrahedral clusters and single spheres. We also validate and extend the analytical constraint approach with direct MD simulations of superstructure nucleation and growth.

Nanoparticle Superlattices as Quasi-Frank-Kasper Phases

I show that all phases reported experimentally in binary nanoparticle superlattices can be described as networks of disclinations in an ideal lattice of regular tetrahedra. A set of simple rules is provided to identify the different disclination types from the Voronoi construction, and it is shown that those disclinations completely screen the positive curvature of the ideal tetrahedral lattice. In this way, this study provides a generalization of the well-known Frank-Kasper phases to binary systems consisting of two types of particles, and with a more general type of disclinations, i.e., quasi-Frank-Kasper phases. The study comprises all strategies in nanoparticle self-assembly, whether driven by DNA or hydrocarbon ligands, and establishes the universal tendency of superlattices to develop icosahedral order, which is facilitated by the asymmetry of the particles. Besides its interest in predicting nanoparticle self-assembly, I discuss the implications for models of the glass transition, micelles of diblock polymers, and dendritic molecules, among many others.

Directionally Interacting Spheres and Rods Form Ordered Phases

The structures formed by mixtures of dissimilarly shaped nanoscale objects can significantly enhance our ability to produce nanoscale architectures. However, understanding their formation is a complex problem due to the interplay of geometric effects (entropy) and energetic interactions at the nanoscale. Spheres and rods are perhaps the most basic geometrical shapes and serve as convenient models of such dissimilar objects. The ordered phases formed by each of these individual shapes have already been explored, however, when mixed, spheres and rods have demonstrated only limited structural organization to date. Here, we show using experiments and theory that the introduction of directional attractions between rod ends and isotropically interacting spherical nanoparticles (NPs) through DNA base pairing leads to the formation of ordered three-dimensional lattices. The spheres and rods arrange themselves in a complex alternating manner, where the spheres can form either a face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice, or a disordered phase, as observed by in situ X-ray scattering. Increasing NP diameter at fixed rod length yields an initial transition from a disordered phase to the HCP crystal, energetically stabilized by rod-rod attraction across alternating crystal layers, as revealed by theory. In the limit of large NPs, the FCC structure is instead stabilized over the HCP by rod entropy. We, therefore, propose that directionally specific attractions in mixtures of anisotropic and isotropic objects offer insight into unexplored self-assembly behavior of noncomplementary shaped particles.

Neural-Network-Biased Genetic Algorithms for Materials Design: Evolutionary Algorithms That Learn

Machine learning has the potential to dramatically accelerate high-throughput approaches to materials design, as demonstrated by successes in biomolecular design and hard materials design. However, in the search for new soft materials exhibiting properties and performance beyond those previously achieved, machine learning approaches are frequently limited by two shortcomings. First, because they are intrinsically interpolative, they are better suited to the optimization of properties within the known range of accessible behavior than to the discovery of new materials with extremal behavior. Second, they require large pre-existing data sets, which are frequently unavailable and prohibitively expensive to produce. Here we describe a new strategy, the neural-network-biased genetic algorithm (NBGA), for combining genetic algorithms, machine learning, and high-throughput computation or experiment to discover materials with extremal properties in the absence of pre-existing data. Within this strategy, predictions from a progressively constructed artificial neural network are employed to bias the evolution of a genetic algorithm, with fitness evaluations performed via direct simulation or experiment. In effect, this strategy gives the evolutionary algorithm the ability to "learn" and draw inferences from its experience to accelerate the evolutionary process. We test this algorithm against several standard optimization problems and polymer design problems and demonstrate that it matches and typically exceeds the efficiency and reproducibility of standard approaches including a direct-evaluation genetic algorithm and a neural-network-evaluated genetic algorithm. The success of this algorithm in a range of test problems indicates that the NBGA provides a robust strategy for employing informatics-accelerated high-throughput methods to accelerate materials design in the absence of pre-existing data.

Colloidal Cluster Assembly into Ordered Superstructures via Engineered Directional Binding

Recent experimental studies have demonstrated a facile route for fabricating large numbers of geometrically uniform colloidal clusters out of submicron DNA-functionalized spheres. These clusters are ideally suited for use as anisotropic building blocks for hierarchical assembly of superstructures with symmetries that are otherwise inaccessible with simple spherical particles. We study computationally the self-assembly of cubic, tetrahedral, and octahedral clusters mediated by "bond spheres" that dock with the clusters at specific preferential sites, providing robust and well-defined directional bonding. We analyze the assembly process with a combination of direct molecular dynamics simulations of superstructure growth and state-of-the-art umbrella sampling techniques to compute nucleation free energy profiles. The simulations confirm the versatility and robustness of hierarchical cluster assembly but also reveal potential obstacles in the form of energetically accessible defect states. We find and study solutions for bypassing these defects that rely on appropriate selection of particle size and interparticle interaction as a function of building block shape and, therefore, provide operational guidelines for future experimental demonstrations.

Generic phase diagram of binary superlattices

Emergence of a large variety of self-assembled superlattices is a dramatic recent trend in the fields of nanoparticle and colloidal sciences. Motivated by this development, we propose a model that combines simplicity with a remarkably rich phase behavior applicable to a wide range of such self-assembled systems. Those systems include nanoparticle and colloidal assemblies driven by DNA-mediated interactions, electrostatics, and possibly, controlled drying. In our model, a binary system of large and small hard spheres (L and S, respectively) interacts via selective short-range ("sticky") attraction. In its simplest version, this binary sticky sphere model features attraction only between S and L particles. We show that, in the limit when this attraction is sufficiently strong compared with [Formula: see text], the problem becomes purely geometrical: the thermodynamically preferred state should maximize the number of [Formula: see text] contacts. A general procedure for constructing the phase diagram as a function of system composition f and particle size ratio r is outlined. In this way, the global phase behavior can be calculated very efficiently for a given set of plausible candidate phases. Furthermore, the geometric nature of the problem enables us to generate those candidate phases through a well-defined and intuitive construction. We calculate the phase diagrams for both 2D and 3D systems and compare the results with existing experiments. Most of the 3D superlattices observed to date are featured in our phase diagram, whereas several more are predicted for future discovery.

Digital Alchemy for Materials Design: Colloids and Beyond

Starting with the early alchemists, a holy grail of science has been to make desired materials by modifying the attributes of basic building blocks. Building blocks that show promise for assembling new complex materials can be synthesized at the nanoscale with attributes that would astonish the ancient alchemists in their versatility. However, this versatility means that making a direct connection between building-block attributes and bulk structure is both necessary for rationally engineering materials and difficult because building block attributes can be altered in many ways. Here we show how to exploit the malleability of the valence of colloidal nanoparticle "elements" to directly and quantitatively link building-block attributes to bulk structure through a statistical thermodynamic framework we term "digital alchemy". We use this framework to optimize building blocks for a given target structure and to determine which building-block attributes are most important to control for self-assembly, through a set of novel thermodynamic response functions, moduli, and susceptibilities. We thereby establish direct links between the attributes of colloidal building blocks and the bulk structures they form. Moreover, our results give concrete solutions to the more general conceptual challenge of optimizing emergent behaviors in nature and can be applied to other types of matter. As examples, we apply digital alchemy to systems of truncated tetrahedra, rhombic dodecahedra, and isotropically interacting spheres that self-assemble diamond, fcc, and icosahedral quasicrystal structures, respectively. Although our focus is on colloidal systems, our methods generalize to any building blocks with adjustable interactions.

Binary nanoparticle superlattices of soft-particle systems

The solid-phase diagram of binary systems consisting of particles of diameter σA = σ and σB = γσ (γ ≤ 1) interacting with an inverse p = 12 power law is investigated as a paradigm of a soft potential. In addition to the diameter ratio γ that characterizes hard-sphere models, the phase diagram is a function of an additional parameter that controls the relative interaction strength between the different particle types. Phase diagrams are determined from extremes of thermodynamic functions by considering 15 candidate lattices. In general, it is shown that the phase diagram of a soft repulsive potential leads to the morphological diversity observed in experiments with binary nanoparticles, thus providing a general framework to understand their phase diagrams. Particular emphasis is given to the two most successful crystallization strategies so far: evaporation of solvent from nanoparticles with grafted hydrocarbon ligands and DNA programmable self-assembly.

Stoichiometric control of DNA-grafted colloid self-assembly

There has been considerable interest in understanding the self-assembly of DNA-grafted nanoparticles into different crystal structures, e.g., CsCl, AlB2, and Cr3Si. Although there are important exceptions, a generally accepted view is that the right stoichiometry of the two building block colloids needs to be mixed to form the desired crystal structure. To incisively probe this issue, we combine experiments and theory on a series of DNA-grafted nanoparticles at varying stoichiometries, including noninteger values. We show that stoichiometry can couple with the geometries of the building blocks to tune the resulting equilibrium crystal morphology. As a concrete example, a stoichiometric ratio of 3:1 typically results in the Cr3Si structure. However, AlB2 can form when appropriate building blocks are used so that the AlB2 standard-state free energy is low enough to overcome the entropic preference for Cr3Si. These situations can also lead to an undesirable phase coexistence between crystal polymorphs. Thus, whereas stoichiometry can be a powerful handle for direct control of lattice formation, care must be taken in its design and selection to avoid polymorph coexistence.

Programming macro-materials from DNA-directed self-assembly

DNA is a powerful tool that can be attached to nano- and micro-objects and direct the self-assembly through base pairing. Since the strategy of DNA programmable nanoparticle self-assembly was first introduced in 1996, it has remained challenging to use DNA to make powerful diagnostic tools and to make designed materials with novel properties and highly ordered crystal structures. In this review, we summarize recent experimental and theoretical developments of DNA-programmable self-assembly into three-dimensional (3D) materials. Various types of aggregates and 3D crystal structures obtained from an experimental DNA-driven assembly are introduced. Furthermore, theoretical calculations and simulations for DNA-mediated assembly systems are described and we highlight some typical theoretical models for Monte Carlo and Molecular Dynamics simulations.