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

Supercrystal Engineering of Nanoarrows Enabled by Tailored Concavity

Self-assembly of nanoparticles into supercrystals represents a powerful approach to create unique and complex superstructures with fascinating properties and novel functions, but the complexity in spatial configuration, and the tunability in lattice structure are still quite limited compared to the crystals formed by atoms and molecules. Herein, shallowly concave gold nanoarrows with a unique concave-convex geometry are synthesized and employed as novel building blocks for shape-directed self-assembly of a wealth of complex 3D supercrystals with unprecedented configurations. The obtained diverse superstructures including six Interlocking-type supercrystals and three Packing-type supercrystals exhibit four types of Bravais lattices (i.e., tP, oI, tI, and oF) and six types of crystallographic space groups (i.e., Pmmm, I222, Pnnm, Ibam, I4/mmm, and Fmmm), which have not been documented in the mesoscale self-assembled systems. It has been revealed that the relative yield of different supercrystal structures is mainly determined by the packing density and deformability of the supercrystals, which are closely related to the tailored concavity of the nanoparticles and is affected by the particle concentration, thus allowing for programmable self-assembly into specific supercrystals through particle shape modulation. The concavity-enabled supercrystal engineering may open a new avenue toward unconventional nanoparticle superstructures with expanded complexity, tunability, and functionality.

Programming patchy particles for materials assembly design

Direct design of complex functional materials would revolutionize technologies ranging from printable organs to novel clean energy devices. However, even incremental steps toward designing functional materials have proven challenging. If the material is constructed from highly complex components, the design space of materials properties rapidly becomes too computationally expensive to search. On the other hand, very simple components such as uniform spherical particles are not powerful enough to capture rich functional behavior. Here, we introduce a differentiable materials design model with components that are simple enough to design yet powerful enough to capture complex materials properties: rigid bodies composed of spherical particles with directional interactions (patchy particles). We showcase the method with self-assembly designs ranging from open lattices to self-limiting clusters, all of which are notoriously challenging design goals to achieve using purely isotropic particles. By directly optimizing over the location and interaction of the patches on patchy particles using gradient descent, we dramatically reduce the computation time for finding the optimal building blocks.

Nanocrystal Assemblies: Current Advances and Open Problems

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

Local Structural Features Elucidate Crystallization of Complex Structures

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

Theory and simulation of ligand functionalized nanoparticles - a pedagogical overview

Synthesizing reconfigurable nanoscale synthons with predictive control over shape, size, and interparticle interactions is a holy grail of bottom-up self-assembly. Grand challenges in their rational design, however, lie in both the large space of experimental synthetic parameters and proper understanding of the molecular mechanisms governing their formation. As such, computational and theoretical tools for predicting and modeling building block interactions have grown to become integral in modern day self-assembly research. In this review, we provide an in-depth discussion of the current state-of-the-art strategies available for modeling ligand functionalized nanoparticles. We focus on the critical role of how ligand interactions and surface distributions impact the emergent, pre-programmed behaviors between neighboring particles. To help build insights into the underlying physics, we first define an "ideal" limit - the short ligand, "hard" sphere approximation - and discuss all experimental handles through the lens of perturbations about this reference point. Finally, we identify theories that are capable of bridging interparticle interactions to nanoscale self-assembly and conclude by discussing exciting new directions for this field.

Geometrically frustrated interactions drive structural complexity in amorphous calcium carbonate

Amorphous calcium carbonate is an important precursor for biomineralization in marine organisms. Key outstanding problems include understanding the structure of amorphous calcium carbonate and rationalizing its metastability as an amorphous phase. Here we report high-quality atomistic models of amorphous calcium carbonate generated using state-of-the-art interatomic potentials to help guide fits to X-ray total scattering data. Exploiting a recently developed inversion approach, we extract from these models the effective Ca⋯Ca interaction potential governing the structure. This potential contains minima at two competing distances, corresponding to the two different ways that carbonate ions bridge Ca2+-ion pairs. We reveal an unexpected mapping to the Lennard-Jones-Gauss model normally studied in the context of computational soft matter. The empirical model parameters for amorphous calcium carbonate take values known to promote structural complexity. We thus show that both the complex structure and its resilience to crystallization are actually encoded in the geometrically frustrated effective interactions between Ca2+ ions.

Targeted Discovery of Low-Coordinated Crystal Structures via Tunable Particle Interactions

Particles interacting via isotropic, multiwell pair potentials have been shown to self-assemble into a range of crystal structures, yet how the characteristics of the underlying interaction potential give rise to the resultant structure remains largely unknown. We have thus developed a functional form for the interaction potential in which all features can be tuned independently. We perform continuous parameter space searches by systematically changing pairs of parameters, controlling the various features of the interaction potential. By enforcing a repulsive first well (controlling particle interactions of the first neighbor shell), we stimulate the formation of low-coordinated assemblies. We report the self-assembly of 20 previously unknown crystal structure types, 14 of which have low coordination numbers. Despite limiting the search to a small region of the vast parameter space of possible particle interactions, a wealth of complexity and symmetry is apparent within these crystal structures, which include clathrates with empty cages and low-symmetry structures. Our findings suggest that an unknown number of previously undiscovered crystal structure configurations are possible through self-assembly, which can serve as interesting design targets for soft condensed matter synthesis.

Conformational Dynamics of mCherry Variants: A Link between Side-Chain Motions and Fluorescence Brightness

The 3-fold higher brightness of the recently developed mCherry-XL red fluorescent protein (FP) compared to its progenitor, mCherry, is due to a significant decrease in the nonradiative decay rate underlying its increased fluorescence quantum yield. To examine the structural and dynamic role of the four mutations that distinguish the two FPs and closely related variants, we employed microsecond time scale, all-atom molecular dynamics simulations. The simulations revealed that the I197R mutation leads to the formation of multiple hydrogen-bonded contacts and increased rigidity of the β-barrel. In particular, mCherryXL showed reduced nanosecond time scale breathing of the gap between the β7 and β10-strands, which was previously shown to be the most flexible region of mCherry. Together with experimental results, the simulations also reveal steric interactions of residue 161 and a network of hydrogen-bonding interactions of the chromophore with residues at positions 59, 143, and 163 that are critical in perturbing the chromophore electronic structure. Finally, we shed light on the conformational dynamics of the conserved residues R95 and S146, which are hydrogen-bonded to the chromophore, and provide physical insights into the observed photophysics. To the best of our knowledge, this is the first study that evaluates the conformational space for a set of closely related FPs generated by directed evolution.

A bottom-up design strategy for controllable self-assembly based on the isotropic double-well potential

Controllable self-assembly of particles or atoms is still challenging in the synthesis of materials with desirable properties that are highly relevant to the microscopic structures determined by the interparticle interactions. To gain insight into how the interactions affect the self-assembly, we designed various kinds of isotropic double-well potentials and simulated the motion of the particles. By controlling the depth and location of the potential wells and the height of the barriers, we studied their effects on the aggregation structures and the related microscopic kinetic processes. We identified five aggregation patterns at different temperatures and eight kinds of crystals, including Frank-Kasper phases, and observed the expansion or contraction of crystals. We found that the system usually stays in a sparse configuration at very low or very high temperatures. The particles typically assemble into a loosely packed cluster at medium temperatures and then deplete into a tightly packed state with a specific pattern. These phenomena can be explained from the perspective of energy. In contrast, very few structures could be obtained for the system guided by a single-well potential under the same simulation conditions. Thus, the interparticle interactions driven by the double-well potential greatly enrich the possible packing morphology of the system. The information obtained from this work helps us to understand how to achieve a specific self-assembled architecture through a reasonable selection of materials.

Symmetry-derived structure directing agents for two-dimensional crystals of arbitrary colloids

We derive properties of self-assembling rings which can template the organization of an arbitrary colloid into any periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings are derivable, and are explicitly reflected by the symmetry group's orbifold symbol. We performed molecular dynamics simulations to observe their self-assembly and found 5 different characteristics which could be easily rationalized on the basis of this symbol. These include systems which undergo chiral phase separation, are addressably complex, exhibit self-limiting growth into clusters, form ordered "rods" in only one-dimension akin to a smectic phase, and those from symmetry groups which are pluripotent and allow one to select rings which exhibit different behaviors. We discuss how the curvature of the ring's edges plays an integral role in achieving correct self-assembly, and illustrate how to obtain these shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.