Lock and key colloids

Crystallization of non-convex colloids: the roles of particle shape and entropy

Particle shape and entropy play critical roles in order-disorder transitions; examples include liquid crystals and crystals formed from hard polyhedra. With few exceptions, colloidal crystals reported in the literature form from convex particles, for which the roles of particle shape and entropy are well explored. However, recent experimental work has shown that a cubic diamond lattice, elusive but long sought after for its wide and robust photonic band gap, can be assembled from non-convex particles. Here, we use simulations to explore the crystallization of colloidal diamond from non-convex tetrahedral-lobed patchy particles (TLPPs). Our results show how the entropic cost of binding, measured using umbrella sampling, can be tuned through subtle changes to the particle geometry. Geometric constraints, uniquely provided by the particle's non-convex features, select the staggered bond conformation required for cubic diamond. These constraints and the entropy associated with them can be geometrically tuned to vary the flexibility of the bonds. Depending on the particle geometry, TLPPs form liquid, diamond, or amorphous structures. Importantly, all geometrical parameters can be controlled in experiments, which should lead to larger crystals with less disorder, improving the resulting photonic band gap.

Processable and controllable all-aqueous gels based on high internal phase water-in-water emulsions

Aqueous two-phase systems (ATPSs) have primarily been developed in the form of emulsions to enhance their utilization in green and biocompatible applications. However, numerous challenges have arisen in forming stable and processable water-in-water (W/W) emulsion systems, as well as in fine-tuning the interconnectivity of their internal structure, which can significantly impact their performance. To effectively address these challenges, we elucidate, for the first time, the root cause of the poor stability of W/W emulsions. Leveraging this insight, we successfully stabilize W/W high internal phase emulsions (W/W HIPEs) characterized by an extremely thin continuous phase. This stabilization enables the fine-tuning of interconnectivity between dispersed droplets through photopolymerization of thin continuous phases, resulting in the fabrication of stable and processable all-aqueous gels. This W/W HIPE-based gel fabrication holds promise as a universal technology for a wide range of applications. It facilitates in situ polymerization of the continuous phase of W/W HIPEs, where target molecules are stored in the dispersed phase. Moreover, this method allows easy adjustment of the external release rate or internal transfer rate of target molecules by adjusting the interconnectivity of the internal structures.

Dynamic and asymmetric colloidal molecules

"Colloidal molecules" represent artificial colloidal clusters replicating the geometries of molecules and exhibiting flexibility and fluctuations similar to macromolecules and proteins. Their dynamic and anisotropic characters make them unique and indispensable building blocks for creating hierarchically organized superstructures. Despite the progress in synthesizing and assembling colloidal molecules, unveiling their dynamic characters is challenging in experiments. Here, we employ real-time three-dimensional imaging and simulations to reveal dynamic colloidal molecule structures in micrometre-sized colloidal-emulsion models with tunable electrostatic interactions. Our findings reveal that colloidal molecules' dynamic structures are inherently asymmetric, with angular symmetry emerging through continuous ordering from a liquid-like configuration. We further develop an effective method to guide the ordering of colloidal molecules towards a desired structure by dynamically adjusting the ionic strength in the solvent during the ordering process. We validate this method using molecular dynamics simulations and propose a practical protocol for its experimental implementation. Our research contributes to a clearer physical understanding of dynamic colloidal molecules and offers potential solutions to the complexities inherent in their formation process.

Structure, dynamics and phase transitions in electric field assembled colloidal crystals and glasses

Field-induced assembly of colloidal particles into structures of desired configurations is extremely relevant from the viewpoint of producing field-assembled micro-swimmers and reconfigurable smart materials. However, the behaviour of colloidal particles under the influence of alternating current (AC) electric fields remains a topic of ongoing investigation due to the complex and nuanced effects of various control parameters. Here, we examine the role of several factors including particle size, zeta potential, voltage and frequency of the applied field in the formation of different structural configurations in an intermediate frequency range (5-50 kHz) and very low conductivity solutions. We observe a wide range of configurations ranging from crystals to glasses that are normally observed at frequency ranges below 1 kHz. Additionally, we investigate the dynamics: the nature of diffusion and active motion in these out-of-equilibrium systems and show how that is directly interlinked with the formation of close-packed or open (non close-packed) structures. Lastly, we investigate the frequency-driven disorder-order-disorder phase transition in colloidal crystals, which is a starting point for building reconfigurable systems. Our findings contribute to a deeper understanding of interlinked roles of various factors in electric field-induced assembly of colloidal particles in the intermediate frequency-low conductivity regime, which is significant for potential applications in micro-robotics and next generation materials.

Curvature-guided depletion stabilizes Kagome superlattices of nanocrystals

Shape-anisotropic nanocrystals and patchy particles have been explored to construct complex superstructures, but most studies have focused on convex shapes. We report that nonconvex, dumbbell-shaped nanocrystals (nanodumbbells) exhibit globally interlocking self-assembly behaviors governed by curvature-guided depletion interactions. By tailoring the local curvature of nanodumbbells, we can precisely and flexibly adjust particle bonding directionality, a level of control rarely achievable with conventional convex building blocks. These nanodumbbells can undergo long-range ordered assembly into various intricate two-dimensional superlattices, including the chiral Kagome lattice. Theoretical calculations reveal that the Kagome lattice is a thermodynamically stable phase, with depletion interactions playing a crucial role in stabilizing these non-close-packed structures. The emergence of Kagome lattices and other unusual structures highlights the vast potential of nonconvex nanocrystals for creating sophisticated architectures.

A Free Energy Model for the Plateau Shear Modulus in Thermosensitive Microgel Suspensions

Polymer microgels exhibit intriguing macroscopic flow properties arising from their unique microscopic structure. Microgel colloids usually comprise a cross-linked polymer network with a radially decaying density profile, resulting in a dense core surrounded by a fuzzy corona. Notably, microgels synthesized from poly(N-isopropylacrylamide) (PNIPAM) are thermoresponsive and capable of adjusting their size and density profile based on temperature. Above the lower critical solution temperature (T LCST ∼ 33 °C), the microgel's polymer network collapses, expulsing water through a reversible process. Conversely, below 33 °C, the microgel's network swells, becoming highly compressible and allowing overpacking to effective volume fractions exceeding one. Under conditions of dense packing, microgels undergo deformation in distinct stages: corona compression and faceting, interpenetration, and finally, isotropic compression. Each stage exhibits a characteristic signature in the dense microgel suspensions' yield stress and elastic modulus. Here, we introduce a model for the linear elastic shear modulus by minimizing a quasi-equilibrium free energy, encompassing all relevant energetic contributions. We validate our model by comparing its predictions to experimental results from oscillatory shear rheology tests on microgel suspensions at different densities and temperatures. Our findings demonstrate that combining macroscopic rheological measurements with the model allows for temperature-dependent characterization of polymer interaction parameters.

Shape-Directed Dynamic Assembly of Active Colloidal Metamachines

Modularly organizing active micromachines into high-grade metamachines makes a great leap for operating the microscopic world in a biomimetic way. However, modulating the nonreciprocal interactions among different colloidal motors through chemical reactions to achieve the controllable construction of active colloidal metamachines with specific dynamic properties remains challenging. Here, we report the phototactic active colloidal metamachines constructed by shape-directed dynamic self-assembly of chemically driven peanut-shaped TiO2 colloidal motors and Janus spherical Pt/SiO2 colloidal motors. The long-range diffusiophoretic attraction generated by the photocatalytic reaction dominates the sensing and collision of peanut TiO2 motors with Janus Pt/SiO2 motors. The coupling of local chemical concentration gradient fields between the two types of motors generates short-range site-selective interactions, promoting the shape-directed assembly toward active colloidal metamachines with well-defined spatial configurations. Metamachines, made of colloidal motors, exhibit configuration-dependent kinematics. The colloidal metamachines can be reversibly reconstructed by adjusting lighting conditions and can move phototactically along a predetermined path under the structured light field. Such chemically driven colloidal metamachines that integrate multiple active agents provide a significant avenue for fabricating active soft matter materials and intelligent robotic systems with advanced applications.

3D Nanofabrication via Directed Material Assembly: Mechanism, Method, and Future

Fabrication of complex three-dimensional (3D) structures at nanoscale is the core of nanotechnology, as it enables the creation of various micro-/nano-devices such as micro-robots, metamaterials, sensors, photonic devices, etc. Among most 3D nanofabrication strategies, the guided material assembly, an efficient bottom-up approach capable of directly constructing designed structures from precise integration of material building blocks, possesses compelling advantages in diverse material compatibility, sufficient driving forces, facile processing steps, and nanoscale resolution. In this review, we focus on assembly-based fabrication methods capable of creating complex 3D nanostructures (instead of periodic or 2.5D-only structures). Recent advances are classified based on the different assembly mechanisms, i.e., assembly driven by chemical reactions, physical interactions, and the synergy of multiple microscopic interactions. The design principles of representative fabrication strategies with an emphasis on their respective advantages, e.g., structural design flexibility, material compatibility, resolution, or applications are analyzed. In the summary and outlook, existing challenges, as well as possible paths to solutions for future development are reviewed. We believe that with recent advances in assembly-based nanofabrication strategies, 3D nanofabrication has achieved tremendous progress in resolution, material generality, and manufacturing cost, for it to make a greater impact in the near future.

Depletion-Induced Tunable Assembly of Complementary Platonic Solids

Multicomponent self-assembly has been explored to create novel metamaterials from nanoparticles of different sizes and compositions, but the assembly of nanoparticles with complementary shapes remains rare. Recent binary assemblies were mediated by DNA base pairing or induced by solvent evaporation. Here, we introduce depletion-induced self-assembly (DISA) as a novel approach to constructing tunable binary lattices. In situ structural analysis in the real and reciprocal spaces demonstrates DISA of a binary mixture of octahedra and tetrahedra into extended supercrystals with Fm3̅m symmetry. The interparticle distance, adjustable by depletant concentration, offers a versatile method for assembling nanoparticles into ordered structures while they remain dispersed in a liquid phase. We show that DISA can control the packing fraction of such binary supercrystals between φ = 0.37 and φ = 0.66, much lower than dense packing in the dry state. These findings highlight DISA's potential for creating complex and highly ordered metamaterials with tailored properties.

Discrete state model of a self-aggregating colloidal system with directional interactions

The construction of coarse-grained descriptions of a system's kinetics is well established in biophysics. One prominent example is Markov state models in protein folding dynamics. In this paper, we develop a coarse-grained, discrete state model of a self-aggregating colloidal particle system inspired by the concepts of Markov state modeling. The specific self-aggregating system studied here involves field-responsive colloidal particles in orthogonal electric and magnetic fields. Starting from particle-resolved (Brownian dynamics) simulations, we define the discrete states by categorizing each particle according to its local structure. We then describe the kinetics between these states as a series of stochastic, memoryless jumps. In contrast to other works on colloidal self-assembly, our coarse-grained approach describes the simultaneous formation and evolution of multiple aggregates from single particles. Our discrete model also takes into account the changes in transition dynamics between the discrete states as the size of the largest cluster grows. We validate the coarse-grained model by comparing the predicted population fraction in each of the discrete states with those calculated directly from the particle-resolved simulations as a function of the largest cluster size. We then predict population fractions in the presence of noise-averaging and in a situation where a model parameter is changed instantaneously after a certain time. Finally, we explore the validity of the detailed balance condition in the various stages of aggregation.

Active Stratification of Colloidal Mixtures for Asymmetric Multilayers

Stratified films offer high performance and multifunctionality, yet achieving fully stratified films remains a challenge. The layer-by-layer method, involving the sequential deposition of each layer, has been commonly utilized for stratified film fabrication. However, this approach is time-consuming, labor-intensive, and prone to leaving defects within the film. Alternatively, the self-stratification process exploiting a drying binary colloidal mixture is intensively developed recently, but it relies on strict operating conditions, typically yielding a heterogeneous interlayer. In this study, an active interfacial stratification process for creating completely stratified nanoparticle (NP) films is introduced. The technique leverages NPs with varying interfacial activity at the air-water interface. With the help of depletion pressure, the lateral compression of NP mixtures at the interface induces individual desorption of less interfacial active NPs into the subphase, while more interfacial active NPs remain at the interface. This simple compression leads to nearly perfect stratified NP films with controllability, universality, and scalability. Combined with a solvent annealing process, the active stratification process enables the fabrication of stratified films comprising a polymeric layer atop a NP layer. This work provides insightful implications for designing drug encapsulation and controlled release, as well as manufacturing transparent and flexible electrodes.

In-situ isomerization and reversible self-assembly of photoresponsive polymeric colloidal molecules enabled by ON and OFF light control

Photocatalytic colloids enable light-triggered nonequilibrium interactions and are emerging as key components for the self-assembly of colloidal molecules (CMs) out of equilibrium. However, the material choices have largely been limited to inorganic substances and the potential for reconfiguring structures through dynamic light control remains underexplored, despite light being a convenient handle for tuning nonequilibrium interactions. Here, we introduce photoresponsive N,O-containing covalent organic polymer (NOCOP) colloids, which display multi-wavelength triggered fluorescence and switchable diffusiophoretic interactions with the addition of triethanolamine. Our system can form various flexible structures, including ABn-type molecules and linear chains. By varying the relative sizes of active to passive colloids, we significantly increase the structural diversity of A2B2-type molecules. Most importantly, we demonstrate in-situ transitions between different isomeric configurations and the reversible assembly of various structures, enabled by on-demand light ON and OFF control of diffusiophoretic interactions. Our work introduces a new photoresponsive colloidal system and a novel strategy for constructing and reconfiguring colloidal assemblies, with promising applications in microrobotics, optical devices, and smart materials.

Effect of non-additive mixing on entropic bonding strength and phase behavior of binary nanocrystal superlattices

Non-additive mixing plays a key role in the properties of molecular fluids and solids. In this work, the potential for athermal order-disorder phase transitions is explored in non-additive binary colloidal nanoparticles that form substitutionally ordered compounds, namely, for equimolar mixtures of octahedra + spheres, which form a CsCl lattice compound, and cubes + spheres, which form a NaCl crystal. Monte Carlo simulations that target phase coexistence conditions were used to examine the effect on compound formation of varying degrees of negative non-additivity created by component size asymmetry and by size-tunable indentations in the polyhedra's facets, intended to allow the nestling of neighboring spheres. Our results indicate that the stabilization of the compound crystal requires a relatively large degree of negative non-additivity, which depends on particle geometry and the packing of the relevant phases. It is found that negative non-additivity can be achieved in mixtures of large spheres and small cubes having no indentations and lead to the athermal crystallization of the NaCl lattice. For similarly sized components, athermal congruent transitions are attainable and non-additivity can be generated through indentations, especially for the cubes + spheres system. Increasing indentation leads to lower phase coexistence free energy and pressure in the cubes + spheres system but has the opposite effect in the octahedra + spheres system. These results indicate a stronger stabilizing effect on the athermal compound phase by the cubes' indentations, where a deeper nestling of the spheres leads to a denser compound phase and a larger reduction in the associated pressure-volume free-energy term.

Engineering Anisotropy into Organized Nanoscale Matter

Programming the organization of discrete building blocks into periodic and quasi-periodic arrays is challenging. Methods for organizing materials are particularly important at the nanoscale, where the time required for organization processes is practically manageable in experiments, and the resulting structures are of interest for applications spanning catalysis, optics, and plasmonics. While the assembly of isotropic nanoscale objects has been extensively studied and described by empirical design rules, recent synthetic advances have allowed anisotropy to be programmed into macroscopic assemblies made from nanoscale building blocks, opening new opportunities to engineer periodic materials and even quasicrystals with unnatural properties. In this review, we define guidelines for leveraging anisotropy of individual building blocks to direct the organization of nanoscale matter. First, the nature and spatial distribution of local interactions are considered and three design rules that guide particle organization are derived. Subsequently, recent examples from the literature are examined in the context of these design rules. Within the discussion of each rule, we delineate the examples according to the dimensionality (0D-3D) of the building blocks. Finally, we use geometric considerations to propose a general inverse design-based construction strategy that will enable the engineering of colloidal crystals with unprecedented structural control.

Potential effects on effective attraction between probes diffusing in colloidal crystal

Considering the significant influence of interparticle potentials on traditional depletion forces, we here employ computer simulations to investigate how varying potentials between particles affect the effective interaction of probes diffusing freely in a 2D colloidal crystal. Our results reveal that attractive potentials between the background particles and probes significantly modify the interprobe effective interactions, whereas long-range repulsive tails among the background particles have minimal impact. Furthermore, we observe contrary temperature dependencies of the effective force for soft and stiff repulsions between the background particles. These findings provide deeper insights into how direct interparticle potentials shape entropic-dominated effective forces mediated by colloidal crystals.

Synthesis and Assembly of Photoresponsive Colloidal Tubes

Inspired by the sophisticated multicomponent and multistage assembly of proteins and their mixtures in living cells, this study rationally designs and fabricates photoresponsive colloidal tubes that can self-assemble and hybrid-assemble when mixed with colloidal spheres and rods. Time-resolved observation and computer simulation reveal that the assembly is driven by phoretic attraction originating from osmotic pressures. These pressures are induced by the chemical concentration gradients generated by the photochemical reaction caused by colloidal tubes in a H2O2 solution under ultraviolet (UV) irradiation. The assembled structure is dictated by the size and shape of the constituent colloids as well as the intensity of the UV irradiation. Additionally, the resulting assembly can undergo self-propelled motion originating from the broken symmetry of the surrounding concentration gradients. This motion can be steered by a magnetic field and used for microscale cargo delivery. The study demonstrates a facile synthesis method for colloidal tubes and highlights their unique potential for controlled, hierarchical self-assembly and hybrid-assembly.

Designing highly efficient interlocking interactions in anisotropic active particles

Cluster formation of microscopic swimmers is key to the formation of biofilms and colonies, efficient motion and nutrient uptake, but, in the absence of other interactions, requires high swimmer concentrations to occur. Here we experimentally and numerically show that cluster formation can be dramatically enhanced by an anisotropic swimmer shape. We analyze a class of model microswimmers with a shape that can be continuously tuned from spherical to bent and straight rods. In all cases, clustering can be described by Michaelis-Menten kinetics governed by a single scaling parameter that depends on particle density and shape only. We rationalize these shape-dependent dynamics from the interplay between interlocking probability and cluster stability. The bent rod shape promotes assembly in an interlocking fashion even at vanishingly low particle densities and we identify the most efficient shape to be a semicircle. Our work provides key insights into how shape can be used to rationally design out-of-equilibrium self-organization, key to creating active functional materials and processes that require two-component assembly with high fidelity.

Economical routes to size-specific assembly of self-closing structures

Programmable self-assembly has seen an explosion in the diversity of synthetic crystalline materials, but developing strategies that target "self-limiting" assemblies has remained a challenge. Among these, self-closing structures, in which the local curvature defines the finite global size, are prone to polymorphism due to thermal bending fluctuations, a problem that worsens with increasing target size. Here, we show that assembly complexity can be used to eliminate this source of polymorphism in the assembly of tubules. Using many distinct components, we prune the local density of off-target geometries, increasing the selectivity of the tubule width and helicity to nearly 100%. We further show that by reducing the design constraints to target either the pitch or the width alone, fewer components are needed to reach complete selectivity. Combining experiments with theory, we reveal an economical limit, which determines the minimum number of components required to create arbitrary assembly sizes with full selectivity.

Spearheading a new era in complex colloid synthesis with TPM and other silanes

Colloid science has recently grown substantially owing to the innovative use of silane coupling agents (SCAs), especially 3-trimethoxysilylpropyl methacrylate (TPM). SCAs were previously used mainly as modifying agents, but their ability to form droplets and condense onto pre-existing structures has enabled their use as a versatile and powerful tool to create novel anisotropic colloids with increasing complexity. In this Review, we highlight the advances in complex colloid synthesis facilitated by the use of TPM and show how this has driven remarkable new applications. The focus is on TPM as the current state-of-the-art in colloid science, but we also discuss other silanes and their potential to make an impact. We outline the remarkable properties of TPM colloids and their synthesis strategies, and discuss areas of soft matter science that have benefited from TPM and other SCAs.

Self-Assembled Ring-Based Complex Colloidal Particles by Lock-And-Key Interaction and Their Self-Assembly into Unusual Colloidal Crystals

Creating hierarchical crystalline materials using simple colloids or nanoparticles is very challenging, as it is usually impossible to achieve hierarchical structures without nonhierarchical colloidal interactions. Here, we present a hierarchical self-assembly (SA) route that employs colloidal rings and anisotropic colloidal particles to form complex colloids and uses them as building blocks to form unusual colloidal columnar liquid crystals or crystals. This route is realized by designing hierarchical SA driving forces that is controlled by the colloidal shape and shape-dependent depletion attraction. Depletion-induced lock-and-key interaction is the first driving force, which ensures a high efficiency (>90%) to load colloidal particles of other shapes such as spheres, spherocylinders, and oblate ellipsoids into rings, providing high-quality building blocks. Their SA into ordered superstructures has to require a second driving force such as higher volume fraction and/or stronger depletion attraction. As a result, unusual hierarchical colloidal (liquid) crystals, which have previously been difficult to fabricate by simple binary assembly, can be achieved. This work presents a significant advancement in the field of hierarchical SA, demonstrating a promising strategy for constructing many unprecedented crystalline materials by the SA route.

Depletion Strategies for Crystallized Layers of Two-Dimensional Nanosheets to Enhance Lithium-Ion Conductivity in Polymer Nanocomposites

The assembly of long-range aligned structures of two-dimensional nanosheets (2DNSs) in polymer nanocomposites (PNCs) is in urgent need for the design of nanoelectronics and lightweight energy-storage materials of high conductivity for electricity or heat. These 2DNS are thin and exhibit thermal fluctuations, leading to an intricate interplay with polymers in which entropic effects can be exploited to facilitate a range of different assemblies. In molecular dynamics simulations of experimentally studied 2DNSs, we show that the layer-forming crystallization of 2DNSs is programmable by regulating the strengths and ranges of polymer-induced entropic depletion attractions between pairs of 2DNSs, as well as between single 2DNSs and a substrate surface, by exclusively tuning the temperature and size of the 2DNS. Enhancing the temperature supports the 2DNS-substrate depletion rather than crystallization of 2DNSs in the bulk, leading to crystallized layers of 2DNSs on the substrate surfaces. On the other hand, the interaction range of the 2DNS-2DNS depletion attraction extends further than the 2DNS-substrate attraction whenever the 2DNS size is well above the correlation length of the polymers, which results in a nonmonotonic dependence of the crystallization layer on the 2DNS size. It is demonstrated that the depletion-tuned crystallization layers of 2DNSs contribute to a conductive channel in which individual lithium ions (Li ions) migrate efficiently through the PNCs. This work provides statistical and dynamical insights into the balance between the 2DNS-2DNS and 2DNS-substrate depletion interactions in polymer-2DNS composites and highlights the possibilities to exploit depletion strategies in order to engineer crystallization processes of 2DNSs and thus to control electrical conductivity.

Depletion-induced crystallization of anisotropic triblock colloids

The intricate interplay between colloidal particle shape and precisely engineered interaction potentials has paved the way for the discovery of unprecedented crystal structures in both two and three dimensions. Here, we make use of anisotropic triblock colloidal particles composed of two distinct materials. The resulting surface charge heterogeneity can be exploited to generate regioselective depletion interactions and directional bonding. Using extensive molecular dynamics simulations and a dimensionality reduction analysis approach, we map out state diagrams for the self-assembly of such colloids as a function of their aspect ratio and for varying depletant features in a quasi two-dimensional set-up. We observe the formation of a wide variety of crystal structures such as a herringbone, brick-wall, tilted brick-wall, and (tilted) ladder-like structures. More specifically, we determine the optimal parameters to enhance crystallization, and investigate the nucleation process. Additionally, we explore the potential of using crystalline monolayers as templates for deposition, thereby creating complex three-dimensional structures that hold promise for future applications.

Rotational diffusion of colloidal microspheres near flat walls

Recently, colloids with an off-center fluorescent core and homogeneous composition have been developed to measure the rotational diffusivity of microparticles using 3D confocal microscopy in refractive index-matched suspensions. Here, we show that the same particles may be imaged using a standard fluorescence microscope to yield their rotational diffusion coefficients. Trajectories of the off-center core may be combined with known expressions for the correlation decay of particle orientations to determine an effective rotational diffusivity. For sedimented particles, we also find the rotational diffusivity about axes perpendicular and parallel to the interface by adding some bright field illumination and simultaneously tracking both the core and the particle. Trajectories for particles of different sizes yield excellent agreement with hydrodynamic models of rotational diffusion near flat walls, taking the sedimentation-diffusion equilibrium into account. Finally, we explore the rotational diffusivity of particles in crowded two-dimensional monolayers, finding a different reduction of the rotational motion about the two axes depending on the colloidal microstructure.

Reconfigurable Assembly of Planar Colloidal Molecules via Chemical Reaction and Electric Polarization

Colloidal molecules, ordered structures assembled from micro- and nanoparticles, serve as a valuable model for understanding the behavior of real molecules and for constructing materials with tunable properties. In this work, we introduce a universal strategy for assembling colloidal molecules consisting of a central active particle surrounded by several passive particles as ligands. During the assembly process, active particles attract the surrounding passive particles through phoresis and osmosis resulting from the chemical reactions on the surface of the active particles, while passive particles repel each other due to the electric polarization induced by an alternating current (AC) electric field. By carefully selecting particles of varying structures and sizes, we have assembled colloidal molecules of symmetric and asymmetric dimers, trimers, and multimers. Furthermore, the coordination number of these colloidal molecules can be regulated in real time and in situ by tuning the interaction forces between the constituent particles. Brownian dynamics simulations reproduced the formation of the colloidal molecules and validated that the self-assembly arises from chemically induced attraction and electrical dipolar repulsion. This strategy for reconfigurable colloidal assemblies poses the potential for designing adaptive micro-nanomachines.

Direct Imaging of "Patch-Clasping" and Relaxation in Robust and Flexible Nanoparticle Assemblies

Polymer patching on inorganic nanoparticles (NPs) enables multifunctionality and directed self-assembly into nonclosely packed optical and mechanical metamaterials. However, experimental demonstration of such assemblies has been scant due to challenges in leveraging patch-induced NP-NP attractions and understanding NP self-assembly dynamics. Here we use low-dose liquid-phase transmission electron microscopy to visualize the dynamic behaviors of tip-patched triangular nanoprisms upon patch-clasping, where polymer patches interpenetrate to form cohesive bonds that connect NPs. Notably, these bonds are longitudinally robust but rotationally flexible. Patch-clasping is found to allow highly selective tip-tip assembly, interconversion between dimeric bowtie and sawtooth configurations, and collective structural relaxation of NP networks. The integration of single particle tracking, polymer physics theory, and molecular dynamics simulation reveals the macromolecular origin of patch-clasping-induced NP dynamics. Our experiment-computation integration can aid the design of stimuli-responsive nanomaterials, such as topological metamaterials for chiral sensors, waveguides, and nanoantennas.

Regioselective Growth of Colloidal Crystals Induced by Depletion Attraction

Colloidal crystals display photonic stopbands that generate reflective structural colors. While micropatterning offers significant value for various applications, the resolution is somewhat limited for conventional top-down approaches. In this work, a simple, single-step bottom-up approach is introduced to produce photonic micropatterns through depletion-mediated regioselective growth of colloidal crystals. Lithographically-featured micropatterns with planar surfaces and nano-needle arrays as substrates are employed. Heterogeneous nucleation is drastically suppressed on nano-needle arrays due to minimal particle-to-needles overlap of excluded volumes, while it is promoted on planar surfaces with large particle-to-plane volume overlap, enabling regioselective growth of colloidal crystals. This strategy allows high-resolution micropatterning of colloidal photonic crystals, with a minimum feature size as small as 10 µm. Stopband positions, or structural colors, are controllable through concentration and depletant and salt, as well as particle size. Notably, secondary colors can be created through structural color mixing by simultaneously crystallizing two different particle sizes into their own crystal grains, resulting in two distinct reflectance peaks at controlled wavelengths. The simple and highly reproducible method for regioselective colloidal crystallization provides a general route for designing elaborate photonic micropatterns suitable for various applications.

Janus particles with tunable patch symmetry and their assembly into chiral colloidal clusters

Janus particles, which have an attractive patch on the otherwise repulsive surface, have been commonly employed for anisotropic colloidal assembly. While current methods of particle synthesis allow for control over the patch size, they are generally limited to producing dome-shaped patches with a high symmetry (C∞). Here, we report on the synthesis of Janus particles with patches of various tunable shapes, having reduced symmetries ranging from C2v to C3v and C4v. The Janus particles are synthesized by partial encapsulation of an octahedral metal-organic framework particle (UiO-66) in a polymer matrix. The extent of encapsulation is precisely regulated by a stepwise, asymmetric dewetting process that exposes selected facets of the UiO-66 particle. With depletion interaction, the Janus particles spontaneously assemble into colloidal clusters reflecting the particles' shapes and patch symmetries. We observe the formation of chiral structures, whereby chirality emerges from achiral building blocks. With the ability to encode symmetry and directional bonding information, our strategy could give access to more complex colloidal superstructures through assembly.

A computational toolbox for the assembly yield of complex and heterogeneous structures

The self-assembly of complex structures from a set of non-identical building blocks is a hallmark of soft matter and biological systems, including protein complexes, colloidal clusters, and DNA-based assemblies. Predicting the dependence of the equilibrium assembly yield on the concentrations and interaction energies of building blocks is highly challenging, owing to the difficulty of computing the entropic contributions to the free energy of the many structures that compete with the ground state configuration. While these calculations yield well known results for spherically symmetric building blocks, they do not hold when the building blocks have internal rotational degrees of freedom. Here we present an approach for solving this problem that works with arbitrary building blocks, including proteins with known structure and complex colloidal building blocks. Our algorithm combines classical statistical mechanics with recently developed computational tools for automatic differentiation. Automatic differentiation allows efficient evaluation of equilibrium averages over configurations that would otherwise be intractable. We demonstrate the validity of our framework by comparison to molecular dynamics simulations of simple examples, and apply it to calculate the yield curves for known protein complexes and for the assembly of colloidal shells.

The entropy-controlled strategy in self-assembling systems

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

Synthesis of dimpled polymer particles and polymer particles with protrusions - Past, present, and future

Since the development of emulsion polymerization techniques, polymer particles have become the epitome of standard colloids due to the exceptional control over size, size distribution, and composition the synthesis methods allow reaching. The exploration of different variations of the synthesis methods has led to the discovery of more advanced techniques, enabling control over their composition and shape. Many early investigations focused on forming particles with protrusions (with one protrusion, called dumbbell particles) and particles with concavities, also called dimpled particles. This paper reviews the literature covering the synthesis, functionalization, and applications of both types of particles. The focus has been on the rationalization of the various approaches used to prepare such particles and on the discussion of the mechanisms of formation not just from the experimental viewpoint but also from the standpoint of thermodynamics. The primary motivation to combine in a single review the preparation of both types of particles has been the observation of similarities among some of the methods developed to prepare dimpled particles, which sometimes include the formation of particles with protrusions and vice versa. The most common applications of these particles have been discussed as well. By looking at the different approaches developed in the literature under one general perspective, we hope to stimulate a more ample use of these particles and promote the development of even more effective synthetic protocols.

Hydrodynamic Anisotropy of Depletion in Nonequilibrium

Active colloids in a bath of inert particles of smaller size cause anisotropic depletion. The active hydrodynamics of this nonequilibrium phenomenon, which is fundamentally different from its equilibrium counterpart and passive particles in an active bath, remains scarcely understood. Here we combine mesoscale hydrodynamic simulation as well as theoretical analysis to examine the physical origin for the active depletion around a self-propelled noninteractive colloid. Our results elucidate that the variable hydrodynamic effect critically governs the microstructure of the depletion zone. Three characteristic states of anisotropic depletion are identified, depending on the strength and stress of activity. This yields a state diagram of depletion in the two-parameter space, captured by developing a theoretical model with the continuum kinetic theory and leading to a mechanistic interpretation of the hydrodynamic anisotropy of depletion. Furthermore, we demonstrate that such depletion in nonequilibrium results in various clusters with ordered organization of squirmers, which follows a distinct principle contrary to that of the entropy scenario of depletion in equilibrium. The findings might be of immediate interest to tune the hydrodynamics-mediated anisotropic interactions and active nonequilibrium organizations in the self-propulsion systems.

Inspired Beyond Nature: Three Decades of Spherical Nucleic Acids and Colloidal Crystal Engineering with DNA

The conception, synthesis, and invention of a nanostructure, now known as the spherical nucleic acid, or SNA, in 1996 marked the advent of a new field of chemistry. Over the past three decades, the SNA and its analogous anisotropic equivalents have provided an avenue for us to think about some of the most fundamental concepts in chemistry in new ways and led to technologies that are significantly impacting fields from medicine to materials science. A prime example is colloidal crystal engineering with DNA, the framework for using SNAs and related structures to synthesize programmable matter. Herein, we document the evolution of this framework, which was initially inspired by nature, and describe how it now allows researchers to chart paths to move beyond it, as programmable matter with real-world significance is envisioned and created.

GraphVAMPnets for uncovering slow collective variables of self-assembly dynamics

Uncovering slow collective variables (CVs) of self-assembly dynamics is important to elucidate its numerous kinetic assembly pathways and drive the design of novel structures for advanced materials through the bottom-up approach. However, identifying the CVs for self-assembly presents several challenges. First, self-assembly systems often consist of identical monomers, and the feature representations should be invariant to permutations and rotational symmetries. Physical coordinates, such as aggregate size, lack high-resolution detail, while common geometric coordinates like pairwise distances are hindered by the permutation and rotational symmetry challenges. Second, self-assembly is usually a downhill process, and the trajectories often suffer from insufficient sampling of backward transitions that correspond to the dissociation of self-assembled structures. Popular dimensionality reduction methods, such as time-structure independent component analysis, impose detailed balance constraints, potentially obscuring the true dynamics of self-assembly. In this work, we employ GraphVAMPnets, which combines graph neural networks with a variational approach for Markovian process (VAMP) theory to identify the slow CVs of the self-assembly processes. First, GraphVAMPnets bears the advantages of graph neural networks, in which the graph embeddings can represent self-assembly structures in high-resolution while being invariant to permutations and rotational symmetries. Second, it is built upon VAMP theory, which studies Markov processes without forcing detailed balance constraints, which addresses the out-of-equilibrium challenge in the self-assembly process. We demonstrate GraphVAMPnets for identifying slow CVs of self-assembly kinetics in two systems: the aggregation of two hydrophobic molecules and the self-assembly of patchy particles. We expect that our GraphVAMPnets can be widely applied to molecular self-assembly.

Shape-Dictated Self-Assembly of Photoresponsive Hybrid Colloids

The shape-dictated self-assembly of hybrid colloids induced by chemical concentration gradients generated by photocatalytic reactions of the colloids is studied. Different shapes enable the formation of assemblies with distinct lattice structures including hexagons, distorted hexagons, and squares, which are corroborated by computer simulations. Furthermore, assemblies change from lattices to chains when increasing the attraction between the colloids. The results show that photoresponsive hybrid colloids possess a unique capability for shape-dependent self-assembly, offering a practical and versatile approach to manipulate self-assembly at the microscale.

Colloidal robotics

Robots have components that work together to accomplish a task. Colloids are particles, usually less than 100 µm, that are small enough that they do not settle out of solution. Colloidal robots are particles capable of functions such as sensing, computation, communication, locomotion and energy management that are all controlled by the particle itself. Their design and synthesis is an emerging area of interdisciplinary research drawing from materials science, colloid science, self-assembly, robophysics and control theory. Many colloidal robot systems approach synthetic versions of biological cells in autonomy and may find ultimate utility in bringing these specialized functions to previously inaccessible locations. This Perspective examines the emerging literature and highlights certain design principles and strategies towards the realization of colloidal robots.

Synthetic strategies for nonporous organosilica nanoparticles from organosilanes

Organosilica nanoparticles refer to silica nanoparticles containing carbon along with organic or functional groups and can be divided into mesoporous organosilica nanoparticles and nonporous organosilica nanoparticles. During the past few decades, considerable efforts have been devoted to the development of organosilica nanoparticles directly from organosilanes. However, most of the reports have focused on mesoporous organosilica nanoparticles, while relatively few are concerned with nonporous organosilica nanoparticles. The synthesis of nonporous organosilica nanoparticles typically involves (i) self-condensation of an organosilane as the single source, (ii) co-condensation of two or more types of organosilanes, (iii) co-condensation of tetraalkoxysilane and an organosilane, and (iv) spontaneous emulsification and the subsequent radical polymerization of 3-(trimethoxysilyl)propyl methacrylate (TPM). This article aims to provide a review on the synthetic strategies of this important type of colloidal particle, followed by a brief discussion on their applications and future perspectives.

Statistics of carrier-cargo complexes

We explore the statistics of assembling soft-matter building blocks to investigate the uptake and encapsulation of cargo particles by carriers engulfing their load. While the such carrier-cargo complexes are important for many applications out of equilibrium, such as drug delivery and synthetic cell encapsulation, we uncover here the basic statistical physics in minimal hard-core-like models for particle uptake. Introducing an exactly solvable equilibrium model in one dimension, we demonstrate that the formation of carrier-cargo complexes can be largely tuned by both the cargo concentration and the carriers' interior size. These findings are intuitively explained by interpreting the internal free space (partition function) of the cargo inside a carrier as its engulfment strength, which can be mapped to an external control parameter (chemical potential) of an additional effective particle species. Assuming a hard carrier membrane, such a mapping can be exactly applied to account for multiple cargo uptake involving various carrier or cargo species and even attractive uptake mechanisms, while soft interactions require certain approximations. We further argue that the Boltzmann occupation law identified within our approach is broken when particle uptake is governed by nonequilibrium forces. Speculating on alternative occupation laws using effective parameters, we put forward a Bose-Einstein-like phase transition associated with polydisperse carrier properties.

Fine-tuning of colloidal polymer crystals by molecular simulation

Through extensive molecular simulations we determine a phase diagram of attractive, fully flexible polymer chains in two and three dimensions. A rich collection of distinct crystal morphologies appear, which can be finely tuned through the range of attraction. In three dimensions these include the face-centered cubic, hexagonal close packed, simple hexagonal, and body-centered cubic crystals and the Frank-Kasper phase. In two dimensions the dominant structures are the triangular and square crystals. A simple geometric model is proposed, based on the concept of cumulative neighbors of ideal crystals, which can accurately predict most of the observed structures and the corresponding transitions. The attraction range can thus be considered as an adjustable parameter for the design of colloidal polymer crystals with tailored morphologies.

Nanoparticle Self-Assembly: From Design Principles to Complex Matter to Functional Materials

The creation of matter with varying degrees of complexities and desired functions is one of the ultimate targets of self-assembly. The ability to regulate the complex interactions between the individual components is essential in achieving this target. In this direction, the initial success of controlling the pathways and final thermodynamic states of a self-assembly process is promising. Despite the progress made in the field, there has been a growing interest in pushing the limits of self-assembly processes. The main inception of this interest is that the intended self-assembled state, with varying complexities, may not be "at equilibrium (or at global minimum)", rendering free energy minimization unsuitable to form the desired product. Thus, we believe that a thorough understanding of the design principles as well as the ability to predict the outcome of a self-assembly process is essential to form a collection of the next generation of complex matter. The present review highlights the potent role of finely tuned interparticle interactions in nanomaterials to achieve the preferred self-assembled structures with the desired properties. We believe that bringing the design and prediction to nanoparticle self-assembly processes will have a similar effect as retrosynthesis had on the logic of chemical synthesis. Along with the guiding principles, the review gives a summary of the different types of products created from nanoparticle assemblies and the functional properties emerging from them. Finally, we highlight the reasonable expectations from the field and the challenges lying ahead in the creation of complex and evolvable matter.

Colloidal antibiotic mimics: selective capture and killing of microorganisms by shape-anisotropic colloids

The development of targeted and efficient antimicrobials for the selective killing of pathogenic bacteria is of great importance, yet remains challenging. Here, we propose a targeted approach to selectively capture and kill microorganisms with colloidal antibiotic mimics that are readily prepared by common chemical syntheses. The mimics are shape-anisotropic colloids, which can selectively capture shape-matching microorganisms due to lock-key depletion attractions. Furthermore, after being modified with gold nanoparticles (AuNPs) and irradiated with near-infrared light, the colloidal mimics can kill the selectively captured microorganisms due to the localized photothermal effect of the AuNPs. The work demonstrates the important ability of anisotropic colloids to selectively capture and precisely kill microorganisms, which holds considerable promise for safe and adaptive antibacterial therapies without the risk of antibiotic resistance.

Competition between deformation and free volume quantified by 3D image analysis of red blood cell

Cells in living organisms are subjected to mechanical strains caused by external forces like overcrowding, resulting in strong deformations that affect cell function. We study the interplay between deformation and crowding of red blood cells (RBCs) in dispersions of nonabsorbing rod-like viruses. We identify a sequence of configurational transitions of RBC doublets, including configurations that can only be induced by long-ranged attraction: highly fluctuating T-shaped and face-to-face configurations at low, and doublets approaching a complete spherical configuration at high, rod concentrations. Complementary simulations are used to explore different energy contributions to deformation as well as the stability of RBC doublet configurations. Our advanced analysis of 3D reconstructed confocal images of RBC doublets quantifies the depletion interaction and the resulting deformation energy. Thus, we introduce a noninvasive, high-throughput platform that is generally applicable to investigate the mechanical response of biological cells to external forces and characterize their mechanical properties.

Molecular Engineering of Colloidal Atoms

Creation of architectures with exquisite hierarchies actuates the germination of revolutionized functions and applications across a wide range of fields. Hierarchical self-assembly of colloidal particles holds the promise for materialized realization of structural programing and customizing. This review outlines the general approaches to organize atom-like micro- and nanoparticles into prescribed colloidal analogs of molecules by exploiting diverse interparticle driving motifs involving confining templates, interactive surface ligands, and flexible shape/surface anisotropy. Furthermore, the self-regulated/adaptive co-assembly of simple unvarnished building blocks is discussed to inspire new designs of colloidal assembly strategies.

Characterization and Optimization of Fluorescent Organosilica Colloids for 3D Confocal Microscopy Prepared Under "Zero-Flow" Conditions

We optimize and characterize the preparation of 3-trimethoxysilyl propyl methacrylate (TPM) colloidal suspensions for three-dimensional confocal microscopy. We revisit a simple synthesis of TPM microspheres by nucleation of droplets from prehydrolyzed TPM oil in a "zero-flow" regime and demonstrate how precise and reproducible control of particle size may be achieved via single-step nucleation with a focus on how the reagents are mixed. We also revamp the conventional dyeing method for TPM particles to achieve uniform transfer of a fluorophore to the organosilica droplets, improving particle identification. Finally, we illustrate how a ternary mixture of tetralin, trichloroethylene, and tetrachloroethylene may be used as a suspension medium which matches the refractive index of these particles while allowing independent control of the density mismatch between particle and solvent.

Self-Assembled Tetratic Crystals by Orthogonal Colloidal Force

Bonding simple building blocks to create crystalline materials with design has been sophisticated in the molecular world, but this is still very challenging for anisotropic nanoparticles or colloids, because the particle arrangements, including position and orientation, cannot be manipulated as expected. Here biconcave polystyrene (PS) discs to present a shape self-recognition route are used, which can control both the position and orientation of particles during self-assembly by directional colloidal forces. An unusual but very challenging two-dimensional (2D) open superstructure-tetratic crystal (TC)-is achieved. The optical properties of the 2D TCs are studied by the finite difference time domain method, showing that the PS/Ag binary TC can be used to modulate the polarization state of the incident light, for example, converting the linearly polarized light into left-handed or right-handed circularly polarized light. This work paves an important way for self-assembling many unprecedented crystalline materials.

Visualizing defect dynamics by assembling the colloidal graphene lattice

Graphene has been under intense scientific interest because of its remarkable optical, mechanical and electronic properties. Its honeycomb structure makes it an archetypical two-dimensional material exhibiting a photonic and phononic band gap with topologically protected states. Here, we assemble colloidal graphene, the analogue of atomic graphene using pseudo-trivalent patchy particles, allowing particle-scale insight into crystal growth and defect dynamics. We directly observe the formation and healing of common defects, like grain boundaries and vacancies using confocal microscopy. We identify a pentagonal defect motif that is kinetically favoured in the early stages of growth, and acts as seed for more extended defects in the later stages. We determine the conformational energy of the crystal from the bond saturation and bond angle distortions, and follow its evolution through the energy landscape upon defect rearrangement and healing. These direct observations reveal that the origins of the most common defects lie in the early stages of graphene assembly, where pentagons are kinetically favoured over the equilibrium hexagons of the honeycomb lattice, subsequently stabilized during further growth. Our results open the door to the assembly of complex 2D colloidal materials and investigation of their dynamical, mechanical and optical properties.

Metal-Organic Framework-Based Colloidal Particle Synthesis, Assembly, and Application

Metal-organic frameworks (MOFs) assembled from metal nodes and organic ligands have received significant attention over the past two decades for their fascinating porous properties and broad applications. Colloidal MOFs (CMOFs) not only inherit the intrinsic properties of MOFs, but can also serve as building blocks for self-assembly to make functional materials. Compared to bulk MOFs, the colloidal size of CMOFs facilitates further manipulation of CMOF particles in a single or collective state in a liquid medium. The resulting crystalline order obtained by self-assembly in position and orientation can effectively improve performance. In this review, we summarize the latest developments of CMOFs in synthesis strategies, self-assembly methods, and related applications. Finally, we discuss future challenges and opportunities of CMOFs in synthesis and assembly, by which we hope that CMOFs can be further developed into new areas for a wider range of applications.

Local and Global Order in Dense Packings of Semi-Flexible Polymers of Hard Spheres

The local and global order in dense packings of linear, semi-flexible polymers of tangent hard spheres are studied by employing extensive Monte Carlo simulations at increasing volume fractions. The chain stiffness is controlled by a tunable harmonic potential for the bending angle, whose intensity dictates the rigidity of the polymer backbone as a function of the bending constant and equilibrium angle. The studied angles range between acute and obtuse ones, reaching the limit of rod-like polymers. We analyze how the packing density and chain stiffness affect the chains' ability to self-organize at the local and global levels. The former corresponds to crystallinity, as quantified by the Characteristic Crystallographic Element (CCE) norm descriptor, while the latter is computed through the scalar orientational order parameter. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies, developing a complete phase diagram as a function of packing density and equilibrium bending angle. A plethora of structures are obtained, ranging between random hexagonal closed packed morphologies of mixed character and almost perfect face centered cubic (FCC) and hexagonal close-packed (HCP) crystals at the level of monomers, and nematic mesophases, with prolate and oblate mesogens at the level of chains. For rod-like chains, a delay is observed between the establishment of the long-range nematic order and crystallization as a function of the packing density, while for right-angle chains, both transitions are synchronized. A comparison is also provided against the analogous packings of monomeric and fully flexible chains of hard spheres.

Solvent-induced assembly of mono- and divalent silica nanoparticles

Particles with attractive patches are appealing candidates to be used as building units to fabricate novel colloidal architectures by self-assembly. Here, we report the synthesis of one-patch silica nanoparticles, which consist of silica half-spheres whose concave face carries in its center a polymeric patch made of grafted polystyrene chains. The multistage synthesis allows for a fine control of the patch-to-particle size ratio from 0.23 to 0.57. The assembly of the patchy nanoparticles can be triggered by reducing the solvent quality for the polystyrene chains. Dimers or trimers can be obtained by tuning the patch-to-particle size ratio. When mixed with two-patch nanoparticles, one-patch nanoparticles control the length of the resulting chains by behaving as colloidal chain stoppers. The present strategy allows for future elaboration of novel colloidal structures by controlled assembly of nanoparticles.

Optimization of non-equilibrium self-assembly protocols using Markov state models

The promise of self-assembly to enable the bottom-up formation of materials with prescribed architectures and functions has driven intensive efforts to uncover rational design principles for maximizing the yield of a target structure. Yet, despite many successful examples of self-assembly, ensuring kinetic accessibility of the target structure remains an unsolved problem in many systems. In particular, long-lived kinetic traps can result in assembly times that vastly exceed experimentally accessible timescales. One proposed solution is to design non-equilibrium assembly protocols in which system parameters change over time to avoid such kinetic traps. Here, we develop a framework to combine Markov state model (MSM) analysis with optimal control theory to compute a time-dependent protocol that maximizes the yield of the target structure at a finite time. We present an adjoint-based gradient descent method that, in conjunction with MSMs for a system as a function of its control parameters, enables efficiently optimizing the assembly protocol. We also describe an interpolation approach to significantly reduce the number of simulations required to construct the MSMs. We demonstrate our approach with two examples; a simple semi-analytic model for the folding of a polymer of colloidal particles, and a more complex model for capsid assembly. Our results show that optimizing time-dependent protocols can achieve significant improvements in the yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.

Light-Activated Colloidal Micromotors with Synthetically Tunable Shapes and Shape-Directed Propulsion

Controlling the propulsion modes of colloidal micromotors, from translational to spinning and helical motion, expands the versatility of their potential applications in microrobotics and micromachinery. Engineering colloidal shapes with designed asymmetry can regulate their propulsion behaviors, yet current methods rely on complicated and costly fabrication processes such as lithography. Herein, we present a solution-based synthesis of light-activated colloidal motors adopting straight and various tunable bent geometries, which feature controlled asymmetry and allow shape-directed propulsions. The keys for our strategy are the synthesis of bent silica rods with a tailored bending position and degree, together with the site-specific installation of a photoactive engine. Upon light illumination, the resulting particles propel autonomously, whereby their shape information is translated to various propulsion modes including linear locomotion, steering, and spinning. This low-cost, scalable method for fabricating micromotors with a high degree of control of shapes could promote study in microscale actuation, in active assembly, and eventually for fabrication of colloidal functional materials.