Revealing pseudorotation and ring-opening reactions in colloidal organic molecules

Nanoalignment by critical Casimir torques

The manipulation of microscopic objects requires precise and controllable forces and torques. Recent advances have led to the use of critical Casimir forces as a powerful tool, which can be finely tuned through the temperature of the environment and the chemical properties of the involved objects. For example, these forces have been used to self-organize ensembles of particles and to counteract stiction caused by Casimir-Liftshitz forces. However, until now, the potential of critical Casimir torques has been largely unexplored. Here, we demonstrate that critical Casimir torques can efficiently control the alignment of microscopic objects on nanopatterned substrates. We show experimentally and corroborate with theoretical calculations and Monte Carlo simulations that circular patterns on a substrate can stabilize the position and orientation of microscopic disks. By making the patterns elliptical, such microdisks can be subject to a torque which flips them upright while simultaneously allowing for more accurate control of the microdisk position. More complex patterns can selectively trap 2D-chiral particles and generate particle motion similar to non-equilibrium Brownian ratchets. These findings provide new opportunities for nanotechnological applications requiring precise positioning and orientation of microscopic objects.

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.

Inverse design of a pyrochlore lattice of DNA origami through model-driven experiments

Sophisticated statistical mechanics approaches and human intuition have demonstrated the possibility of self-assembling complex lattices or finite-size constructs. However, attempts so far have mostly only been successful in silico and often fail in experiment because of unpredicted traps associated with kinetic slowing down (gelation, glass transition) and competing ordered structures. Theoretical predictions also face the difficulty of encoding the desired interparticle interaction potential with the experimentally available nano- and micrometer-sized particles. To overcome these issues, we combine SAT assembly (a patchy-particle interaction design algorithm based on constrained optimization) with coarse-grained simulations of DNA nanotechnology to experimentally realize trap-free self-assembly pathways. We use this approach to assemble a pyrochlore three-dimensional lattice, coveted for its promise in the construction of optical metamaterials, and characterize it with small-angle x-ray scattering and scanning electron microscopy visualization.

Pickering stabilization mechanism revealed through direct imaging of particles with tuneable contact angle in a phase-separated binary solvent

Pickering emulsions have attracted increasing attention from multiple fields, including food, cosmetics, healthcare, pharmaceutical, and agriculture. Their stability relies on the presence of colloidal particles instead of surfactant at the droplet interface, providing steric stabilization. Here, we demonstrate the microscopic attachment and detachment of particles with tunable contact angle at the interface underlying the Pickering emulsion stability. We vary the interfacial tension continuously by varying the temperature offset of a phase-separated binary liquid from its critical point, and employ confocal microscopy to directly observe the particles at the interface to determine their coverage and contact angle as a function of the varying interfacial tension. When the interfacial tension decreases upon approaching the binary liquid's critical point, the contact angle and detachment energy (ΔE) drop, and the particles move out of the interface. Microscopic imaging suggests necking and capillary interactions lead to clustering of the particles, before they eventually desorb from the interface. Macroscopic measurements show that concomitantly, coalescence takes place, and the emulsion loses its stability. These results reveal the interplay of interfacial energies, contact angle and surface coverage that underlies the Pickering emulsion stability, opening up ways to manipulate and design the stability through the microscopic behavior of the adsorbed particles.

Uniform, convex structuring of polymeric colloids via site-selected swelling

Non-spherical, polymeric colloids serve as building blocks for advanced functional materials. We propose a novel method to produce morphologically controlled, non-spherical particles by generating site-selected, convex structures on polystyrene (PS) particles. It consists of two simple procedures: a monolayer of PS particles is illuminated with UV light and is subsequently immersed in a fluorinated solvent (HFIP). UV irradiation generates site-selected, oxidized domains on PS particles with a different solvent affinity than unoxidized PS, and HFIP immersion preferentially swells the oxidized domains. Such swelling gives rise to site-selected, convex structures on PS particles. By adjusting UV irradiation conditions, including incident and azimuth angles, the oxidized sites, i.e., the swelled portions, can be accurately situated, allowing us to produce various convex shapes, including chiral shapes at desired positions on PS particles.

Selective Vapor Condensation for the Synthesis and Assembly of Spherical Colloids with a Precise Rough Patch

Patchy particles occupy an increasingly important space in soft matter research due to their ability to assemble into intricate phases and states. Being able to fine-tune the interactions among these particles is essential to understanding the principles governing the self-assembly processes. However, current fabrication techniques often yield patches that deviate chemically and physically from the native particles, impeding the identification of the driving forces behind self-assembly. To overcome this challenge, we propose a new approach to synthesizing spherical colloids with a well-defined rough patch on their surface. By treating polystyrene microspheres with vapors of a good solvent, here an acetone-water mixture, we achieve selective polymer corrugation on the particle surface resulting in a chemically similar yet rough surface patch. The key step is the selective condensation of the acetone-water vapors on the apex of the polystyrene microparticles immobilized on a substrate, which leads to rough patch formation. We leverage the ability to tune the vapor-liquid equilibrium of the volatile acetone-water mixture to precisely control the polymer corrugation on the particle surface. We demonstrate the dependence of patch formation on particle and substrate wettability, with the condensation occurring on the particle apex only when it is more wettable than the substrate, which is consistent with Volmer's classical nucleation theory. By combining experiments and molecular dynamics simulations, we identify the role of the rough patch in the depletion interaction-driven self-assembly of the microspheres, which is crucial for designing programmable supracolloidal structures.

Activity affects the stability, deformation and breakage dynamics of colloidal architectures

Living network architectures, such as the cytoskeleton, are characterized by continuous energy injection, leading to rich but poorly understood non-equilibrium physics. There is a need for a well-controlled (experimental) model system that allows basic insight into such non-equilibrium processes. Activated self-assembled colloidal architectures can fulfill this role, as colloidal patchy particles can self-assemble into colloidal architectures such as chains, rings and networks, while self-propelled colloidal particles can simultaneously inject energy into the architecture, alter the dynamical behavior of the system, and cause the self-assembled structures to deform and break. To gain insight, we conduct a numerical investigation into the effect of introducing self-propelled colloids modeled as active Brownian particles, into self-assembling colloidal dispersions of dipatch and tripatch particles. For the interaction potential, we use a previously designed model that accurately can reproduce experimental colloidal self-assembly via the critical Casimir force [Jonas et al., J. Chem. Phys., 2021, 135, 034902]. Here, we focus primarily on the breakage dynamics of three archetypal substructures, namely, dimers, chains, and rings. We find a rich response behavior to the introduction of self-propelled particles, in which the activity can enhance as well as reduce the stability of the architecture, deform the intact structures and alter the mechanisms of fragmentation. We rationalize these findings in terms of the rate and mechanisms of breakage as a function of the direction and magnitude of the active force by separating the bond breakage process into two stages: escaping the potential well and separation of the particles. The results set the stage for investigating more complex architectures.

Colloidal Self-Assembly: From Passive to Active Systems

Self-assembly fundamentally implies the organization of small sub-units into large structures or patterns without the intervention of specific local interactions. This process is commonly observed in nature, occurring at various scales ranging from atomic/molecular assembly to the formation of complex biological structures. Colloidal particles may serve as micrometer-scale surrogates for studying assembly, particularly for the poorly understood kinetic and dynamic processes at the atomic scale. Recent advances in colloidal self-assembly have enabled the programmable creation of novel materials with tailored properties. We here provide an overview and comparison of both passive and active colloidal self-assembly, with a discussion on the energy landscape and interactions governing both types. In the realm of passive colloidal assembly, many impressive and important structures have been realized, including colloidal molecules, one-dimensional chains, two-dimensional lattices, and three-dimensional crystals. In contrast, active colloidal self-assembly, driven by optical, electric, chemical, or other fields, involves more intricate dynamic processes, offering more flexibility and potential new applications. A comparative analysis underscores the critical distinctions between passive and active colloidal assemblies, highlighting the unique collective behaviors emerging in active systems. These behaviors encompass collective motion, motility-induced phase segregation, and exotic properties arising from out-of-equilibrium thermodynamics. Through this comparison, we aim to identify the future opportunities in active assembly research, which may suggest new application domains.

Networks of Limited-Valency Patchy Particles

Equilibrium gels provide physically attractive counterparts of nonequilibrium gels, allowing statistical understanding and design of the equilibrium gel structure. Here, we assemble two-dimensional equilibrium gels from limited-valency "patchy" colloidal particles and follow their evolution at the particle scale to elucidate cluster-size distributions and free energies. By finely adjusting the patch attraction with critical Casimir forces, we let a mixture of two-valent and pseudo-three-valent patchy particles approach the percolated network state through a set of equilibrium states. Comparing this equilibrium route with a deep quench, we find that both routes approach the percolated state via the same equilibrium states, revealing that the network topology is uniquely set by the particle bond angles, independent of the formation history. The limited-valency system follows percolation theory remarkably well, approaching the percolation point with the expected universal exponents.

Dynamic surface chemistry and interparticle interactions mediating chemically fueled dissipative assembly of colloids

HYPOTHESIS

Dissipative assembly of colloids involves using a chemical fuel to temporarily activate organic colloid surface ligands to an assembly prone state. Colloids assemble into transient aggregates that disintegrate after the fuel is consumed. The underlying colloidal interactions controlling dissipative assembly have not been rigorously identified or quantified. We expect that fuel concentration dependent dissipative assembly behavior can be reconciled with measurements of dynamic colloid surface chemistry and colloidal interactions.

EXPERIMENTS

Carbodiimide chemistry was utilized to induce dissipative assembly of carboxylic acid functionalized polystyrene colloids. We measured aggregation kinetics, colloid surface hydrophobicity, and zeta potential as a function of time, which established that colloids underwent dissipative assembly for fuel concentrations between 5 and 12.5 mM and irreversible aggregation at higher fuel concentrations due to transient changes in surface chemistry.

FINDINGS

We formulated a pairwise colloidal interaction potential model including hydrophobic interactions quantified by fluorescence binding experiments. Fuel concentrations causing dissipative assembly displayed a transient increase in secondary minimum depth and a primary maximum much larger than the thermal potential. Fuel concentrations leading to irreversible aggregation displayed a primary maximum smaller than the thermal potential. This is the first study to quantify surface chemistry and interparticle interactions during dissipative colloid assembly and represents a foundational step in rationally designing more complex dissipative assembly systems.

Phases of surface-confined trivalent colloidal particles

Patchy colloids promise the design and modelling of complex materials, but the realization of equilibrium patchy particle structures remains challenging. Here, we assemble pseudo-trivalent particles and elucidate their phase behaviour when confined to a plane. We observe the honeycomb phase, as well as more complex amorphous network and triangular phases. Structural analysis performed on the three condensed phases reveals their shared structural motifs. Using a combined experimental and simulation approach, we elucidate the energetics of these phases and construct the phase diagram of this system, using order parameters to determine the phase coexistence lines. Our results reveal the rich phase behaviour that a relatively simple patchy particle system can display, and open the door to a larger joined simulation and experimental exploration of the full patchy-particle phase space.

Potential Energy Surfaces Sampled in Cremer-Pople Coordinates and Represented by Common Force Field Functionals for Small Cyclic Molecules

The complex conformations of the cyclic moieties impact the physical and chemical properties of molecules. In this work, we chose 22 molecules of four-, five-, and six-membered rings and performed a thorough conformational sampling using Cremer-Pople coordinates. With consideration of symmetries, we obtained a total of 1504 conformational structures for four-membered, 5576 for five-membered, and 13509 for six-membered rings. All well-known and many less well-known conformers for each molecule were identified. We represented the potential energy surfaces (PESs) by fitting the data to common analytical force field (FF) functional forms. We found that the general features of PESs can be described by the essential FF functional forms; however, the accuracy of representation can be improved remarkably by including the torsion-bond and torsion-angle coupling terms. The best fit yields R-squared (R²) values close to 1.0 and mean absolute errors in energy less than 0.3 kcal/mol.

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.

Sorting of heterogeneous colloids by AC-dielectrophoretic forces in a microfluidic chip with asymmetric orifices

HYPOTHESIS

The synthesis of compositionally heterogeneous particles is central to the development of complex colloidal units for self-assembly and self-propulsion. Yet, as the complexity of particles grows, synthesis becomes more prone to "errors". We hypothesize that alternating-current dielectrophoretic forces can efficiently sort Janus particles, as a function of patch size and material, and colloidal dumbbells by size.

EXPERIMENTS

We prepared Janus particles with different patch size and material by physical vapor deposition and colloidal dumbbells via capillarity-assisted particle assembly. We then performed sorting experiments in a microfluidic chip comprising electrodes with asymmetric orifices, specifically exploiting the dielectric contrast between different portions of the particles or their size difference to steer them towards different outlets.

FINDINGS

We calculated that the DEP force for Janus particles may switch from positive to negative as a function of composition at a critical AC frequency, thus enabling sorting different particles crossing the electrodes' region. The predictions are confirmed by optical microscopy experiments. We also show that intact and "broken" dumbbells can be simply separated as they experience different DEP forces. The integration of multiple asymmetric orifices leads a larger zone with high field gradient to increase separation efficiency and makes it a promising tool to select precise particle populations, isolating fractions with narrowly distributed characteristics.

Brownian motion of flexibly linked colloidal rings

Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on the conformation and diffusion of molecular ring polymers simultaneously are challenging due to their inherently small size. Here, we study an experimental model system for cyclic polymers, that consists of rings of flexibly linked micron-sized colloids with n=4-8 segments. We characterize the conformations of these flexible colloidal rings and find that they are freely jointed up to steric restrictions. We measure their diffusive behavior and compare it to hydrodynamic simulations. Interestingly, flexible colloidal rings have a larger translational and rotational diffusion coefficient compared to colloidal chains. In contrast to chains, their internal deformation mode shows slower fluctuations for n≲8 and saturates for higher values of n. We show that constraints stemming from the ring structure cause this decrease in flexibility for small n and infer the expected scaling of the flexibility as function of ring size. Our findings could have implications for the behavior of both synthetic and biological ring polymers, as well as for the dynamic modes of floppy colloidal materials.

Advances in Colloidal Building Blocks: Toward Patchy Colloidal Clusters

The scalable synthetic route to colloidal atoms has significantly advanced over the past two decades. Recently, colloidal clusters with DNA-coated cores called "patchy colloidal clusters" have been developed, providing a directional bonding with specific angle of rotation due to the shape complementarity between colloidal clusters. Through a DNA-mediated interlocking process, they are directly assembled into low-coordination colloidal structures, such as cubic diamond lattices. Herein, the significant progress in recent years in the synthesis of patchy colloidal clusters and their assembly in experiments and simulations is reviewed. Furthermore, an outlook is given on the emerging approaches to the patchy colloidal clusters and their potential applications in photonic crystals, metamaterials, topological photonic insulators, and separation membranes.

Extended Wertheim theory predicts the anomalous chain length distributions of divalent patchy particles under extreme confinement

Colloidal patchy particles with divalent attractive interaction can self-assemble into linear polymer chains. Their equilibrium properties in 2D and 3D are well described by Wertheim's thermodynamic perturbation theory which predicts a well-defined exponentially decaying equilibrium chain length distribution. In experi- mental realizations, due to gravity, particles sediment to the bottom of the suspension forming a monolayer of particles with a gravitational height smaller than the particle diameter. In accordance with experiments, an anomalously high monomer concentration is observed in simulations which is not well understood. To account for this observation, we interpret the polymerization as taking place in a highly confined quasi-2D plane and extend the Wertheim thermodynamic perturbation theory by defining addition reactions constants as functions of the chain length. We derive the theory, test it on simple square well potentials, and apply it to the experimental case of synthetic colloidal patchy particles immersed in a binary liquid mixture that are described by an accurate effective critical Casimir patchy particle potential. The important interaction parameters entering the theory are explicitly computed using the integral method in combination with Monte Carlo sampling. Without any adjustable parameter, the predictions of the chain length distribution are in excellent agreement with explicit simulations of self-assembling particles. We discuss generality of the approach, and its application range.

Self-assembly of colloidal cube superstructures with critical Casimir attractions

The structure of self-assembled materials is determined by the shape and interactions of the building blocks. Here, we investigate the self-assembly of colloidal 'superballs', i.e. cubes with rounded corners, by temperature-tunable critical Casimir forces to obtain insight into the coupling of a cubic shape and short range attractions. The critical Casimir force is a completely reversible and controllable attraction that arises in a near-critical solvent mixture. Using confocal microscopy and particle tracking, we follow the self-assembly dynamics and structural transition in a quasi-2D system. At low attraction, we observe the formation of small clusters with square symmetry. When the attraction is increased, a transition to a rhombic Λ₁-lattice is observed. We explain our findings by the change in contact area at faces and corners of the building blocks combined with the increase in attraction strength and range of the critical Casimir force. Our results show that the coupling between the rounded cubic shape and short-range attraction plays a crucial role for the superstructures that form and provide new insights for the active assembly control of micro and nanocubes.

Revealing viscoelastic bending relaxation dynamics of isolated semiflexible colloidal polymers

The viscoelastic properties of filaments and biopolymers play a crucial role in soft and biological materials from biopolymer networks to novel synthetic metamaterials. Colloidal particles with specific valency allow mimicking polymers and more complex molecular structures at the colloidal scale, offering direct observation of their internal degrees of freedom. Here, we elucidate the time-dependent viscoelastic response in the bending of isolated semi-flexible colloidal polymers, assembled from dipatch colloidal particles by reversible critical Casimir forces. By tuning the patch-patch interaction strength, we adjust the polymers' viscoelastic properties, and follow spontaneous bending modes and their relaxation directly on the particle level. We find that the elastic response is well described by that of a semiflexible rod with persistence length of order 1000 μm, tunable by the critical Casimir interaction strength. We identify the viscous relaxation on longer timescales to be due to internal friction, leading to a wavelength-independent relaxation time similar to single biopolymers, but in the colloidal case arising from the contact mechanics of the bonded patches. These tunable mechanical properties of assembled colloidal filaments open the door to "colloidal architectures", rationally designed (network) structures with desired topology and mechanical properties.

Revealing Polymerization Kinetics with Colloidal Dipatch Particles

Limited-valency colloidal particles can self-assemble into polymeric structures analogous to molecules. While their structural equilibrium properties have attracted wide attention, insight into their dynamics has proven challenging. Here, we investigate the polymerization dynamics of semiflexible polymers in 2D by direct observation of assembling divalent particles, bonded by critical Casimir forces. The reversible critical Casimir force creates living polymerization conditions with tunable chain dissociation, association, and bending rigidity. We find that unlike dilute polymers that show exponential size distributions in excellent agreement with Flory theory, concentrated samples exhibit arrest of rotational and translational diffusion due to a continuous isotropic-to-nematic transition in 2D, slowing down the growth kinetics. These effects are circumvented by the addition of higher-valency particles, cross linking the polymers into networks. Our results connecting polymer flexibility, polymer interactions, and the peculiar isotropic-nematic transition in 2D offer insight into the polymerization processes of synthetic two-dimensional polymers and biopolymers at membranes and interfaces.

Multipoint Lock-and-Key Assembly of Particles with Anisotropic Dents toward Modeling Rigid Macromolecules in a Colloidal Scale

Multipoint lock-and-key particle assembly, consisting of lock particles with multiple anisotropic dents and rod-shaped particles as key particles, is developed for colloidal modeling application. The lock particles were connected with each other at a key particle as their joint in the presence of depletants, forming rigid colloidal molecules imitating rigid polymers (e.g., polymers containing aromatic rings and intramolecular hydrogen bonds). A single-particle level observation was conducted to visualize the colloidal polymerization of the particle assembly. Motion trajectories of the lock particles observed by optical microscopy indicated that the particle diffusivity was dramatically lowered when the lock particle connected with another one, suggesting that particle diffusion was suppressed by particle assembly formation. Because the kinetic and regioselectivity of colloidal polymerization are assumed to be analogous to those at the atomic scale, the proposed lock-and-key assembly can be a promising colloidal model for atomic-scale polymers associated with their micro-Brownian motion.

A temperature-dependent critical Casimir patchy particle model benchmarked onto experiment

Synthetic colloidal patchy particles immersed in a binary liquid mixture can self-assemble via critical Casimir interactions into various superstructures, such as chains and networks. Up to now, there are no quantitatively accurate potential models that can simulate and predict this experimentally observed behavior precisely. Here, we develop a protocol to establish such a model based on a combination of theoretical Casimir potentials and angular switching functions. Using Monte Carlo simulations, we optimize several material-specific parameters in the model to match the experimental chain length distribution and persistence length. Our approach gives a systematic way to obtain accurate potentials for critical Casimir induced patchy particle interactions and can be used in large-scale simulations.