Designing conditions to enable interfacial colloidal crystallization on three-dimensional (3D) surface topographies requires understanding how particles interact with each other, surfaces, solution species, and gravity. The net interaction, or potential energy landscape, can produce diverse states including dispersed, aggregated, deposited, arrested, and sedimented configurations, often more easily than near-equilibrium interfacial crystalline states. Although nearly neutrally buoyant particles at fluid interfaces have been well studied, less progress has been made in determining competing interactions necessary to produce interfacial colloidal crystals on fluid-solid surface topographies. In this work, we directly measure and model the interactions that control interfacial colloidal crystallization on 3D surface topographies with varying elevation and curvature. Our results demonstrate crystallization for different colloidal materials and sizes in solvent mixtures containing charged surfactants without density or refractive index matching. Conditions for interfacial crystallization are designed via systematic development of direct measurements and models of kT-scale energy landscapes balancing buoyancy, electrostatics, and depletion interactions. Unique crystal morphologies are obtained for different particle materials and dimensions, which shows a dependence on the balance of gravitational and pair interactions.

We report AC electric field mediated feedback control over the reversible assembly, disassembly, and reconfiguration of elliptical prism colloidal particles between liquid, nematic, and crystal states with continuously varying orientational and positional order. Accessible states are first systematically identified by varying field parameters and quantifying microstructures with nematic and crystallinity order parameters. The same order parameters vs time are used as reaction coordinates to track nonequilibrium microstructure evolution between states. A proportional feedback controller for reaction coordinate trajectories is designed to target microstructures with different degrees of order, where gain constants are tuned to maximize transition rates between states orders of magnitude faster than diffusion limited rates (on second to minute time scales). The resulting feedback control approach is demonstrated for time-dependent reaction coordinate trajectories including sinusoidal, step changes, and programmed multistate profiles. Our results and findings demonstrate a generalizable scalable approach to formally control navigation of dynamic pathways between microstructural states in a system of anisotropic colloidal particles, which can be used to control processing of particle-based materials, coatings, and devices.

Induced-charge electroosmosis (ICEO) offers a practical approach to drive microscale flows by application of AC electric fields across polarizable surfaces, enabling diverse functions including microfluidic pumping, active cargo transport, and biosensing. While ICEO along pristine surfaces is well-understood, practical applications of ICEO often require surface modifications that affect ICEO flows in a manner that is poorly understood. Here, this study introduces dielectrophoretic (DEP) polarizability measurement, DPM, as a method to study effects of surface modifications on surface polarizability and ICEO flows. The method entails DEP trapping of probe particles and analysis of their equilibrium motions to measure polarizability. This DPM-generated polarizability data is then used to predict effects of surface modifications on ICEO flows and reveal the contribution of additional factors affecting ICEO. It compares predictions with experimentally observed changes to the speed of Janus particles traveling by ICEO-driven induced-charge electrophoresis. This study shows that DPM enables prediction of decreased particle speed upon protein capture by functional Janus particles and reveals that increased speed of polymer-modified Janus particles likely arises from hydrodynamic factors. Overall, this work lays the foundation for investigating new ICEO-driven systems with applications in complex environments, potentially including those encountered in biosensing, remediation, or cargo delivery.

A widely used model system in rheological studies of colloidal gels consists of octadecyl-coated silica particles that undergo thermoreversible gelation in specific suspending media. Their standard synthesis protocol involves an etherification of octadecanol and suffers from poor reproducibility with varying grafting densities and, therefore, transition temperatures. To overcome this limitation, we present here an alternative approach using an amine-yne click-like reaction to graft octadecyl chains onto the particle surface with high fidelity. Suspended in tetradecane, these particles exhibit a reversible liquid-solid transition below 20 °C─making them ideal for comparative studies, particularly by avoiding complications in the rheological characterization due to loading history or thixotropic effects. By fine-tuning the reaction conditions, we precisely control the grafting density─and thus the gelation. The resulting interparticle interactions can be described as a superposition of temperature-dependent forces: repulsion at high temperatures, van der Waals attraction, and temperature-dependent chain-chain interactions, and their resulting potentials can be validated with AFM measurements. The accurate tuning of interparticle potentials makes this model system ideally suited for quantitative comparisons between experiments and simulations across relevant length scales.

We simulate and model diffusion of spherical colloids of radius, a, on spherical surfaces of radius, R, as a function of relative size and surface concentration. Using Brownian dynamics simulations, we quantify diffusion and microstructure at different concentrations ranging from single particles to dense crystalline states. Self-diffusion and structural metrics (pair distribution, local density, and topological charge) are indistinguishable between spheres and planes for all concentrations up to dense liquid states. For concentrations approaching and greater than the freezing transition, smaller spheres with higher curvature show increased diffusivities and nonuniform density/topological defect distributions, which differ qualitatively from planar surfaces. The total topological charge varies quadratically with sphere radius for dense liquid states and linearly with sphere radius for dense crystals with icosahedrally organized grain scars. Between the dense liquid and dense crystal states on spherical surfaces is a regime of fluctuating and interacting defect clusters. We show local density governs self-diffusion in dense liquids on flat and spherical surfaces via the pair distribution. In contrast, dynamic topological defects couple to finite diffusivities through freezing and in low density crystal states on spherical surfaces, where neither exist on flat surfaces. Simulations of colloids on spherical surfaces show that self-diffusion, local density, and topological defects are curvature-independent until freezing, after which topological charge distribution mediates curvature-dependent diffusion.

We report direct measurements of potential energy landscapes for different shaped colloidal particles interacting with nonuniform AC electric fields. Epoxy particle shapes investigated include disks, ellipses, squares, rectangles, and rhombuses, which are all part of the superelliptical prism shape class and are chosen to systematically vary particle anisotropy and corner features. The measurement configuration consists of noninteracting single particles sedimented onto microscope slides within electric fields between parallel coplanar electrodes. Thermally sampled positions and orientations of single particles in nonuniform fields are tracked in an optical microscope, and measured potential energy landscapes are obtained via Boltzmann inversions. We develop a new analytically simple model that captures all measured energy landscapes for superelliptical prism shaped colloidal particles with electrostatic double layers. The model recovers known validated potentials for spherical and ellipsoidal particles, and therefore captures energy landscapes for a variety of different colloidal particle sizes, shapes, and materials reported in prior studies.

Microrobots have the potential for diverse applications, including targeted drug delivery and minimally invasive surgery. Despite advancements in microrobot design and actuation strategies, achieving precise control over their motion remains challenging due to the dominance of viscous drag, system disturbances, physicochemical heterogeneities, and stochastic Brownian forces. Here, a precise control over the interfacial motion of model microellipsoids is demonstrated using time-varying rotating magnetic fields. The impacts of microellipsoid aspect ratio, field characteristics, and magnetic properties of the medium and the particle on the motion are investigated. The role of mobile micro-vortices generated is highlighted by rotating microellipsoids in capturing, transporting, and releasing cargo objects. Furthermore, an approach is presented for controlled navigation through mazes based on real-time particle and obstacle sensing, path planning, and magnetic field actuation without human intervention. The study introduces a mechanism of directing motion of microparticles using rotating magnetic fields, and a control scheme for precise navigation and delivery of micron-sized cargo using simple microellipsoids as microbots.

We report a model to predict equilibrium density profiles for different shaped colloids in two-dimensional liquid, nematic, and crystal states in nonuniform external fields. The model predictions are validated against Monte Carlo simulations and optical microscopy experiments for circular, square, elliptical, and rectangular colloidal particles in AC electric fields between parallel electrodes. The model to predict the densities of all states of different shaped particles is based on a balance of the local quasi-2D osmotic pressure against a compressive force due to induced dipole-field interactions. The osmotic force balance employs equations of state for hard ellipse liquid, nematic, and crystal state osmotic pressures, which are extended to additional particle shapes. The resulting simple analytical model is shown to accurately predict particle densities within liquid, liquid crystal, and crystal states for a broad range of particle shapes, system sizes, and field conditions. These findings provide a basis for quantitative design and control of fields to assemble and reconfigure colloidal particles in interfacial materials and devices.

We report total internal reflection microscopy measurements of 3D trajectories of ensembles of micron sized colloidal particles near interfaces with and without adsorbed macromolecules. Evanescent wave scattering reveals nanometer scale motion normal to planar surfaces and sub-diffraction limit lateral motion is resolved via image analysis. Equilibrium and non-equilibrium analyses of particle trajectories reveal self-consistent position dependent energies (energy landscapes) and position dependent diffusivities (diffusivity landscapes) both perpendicular and parallel to interfaces. For bare colloids and surfaces, electrostatic and hydrodynamic interactions are accurately quantified with established analytical theories. For colloids and surfaces with adsorbed macromolecules, conservative forces are accurately quantified with models for interactions between brush layers, whereas directly measured position dependent diffusivities require novel models of spatially varying permeability within adsorbed layers. Agreement between spatially resolved interactions and diffusivities and rigorous simplified models provide a basis to consistently interpret, predict, and design colloidal transport in the presence of adsorbed macromolecules for diverse applications. We report direct measurements and simplified models of 3D trajectories of ensembles of micron sized colloidal particles near interfaces with and without adsorbed macromolecules.

We report the controlled interfacial assembly and reconfiguration of rectangular prism colloidal particles between microstructures of varying positional and orientational order including stable, metastable, and transient states. Structurally diverse states are realized by programming time dependent electric fields that mediate dipolar interactions determining particle position, orientation, compression, and chaining. We identify an order parameter set that defines each state as a combination of the positional and orientational order. These metrics are employed as reaction coordinates to capture the microstructure evolution between initial and final states upon field changes. Assembly trajectory manifolds between states in the low-dimensional reaction coordinate space reveal a dynamic pathway map including information about pathway accessibility, reversibility, and kinetics. By navigating the dynamic pathway map, we demonstrate reconfiguration between states on minute time scales, which is practically useful for particle-based materials processing and device responses. Our findings demonstrate a conceptually general approach to discover dynamic pathways as a basis to control assembly and reconfiguration of self-organizing building blocks that respond to global external stimuli.

We construct a reduced, data-driven, parameter dependent effective stochastic differential equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian dynamics simulations. We use diffusion maps (a manifold learning algorithm) to identify a set of useful latent observables. In this latent space we identify an eSDE using a deep learning architecture inspired by numerical stochastic integrators and compare it with the traditional Kramers-Moyal expansion estimation. We show that the obtained variables and the learned dynamics accurately encode the physics of the Brownian dynamic simulations. We further illustrate that our reduced model captures the dynamics of corresponding experimental data. Our dimension reduction/reduced model identification approach can be easily ported to a broad class of particle systems dynamics experiments/models.

Deposition of silica microparticles on glass substrates was measured as a function of cationic polymer-anionic surfactant composition and shear rate. Particles were initially deposited in quiescent conditions in different polymer-surfactant compositions, which were chosen based on prior measurements of composition-dependent polymer-surfactant interactions and deposition behavior (up to 0.5 wt % polymer and 12 wt % surfactant). Programmed shear and dilution profiles in a flow cell together with optical microscopy observation were used to continuously track particle deposition, detachment, and redeposition. Knowledge of the shear-dependent torque on each particle provides information on adhesive torque mediated by polymer-surfactant complexes. Detachment of colloids initially deposited by depletion interactions occurs at low shear rates (∼100 s-1) due to lack of tangential forces or an adhesive torque. Further dilution produced redeposition of particles that resisted detachment (up to ∼2000 s-1) as the result of strong cationic polymer bridge formation, presumably due to preferential surfactant removal. Dilution from different initial compositions indicates a pathway dependence of polymer-surfactant de-complexation into shear-resistant cationic bridges. These findings demonstrate the ability to program deposition behavior via the informed design of initial polymer-surfactant compositions and shear profiles. The particle trajectory analysis developed in this work provides an assay to screen composition-dependent colloidal deposition in diverse materials and applications.

We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1–9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid–nematic, fluid–crystal, and fluid–nematic–crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal–nematic and crystal–fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications.

We measure and model monolayers of concentrated diffusing colloidal probes interacting with polymerized liquid crystal (PLC) planar surfaces. At topological defects in local nematic director profiles at PLC surfaces, we observe time-averaged two-dimensional particle density profiles of diffusing colloidal probes that closely correlate with spatial variations in PLC optical properties. An inverse Monte Carlo analysis of particle concentration profiles yields two-dimensional PLC interfacial energy landscapes on the kT-scale, which is the inherent scale of many interfacial phenomena (e.g., self-assembly, adsorption, diffusion). Energy landscapes are modelled as the superposition of macromolecular repulsion and van der Waals attraction based on an anisotropic dielectric function obtained from the liquid crystal birefringence. Modelled van der Waals landscapes capture most net energy landscape variations and correlate well with experimental PLC director profiles around defects. Some energy landscape variations near PLC defects indicate either additional local repulsive interactions or possibly the need for more rigorous van der Waals models with complete spectral data. These findings demonstrate direct, sensitive measurements of kT-scale van der Waals energy landscapes at PLC interfacial defects and suggest the ability to design interfacial anisotropic materials and van der Waals energy landscapes for colloidal assembly.

We report interactions between adsorbed copolymers of poly(ethylene glycol) (PEG) in the presence of two abundant blood proteins, serum albumin and an immunoglobulin G, up to physiological blood concentrations. We directly and nonintrusively measure interactions between PEG triblock copolymers (PEG-PPO-PEG) adsorbed to hydrophobic colloids and surfaces using Total Internal Reflection Microscopy, which provides kT- and nanometer-scale resolution of interaction potentials (energy vs separation). In the absence of protein, adsorbed PEG copolymer repulsion is consistent with dimensions and architectures of PEG brushes on both colloids and surfaces. In the presence of proteins, we observe concentration dependent depletion attraction and no change to brush repulsion, indicating protein exclusion from PEG brushes. Because positive and negative protein adsorption are mutually exclusive, our observations of concentration dependent depletion attraction with no change to brush repulsion unambiguously indicate the absence of protein coronas at physiological protein concentrations. These findings demonstrate a direct sensitive approach to determine interactions between proteins and particle/surface coatings important to diverse biotechnology applications.

We report computer simulations of two-dimensional convex hard superellipse particle phases vs. particle shape parameters including aspect ratio, corner curvature, and sidewall curvature. Shapes investigated include disks, ellipses, squares, rectangles, and rhombuses, as well as shapes with non-uniform curvature including rounded squares, rounded rectangles, and rounded rhombuses. Using measures of orientational order, order parameters, and a novel stretched bond orientational order parameter, we systematically identify particle shape properties that determine liquid crystal and crystalline phases including their coarse boundaries and symmetry. We observe phases including isotropic, nematic, tetratic, plastic crystals, square crystals, and hexagonal crystals (including stretched variants). Our results catalog known benchmark shapes, but include new shapes that also interpolate between known shapes. Our results indicate design rules for particle shapes that determine two-dimensional liquid, liquid crystalline, and crystalline microstructures that can be realized via particle assembly.

We report the development of novel mineralized protein microcapsules to address critical challenges in the environmental impact and performance of consumer, pharmaceutical, agrochemical, cosmetic, and paint products. We designed environment-friendly capsules composed of proteins and biominerals as an alternative to solid microplastic particles or core-shell capsules made of nonbiodegradable synthetic polymeric resins. We synthesized mineralized capsule surface morphologies to mimic the features of natural pollens, which dramatically improved the deposition of high value-added fragrance chemicals on target substrates in realistic application conditions. A mechanistic model accurately captures the observed enhanced deposition behavior and shows how surface features generate an adhesive torque that resists shear detachment. Mineralized protein capsule performance is shown to depend both on material selection that determines van der Waals attraction and on capsule-substrate energy landscapes as parameterized by a geometric taxonomy for surface morphologies. These findings have broad implications for engineering multifunctional environmentally friendly delivery systems.

Assembling different shaped particles into ordered microstructures is an open challenge in creating multifunctional particle-based materials and devices. Here, we report the two-dimensional (2D) AC electric field mediated assembly of different shaped colloidal particles into amorphous, liquid crystalline, and crystalline microstructures. Particle shapes investigated include disks, ellipses, squares, and rectangles, which show how systematic variations in anisotropy and corner curvature determine the number and type of resulting microstructures. AC electric fields induce dipolar interactions to control particle positional and orientational order. Microstructural states are determined via particle tracking to compute order parameters, which agree with computer simulations and show how particle packing and dipolar interactions together produce each structure. Results demonstrate how choice of particle shape and field conditions enable kinetically viable routes to assemble nematic, tetratic, and smectic liquid crystal structures as well as crystals with stretched 4- and 6-fold symmetry. Results show it is possible to assemble all corresponding hard particle phases, but also show how dipolar interactions influence and produce additional microstructures. Our findings provide design rules for the assembly of diverse microstructures of different shaped particles in AC electric fields, which could enable scalable and reconfigurable particle-based materials, displays, and printing technologies.

We match experimental and simulated configurations of anisotropic epoxy colloidal particles in high frequency AC electric fields by identifying analytical potentials for dipole-field and dipole-dipole interactions. We report an inverse Monte Carlo simulation algorithm to determine optimal fits of analytical potentials by matching simulated and experimental distribution functions for non-uniform liquid, liquid crystal, and crystal microstructures in varying amplitude electric fields. Two potentials that include accurate particle volume and dimensions along with a concentration dependent prefactor quantitatively capture experimental observations. At low concentrations, an effective ellipsoidal point dipole potential works well, whereas a novel stretched point dipole potential is found to be suitable at all concentrations, field amplitudes, and degrees of ordering. The simplicity, accuracy, and adjustability of the stretched point dipole potential suggest it can be applied to model field mediated microstructures and assembly of systematically varying anisotropic particle shapes.

Spontaneous emulsification of 3-(trimethoxysilyl) propyl methacrylate (TPM) can produce complex and active colloids, nanoparticles, or monodisperse Pickering emulsions. Despite the applicability of TPM in particle synthesis, the nucleation and growth mechanisms of TPM emulsions are still poorly understood. We investigate droplet formation and growth of TPM in aqueous solutions under quiescent conditions. Our results show that in the absence of stirring the mechanisms of diffusion and stranding likely drive the spontaneous emulsification of TPM through the formation of co-soluble species during hydrolysis. In addition, turbidity and dynamic light scattering experiments show that the pH modulates the growth mechanism. At pH 10.1, the droplets grow via Ostwald ripening, while at pH 11.5, the droplets grow via monomer addition. Adding surfactants [Tween, sodium dodecyl sulfate (SDS), or cetyltrimethylammonium bromide] leads to <100 nm droplets that are kinetically stable. The growth of Tween droplets occurs through addition of TPM species while the number density of droplets is kept constant. In addition, in the presence of the ionic surfactant SDS, electrostatic repulsion between the solubilized TPM species and SDS leads to a significant increase in the number density of droplets as well as additional nucleation events. Finally, imaging of the solubilization of TPM in capillaries shows that in the absence of a surfactant, TPM hydrolysis is likely the rate-limiting step for emulsification, whereas the presence of silica particles in the aqueous phase likely acts as a catalyst of TPM hydrolysis. Our experiments highlight the importance of diffusion and solubilization of TPM species in the aqueous phase in the nucleation and growth of droplets.