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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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We report a feedback control method to remove grain boundaries and produce circular shaped colloidal crystals using morphing energy landscapes and reinforcement learning-based policies. We demonstrate this approach in optical microscopy and computer simulation experiments for colloidal particles in ac electric fields. First, we discover how tunable energy landscape shapes and orientations enhance grain boundary motion and crystal morphology relaxation. Next, reinforcement learning is used to develop an optimized control policy to actuate morphing energy landscapes to produce defect-free crystals orders of magnitude faster than natural relaxation times. Morphing energy landscapes mechanistically enable rapid crystal repair via anisotropic stresses to control defect and shape relaxation without melting. This method is scalable for up to at least N = 103 particles with mean process times scaling as N 0.5 Further scalability is possible by controlling parallel local energy landscapes (e.g., periodic landscapes) to generate large-scale global defect-free hierarchical structures.

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Total internal reflection microscopy (TIRM) is used to directly, sensitively, and simultaneously measure colloidal interactions, dynamics, and deposition for a broad range of polymer-surfactant compositions. A deposition state diagram containing comprehensive information about particle interactions, trajectories, and deposition behavior is obtained for polymer-surfactant compositions covering four decades in both polymer and surfactant concentrations. Bulk polymer-surfactant phase behavior and surface properties are characterized to provide additional information to interpret mechanisms. Materials investigated include cationic acrylamide-acrylamidopropyltrimonium copolymer (AAC), sodium lauryl ether sulfate (SLES) surfactant, silica colloids, and glass microscope slides. Measured colloid-substrate interaction potentials and deposition behavior show nonmonotonic trends vs polymer-surfactant composition and appear to be synergistic in the sense that they are not easily explained as the superposition of single-component-mediated interactions. Broad findings show that at some compositions polymer-surfactant complexes mediate bridging and depletion attractions that promote colloidal deposition, whereas other compositions produce electrosteric repulsion that deters colloidal deposition. These findings illustrate mechanisms underlying colloid-surface interactions in polymer-surfactant mixtures, which are important to controlling selective colloidal deposition in multicomponent formulation applications.

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Controlling active colloidal particle swarms could enable useful microscopic functions in emerging applications at the interface of nanotechnology and robotics. Here, we present a computational study of controlling self-propelled colloidal particle propulsion speeds to cooperatively capture and transport cargo particles, which otherwise produce random dispersions. By sensing swarm and cargo coordinates, each particle's speed is actuated according to a control policy based on multiagent assignment and path planning strategies that navigate stochastic particle trajectories to targets around cargo. Colloidal swarms are shown to dynamically cage cargo at their center via inward radial forces while simultaneously translating via directional forces. Speed, power, and efficiency of swarm tasks display emergent coupled dependences on swarm size and pair interactions and approach asymptotic limits indicating near-optimal performance. This scheme exploits unique interactions and stochastic dynamics in colloidal swarms to capture and transport microscopic cargo in a robust, stable, error-tolerant, and dynamic manner.

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A method is reported to determine equilibrium concentration profiles and local phase behavior of colloids on multi-dimensional energy landscapes. A general expression is derived based on local particle concentration and osmotic pressure differences that are balanced by forces on colloids due to energy landscape gradients. This analysis is applied to colloidal particles in high frequency AC electric fields within octupolar electrodes, where the energy landscape can be shaped in two dimensions. These results are also directly applicable to any particles having induced dipoles in spatially non-uniform electromagnetic fields. Predictions based on modeling colloids with an effective hard disk equation of state indicate inhomogeneous solid and fluid states coexisting on different shaped energy landscapes including multiple minima. Model predictions show excellent agreement with time-averaged Brownian dynamic simulations at equilibrium. Findings demonstrate a general approach to understand colloidal phase behavior on energy landscapes due to external fields, which could enable control of colloidal microstructures on morphing energy landscapes and the inverse design of fields to assemble hierarchically structured colloidal materials.

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Nanoemulsions are a versatile means to create a variety of consumer products and complex materials. Producing nanoemulsions with a high volume fraction of the dispersed phase is generally limited to mechanically intensive processes, such as high-pressure homogenization, and often results in polydisperse droplet size distributions. Low-energy methods, such as spontaneous emulsification, can produce monodispersed droplets, but the volume fraction of the dispersed phase is usually much lower. Here, we report on the spontaneous emulsification of 3-(trimethoxysilyl) propyl methacrylate (TPM) into an alkaline aqueous phase (pH > 10.0) that contains surfactants (Tween 20, sodium dodecyl sulfate (SDS), or cetyltrimethylammonium bromide (CTAB)). The nanoemulsions are monodisperse with droplet diameters that range between 15 and 500 nm. The small droplet size is due to the presence of surfactants that stabilize the droplets against coalescence. The spontaneous emulsion process can produce emulsions with a dispersed volume fraction of up to 10% in CTAB solutions and up to 30% using Tween 20 and SDS. After the emulsification process, the TPM droplets can be polymerized to produce nanoparticles. Using dynamic light scattering and scanning electron microscopy, we characterize the relationship between the surfactant concentration and the size of the droplets in the nanoemulsions. We find that the droplet diameter is primarily determined by the molar ratio of oil to surfactant. We also find that the pH in the aqueous phase also modulates the droplet diameter when using an ionic surfactant. This work expands the spontaneous emulsification of TPM in the absence of stabilizing particles to the nanoscale while producing one of the highest volume fractions of nanoemulsion droplets obtained via a low-energy mechanism.

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Mosquito compound eyes are elaborate multifunctional hierarchical structures. The presence of ordered curved features spanning length scales of nanometers to millimeters provides the mosquito eye with a wide field of view, an infinite depth of field, and antifogging properties. Developing bio-inspired compound lenses is challenging because of the need to mimic all characteristic curvatures along with their functionalities. Herein, we show how the curvature inherent to nanoparticles, emulsion droplets, and liquid marbles can be employed to mimic the hierarchical structure and functionality of mosquito compound eyes. At the nanometer to micrometer length scale we employ nanoparticle-stabilized emulsion droplets of photocurable oil to form microlenses with nanoscale surface features. After polymerization, the microlenses form a monolayer on an oil droplet to create an optically clear, millimeter scale, liquid marble that functions as a compound lens. We characterize the optical and surface properties of the compound lenses and find that they reproduce the functionality of the mosquito eye. Additionally, we exploit the mobility and reconfigurability of liquid marbles to create arrays (centimeter scale) of compound lenses and other types of functional lenses such as the Janus lens that magnifies the image acquired by the compound lens. Simple and scalable methods to create compound lenses could aid in the development of miniaturized advanced vision systems.

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Simulations and experiments are reported for nonequilibrium steady-state assembly of small colloidal crystal clusters in rotating magnetic fields vs frequency and amplitude. High-dimensional trajectories of particle coordinates from image analysis of experiments and from Stokesian Dynamic computer simulations are fit to low-dimensional reaction coordinate based Fokker-Planck and Langevin equations. The coefficients of these equations are effective energy and diffusivity landscapes that capture configuration-dependent energy and friction for nonequilibrium steady-state dynamics. Two reaction coordinates that capture condensation and anisotropy of dipolar chains folding into crystals are sufficient to capture high-dimensional experimental and simulated dynamics in terms of first passage time distributions. Our findings illustrate how field-mediated nonequilibrium steady-state colloidal assembly dynamics can be modeled to interpret and design pathways toward target microstructures and morphologies.