Field-Directed Motion, Cargo Capture, and Closed-Loop Controlled Navigation of Microellipsoids.

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.

Direct measurements & simplified models of colloidal interactions & diffusion with adsorbed macromolecules.

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.

Diffusion, density, and defects on spheres.

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.

Colloidal Deposition by Polymer-Surfactant Complexes with Dilution and Shear.

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.

Energy landscapes on polymerized liquid crystal interfaces.

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.

Anisotropic particle multiphase equilibria in nonuniform fields.

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.

Design rules for 2D field mediated assembly of different shaped colloids into diverse microstructures.

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.

Hard superellipse phases: particle shape anisotropy & curvature.

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.

Droplet Formation and Growth Mechanisms in Reaction-Induced Spontaneous Emulsification of 3-(Trimethoxysilyl) Propyl Methacrylate.

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.

Anisotropic colloidal interactions & assembly in AC electric fields.

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.

Surfactant-Stabilized Spontaneous 3-(Trimethoxysilyl) Propyl Methacrylate Nanoemulsions.

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.

Spatially varying colloidal phase behavior on multi-dimensional energy landscapes.

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.

Ionic Strength-Dependent Interactions and Dimensions of Adsorbed Zwitterionic Copolymers.

We report direct measurements of ionic strength-dependent interactions between different molecular weights of zwitterionic triblock copolymers adsorbed to hydrophobic colloids and surfaces. The zwitterionic copolymers investigated include phosphorylcholine [poly(2-methacryloyloxyethyl phosphorylcholine) (PMPC)] and sulfopropylbetaine [poly(3-( N-2-methacryloyloxyethyl- N, N-dimethyl)ammonatopropanesulfonate) (PMAPS)] end blocks separated by poly(propylene oxide) center blocks. The range of repulsion between adsorbed PMAPS copolymer layers increases with increasing NaCl from 0.01 to 3 M, and layer thicknesses range from ∼50 to 100% of the PMAPS block contour length. In contrast, repulsion between PMPC layers does not change for 0.01-3 M NaCl, and layers remain near full extension at their contour length. NaCl-dependent interactions and inferred layer dimensions correlate with hydrodynamic layer thickness and polymer second virial coefficients. These results suggest that the interaction range and layer thickness of adsorbed zwitterionic copolymers arise from a balance of intramolecular dipolar attraction and repulsion possibly mediated by water solvation. The balance between these competing effects and resulting ionic strength dependence is determined by specific zwitterionic moieties.

Non-equilibrium steady-state colloidal assembly dynamics.

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.

Competitive Adsorption between Nanoparticles and Surface Active Ions for the Oil-Water Interface.

Nanoparticles (NPs) can add functionality (e.g., catalytic, optical, rheological) to an oil-water interface. Adsorption of ∼10 nm NPs can be reversible; however, the mechanisms for adsorption and its effects on surface pressure remain poorly understood. Here we demonstrate how the competitive reversible adsorption of NPs and surfactants at fluid interfaces can lead to independent control of both the adsorbed amount and surface pressure. In contrast to prior work, both species investigated (NPs and surfactants) interact reversibly with the interface and without the surface active species binding to NPs. Independent measurements of the adsorption and surface pressure isotherms allow determination of the equation of state (EOS) of the interface under conditions where the NPs and surfactants are both in dynamic equilibrium with the bulk phase. The adsorption and surface pressure measurements are performed with gold NPs of two different sizes (5 and 10 nm), at two pH values, and across a wide concentration range of surfactant (tetrapentylammonium, TPeA+) and NPs. We show that free surface active ions compete with NPs for the interface and give rise to larger surface pressures upon the adsorption of NPs. Through a competitive adsorption model, we decouple the contributions of NPs wetting at the interface and their surface activity on the measured surface pressure. We also demonstrate reversible control of adsorbed amount via changes in the surfactant concentration or the aqueous phase pH.

Measurement of Anisotropic Particle Interactions with Nonuniform ac Electric Fields.

Optical microscopy measurements are reported for single anisotropic polymer particles interacting with nonuniform ac electric fields. The present study is limited to conditions where gravity confines particles with their long axis parallel to the substrate such that particles can be treated using quasi-2D analysis. Field parameters are investigated that result in particles residing at either electric field maxima or minima and with long axes oriented either parallel or perpendicular to the electric field direction. By nonintrusively observing thermally sampled positions and orientations at different field frequencies and amplitudes, a Boltzmann inversion of the time-averaged probability of states yields kT-scale energy landscapes (including dipole-field, particle-substrate, and gravitational potentials). The measured energy landscapes show agreement with theoretical potentials using particle conductivity as the sole adjustable material property. Understanding anisotropic particle-field energy landscapes vs field parameters enables quantitative control of local forces and torques on single anisotropic particles to manipulate their position and orientation within nonuniform fields.

Nanoparticle adsorption dynamics at fluid interfaces.

Understanding the dynamic adsorption of nanoparticles (NPs) at fluid interfaces is important for stabilizing emulsions and for the preparation of 2D NP-based materials. Here we show that the Ward-Tordai equations commonly employed to describe the dynamics of surfactant adsorption at a fluid interface combined with a Frumkin adsorption isotherm can be employed to model the diffusion-limited adsorption of NPs onto a fluid interface. In contrast to surfactants, an additional wetting equation of state (EOS) must be incorporated to characterize the dynamic interfacial tension during the adsorption of NPs to the oil-water interface. Our results show agreement between the model and experiments with NP area fractions <0.3. Slower dynamics are observed at larger area fractions, which are speculated to arise from polydispersity or re-organization at the interface. We show the model can be extended to the competitive adsorption between the NPs and a surface active species.

Energy landscapes for ellipsoids in non-uniform AC electric fields.

We report a closed-form analytical model for energy landscapes of ellipsoidal particles in non-uniform high-frequency AC electric fields to identify all possible particle positions and orientations. Three-dimensional equilibrium positions and orientations of prolate (rx = ry < rz), oblate (rx = rz > ry), and scalene (rx≠ry≠rz) ellipsoids are reported vs. field frequency and amplitude, which are determined from energy landscape minima. For ellipsoids within non-uniform electric fields between co-planar parallel electrodes, the number of configurations of position and orientation is 6 for prolate, 5 for oblate, and 9 for scalene ellipsoids. In addition, for coplanar electrodes, conditions are identified when particles can be treated using a quasi-2D analysis in the plane of their most probable elevation near an underlying surface. The reported expressions are valid for time-averaged interactions of ellipsoid particles in arbitrary AC electric field configurations, such that our results are applicable to electromagnetic tweezers interacting with particles having an appropriate material property contrast with the medium in the frequency range of interest.

General Potential for Anisotropic Colloid-Surface Interactions.

A general closed-form, analytical potential is developed for the interaction of planar surfaces with superellipsoidal particles (which includes shapes such as spheres, ellipsoids, cylinders, polygons, superspheres, etc.). The Derjaguin approximation is used with DLVO half-space interactions (e.g., electrostatics and van der Waals) to yield potentials for arbitrary particle-wall separation and orientation. The resulting potential is a function of the minimum distance between surfaces and the particle's local Gaussian curvature at the minimum distance position. The validity of the solution is reported in terms of the local Gaussian curvature (Γ) and characteristic interaction range (e.g., Debye length, κ-1, for electrostatics) based on the limits of the Derjaguin approximation. This solution is limited for superellipsoids with convex shapes and orientations where the condition κ/Γ1/2 > 2 is satisfied. The potentials reported in this work should be useful for modeling a wide range of natural and synthetic nonspherical and anisotropic colloidal particles in environmental, biological, and advanced material applications.

Interfacial and Confined Colloidal Rod Diffusion.

Optical microscopy is used to measure translational and rotational diffusion of colloidal rods near a single wall, confined between parallel walls, and within quasi-2D porous media as a function of rod aspect ratio and aqueous solution ionic strength. Translational and rotational diffusivities are obtained as rod particles experience positions closer to boundaries and for larger aspect ratios. Models based on position dependent hydrodynamic interactions quantitatively capture diffusivities in all geometries and indicate particle-wall separations in agreement with independent estimates based on electrostatic interactions. Short-time translational diffusion in quasi-2D porous media is insensitive to porous media area fraction, which appears to arise from a balance of hydrodynamic hindrance and enhanced translation due to parallel alignment along surfaces. Findings in this work provide a basis to interpret and predict interfacial and confined colloidal rod transport relevant to biological, environmental, and synthetic material systems.