Directed assembly of small binary clusters of magnetizable ellipsoids.

We report the effect of shape anisotropy and material properties on the directed assembly of binary suspensions composed of magnetizable ellipsoids. In a Monte Carlo simulation, we implement the ellipsoid-dipole model to calculate the pairwise dipolar interaction energy as a function of position and orientation. The analysis explores dilute suspensions of paramagnetic and diamagnetic ellipsoids with different aspect ratios in a superparamagnetic medium. We analyze the local order of binary structures as a function of particle aspect ratio, medium permeability, and dipolar interaction strength. Our results show that local order and symmetry are tunable under the influence of a uniform magnetic field when one component of the structure is dilute with respect to the other. The simulation results match previously reported experiments on the directed assembly of binary suspension of spheres. Additionally, we report the conditions on particle aspect ratios and medium properties for various structures with rotational symmetries, as well as open and enclosed structures under the influence of a uniform magnetic field.

Synergistic interactions of binary suspensions of magnetic anisotropic particles.

We report the effect of the dipole-dipole interaction and shape anisotropy in suspensions of permanently magnetized anisotropic particles. We quantify the dipolar interaction energy using an ellipsoid-dipole model to describe particles with similar or dissimilar shapes. The expression captures the physics of the point-dipole interaction energy between uniformly magnetized spherical particles. Additionally, we report Monte Carlo simulations to describe the effect of dipolar interaction and shape anisotropy under different field strengths. Results show that the shape anisotropy and dipolar interactions modify the head-to-tail interaction with respect to spheres, promoting dendritic and barbed-wire structures in uniform ellipsoids and binary mixtures, respectively. Furthermore, competing entropic and energy interactions generate a synergistic effect reducing the magnetic response of binary suspensions.

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.

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.

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.

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.

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.

Surface Morphology-Enhanced Delivery of Bioinspired Eco-Friendly Microcapsules.

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.

Direct Measurements of kT-Scale Capsule-Substrate Interactions and Deposition Versus Surfactants and Polymer Additives.

We report a novel approach to directly measure the interactions and deposition behavior of functional capsule delivery systems on glass substrates versus the concentration of an anionic surfactant sodium lauryl ether sulfate (SLES) and a cationic acrylamide-acrylamidopropyltrimonium copolymer (AAC). Analyses of three-dimensional optical microscopy trajectories were used to quantify lateral diffusive dynamics, deposition lifetimes, and potentials of mean force for different solution conditions. In the absence of additives, negatively charged capsule surfaces yield electrostatic repulsion with the negatively charged substrate, which inhibits deposition. With an increasing SLES concentration below the critical micelle concentration (CMC), capsule-substrate electrostatic repulsion is mediated by the charged surfactant solution that decreases the Debye length. Above the SLES CMC, depletion attraction causes enhanced deposition until eventually depletion repulsion inhibits deposition at concentrations ∼10 wt %. Addition of an ACC causes deposition via capsule-substrate bridging at all concentrations; the weakest deposition occurs at intermediate AAC concentrations from a competition of steric repulsion and attraction via a few extended bridges. The novel measurements and models of capsule interactions and deposition on substrates in this work provide a basis to fundamentally understand and rationally design complex rinse-off cleansing formulations with optimal characteristics.

Magnetic Assembly and Cross-Linking of Nanoparticles for Releasable Magnetic Microstructures.

This article describes a versatile method to fabricate magnetic microstructures with complex two-dimensional geometric shapes using magnetically assembled iron oxide (Fe3O4) and cobalt ferrite (CoFe2O4) nanoparticles. Magnetic pole patterns are imprinted into magnetizable media, onto which magnetic nanoparticles are assembled from a colloidal suspension into defined shapes via the shaped magnetic field gradients. The kinetics of this assembly process are studied by evaluation of the microstructure features (e.g., line width and height) as a function of time, particle type, and volume fraction. After assembly, the iron oxide particles are cross-linked in situ and subsequently released by dissolving a sacrificial layer. The free-floating magnetic structures are shown to retain their patterned shape during manipulation with external magnetic fields.