kT-scale colloidal interactions in high frequency inhomogeneous AC electric fields. I. Single particles

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.

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.

Directed Assembly of Particles for Additive Manufacturing of Particle-Polymer Composites

Particle-polymer dispersions are ubiquitous in additive manufacturing (AM), where they are used as inks to create composite materials with applications to wearable sensors, energy storage materials, and actuation elements. It has been observed that directional alignment of the particle phase in the polymer dispersion can imbue the resulting composite material with enhanced mechanical, electrical, thermal or optical properties. Thus, external field-driven particle alignment during the AM process is one approach to tailoring the properties of composites for end-use applications. This review article provides an overview of externally directed field mechanisms (e.g., electric, magnetic, and acoustic) that are used for particle alignment. Illustrative examples from the AM literature show how these mechanisms are used to create structured composites with unique properties that can only be achieved through alignment. This article closes with a discussion of how particle distribution (i.e., microstructure) affects mechanical properties. A fundamental description of particle phase transport in polymers could lead to the development of AM process control for particle-polymer composite fabrication. This would ultimately create opportunities to explore the fundamental impact that alignment has on particle-polymer composite properties, which opens up the possibility of tailoring these materials for specific applications.

Electric-Field-Driven Assembly of Dipolar Spheres Asymmetrically Confined between Two Electrodes

Externally applied electric fields have previously been utilized to direct the assembly of colloidal particles confined at a surface into a large variety of colloidal oligomers and nonclose-packed honeycomb lattices (J. Am. Chem. Soc. 2013, 135, 7839-7842). The colloids under such confinement and fields are observed to spontaneously organize into bilayers near the electrode. To extend and better understand how particles can come together to form quasi-two-dimensional materials, we have performed Monte Carlo simulations and complementary experiments of colloids that are strongly confined between two electrodes under an applied alternating current electric field, controlling field strength and particle area fraction. Of particular importance, we control the fraction of particles in the upper vs lower plane, which we describe as asymmetric confinement, and which effectively modulates the coordination number of particles in each plane. We model the particle-particle interactions using a Stockmayer potential to capture the dipolar interactions induced by the electric field. Phase diagrams are then delineated as a function of the control parameters, and a theoretical model is developed in which the energies of several idealized lattices are calculated and compared. We find that the resulting theoretical phase diagrams agree well with simulation. We have not only reproduced the structures observed in experiments using parameters that are close to experimental conditions but also found several previously unobserved phases in the simulations, including a network of rectangular bands, zig zags, and a sigma lattice, which we were then able to confirm in experiment. We further propose a simple way to precisely control the number ratio of particles between different planes, that is, superimposing a direct current electric field with the alternating current electric field, which can be implemented conveniently in experiments. Our work demonstrates that a diverse collection of materials can be assembled from relatively simple ingredients, which can be analyzed effectively through comparison of simulation, theory, and experiment. Our model further explains possible pathways between different phases and provides a platform for examining phases that have yet to be observed in experiments.

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 (r_x = r_y < r_z), oblate (r_x = r_z > r_y), and scalene (r_x≠r_y≠r_z) 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.

Tunable two-dimensional assembly of colloidal particles in rotating electric fields

Tunable interparticle interactions in colloidal suspensions are of great interest because of their fundamental and practical significance. In this paper we present a new experimental setup for self-assembly of colloidal particles in two-dimensional systems, where the interactions are controlled by external rotating electric fields. The maximal magnitude of the field in a suspension is 25 V/mm, the field homogeneity is better than 1% over the horizontal distance of 250 μm, and the rotation frequency is in the range of 40 Hz to 30 kHz. Based on numerical electrostatic calculations for the developed setup with eight planar electrodes, we found optimal experimental conditions and performed demonstration experiments with a suspension of 2.12 μm silica particles in water. Thanks to its technological flexibility, the setup is well suited for particle-resolved studies of fundamental generic phenomena occurring in classical liquids and solids, and therefore it should be of interest for a broad community of soft matter, photonics, and material science.

Characterizing gelatin hydrogel viscoelasticity with diffusing colloidal probe microscopy

In this study, we investigate viscoelasticity in gelatin hydrogels using diffusing colloidal probe microscopy (DCPM) to directly measure the elastic potential energy interaction between colloidal probes and the underlying viscoelastic media. Gelatin samples are prepared in four different concentrations between 0.3wt% and 0.6wt% to examine changes in viscoelasticity with concentration. A force balance describing the interaction between the colloidal probes and the hydrogel as a spring-damper system lead to a simple model for mean square displacement. A histogram of locations sampled by the colloidal probes is directly related to the elastic potential energy and the effective spring constant of the gelatin hydrogels. The effective spring constant is a fixed parameter used in the mean square displacement model to find effective viscosity. These parameters are comparable to viscoelastic parameters obtain by a microrheology analysis of two-dimensional mean square displacements. These results can serve as a guide for assessing hydrogel systems where viscoelastic properties are an important factor in biomaterial design.

Diffusing colloidal probes of cell surfaces

Measurements and analyses are reported to quantify dynamic and equilibrium interactions between colloidal particles and live cell surfaces using dark field video microscopy. Two-dimensional trajectories of micron-sized polyethylene glycol (PEG)-coated silica colloids relative to adherent epithelial breast cancer cell perimeters are determined allowing measurement of position dependent diffusivities and interaction potentials. PEG was chosen as the material system of interest to assess non-specific interactions with cell surfaces and establishes a basis for investigation of specific interactions in future studies. Analysis of measured potential energies on cell surfaces reveals the spatial dependence in cell topography. With the measured cell topography and models for particle-cell surface hydrodynamic interactions, excellent agreement is obtained between theoretical and measured colloidal transport on cell surfaces. Quantitative analyses of association lifetimes showed that PEG coatings act to stabilize colloids above the cell surface through net repulsive, steric interactions. Our results demonstrate a self-consistent analysis of diffusing colloidal probe interactions due to conservative and non-conservative forces to characterize biophysical cell surface properties.

Controlling colloidal particles with electric fields

In this instructional review, we discuss how to control individual colloids and ensembles of colloids using electric fields. We provide background on the electrokinetic transport mechanisms and kT-scale equilibrium colloidal interactions that enable such control. We also describe the experimental configurations, microscopy methods, image analyses, and material systems for which these mechanisms have been successfully employed. Methods are presented for creating various structures including colloidal chains, quasi-2D colloidal crystals, and 3D colloidal crystals. We also describe electric-field-mediated feedback control of the colloidal crystal size as well as colloidal crystal assembly and disassembly. Finally, we discuss future extensions of these methods that aim to incorporate accurate colloidal crystallization dynamic models into electric-field-mediated feedback control to allow rapid assembly, disassembly, and repair of defect-free colloidal structures.

Colloidal crystal grain boundary formation and motion

The ability to assemble nano- and micro- sized colloidal components into highly ordered configurations is often cited as the basis for developing advanced materials. However, the dynamics of stochastic grain boundary formation and motion have not been quantified, which limits the ability to control and anneal polycrystallinity in colloidal based materials. Here we use optical microscopy, Brownian Dynamic simulations, and a new dynamic analysis to study grain boundary motion in quasi-2D colloidal bicrystals formed within inhomogeneous AC electric fields. We introduce "low-dimensional" models using reaction coordinates for condensation and global order that capture first passage times between critical configurations at each applied voltage. The resulting models reveal that equal sized domains at a maximum misorientation angle show relaxation dominated by friction limited grain boundary diffusion; and in contrast, asymmetrically sized domains with less misorientation display much faster grain boundary migration due to significant thermodynamic driving forces. By quantifying such dynamics vs. compression (voltage), kinetic bottlenecks associated with slow grain boundary relaxation are understood, which can be used to guide the temporal assembly of defect-free single domain colloidal crystals.

Multiple electrokinetic actuators for feedback control of colloidal crystal size

We report a feedback control method to precisely target the number of colloidal particles in quasi-2D ensembles and their subsequent assembly into crystals in a quadrupole electrode. Our approach relies on tracking the number of particles within a quadrupole electrode, which is used in a real-time feedback control algorithm to dynamically actuate competing electrokinetic transport mechanisms. Particles are removed from the quadrupole using DC-field mediated electrophoretic-electroosmotic transport, while high-frequency AC-field mediated dielectrophoretic transport is used to concentrate and assemble colloidal crystals. Our results show successful control of the size of crystals containing 20 to 250 colloidal particles with less than 10% error. Assembled crystals are characterized by their radius of gyration, crystallinity, and number of edge particles, and demonstrate the expected size-dependent properties. Our findings demonstrate successful ensemble feedback control of the assembly of different sized colloidal crystals using multiple actuators, which has broad implications for control over nano- and micro- scale assembly processes involving colloidal components.

High density single-molecule-bead arrays for parallel single molecule force spectroscopy

The assembly of a highly parallel force spectroscopy tool requires careful placement of single-molecule targets on the substrate and the deliberate manipulation of a multitude of force probes. Since the probe must approach the target biomolecule for covalent attachment, while avoiding irreversible adhesion to the substrate, the use of polymer microspheres as force probes to create the tethered bead array poses a problem. Therefore, the interactions between the force probe and the surface must be repulsive at very short distances (<5 nm) and attractive at long distances. To achieve this balance, the chemistry of the substrate, force probe, and solution must be tailored to control the probe-surface interactions. In addition to an appropriately designed chemistry, it is necessary to control the surface density of the target molecule in order to ensure that only one molecule is interrogated by a single force probe. We used gold-thiol chemistry to control both the substrate's surface chemistry and the spacing of the studied molecules, through binding of the thiol-terminated DNA and an inert thiol forming a blocking layer. For our single molecule array, we modeled the forces between the probe and the substrate using DLVO theory and measured their magnitude and direction with colloidal probe microscopy. The practicality of each system was tested using a probe binding assay to evaluate the proportion of the beads remaining adhered to the surface after application of force. We have translated the results specific for our system to general guiding principles for preparation of tethered bead arrays and demonstrated the ability of this system to produce a high yield of active force spectroscopy probes in a microwell substrate. This study outlines the characteristics of the chemistry needed to create such a force spectroscopy array.