Anomalous particle rotation and resulting microstructure of colloids in AC electric fields

Large Scale Zigzag Pattern Emerging from Circulating Active Shakers

We report the emergence of large zigzag bands in a population of reversibly actuated magnetic rotors that behave as active shakers, namely squirmers that shake the fluid around them without moving. The shakers collectively organize into dynamic structures displaying self-similar growth and generate topological defects in the form of cusps that connect vortices of rolling particles with alternating chirality. By combining experimental analysis with particle-based simulation, we show that the special flow field created by the shakers is the only ingredient needed to reproduce the observed spatiotemporal pattern. We unveil a self-organization scenario in a collection of driven particles in a viscoelastic medium emerging from the reduced particle degrees of freedom, as here the frozen orientational motion of the shakers.

Emergence of Colloidal Patterns in ac Electric Fields

Suspended microparticles subjected to ac electrical fields collectively organize into band patterns perpendicular to the field direction. The bands further develop into zigzag shaped patterns, in which the particles are observed to circulate. We demonstrate that this phenomenon can be observed quite generically by generating such patterns with a wide range of particles: silica spheres, fatty acid, oil, and coacervate droplets, bacteria, and ground coffee. We show that the phenomenon can be well understood in terms of second order electrokinetic flow, which correctly predicts the hydrodynamic interactions required for the pattern formation process. Brownian particle simulations based on these interactions accurately recapitulate all of the observed pattern formation and symmetry-breaking events, starting from a homogeneous particle suspension. The emergence of the formed patterns can be predicted quantitatively within a parameter-free theory.

Tuning the Morphology of Protein-Inorganic Calcium-Phosphate Supraparticles via Directed Assembly

Understanding the phenomena that govern complex interfacial and directed assemblies is essential for both control and scale-up of particle syntheses. The present work describes an effort to understand, control, and tune the formation of protein-inorganic calcium-phosphate supraparticles that are produced at an oscillating air-water interface created by end-over-end rotation of the synthesis solution. Supraparticles were synthesized under an array of different conditions that varied reagent concentration, the presence of additives, tube size, and rotational speed. Paired with a fluid mechanics model of the end-over-end rotation and dimensional analysis, the sensitivity of the synthesis to physicochemical and mechanical parameters was determined. Surface tension and bubble formation were found to be important criteria for changing the size distribution of supraparticles. Thresholds for the values of the Froude, Iribarren, and rotational Reynolds numbers were identified for narrowing particle size distribution. These results both guide the specific protein-inorganic supraparticle synthesis described here and inform future manipulation and scale-up of other complex interfacial colloidal assemblies.

An Expanded State Diagram for the Directed Self-Assembly of Colloidal Suspensions in Toggled Fields

The suspension structure and assembly kinetics of micrometer-diameter paramagnetic spheres in toggled magnetic fields are investigated at a constant field strength H = 1750A·m^-1 while toggling the field on and off over the frequency range 0.3<f<5 Hz and duty ratio values (the fraction of time the field is on over one toggle period) 0.05 ≤ ξ ≤ 0.8. Five microstructures form after sufficient time in the toggled field, fluid, columnar, percolated, ellipsoidal-shaped, and perpendicular, and their kinetic pathways are identified. For ellipsoidal-shaped microstructures, diffusion-driven particle aggregation at early times gives way to a fluid-like breakup. For columnar and percolated structures, this coarsening arrests before breakup. As the toggling duty cycle decreases, the range of frequencies for each structure narrows, giving way to an unstructured fluid; below ξ<0.1, only the fluid state is observed. The existence of fluid, columnar, percolated, and ellipsoidal-shaped microstructures agrees well with those predicted by the theoretical and computational work of Sherman et al. (Sherman, Z. M.; Rosenthal, H.; Swan, J. W. Langmuir 2018, 34, 1029-1041). Microstructures that connect perpendicularly to the magnetic field are identified for 0.1 ≤ ξ ≤ 0.3 and 1.6<f<3.7 Hz. Perpendicular microstructures also exhibit emergent dynamics with continuous rotation, breakup, and coalescence events.

Directed Self-Assembly of Patchy Microgels into Anisotropic Nanostructures

Multi-geometry nanostructures with high-order, complex, and controllable geometries have attracted extensive attention in the development of functional nanomaterials. A simple and versatile strategy is proposed to construct various anisotropic nanostructures through the directed self-assembly (DSA) of patchy microgels. A general criterion for interaction parameters is developed by the variance analysis method to achieve the formation of 1D nanorods by the single directional DSA process, and 2D or 3D polymorphs including V/T/h/cross shapes, multiple arms, multi-directional bending, single/multiple rings, nanocages, etc., by the multi-directional DSA process of binary microgel blends. At the optimum interaction parameters, the nanorods exhibit the quickest formation process and the most thermodynamically stable geometry, while the various 2D or 3D assemblies exhibit controlled jointing behaviors for versatile assembly geometries. The number of recognition sites on the patchy microgel surface guides the aggregation modes of microgels during the DSA process. These assemblies can bear large curvature variance with the increase of shear rates due to the high flexibility and the ability of adjusting orientation spontaneously. The DSA behavior of patchy microgels differs from the traditional self-assembly process of block copolymers, which may open a new route for guiding the formation of controllable nanoparticle architectures.

Approaches to self-assembly of colloidal monolayers: A guide for nanotechnologists

Self-assembly of quasi-spherical colloidal particles in two-dimensional (2D) arrangements is essential for a wide range of applications from optoelectronics to surface engineering, from chemical and biological sensing to light harvesting and environmental remediation. Several self-assembly approaches have flourished throughout the years, with specific features in terms of complexity of the implementation, sensitivity to process parameters, characteristics of the final colloidal assembly. Selecting the proper method for a given application amidst the vast literature in this field can be a challenging task. In this review, we present an extensive classification and comparison of the different techniques adopted for 2D self-assembly in order to provide useful guidelines for scientists approaching this field. After an overview of the main applications of 2D colloidal assemblies, we describe the main mechanisms underlying their formation and introduce the mathematical tools commonly used to analyse their final morphology. Subsequently, we examine in detail each class of self-assembly techniques, with an explanation of the physical processes intervening in crystallization and a thorough investigation of the technical peculiarities of the different practical implementations. We point out the specific characteristics of the set-ups and apparatuses developed for self-assembly in terms of complexity, requirements, reproducibility, robustness, sensitivity to process parameters and morphology of the final colloidal pattern. Such an analysis will help the reader to individuate more easily the approach more suitable for a given application and will draw the attention towards the importance of the details of each implementation for the final results.

Multidirectional colloidal assembly in concurrent electric and magnetic fields

Dipolar interactions between nano- and micron sized colloids lead to their assembly into domains with well-defined local order. The particles with a single dipole induced by an external field assemble into linear chains and clusters. However, to achieve the formation of multidirectionally organized nano- or microassemblies with tunable physical characteristics, more sophisticated interaction tools are needed. Here we demonstrate that such complex interactions can be introduced in the form of two independent, non-interacting dipoles (double-dipoles) within a microparticle. We show how this can be achieved by the simultaneous application of alternating current (AC)-electric field and uniform magnetic field to dispersions of superparamagnetic microspheres. Depending on their timing and intensity, concurrent electric and magnetic fields lead to the formation of bidirectional particle chains, colloidal networks, and discrete crystals. We investigate the mechanistic details of the assembly process, and identify and classify the non-equilibrium states formed. The morphologies of different experimental states are in excellent correlation with our theoretical predictions based on Brownian dynamics simulations combined with a structural analysis based on local energy parameters. This novel methodology of introducing and interpreting double-dipolar particle interactions may assist in the assembly of colloidal coatings, dynamically reconfigurable particle networks, and bidirectional active structures.

Collapse of DNA under alternating electric fields

Recent studies have shown that double-stranded DNA can collapse in the presence of a strong electric field. Here we provide an in-depth study of the collapse of DNA under weak confinement in microchannels as a function of buffer strength, driving frequency, applied electric-field strength, and molecule size. We find that the critical electric field at which DNA molecules collapse (tens of kV/m) is strongly dependent on driving frequency (100-800 Hz) and molecular size (20-160 kbp), and weakly dependent on the ionic strength (8-60 mM). We argue that an apparent stretching at very high electric fields is an artifact of the finite frame time of video microscopy.

Electric-field-induced phase separation and homogenization dynamics in colloidal suspensions of dichroic rod-shaped pigment particles

We report a reversible phase separation phenomenon in nonpolar colloidal suspensions of rod-shaped dichroic pigment particles in an electric field. The voltage-frequency phase diagram features a variety of phases with different morphologies. Single static particle-rich islands, chains of islands, and dynamic patterns were found in this system. We demonstrate that those patterns exhibit complex relaxation dynamics toward the homogeneous field-free state once the external field is removed.

An electric-field induced dynamical state in dispersions of charged colloidal rods

The response of concentrated dispersions of charged colloids to low-frequency electric fields is governed by field-induced inter-colloidal interactions resulting from the polarization of electric double layers and the layer of condensed ions, association and dissociation of condensed ions, as well as hydrodynamic interactions through field-induced electro-osmotic flow. The phases and states that can be formed by such field-induced interactions are an essentially unexplored field of research. Experiments on concentrated suspensions of rod-like colloids (fd-virus particles), within the isotropic-nematic phase coexistence region, showed that a number of phases/states are induced, depending on the field amplitude and frequency [Soft Matter, 2010, 6, 273]. In particular, a dynamical state is found where nematic domains form and melt on a time scale of the order of seconds. We discuss the microscopic origin of this dynamical state, which is attributed to the cyclic, electric-field induced dissociation and association of condensed ions. A semi-quantitative theory is presented for the dynamics of melting and formation of nematic domains, including a model for the field-induced dissociation/association of condensed ions. The resulting equation of motion for the orientational order parameter is solved numerically for parameters complying with the fd-virus system. A limit-cycle is found, with a cycling-time that diverges at the transition line in the field-amplitude versus frequency plane where the dynamical state first appears, in accord with experimental findings.

Directed assembly of Janus particles under high frequency ac-electric fields: effects of medium conductivity and colloidal surface chemistry

The manipulation and assembly of polystyrene-based Janus particles of varied surface chemistry on one hemispherical particle surface under high frequency nonuniform ac-electric fields is examined experimentally by in situ microscopic observation. Strong effects of ac-field frequency, medium conductivity, and particle surface chemistry on the structure of Janus colloidal assembly are observed. At low medium conductivity, σ(m) from 0.0007 S/m to 0.0153 S/m, pearl chains of Janus particles are observed over the ac-frequency range from 25 kHz to 20 MHz, indicating the dielectrophoresis (DEP)-directed assembly. In contrast, the chaining of Janus particles is disrupted in a certain frequency range at high σ(m) from 0.0153 S/m to 0.116 S/m, suggesting the combining effects of both induced-charge electrophoresis (ICEP) and DEP. The critical transition frequency for the onset of the fractal aggregation at high σ(m) from 0.0153 S/m to 0.116 S/m is experimentally determined, showing a good agreement with the theoretically predicted upper ICEP frequency limit. Additionally, it is demonstrated that by using zwitterionic Janus particles, the assembled structure of Janus particles under ac-fields can be modified by the chemical coatings on each hemispherical surface of Janus particles.

Directed self-assembly of colloidal crystals by dielectrophoretic ordering

In this Article, we report the dielectrophoretic assembly of colloidal particles and show how the kinetics of assembly and degree of ordering depend on the particle size, charge, solution ionic strength, and field strength and frequency. A special dielectrophoresis (DEP) sample cell is constructed and validated to quantitatively measure directed self-assembly via sequential light scattering and optical microscopy measurements. Our results confirm the recently established scaling for the order-disorder transition and extend it to higher scaled frequencies. The limiting scaling of the order-disorder transition and particle electrophoretic mobility are correctly predicted by the standard electrokinetic model (SEKM). In particular, the order-disorder transition line is predicted from the particle properties using a recently proposed empirical scaling law and the SEKM over an order of magnitude in particle size.

Directed self-assembly of nanoparticles

Within the field of nanotechnology, nanoparticles are one of the most prominent and promising candidates for technological applications. Self-assembly of nanoparticles has been identified as an important process where the building blocks spontaneously organize into ordered structures by thermodynamic and other constraints. However, in order to successfully exploit nanoparticle self-assembly in technological applications and to ensure efficient scale-up, a high level of direction and control is required. The present review critically investigates to what extent self-assembly can be directed, enhanced, or controlled by either changing the energy or entropy landscapes, using templates or applying external fields.

Electrokinetic vortices and traveling waves in nondilute colloidal dispersions

We report a diverse set of coherent fluid flow instabilities, particle patterns, and traveling waves that develop when an ac electric field is applied to nondilute colloidal dispersions with volume fractions that span 3 orders of magnitude. Novel observed phenomena include the following: vortices with steady and unsteady axes of rotation, unsteady time evolution of vortices formation and vortex merging, as well as traveling waves that propagate through the dispersion. Vortical flows are influenced by strong interactions between particle electrical dipoles as well as electric body forces due to electric fields coupled with gradients in particle volume fraction. We use a 1D Burgers equation to predict the existence of traveling waves in colloidal dispersions.

Angelo SK, González P, Keating CD, Fichthorn KA. Assembly of gold nanowires by sedimentation from suspension: Experiments and simulation

We investigated the ordering of gold nanowires that settled from aqueous suspension onto a glass substrate due to gravity. The nanowires, ca. 300 nm in cross-sectional diameter and ca. 2, 4, or 7 microns in length, were coated with 2-mercaptoethanesulfonic acid to provide electrostatic repulsion and prevent aggregation. The layer of nanowires in direct contact with the substrate was examined from below using optical microscopy and found to exhibit smectic-like ordering. The extent of smectic ordering depended on nanowire length with the shortest (2 μm) nanowires exhibiting the best ordering. To understand the assembly in this system, we used canonical Monte Carlo simulations to model the two-dimensional ordering of the nanowires on a substrate. We accounted for van der Waals and electrostatic interactions between the nanowires. The simulations reproduced the experimental trends and showed that roughness at the ends of the nanowires, which locally increased electrostatic repulsion, is critical to correctly predicting the experimentally observed smectic ordering.

Assemble-and-stretch method for creating two- and three-dimensional structures of anisotropic particles

We fabricate two-dimensional ordered arrays of anisotropic particles by embedding hexagonally close-packed monolayers of spherical latex particles in polymer films and subjecting them to an extensional strain. Furthermore, by stacking several films, we create three-dimensional structures. An important advantage of this approach is the ability to independently control the particle orientation in each layer of the structure. Additionally, the symmetry of a layer is controlled by the orientation of the original array of spherical particles versus the stretch direction. This technique may be readily used to generate structures for photonic applications, as well as to aid fundamental studies of packing of anisotropic particles.

One- and two-dimensional assembly of colloidal ellipsoids in ac electric fields

We investigate the assembly of colloidal ellipsoids in ac electric fields. Polystyrene latex ellipsoids with aspect ratios 3.0, 4.3, and 7.6 orient with the applied field and, at sufficient field strengths, interact to form particle chains at an angle with respect to the field. The characteristic chain angle decreases with increasing aspect ratio. The angled chains combine laterally to form an open centered rectangular two-dimensional structures belonging to the c2mm plane group. This chaining and assembly behavior is explained based on calculations of the particle pair interactions explicitly accounting for the electric field and shape of the ellipsoids.