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The assembly of colloidal particles into ordered structures is of great importance to a variety of nanoscale applications where the precise control and placement of particles is essential. A fundamental understanding of this assembly mechanism is necessary to not only predict, but also to tune the desired properties of a given system. Here, we use constructal theory to develop a theoretical model to explain this mechanism with respect to van der Waals and double layer interactions. Preliminary results show that the particle aggregation behavior depends on the initial lattice configuration and solvent properties. Ultimately, our model provides the first constructal framework for predicting the self-assembly of particles and could be expanded upon to fit a range of colloidal systems.

The assembly of colloidal particles into ordered structures is of great importance to a variety of nano-scale applications. Here, we use constructal theory to develop a theoretical model to describe the assembly mechanism with respect to van der Waals and double layer interactions.

Micron-scale colloidal particles suspended in electrolyte solutions have been shown to exhibit a distinct bifurcation in their average height above the electrode in response to oscillatory electric fields. Recent work by Hashemi Amrei et al. ( Phys. Rev. Lett., 2018, 121, 185504) revealed that a steady, long-range asymmetric rectified electric field (AREF) is formed when an oscillatory potential is applied to an electrolyte with unequal ionic mobilities. In this work, we use confocal microscopy to test the hypothesis that a force balance between gravity and an AREF-induced electrophoretic force is responsible for the particle height bifurcation observed in some electrolytes. We demonstrate that at sufficiently low frequencies, particles suspended in electrolytes with large ionic mobility mismatches exhibit extreme levitation away from the electrode surface (up to 50 particle diameters). This levitation height scales approximately as the inverse square root of the frequency for both NaOH and KOH solutions. Moreover, larger particles levitate smaller distances, while the magnitude of the applied field has little effect above a threshold voltage. A force balance between the AREF-induced electrophoresis and gravity reveals saddle node bifurcations in the levitation height with respect to the frequency, voltage, and particle size, yielding stable fixed points above the electrode that accord with the experimental observations. These results point toward a low-energy, non-fouling method for concentrating colloids at specific locations far from the electrodes.

Electronic displays are nearly ubiquitous in modern society. With the drive to lower power consumption, reflective displays based on reversible electrophoretic deposition of nanoparticles have emerged as a candidate next generation display technology. Understanding the origins of color in these displays is challenging because the color is determined by the transient arrangement of particles in the electric field. In this article, a new technique, based on small angle x-ray scattering, is developed to simultaneously interrogate nanoparticle arrangement and measure color while the display is in operation. Furthermore, a particle-based numerical model of electrophoretic deposition is demonstrated to quantitatively predict transient interparticle distances during operation.

Many industrial processes generate “oily wastewaters”, characterized by low volume fractions of micrometer-scale, oil-in-water droplets that are difficult to separate by mechanical or chemical means. High dc voltages are traditionally applied for the electrical demulsification of water-in-oil emulsions. In this work, we demonstrate that oil-in-NaOH contaminated wastewater emulsions respond to low-voltage, low-frequency oscillatory fields by aggregating near the electrodes. Optical microscopy shows that droplets initially separate upon the application of an ∼10 Hz oscillatory field but slowly form aggregates over longer time scales of several minutes. The rate of aggregation varies nonmonotonically with the applied field strength, exhibiting a peak near 3 Vpp and decreasing at higher strengths. Finally, we demonstrate that a combination of low-frequency fields with a small dc offset induces coalescence to break the emulsion. These results point toward a low-energy, nonchemical method for recovering oils fr...

Micron-scale particles suspended in various aqueous electrolytes have been widely observed to aggregate near electrodes in response to oscillatory electric fields, a phenomenon believed to result from electrically induced flows around the particles. Previous work has focused on elucidating the effects of the applied field strength, frequency, and electrolyte type on the aggregation rate of particles, with less attention paid to the ionic strength. Here we demonstrate that an applied field causes micron-scale particles in aqueous NaCl to rapidly aggregate over a wide range of ionic strengths, but with significant differences in aggregation morphology. Optical microscopy observations reveal that at higher ionic strengths (∼1 mM) particles arrange as hexagonally closed-packed (HCP) crystals, but at lower ionic strengths (∼0.05 mM) the particles arrange in randomly closed-packed (RCP) structures. We interpret this behavior in terms of two complementary effects: an increased particle diffusivity at lower ionic strengths due to increased particle height over the electrode and the existence of a deep secondary minimum in the particle pair interaction potential at higher ionic strength that traps particles in close proximity to one another. The results suggest that electrically induced crystallization will readily occur only over a narrow range of ionic strengths.

We demonstrate that application of an oscillatory electric field to a liquid yields a long-range steady field, provided the ions present have unequal mobilities. The main physics is illustrated by a two-ion harmonic oscillator, yielding an asymmetric rectified field whose time average scales as the square of the applied field strength. Computations of the fully nonlinear electrokinetic model corroborate the two-ion model and further demonstrate that steady fields extend over large distances between two electrodes. Experimental measurements of the levitation height of micron-scale colloids versus applied frequency accord with the numerical predictions. The heretofore unsuspected existence of a long-range steady field helps explain several long-standing questions regarding the behavior of particles and electrically induced fluid flows in response to oscillatory potentials.

Micrometer-scale particles suspended in NaCl solutions aggregate laterally near the electrode upon application of a low-frequency (∼100 Hz) field, but the same particles suspended in NaOH solutions are instead observed to separate laterally. The underlying mechanism for the electrolyte dependence remains obscure. Recent work by Woehl et al. (PRX, 2015) revealed that, contrary to previous reports, particles suspended in NaOH solutions indeed aggregate under some conditions while simultaneously exhibiting a distinct bifurcation in average height above the electrode. Here we elaborate on this observation by demonstrating the existence of a critical frequency (∼25 Hz) below which particles in NaOH aggregate laterally and above which they separate. The results indicate that the current demarcation of electrolytes as either aggregating or separating is misleading and that the key role of the electrolyte instead is to set the magnitude of a critical frequency at which particles transition between the two behaviors.

Application of an oscillatory electric field is known to alter the separation distance between micron-scale colloidal particles and an adjacent electrode. This behavior is believed to be partially due to a lift force caused by electrohydrodynamic flow generated around each particle, with previous work focused on identifying a single steady-state “height” of the individual particles over the electrode. Here, we report the existence of a pronounced bifurcation in the particle height in response to low-frequency electric fields. Optical and confocal microscopy observations reveal that application of a ∼100 Hz field induces some of the particles to rapidly move several particle diameters up from the electrode, while the others move closer to the electrode. Statistics compiled from repeated trials demonstrate that the likelihood for a particle to move up follows a binomial distribution, indicating that the height bifurcation is random and does not result from membership in some distinct subpopulation of particles. The fraction of particles that move up increases with increased applied potential and decreased frequency, in a fashion qualitatively consistent with an energy landscape predicated on competition between electrohydrodynamic flow, colloidal interactions, and gravitational forces. Taken together, the results provide evidence for the existence of a deep tertiary minimum in the effective electrode-particle interaction potential at a surprisingly large distance from the electrode.