Electrochemistry Beyond Solutions: Modeling Particle Self-Crowding of Nanoparticle Suspensions.

Nanoparticle suspensions hold promise to transform functionality of next-generation electrochemical systems including batteries, capacitors, wastewater treatment, and sensors, challenging the limits of existing electrochemical models. Classical solution-based electrochemistry assumes that charge is transported and transferred by point-like carriers. Herein, we examine the electrochemistry of a model aqueous suspension of nondissolvable electroactive nanoparticles over a wide concentration range using a rotating disk electrode. Past a concentration and rotation rate threshold, the electrochemistry deviates from solution theory with a maximum attainable current due to particle "self-crowding" where reacted particles on the electrode surface reduce the area accessible for charge transfer by unreacted particles. The observed response is rationalized with an analytical model considering the physical adsorption/desorption kinetics and interfacial transport of nondissolvable finite-size charge carriers. Experimental validation shows the model to be applicable across a range of electrode sizes and thus suitable for engineering electrochemical systems employing nondissolvable nanoparticle suspensions.

The surface diffusivity of nanoparticles physically adsorbed at a solid-liquid interface.

This work proposes an analytical model considering the effects of hydrodynamic drag and kinetic barriers induced by liquid solvation forces to predict the translational diffusivity of a nanoparticle on an adsorbing surface. Small nanoparticles physically adsorbed to a well-wetted surface can retain significant in-plane mobility through thermally activated stick-slip motion, which can result in surface diffusivities comparable to the bulk diffusivity due to free-space Brownian motion. Theoretical analysis and molecular dynamics simulations in this work show that the surface diffusivity is enhanced when (i) the Hamaker constant is smaller than a critical value prescribed by the interfacial surface energy and particle dimensions, and (ii) the nanoparticle is adsorbed at specific metastable separations of molecular dimensions away from the wall. Understanding and controlling this phenomenon can have significant implications for technical applications involving mass, charge, or energy transport by nanomaterials dispersed in liquids under micro/nanoscale confinement, such as membrane-based separation and ultrafiltration, surface electrochemistry and catalysis, and interfacial self-assembly.

The effects of surface hydration on capillary adhesion under nanoscale confinement.

Nanoscale phenomena such as surface hydration and the molecular layering of liquids under strong nanoscale confinement play a critical role in liquid-mediated surface adhesion that is not accounted for by available models, which assume a uniform liquid density with or without considering surface forces and associated disjoining pressure effects. This work introduces an alternative theoretical description that via the potential of mean force (PMF) considers the strong spatial variation of the liquid number density under nanoscale confinement. This alternative description based on the PMF predicts a dual effect of surface hydration by producing: (i) strong spatial oscillations of the local liquid density and pressure and, more importantly, (ii) a configuration-dependent liquid-solid surface energy under nanoscale confinement. Theoretical analysis and molecular dynamics simulations for the case of an axisymmetric water bridge with nanoscale heights show that the latter hydration effect is critical for the accurate prediction of the surface energy and adhesion forces when a small volume of liquid is nanoscopically confined by two surfaces approaching contact.

Toward controlling wetting hysteresis with nanostructured surfaces derived from block copolymer self-assembly.

The synthesis of nanostructured surfaces via block copolymer (BCP) self-assembly enables a precise control of the surface feature shape within a range of dimensions of the order of tens of nanometers. This work studies how to exploit this ability to control the wetting hysteresis and liquid adhesion forces as the substrate undergoes chemical aging and changes in its intrinsic wettability. Via BCP self-assembly we fabricate nanostructured surfaces on silicon substrates with a hexagonal array of regular conical pillars having a fixed period (52 nm) and two different heights (60 and 200 nm), which results in substantially different lateral and top surface areas of the nanostructure. The wetting hysteresis of the fabricated surfaces is characterized using force-displacement measurements under quasistaic conditions and over sufficiently long periods of time for which the substrate chemistry and surface energy, characterized by the Young contact angle, varies significantly. The experimental results and theoretical analysis indicate that controlling the lateral and top area of the nanostructure not only controls the degree of wetting hysteresis but can also make the advancing and receding contact angles less susceptible to chemical aging. These results can help rationalize the design of nanostructured surfaces for different applications such as self-cleaning, enhanced heat transfer, and drag reduction in micro/nanofluidic devices.

Viscous liquid-liquid wetting and dewetting of textured surfaces.

We experimentally investigate the spreading and receding behavior of small water droplets immersed in viscous oils on grid-patterned surfaces using synchronized bottom and profile views. In particular, the evolution of apparent advancing and receding contact angles of droplets fed at constant flow rate is studied as a function of grid surface coverage and height for a wide range of external phase viscosity. Detailed examination of droplet aspect ratio during inflation process provides an averaging method for characterization of quasi-static advancing angles on heterogeneous surfaces. Droplets spreading in partial Cassie state on planar microfluidic grids are also shown to capture oil patches that further evolve into trapped oil droplets depending on grid aspect ratio. The natural retraction velocity of thin water films is examined based on external phase velocity and regime maps of trapped droplets are delineated based on control parameters.

Diffusion in a rough potential: Dual-scale structure and regime crossovers.

Diffusion in a "rough" potential parameterized by a reaction coordinate q is relevant to a wide spectrum of problems ranging from protein folding and charge transport in complex media to colloidal stabilization and self-assembly. This work studies the case of a potential having a coarse-scale structure with characteristic energy barrier ΔU and period ℓ and fine-scale "roughness" of magnitude ΔU' ≲ ΔU and small period ℓ' ≪ ℓ. The numerical solution of the Smoluchowski equation and analytical predictions from Kramers theory document distinct regimes at different distances |Δq| = |q - qE| from stable equilibrium at q = qE. The physical diffusivity D prescribed by dissipative effects can be observed farther than a distance |Δq'| ∝ (ΔU'/ℓ' + ΔU/ℓ). Rescaling the physical diffusivity to account for the fine-scale "roughness" is strictly valid when |Δq| < ΔqI ∝ (ΔU'/ℓ' - ΔU/ℓ). Farther than a critical distance ΔqII ∝ ΔU/ℓ, the diffusion process is free of coarse-scale metastable states, which facilitates determining the effective diffusivity D' from the reaction coordinate trajectory. Closer to equilibrium, the coarse-scale structure induces two diffusive regimes: nearly logarithmic evolution for ΔqII > |Δq| > ΔqIII and exponential decay over time for |Δq| < ΔqIII ∝ 1/ℓ. The effective diffusivity derived in this work is sensitive to the coarse- and fine-scale energy barriers and periods and for ℓ'/ℓ → 0 and ΔU'/kBT ≫ 1 agrees closely with mean first-passage time estimates currently employed, which depend solely on the fine-scale energy barrier.

Dynamic Effects on the Mobilization of a Deposited Nanoparticle by a Moving Liquid-Liquid Interface.

Using molecular dynamics simulations, we investigate the fate of a nanoparticle deposited on a solid surface as a liquid-liquid interface moves past it, depending on the wetting of the solid by the two liquids and the magnitude of the driving force. Interfacial pinning is observed below a critical value of the driving force. Above the critical driving force for pinning and for large contact angle values we observe stick-slip motion, with intermittent interfacial pinning and particle sliding at the interface. At low contact angles we observe that particle rolling precedes detachment, which indicates the importance of dynamic effects not present in static models. The findings in this work indicate that particle mobilization, and removal efficiencies, originating in dynamic liquid-liquid interfaces can be significantly underestimated by static models.

Colloidal Particle Adsorption at Water-Water Interfaces with Ultralow Interfacial Tension.

Using fluorescence confocal microscopy we study the adsorption of single latex microparticles at a water-water interface between demixing aqueous solutions of polymers, generally known as a water-in-water emulsion. Similar microparticles at the interface between molecular liquids have exhibited an extremely slow relaxation preventing the observation of expected equilibrium states. This phenomenon has been attributed to "long-lived" metastable states caused by significant energy barriers ΔF∼γA_{d}≫k_{B}T induced by high interfacial tension (γ∼10^{-2} N/m) and nanoscale surface defects with characteristic areas A_{d}≃10-30 nm^{2}. For the studied water-water interface with ultralow surface tension (γ∼10^{-4} N/m) we are able to characterize the entire adsorption process and observe equilibrium states prescribed by a single equilibrium contact angle independent of the particle size. Notably, we observe crossovers from fast initial dynamics to slower kinetic regimes analytically predicted for large surface defects (A_{d}≃500 nm^{2}). Moreover, particle trajectories reveal a position-independent damping coefficient that is unexpected given the large viscosity contrast between phases. These observations are attributed to the remarkably diffuse nature of the water-water interface and the adsorption and entanglement of polymer chains in the semidilute solutions. This work offers some first insights on the adsorption dynamics or kinetics of microparticles at water-water interfaces in biocolloidal systems.

Colloidal particle adsorption at liquid interfaces: capillary driven dynamics and thermally activated kinetics.

The adsorption of single colloidal microparticles (0.5-1 µm radius) at a water-oil interface has been recently studied experimentally using digital holographic microscopy [Kaz et al., Nat. Mater., 2012, 11, 138-142]. An initially fast adsorption dynamics driven by capillary forces is followed by an unexpectedly slow relaxation to equilibrium that is logarithmic in time and can span hours or days. The slow relaxation kinetics has been attributed to the presence of surface "defects" with nanoscale dimensions (1-5 nm) that induce multiple metastable configurations of the contact line perimeter. A kinetic model considering thermally activated transitions between such metastable configurations has been proposed [Colosqui et al., Phys. Rev. Lett., 2013, 111, 028302] to predict both the relaxation rate and the crossover point to the slow logarithmic regime. However, the adsorption dynamics observed experimentally before the crossover point has remained unstudied. In this work, we propose a Langevin model that is able to describe the entire adsorption process of single colloidal particles by considering metastable states produced by surface defects and thermal motion of the particle and liquid interface. Invoking the fluctuation dissipation theorem, we introduce a drag term that considers significant dissipative forces induced by thermal fluctuations of the liquid interface. Langevin dynamics simulations based on the proposed adsorption model yield close agreement with experimental observations for different microparticles, capturing the crossover from (fast) capillary driven dynamics to (slow) thermally activated kinetics.

Wetting Driven by Thermal Fluctuations on Terraced Nanostructures.

Theoretical analysis and fully atomistic molecular dynamics simulations reveal a Brownian ratchet mechanism by which thermal fluctuations drive the net displacement of immiscible liquids confined in channels or pores with micro- or nanoscale dimensions. The thermally driven displacement is induced by surface nanostructures with directional asymmetry and can occur against the direction of action of wetting or capillary forces. Mean displacement rates in molecular dynamics simulations are predicted via analytical solution of a Smoluchowski diffusion equation for the position probability density. The proposed physical mechanisms and derived analytical expressions can be applied to engineer surface nanostructures for controlling the dynamics of diverse wetting processes such as capillary filling, wicking, and imbibition in micro- or nanoscale systems.

Nanoparticles at liquid interfaces: rotational dynamics and angular locking.

Nanoparticles with different surface morphologies that straddle the interface between two immiscible liquids are studied via molecular dynamics simulations. The methodology employed allows us to compute the interfacial free energy at different angular orientations of the nanoparticle. Due to their atomistic nature, the studied nanoparticles present both microscale and macroscale geometrical features and cannot be accurately modeled as a perfectly smooth body (e.g., spheres and cylinders). Under certain physical conditions, microscale features can produce free energy barriers that are much larger than the thermal energy of the surrounding media. The presence of these energy barriers can effectively "lock" the particle at specific angular orientations with respect to the liquid-liquid interface. This work provides new insights on the rotational dynamics of Brownian particles at liquid interfaces and suggests possible strategies to exploit the effects of microscale features with given geometric characteristics.

Kinetic trapping of nanoparticles by solvent-induced interactions.

Theoretical analysis based on mean field theory indicates that solvent-induced interactions (i.e. structural forces due to the rearrangement of wetting solvent molecules) not considered in DLVO theory can induce the kinetic trapping of nanoparticles at finite nanoscale separations from a well-wetted surface, under a range of ubiquitous physicochemical conditions for inorganic nanoparticles of common materials (e.g., metal oxides) in water or simple molecular solvents. This work proposes a simple analytical model that is applicable to arbitrary materials and simple solvents to determine the conditions for direct particle-surface contact or kinetic trapping at finite separations, by using experimentally measurable properties (e.g., Hamaker constants, interfacial free energies, and nanoparticle size) as input parameters. Analytical predictions of the proposed model are verified by molecular dynamics simulations and numerical solution of the Smoluchowski diffusion equation.

Colloidal adsorption at fluid interfaces: regime crossover from fast relaxation to physical aging.

The adsorption of a colloidal particle at a fluid interface is studied theoretically and numerically, documenting distinctly different relaxation regimes. The adsorption of a perfectly smooth particle is characterized by a fast exponential relaxation to thermodynamic equilibrium where the interfacial free energy reaches the global minimum. The short relaxation time is given by the ratio of viscous damping to capillary forces. Physical and/or chemical heterogeneities, however, can result in multiple minima of the free energy giving rise to metastability. In the presence of metastable states we observe a crossover to a slow logarithmic relaxation reminiscent of physical aging in glassy systems; sufficiently close to equilibrium the slow relaxation becomes exponential. The long relaxation time is determined by the Kramers escape rate from metastable states. Derived analytical expressions yield quantitative agreement with molecular dynamics simulations and recent experimental observations. This work provides new insights on the adsorption of colloidal particles with surface microstructure.

Hydrodynamically driven colloidal assembly in dip coating.

We study the hydrodynamics of dip coating from a suspension and report a mechanism for colloidal assembly and pattern formation on smooth substrates. Below a critical withdrawal speed where the coating film is thinner than the particle diameter, capillary forces induced by deformation of the free surface prevent the convective transport of single particles through the meniscus beneath the film. Capillary-induced forces are balanced by hydrodynamic drag only after a minimum number of particles assemble within the meniscus. The particle assembly can thus enter the thin film where it moves at nearly the withdrawal speed and rapidly separates from the next assembly. The interplay between hydrodynamic and capillary forces produces periodic and regular structures below a critical ratio Ca(2/3)/sqrt[Bo] < 0.7, where Ca and Bo are the capillary and Bond numbers, respectively. An analytical model and numerical simulations are presented for the case of two-dimensional flow with circular particles in suspension. The hydrodynamically driven assembly documented here is consistent with stripe pattern formations observed experimentally in dip coating.

Design, Fabrication, and Analysis of a Capillary Diode for Potential Application in Water-Oil Separation.

A capillary device is designed and fabricated in glass to work as a fluidic diode with vanishingly small hydrodynamic conductance for imbibition of water within a finite range of immersion depths. This is attained through patterning a section of predefined length on the device surfaces using a single-step laser-based ablation process and without resorting to chemical treatment of the hydrophilic glass substrate. While the studied device works as a fluidic diode for water, it can behave as a conventional capillary slit for the imbibition of oils (e.g., alkanes, silicone oils) with low surface tension. A prototype device with simple geometric design is demonstrated for selective adsorption and separation of water and oil in vertical imbibition experiments at controlled immersion depths. Efficient devices for passive separation of water and oil can be designed based on the demonstrated physical mechanism and the analytical model proposed in this work.

Physical ageing of spreading droplets in a viscous ambient phase.

In this work, we study the spontaneous spreading of water droplets immersed in oil and report an unexpectedly slow kinetic regime not described by previous spreading models. We can quantitatively describe the observed regime crossover and spreading rate in the late kinetic regime with an analytical model considering the presence of periodic metastable states induced by nanoscale topographic features (characteristic area ~4 nm2, height ~1 nm) observed via atomic force microscopy. The analytical model proposed in this work reveals that certain combinations of droplet volume and nanoscale topographic parameters can significantly hinder or promote wetting processes such as spreading, wicking, and imbibition.

Mesoscopic model for microscale hydrodynamics and interfacial phenomena: slip, films, and contact-angle hysteresis.

We present a model based on the lattice Boltzmann equation that is suitable for the simulation of dynamic wetting. The model is capable of exhibiting fundamental interfacial phenomena such as weak adsorption of fluid on the solid substrate and the presence of a thin surface film within which a disjoining pressure acts. Dynamics in this surface film, tightly coupled with hydrodynamics in the fluid bulk, determine macroscopic properties of primary interest: the hydrodynamic slip; the equilibrium contact angle; and the static and dynamic hysteresis of the contact angles. The pseudo-potentials employed for fluid-solid interactions are composed of a repulsive core and an attractive tail that can be independently adjusted. This enables effective modification of the functional form of the disjoining pressure so that one can vary the static and dynamic hysteresis on surfaces that exhibit the same equilibrium contact angle. The modeled fluid-solid interface is diffuse, represented by a wall probability function that ultimately controls the momentum exchange between solid and fluid phases. This approach allows us to effectively vary the slip length for a given wettability (i.e., a given static contact angle) of the solid substrate.

High-order hydrodynamics via lattice Boltzmann methods.

In this work, closure of the Boltzmann-Bhatnagar-Gross-Krook (Boltzmann-BGK) moment hierarchy is accomplished via projection of the distribution function f onto a space H(N) spanned by N-order Hermite polynomials. While successive order approximations retain an increasing number of leading-order moments of f , the presented procedure produces a hierarchy of (single) N-order partial-differential equations providing exact analytical description of the hydrodynamics rendered by ( N-order) lattice Boltzmann-BGK (LBBGK) simulation. Numerical analysis is performed with LBBGK models and direct simulation Monte Carlo for the case of a sinusoidal shear wave (Kolmogorov flow) in a wide range of Weissenberg number Wi=taunuk(2) (i.e., Knudsen number Kn=lambdak=square root Wi); k is the wave number, [corrected] tau is the relaxation time of the system, and lambda approximately tauc(s) is the mean-free path, where c(s) is the speed of sound. The present results elucidate the applicability of LBBGK simulation under general nonequilibrium conditions.