Diffusiophoresis in ionic surfactants: effect of micelle formation

Artificial chemotaxis under electrodiffusiophoresis

HYPOTHESIS

Through a large parameter space, electric fields can tune colloidal interactions and forces leading to diverse static and dynamical structures. So far, however, field-driven interactions have been limited to dipole-dipole and hydrodynamic contributions. Nonetheless, in this work, we propose that under the right conditions, electric fields can also induce interactions based on local chemical fields and diffusiophoretic flows.

EXPERIMENTS

Herein, we present a strategy to generate and measure 3D chemical gradients under electric fields. In this approach, faradaic reactions at electrodes induce global pH gradients that drive long-range transport through electrodiffusiophoresis. Simultaneously, the electric field induces local pH gradients by driving the particle's double layer far from equilibrium.

FINDINGS

As a result, while global pH gradients lead to 2D focusing away from electrodes, local pH gradients induce aggregation in the third dimension. Evidence points to a mechanism of interaction based on diffusiophoresis. Interparticle interactions display a strong dependence on surface chemistry, zeta potential and diameter of particles. Furthermore, pH gradients can be readily tuned by adjusting the voltage and frequency of the electric field. For large Péclet numbers, we observed a collective chemotactic-like collapse of particles. Remarkably, such collapse occurs without reactions at a particle's surface. By mixing particles with different sizes, we also demonstrate, through experiments and Brownian dynamics simulations, the emergence of non-reciprocal interactions, where small particles are more drawn towards large ones.

Diffusiophoretic Transport of Charged Colloids in Ionic Surfactant Gradients Entirely below versus Entirely above the Critical Micelle Concentration

When placed in an ionic surfactant gradient, charged colloids will undergo diffusiophoresis at a velocity, uDP = MDP∇ ln S, where MDP is the diffusiophoretic mobility and S is the surfactant concentration. The diffusiophoretic mobility depends in part on the charges and diffusivities of the surfactants and their counterions. Since micellization decreases surfactant diffusivity and alters charge distributions in a surfactant solution, MDP of charged colloids in ionic surfactant gradients may differ significantly when surfactant concentrations are above or below the critical micelle concentration (CMC). The role of micelles in driving diffusiophoresis is unclear, and a previously published model that accounts for micellization suggests the possibility of a change in the sign of MDP above the CMC [Warren, P. B.; . Soft Matter 2019, 15, 278-288]. In the current study, microfluidic channels were used to measure the transport of negatively charged polystyrene colloids in sodium dodecyl sulfate (SDS) surfactant gradients established at SDS concentrations that are either fully above or fully below the CMC. Interpretation of diffusiophoresis was aided by measurements of the colloid electrophoretic mobility as a function of SDS concentration. A numerical transport model incorporating the prior diffusiophoretic mobility model for ionic surfactant gradients was implemented to elucidate signatures of positive and negative diffusiophoretic mobilities and compare with experiments. The theoretically predicted sign of the diffusiophoretic mobility below the CMC was determined to be particularly sensitive to uncertainty in colloid and surfactant properties, while above the CMC, the mobility was consistently predicted to be positive in the SDS concentration range considered in the experiments conducted here. In contrast, experiments only showed signatures of a negative diffusiophoretic mobility for these negatively charged colloids with no change of sign. Colloid diffusiophoretic transport measured in micellar solutions was more extensive than that below the CMC with the same ∇ ln S.

Effect of polymer/surfactant complexation on diffusiophoresis of colloids in surfactant concentration gradients

HYPOTHESIS

A concentration gradient of surfactants in the presence of polymers that non-covalently associate with surfactants will exhibit a continually varying distribution of complexes with different composition, charge, and size. Since diffusiophoresis of colloids suspended in a solute concentration gradient depends on the relaxation of the gradient and on the interactions between solutes and particles, polymer/surfactant complexation will alter the rate of diffusiophoresis driven by surfactant gradients relative to that observed in the same concentration gradient in the absence of polymers.

EXPERIMENTS

A microfluidic device was used to measure diffusiophoresis of colloids suspended in solutions containing a gradient of sodium dodecylsulfate (SDS) in the presence or absence of a uniform concentration of Pluronic P123 poly(ethylene oxide-b-propylene oxide-b-ethylene oxide) nonionic triblock copolymers. To interpret the effect of P123 on the rate of colloid diffusiophoresis, electrophoretic mobility and dynamic light scattering measurements of the colloid/solute systems were performed, and a numerical model was constructed to account for the effects of complexation on diffusiophoresis.

FINDINGS

Polymer/surfactant complexation in solute gradients significantly enhanced diffusiophoretic transport of colloids. Large P123/SDS complexes formed at low SDS concentrations yielded low collective solute diffusion coefficients that prolonged the existence of strong concentration gradients relative to those without P123 to drive diffusiophoresis.

Diffusiophoresis of a spherical particle in porous media

Recent experiments by Doan et al. (Nano Lett., 2021, 21, 7625-7630) demonstrated and measured colloid diffusiophoresis in porous media but existing theories cannot predict the observed colloid motion. Here, using regular perturbation method, we develop a mathematical model that can predict the diffusiophoretic motion of a charged colloidal particle driven by a binary monovalent electrolyte concentration gradient in a porous medium. The porous medium is modeled as a Brinkman medium with a constant Darcy permeability. The linearized Poisson-Boltzmann equation is employed to model the equilibrium electric potential distribution that is driven out-of-equilibrium under diffusiophoresis. We report three key findings. First, we demonstrate that colloid diffusiophoresis could be drastically hindered in a porous medium due to the additional hydrodynamic drag compared to diffusiophoresis in a free electrolyte solution. Second, we show that the variation of the diffusiophoretic motion with respect to a change in the electrolyte concentration in a porous medium could be qualitatively different from that in a free electrolyte solution. Third, our results match quantitatively with experimental measurements, highlighting the predictive power of the present model. The mathematical model developed here could be employed to design diffusiophoretic colloid transport in porous media, which are central to applications such as nanoparticle drug delivery and enhanced oil recovery.

Diffusiophoretic Movements of Polystyrene Particles in a H-Shaped Channel for Inorganic Salts, Carboxylic Acids, and Organic Salts

Diffusiophoresis is the movement of particles as a result of a concentration gradient, where the particles can move toward higher concentrations. The magnitude of the movement is largest for the electrolyte solute and depends upon the relative concentration gradient, surface potential, and diffusivity contrast between the cation and anion. Here, diffusiophoresis of ordinary polystyrene particles is studied in a H-shaped channel for different solutes. The experimental results are compared to a numerical model, which is solely based on the concentration gradient, surface potential, and diffusivity contrast. The surface potential of the particles was measured to use as input for the numerical model. The diffusiophoretic movement of the experiments aligns well with the theoretical predicted movement for the inorganic (lithium chloride and sodium bicarbonate) and organic (lithium formate, sodium formate, and potassium formate) salts measured. However, for the carboxylic acids (formic, acetic, and oxalic acids) measured, the theoretical model and experiment do not align because they are weak acids and only partially dissociate, creating a driving force for diffusiophoresis. Overall, the H-shaped channel can be used in the future as a platform to measure diffusiophoretic movement for more complex systems, for example, with mixtures and asymmetric valence electrolytes.

Influence of fluid flows on electric double layers in evaporating colloidal sessile droplets

A model is developed for describing the transport of charged colloidal particles in an evaporating sessile droplet on the electrified metal substrate in the presence of a solvent flow. The model takes into account the electric charge of colloidal particles and small ions produced by electrolytic dissociation of the active groups on the colloidal particles and solvent molecules. We employ a system of self-consistent Poisson and Nernst-Planck equations for electric potential and average concentrations of colloidal particles and ions with the appropriate boundary conditions. The fluid dynamics, temperature distribution and evaporation process are described with the Navier-Stokes equations, equations of heat conduction and vapor diffusion in air, respectively. The developed model is used to carry out a first-principles numerical simulation of charged silica colloidal particle transport in an evaporating aqueous droplet. We find that electric double layers can be destroyed by a sufficiently strong fluid flow.

A Trace Amount of Surfactants Enables Diffusiophoretic Swimming of Bacteria

From birth to health, surfactants play an essential role in our lives. Due to the importance, their environmental impacts are well understood. One of the aspects that has been extensively studied is their impact on bacteria, particularly on their motility. Here, we uncover an alternate chemotactic strategy triggered by surfactants-diffusiophoresis. We show that even a trace amount of ionic surfactants, down to a single ppm level, can promote the bacterial diffusiophoresis by boosting the surface charge of the cells. Because diffusiophoresis is driven by the surface-solute interactions, surfactant-enhanced diffusiophoresis is observed regardless of the types of bacteria. Whether Gram-positive or -negative, flagellated or nonflagellated, the surfactants enable fast migration of freely suspended bacteria, suggesting a ubiquitous locomotion mechanism that has been largely overlooked. We also demonstrate the implication of surfactant-enhanced bacterial diffusiophoresis on the rapid formation of biofilms in flow networks, suggesting environmental and biomedical implications.

Diffusiophoresis in Multivalent Electrolytes

Diffusiophoresis is the spontaneous movement of colloidal particles in a concentration gradient of solutes. As a small-scale phenomenon that harnesses energy from concentration gradients, diffusiophoresis may prove useful for passively manipulating particles in lab-on-a-chip applications as well as configurations involving interfaces. Though naturally occurring ions are often multivalent, experimental studies of diffusiophoresis have been mostly limited to monovalent electrolytes. In this work, we investigate the motion of negatively charged polystyrene particles in one-dimensional salt gradients for a variety of multivalent electrolytes. We develop a one-dimensional model and obtain good agreement between our experimental and modeling results with no fitting parameters. Our results indicate that the ambipolar diffusivity, which is dependent on the valence combination of cations and anions, dictates the speed of the diffusiophoretic motion of the particles by controlling the time scale at which the electrolyte concentration evolves. In addition, the ion valences also modify the electrophoretic and chemiphoretic contributions to the diffusiophoretic mobility of the particles. Our results are applicable to systems where the chemical concentration gradient is comprised of multivalent ions, and motivate future research to manipulate particles by exploiting ion valence.

Colloid Separation by CO2-Induced Diffusiophoresis

We present a microfluidic crossflow separation of colloids enabled by the dissolution of CO₂ gas in aqueous suspensions. The dissolved CO₂ dissociates into H⁺ and HCO₃^- ions, which are efficient candidates for electrolytic diffusiophoresis, because of the fast diffusion of protons. By exposing CO₂ gas to one side of a microfluidic flow channel, a crossflow gradient can be created, enabling the crossflow diffusiophoresis of suspended particles. We develop a simple two-dimensional model to describe the coupled transport dynamics that is due to the competition of advection and diffusiophoresis. Furthermore, we show that oil nanoemulsions can be effectively separated by utilizing highly charged particles as a carrier vehicle, which is otherwise difficult to achieve. These results demonstrate a portable, versatile method for separating particles in broad applications including oil extraction, drug delivery, and bioseparation.

Diffusion of multiple electrolytes cannot be treated independently: model predictions with experimental validation

We study the diffusion of multiple electrolytes in a one-dimensional pore. We model the scenario where an electrolyte is in contact with a reservoir of another electrolyte, such that the cation of the two electrolytes is common. The model reveals that several factors influence the ion concentration profiles: (i) relative diffusivities of the ions, (ii) ratio of the electrolyte concentrations in the pore and the reservoir, and (iii) the valence of the ions. We demonstrate that it is crucial to consider the interaction between ion fluxes as treating the electrolytes independently, as is sometimes proposed, does not completely capture the dynamics of ion transport. We validate our numerical predictions by conducting experiments with sodium fluorescein salt in the pore and sodium chloride/sodium sulphate/sodium hydroxide in the reservoir. Our visualization and results demonstrate that ion diffusivities and concentrations in the reservoir can influence the diffusion rates of fluorescein, which underscores that ion fluxes are coupled and that multiple electrolytes cannot be treated independently. These results should be useful to the wide range of situations where concentration variations are imposed on systems with an existing background electrolyte.