Recent developments in electrokinetics of salt-free concentrated suspensions

Effects of finite counterion size and nonhomogeneous permittivity and viscosity of the solution on the electrokinetics of a concentrated salt-free colloid

In the present work, a general model of the electrokinetics and dielectric response of a concentrated salt-free colloid is developed which includes consideration of the finite size of the counterions released by the particles to the solution, a nonhomogeneous permittivity of the solution, the existence of Born and dielectrophoretic forces acting on the counterions, and especially the fact that the solution viscosity and diffusion counterion coefficient are allowed to be functions of the local counterion concentration. These effects have recently been discussed by J. J. López-García et al. [Phys. Rev. Fluids 4, 103702 (2019)10.1103/PhysRevFluids.4.103702] in the case of dilute colloids in general electrolyte solutions. The objective of this work is to explore the new effects and their influence on the electrokinetic response of concentrated salt-free systems. Present results confirm previous findings regarding the important increases of the dc electrophoretic mobility and dc electrical conductivity, as well as huge increments of the dynamic electrophoretic mobilities at high frequencies when finite-ion-size effects were taken into account. In addition, consideration of the viscosity of the solution and of the counterion diffusion coefficient as functions of the local counterion concentration leads to a decrease of the magnitude of the previous electrokinetic results. The theory incorporates a more convenient hard-sphere hydrodynamic model to account for the nonhomogeneous viscosity of the solution than others proposed in previous works in the literature. A comparison is elaborated on between electrokinetic and dielectric responses with different levels of complexity of the theoretical model, starting from the case of pointlike counterions and following with the inclusion in sequence of additional aspects such as finite counterion size, nonhomogeneous electrical permittivity with associated Born and dielectrophoretic effects, and, finally, position-dependent viscosity and diffusion counterion coefficient, and clearly shows the influence of individual effects on the general electrokinetic response and especially the relevant role the nonhomogeneous viscosity on the dc and ac electrokientic behavior of salt-free colloids.

Electrokinetic effects of ambient and excess carbonization of dielectric surfaces in aqueous environments

The charge state of surfaces in contact with aqueous electrolytes is crucial for the performance and stability of dielectric surfaces in general and lyophobic colloids in particular. Thus far the role of adsorbed molecular CO2 remained largely unexplored. The aim of the present investigation is to study the de-charging and re-charging for two model surfaces upon addition of CO2 and/or 1:1 electrolytes (NaCl, HCl) under precisely controlled boundary conditions up to millimolar concentrations of additives. Starting from the salt- and CO2-free state, the ζ-potential magnitudes drop linearly with the logarithm of the CO2-concentrations over several orders of magnitude in CO2-concentrations. Hydrophobic Polystyrene nearly fully discharges, hydrophilic SiO2 reveals a 60% charge reduction. From the surface specific effects of instead adding NaCl or HCl, we discriminate and parameterize empirically the relative contribution of three individual mechanisms for decreasing the ζ-potential magnitudes (screening, pH-driven charge regulation, dielectric charge regulation) combining during CO2-addition. Moreover, depending on the achieved CO2-induced de-charging, the behavior upon subsequent addition of NaCl and HCl switches between two limiting cases. Screening dominates for surfaces in the native state without CO2, but a significant re-charging is observed for surfaces conditioned under excess CO2-concentrations.

Electrokinetic and dielectric response of a concentrated salt-free colloid: Different approaches to counterion finite-size effects

In the present work, a general model is developed for the electrokinetics and dielectric response of a concentrated salt-free colloid that takes into account the finite size of the counterions released by the particles to the solution. The effects associated with the counterion finite size have been addressed using a hard-sphere model approach elaborated by Carnahan and Starling [N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969)0021-960610.1063/1.1672048]. A more simple description of the finite size of the counterions based on that by Bikerman has also been considered for comparison. The studies carried out in this work include predictions on the effect of the finite counterion size on the equilibrium properties of the colloid and its electrokinetic and dielectric response when it is subjected to constant or alternating electric fields. The results show how important the counterion finite-size effects are for most of the electrokinetic and dielectric properties of highly charged and concentrated colloids, mainly for the static and dynamic electrophoretic mobilities. Furthermore, new insights are provided on the counterion condensation effect when counterions are allowed to have finite size. Focus is placed on the changes undergone by their concentration in the condensation layer for low-salt and highly charged colloids.

Electrokinetic detection of the salt-free condition in colloids. Application to polystyrene latexes

Because of their singular phenomenology, the so-called salt-free colloids constitute a special family of dispersed systems. Their main characteristic is that the dispersion medium ideally contains only the solvent and the ions compensating exactly the surface charge of the particles. These ions (often called released counterions) come into the solution when the surface groups responsible for the particles charge get ionized. An increasing effort is nowadays dedicated to rigorously compare theoretical model predictions for ideal salt-free suspensions, where only the released counterions are supposed to be present in solution, with appropriately devised experiments dealing with colloids as close as possible to the ideal salt-free ones. Of course, if the supporting solution is aqueous, the presence of atmospheric contamination and any other charged species different from the released counterions in the solution must be avoided. Because this is not an easy task, the presence of dissolved atmospheric CO₂ and of H⁺ and OH^- from water dissociation cannot be fully discarded in aqueous salt-free solutions (often denominated realistic in such case). Ultimately, at some point, the role of the released counterions will be comparable or even larger in highly charged concentrated colloids than that of added salts. These topics are covered in the present contribution. The model results are compared with experimental data on the dynamic mobility and dielectric dispersion of polystyrene spheres of various charges and sizes. As a rule, it is found that the model correctly predicts the significance of alpha and Maxwell-Wagner-O'Konski relaxations. Positions and amplitudes of such relaxations are well predicted, although it is necessary to assume that the released counterions are potassium or sodium instead of protons, otherwise the frequency spectra of experimental mobility and permittivity differ very significantly from those theoretically calculated. The proposed electrokinetic evaluation is an ideal tool for detecting in situ the possible contamination (or incomplete ion exchange of the latexes). A satisfactory agreement is found when potassium counterions are assumed to be in solution, mostly if one considers that the comparison is carried out without using any adjustable parameters.

Electrophoretic Mobility and Electric Conductivity of Salt-Free Suspensions of Charged Soft Particles

A unit cell model is employed to analyze the electrophoresis and electric conduction in a concentrated suspension of spherical charged soft particles (each is a hard core coated with a porous polyelectrolyte layer) in a salt-free medium. The linearized Poisson–Boltzmann equation applicable to a unit cell is solved for the equilibrium electrostatic potential distribution in the liquid solution containing the counterions only surrounding a soft particle. The counterionic continuity equation and modified Stokes/Brinkman equations are solved for the ionic electrochemical potential energy and fluid velocity distributions, respectively. Closed-form formulas for the electrophoretic mobility of the soft particles and effective electric conductivity of the suspension are derived, and the effect of particle interactions on these transport characteristics is interesting and significant. Same as the case in a suspension containing added electrolytes under the Debye–Hückel approximation, the scaled electrophoretic mobility in a salt-free suspension is an increasing function of the fixed charge density of the soft particles and decreases with increases in the core-to-particle radius ratio, ratio of the particle radius to the permeation length in the porous layer, and particle volume fraction, keeping the other parameters unchanged. The normalized effective electric conductivity of the salt-free suspension also increases with an increase in the fixed charge density and with a decrease in the core-to-particle radius ratio, but is not a monotonic function of the particle volume fraction.

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.

Influence of ion size effects on the electrokinetics of aqueous salt-free colloids in alternating electric fields

Electrokinetics is the science of the physical phenomena appearing at the solid-liquid interface of dispersed particles subjected to external fields. Techniques based on electrokinetic phenomena constitute an important set of tools for the electrical characterization of colloids because of their sensitivity to the properties of particle-solution interfaces. Their rigorous description may require inclusion of the effects of finite size of chemical species in the theoretical models, and, particularly in the case of salt-free (no external salt added) aqueous colloids, also consideration of water dissociation and possible carbon dioxide contamination in the aqueous solution. A new ac electrokinetic model is presented for concentrated salt-free spherical colloids for arbitrary characteristics of the particles and aqueous solution, including finite-size effects of chemical species by appropriate modifications of the chemical reaction equations to include such non-ideal aspects. The numerical solution of the electrokinetic equations in an alternating electric field has also been carried out by using a realistic non-equilibrium scenario accounting for association-dissociation processes in the chemical reactions. The results demonstrate the importance of including finite-size effects in the electrokinetic response of the colloid, mainly at high frequencies of the electric field, and for highly charged colloids. Findings of previous models for pointlike ions or for ideal salt-free colloids including finite ion size effects are recovered with the present model, for the appropriate limiting conditions.

The extent of counterion dissociation at the interface of cationic diblock copolymer nanoparticles in non-polar solvents

HYPOTHESIS

Diblock copolymer nanoparticles prepared in non-polar solvents that are sterically stabilized but possess ionic functionality from the inclusion of cationic comonomers in the stabilizer shell are known to exhibit complex electrokinetic behavior (Chem. Sci. 9 (2018) 922-934). For example, core-shell nanoparticles with cationic comonomers located solely within the shell layer have lower magnitude electrophoretic mobilities than nanoparticles containing the same cationic comonomers located within the core, whereas nanoparticles prepared using a minor fraction of steric stabilizer chains containing cationic comonomer repeat units have comparable electrophoretic mobilities to nanoparticles prepared with this cationic comonomer solely located within the core. We hypothesize that these observations can be explained in terms of the strength of the Coulombic interaction between counterions and the nanoparticle interface.

EXPERIMENTS

The highly-fluorinated anionic counterion associated with these cationic nanoparticles is studied by ¹⁹F nuclear magnetic resonance (NMR) spectroscopy in n-dodecane. This revealed only one type of ¹⁹F environment for a soluble macromolecular cation (the oil-soluble steric stabilizer chains used to prepare the nanoparticles), whereas two distinct environments were observed for the sterically-stabilized cationic nanoparticles. Both ¹⁹F diffusion NMR and ¹⁹F-¹³C heteronuclear single quantum correlation (HSQC) measurements support the existence of two environments for this counterion.

FINDINGS

The existence of two distinct ¹⁹F environments for the highly-fluorinated anion associated with the sterically-stabilized nanoparticles demonstrates the presence of spectroscopically distinguishable populations of ion pairs and of fully dissociated free anions. ¹⁹F NMR spectra recorded for sterically-stabilized nanoparticles with a fully ionic shell (all stabilizer chains containing the cationic comonomer) and those with a partly ionic shell (10% of stabilizer chains containing the cationic comonomer) reveal a higher proportion of dissociated anions in the partly ionic case. This suggests a stronger Coulombic interaction between counterions and the cationic interface when the shell is fully ionic, which accounts for the observed reduction in the magnitude of the electrophoretic mobility.

AC Electrokinetics of Salt-Free Multilayered Polymer-Grafted Particles

Interest in the electrical properties of the interface between soft (or polymer-grafted) nanoparticles and solutions is considerable. Of particular significance is the case of polyelectrolyte-coated particles, mainly taking into account that the layer-by-layer procedure allows the control of the thickness and permeability of the layer, and the overall charge of the coated particle. Like in simpler systems, electrokinetic determinations in AC fields (including dielectric dispersion in the 1 kHz-1 MHz frequency range and dynamic electrophoresis by electroacoustic methods in the 1-18 MHz range) provide a large amount of information about the physics of the interface. Different models have dealt with the electrokinetics of particles coated by a single polymer layer, but studies regarding multi-layered particles are far scarcer. This is even more significant in the case of so-called salt-free systems; ideally, the only charges existing in this case consist of the charge in the layer(s) and the core particle itself, and their corresponding countercharges, with no other ions added. The aims of this paper are as follows: (i) the elaboration of a model for the evaluation of the electrokinetics of multi-grafted polymer particles in the presence of alternating electric fields, in dispersion media where no salts are added; (ii) to carry out an experimental evaluation of the frequency dependence of the dynamic (or AC) electrophoretic mobility and the dielectric permittivity of suspensions of polystyrene latex spherical particles coated with successive layers of cationic, anionic, and neutral polymers; and (iii) finally, to perform a comparison between predictions and experimental results, so that it can be demonstrated that the electrokinetic analysis is a useful tool for the in situ characterization of multilayered particles.

Electrolytic conductivity of ionic polymers in a nonpolar solvent

The electrolytic conductivity of two electrolytes as solutions in the nonpolar solvent, n -dodecane, as a function of concentration has been studied. One was a small molecule electrolyte (tetraalkyl cation and a highly fluorinated tetraphenylborate anion), and the other was a macromolecular electrolyte (cation-containing poly(alkyl methacrylate) chain with the same anion). Two series of the macromolecular cation were prepared: one with entirely cation-containing molecules and the other with a small proportion (10%) cation-containing and the rest nonionic. The conductivity data were qualitatively similar for all systems, which formed both single ions and triple ions. The data from the two series of macromolecular electrolytes were particularly informative to understand some recent and counterintuitive electrokinetic data for particles that were stabilized by these polymers. Reducing the proportion of cationic chains in the stabilizer of the particles was found to increase their electrophoretic mobility. In the conductivity data in this study, reducing the proportion of cationic chains in solution was found to increase the magnitude of the single-ion equilibrium constant and suppress the formation of triple ions. These data should support the development of models to understand these electrokinetic results.

Non-monotonic concentration dependence of the electro-phoretic mobility of charged spheres in realistic salt free suspensions

Using super-heterodyne Doppler velocimetry with multiple scattering correction, we extend the optically accessible range of concentrations in experiments on colloidal electro-kinetics. Here, we measured the electro-phoretic mobility and the DC conductivity of aqueous charged sphere suspensions covering about three orders of magnitude in particle concentrations and transmissions as low as 40%. The extended concentration range for the first time allows the demonstration of a non-monotonic concentration dependence of the mobility for a single particle species. Our observations reconcile previous experimental observations made on other species over restricted concentration ranges. We compare our results to the state-of-the-art theoretical calculations using a constant particle charge and the carefully determined experimental boundary conditions as input. In particular, we consider the so-called realistic salt free conditions, i.e., we respect the release of counterions by the particles, the solvent hydrolysis, and the formation of carbonic acid from dissolved neutral CO₂. We also compare our results to previous results obtained under similarly well-defined conditions. This allows identification of three distinct regions of differing density dependence. There is an ascent during the build-up of double layer overlap, which is not expected by theory, an extended plateau region in quantitative agreement with theoretical expectation based on a constant effective charge and a sudden decrease, which occurs way before the expected gradual decrease. Our observations suggest a relation of the non-monotonic behavior to a decrease in particle charge, and we tentatively discuss possibly underlying mechanisms.

Colloidal electro-phoresis in the presence of symmetric and asymmetric electro-osmotic flow

We characterize the electro-phoretic motion of charged sphere suspensions in the presence of substantial electro-osmotic flow using a recently introduced small angle super-heterodyne dynamic light scattering instrument (ISASH-LDV). Operation in integral mode gives access to the particle velocity distribution over the complete cell cross-section. Obtained Doppler spectra are evaluated for electro-phoretic mobility, wall electro-osmotic mobility and particle diffusion coefficient. Simultaneous measurements of differing electro-osmotic mobilities leading to asymmetric solvent flow are demonstrated in a custom made electro-kinetic cell fitting standard microscopy slides as exchangeable sidewalls. The scope and range of our approach are discussed demonstrating the possibility of an internal calibration standard and using the simultaneously measured electro-kinetic mobilities in the interpretation of a microfluidic pumping experiment involving an inhomogeneous electric field and a complex solvent flow pattern.

Synthesis and electrokinetics of cationic spherical nanoparticles in salt-free non-polar media

Cationic diblock copolymer nanoparticles have been prepared in n-dodecane via polymerization-induced self-assembly (PISA). A previously reported poly(stearyl methacrylate)-poly(benzyl methacrylate) (PSMA-PBzMA) PISA formulation (Chem. Sci. 2016, 7, 5078-5090) was modified by statistically copolymerizing an oil-soluble cationic methacrylic monomer, (2-(methacryloyloxy)ethyl)trimethylammonium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate, with either SMA or BzMA, to produce either charged shell or charged core nanoparticles. The electrokinetics were studied as a function of many variables (function of volume function, particle size, solvent viscosity, and number of ions per chain). These data are consistent with electrophoresis controlled by counterion condensation, which is typically observed in salt-free media. However, there are several interesting and unexpected features of interest. In particular, charged shell nanoparticles have a lower electrophoretic mobility than the equivalent charged core nanoparticles, and the magnitude of the electrophoretic mobility increases as the fraction of cationic stabilizer chains in the shell layer is reduced. These results show that cationic PSMA-PBzMA spheres provide an interesting new example of electrophoretic nanoparticles in non-polar solvents. Moreover, they should provide an ideal model system to evaluate new electrokinetic theories.

Solid Separation from a Mixed Suspension through Electric-Field-Enhanced Crystallization

When applied to a pure component suspension in an apolar solvent, a strong inhomogeneous electric field induces particle movement, and the particles are collected at the surface of one of the two electrodes. This new phenomenon was used to separately isolate two organic crystalline compounds, phenazine and caffeine, from their suspension in 1,4-dioxane. First, crystals of both compounds were collected at different electrodes under the influence of an electric field. Subsequent cooling crystallization enabled the immobilization and growth of the particles on the electrodes, which were separately collected after the experiment with purities greater than 91 %. This method can be further developed into a technique for crystal separation and recovery in complex multicomponent suspensions of industrial processes.