Diffuse Layer Potential Research Articles

Analytical solutions for viscoelectric effects in electrokinetic nanochannels.

Understanding electrokinetic transport in nanochannels and nanopores is essential for emerging biological and electrochemical applications. The viscoelectric effect is an important mechanism implicated in the increase of local viscosity due to the polarization of a solvent under a strong electric field. However, most analyses of the viscoelectric effect have been limited to numerical analyses. In this work, we present a set of analytical solutions applicable to the physical description of viscoelectric effects in nanochannel electrokinetic systems. To achieve such closed-form solutions, we employ the Debye-Hückel approximation of small diffuse charge layer potentials compared to the thermal potential. We analyze critical parameters, including electroosmotic flow profiles, electroosmotic mobility, flow rate, and channel conductance. We compare and benchmark our analytical solutions with published predictions from numerical models. Importantly, we leverage these analytical solutions to identify essential thermophysical and nondimensional parameters that govern the behavior of these systems. We identify scaling parameters and relations among surface charge density, ionic strength, and nanochannel height.

Electrochemical Perspective on Hematite–Malonate Interactions

Organic matter (OM) interactions with minerals are essential in OM preservation against decomposition in the environment. Here, by combining potentiometric and electrophoretic measurements, we probed the mode of coordination and the role of pH-dependent electrostatic interactions between organic acids and an iron oxide surface. Specifically, we show that malonate ions adsorbed to a hematite surface in a wide pH window between 3 and 8.7 (point of zero charge). The mode of interactions varied with this pH range and depended on the acid and surface acidity constants. In the acidic environment, hematite surface potential was highly positive (+47 mV, pH 3). At pH < 4 malonate adsorption reduced the surface potential (+30 mV at pH 3) but had a negligible effect on the diffuse layer potential, consistent with the inner-sphere malonate complexation. Here, the specific and electrostatic interactions were responsible for the malonate partial dehydration and surface accumulation. These interactions weakened with an increasing pH and near PZC, the hematite surface charge was neutral on average. Adsorbed malonates started to desorb from the surface with less pronounced accumulation in the diffuse layer, which was reflected in zeta potential values. The transition between specific and non-specific sorption regimes was smooth, suggesting the coexistence of the inner- and outer-sphere complexes with a relative ratio that varied with pH.

Surface charge density and diffuse layer properties of highly defined 2:1 layered silicate platelets

Clays are not only ubiquitous in nature, but they are also used in huge quantities in a broad range of industrial applications, such as thixotropic drilling fluids, ore pelletizers, waste disposal sealants, or fillers in polymer nanocomposites. In order to model environmental processes or to design new materials on a rational base, it is of prime importance to determine and possibly modify the interfacial properties of clay platelets at the solid/electrolyte interface. In this context, the fundamental question rises how far the stoichiometric interlayer charges as determined by the composition of the silicate layer correlates with the diffuse double-layer properties. Here, this question is addressed by means of a series of purposely synthesized sodium 2:1 layered silicates with defined composition and hence interlayer charge densities, respectively. Platelets of layered silicates of large enough diameter to perform AFM colloidal probe measurements were produced by melt synthesis. For comparison also, a natural muscovite mica has been included in this study. The diffuse layer properties in electrolyte solution have been determined by direct force measurements using the colloidal probe AFM technique and by electrokinetic measurements, respectively. We find that the diffuse layer potential decreases with increasing interlayer charge of the 2:1 layered silicates. This counterintuitive finding is attributed to ion adsorption and was further corroborated by determining the quantitative adsorption of polyelectrolytes, namely poly(amidoamine) dendrimers.Graphical abstract

Equilibrium thickness of foam films and adsorption of ions at surfaces: Water and aqueous solutions of sodium chloride, hydrochloric acid, and sodium hydroxide

HypothesisThe origin of negative surface charge at water/air interface is still not clear. The most probable origin is specific adsorption of OH− ions. From diffuse layer potential, we can evaluate the surface density of ions in the Stern layer which can be a measure for the specific adsorption of ions and determines whether the surface charge is solely due to the specific adsorption of OH− ions. ExperimentsEquilibrium thickness of foam films of pure water and aqueous solutions of NaCl, HCl, and NaOH was measured as a function of disjoining pressure for water and as a function of concentration for the aqueous solutions at 298.15 K. Quartz-glass cells thoroughly cleaned and immersed in pure water before use were used for the measurement. FindingsApplication of a modified Poisson-Boltzmann equation to the equilibrium film thickness gave the diffuse layer potential and the surface density of ions in the Stern layer. From the concentration dependence of the surface density, it was concluded that not only OH− ions but also Cl− ions and HCO3− and/or CO32− ions adsorb specifically at the water/air interface.

Theoretical Concepts of the Modification Effect on the Interparticle Energy of the Polymer-Mineral Dispersions for 3D Printing

The molecular gravity and electrostatic repulsion energies were calculated taking into account the structural forces between the modified particles of the polymer-chalk dispersion, which was chosen as a model polymer-chalk system when studying systems for the innovative construction industry using additive technologies (3D printing). In the above calculations, differences for the studied systems are taken into account in such quantities as the complex Hamaker constant, the ionic strength of the solution, and the diffuse layer potential. The calculation of the total potential curves of modified and unmodified polymer-chalk dispersions and the contribution of various factors of aggregative stability analysis showed that as a result of the adsorption of modifier molecules on the particles surface, the action of molecular attraction forces is overcome by the combined action of electrostatic and adsorption-solvate factors of aggregative stability.

Frumkin correction of corrosion electric field generated by 921A-B10 galvanic couple

In order to study the Frumkin correction effect of corrosion electric field generated by 921A-B10 galvanic couple in different concentrations of NaCl solution, the electric double layer (EDL) capacitance of 921A steel and B10 copper alloy at the galvanic potential was acquired by electrochemical impedance spectroscopy (EIS), which was calculated for the experimental value of diffuse layer potential. The theoretical value of diffuse layer potential was got by the theoretical relationship between the diffuse layer potential and the total potential difference of EDL and concentration of supporting electrolyte. According to the Frumkin correction theory, the modified Tafel equation related to diffuse layer potential was obtained. Furthermore, the uncorrected and corrected Tafel equation was used as the boundary condition of the boundary element model (BEM) of corrosion electric field for 921A-B10 galvanic couple, thus the corrosion electric field distribution before and after Frumkin correction was obtained and compared with the experimental results. The results show that the correction effect is 35.6% and 8.8% when the concentration of NaCl is 0.012 M and 0.6 M, respectively. Therefore, it is necessary to correct the Tafel boundary condition during simulation, especially under low electrolyte concentration. The Frumkin correction can greatly reduce the error between results of simulation and experiment.

Sorption of Eu(III) on quartz at high salt concentrations

Sorption of Eu(III) onto quartz from highly saline solutions (up to 5 M NaCl) for pHc 2–9 ha s been studied by measuring sorption edges. The acid-base titrations of the silica surface suggest the rather unusual presence of two different sites that has been the object of recent discussions in the literature. Europium uptake results show the usual behaviour with a steep pH-edge and nearly complete removal at sufficiently high pH. Previous spectroscopic data on this system suggest the presence of two bidentate surface complexes with different proton stoichiometry. Based on this, a self-consistent Surface Complexation Model (SCM) was fitted to the full set of experimental data, from 0.1 to 5 M NaCl, using a coupled Pitzer/surface complexation approach. The Pitzer model was applied to aqueous species. A Basic Stern Model was used for interfacial electrostatics of the system, which includes ion-specific effects via ion-pair formation. Parameter fitting was done using the general parameter estimation software UCODE coupled to a modified version of FITEQL2 involving separate calculations of the respective ionic strength corrections. At high ionic strength (>1 M), the surface potential is strongly screened by ion-pair formation and the diffuse layer potential is negligibly low, which justifies the extension of the standard electrostatic model to these harsh conditions. Overall, our model is able to describe the full set of analysed data. To the knowledge of the authors this is the first comprehensive work studying solid surface titrations and cation uptake up to high salt levels and applying electrostatics models to describe the solid interface at these particular conditions. It is expected that these first systematic data acquisition along with the detailed modelling can serve as a benchmark for the modelling of future studies on sorption in highly saline systems.

Role of TiO2 Anatase Surface Morphology on Organophosphorus Interfacial Chemistry

Optimization of physicochemical properties of TiO2 anatase for organophosphorus remediation remains challenging. One approach is to use anatase nanofibers, prepared from hydrothermally synthesized titanates. Charge densities and potentials of anatase nanofibers were determined from atomic force microscopy force–curve measurements using the modified Derjaguin, Landau, Verwey, Overbeek theory, which includes roughness and hydration forces, in the pH range 4–9. Calculated values were −0.007 to −0.03 C m–2 and −70 to −150 mV, respectively. In contrast, at neutral pH, the magnitudes of diffuse layer surface charge densities and potentials have a minimum in anatase nanoparticles. These observations and zeta-potential results suggest that nanofiber surfaces are more acidic compared with nanoparticles. This is consistent with nanofibers having ∼3-fold higher adsorption for organophosphorus methyl parathion (pH ≈ 7). The resulting adsorption includes contributions from (1) charge accumulation at local coordination...

Measuring Inner Layer Capacitance with the Colloidal Probe Technique

The colloidal probe technique was used to measure the inner layer capacitance of an electrical double layer. In particular, the forces were measured between silica surfaces and sulfate latex surfaces in solutions of monovalent salts of different alkali metals. The force profiles were interpreted with Poisson-Boltzmann theory with charge regulation, whereby the diffuse layer potential and the regulation properties of the interface were obtained. While the diffuse layer potential was measured in this fashion in the past, we are able to extract the regulation properties of the inner layer, in particular, its capacitance. We find systematic trends with the type of alkali metal ion and the salt concentration. The observed trends could be caused by difference in ion hydration, variation of the binding capacitance, and changes of the effective dielectric constant within the Stern layer. Our results are in agreement with recent experiments involving the water-silica interface based on a completely independent method using X-ray photoelectron spectroscopy in a liquid microjet. This agreement confirms the validity of our approach, which further provides a means to probe other types of interfaces than silica.

The relationship between inner surface potential and electrokinetic potential from an experimental and theoretical point of view

Environmental contextInterfacial properties of colloid and nanoparticles are directly related to the reactivity and surface densities of existing surface sites. Surface characterisation of particles provides only some kind of average surface properties. Analysis of well-defined monocrystal surfaces, which form the surface of the single particle, leads to a better understanding of surface reactions and mutual interactions of adjacent crystal planes on average surface properties. AbstractThe contact of small solid particles and macroscopic flat planes with aqueous electrolyte solutions results in the accumulation of ions at the interface and the formation of the electrical interfacial layer. Analysis of well-defined monocrystal surfaces, which are the building blocks of a single particle, leads to a better understanding of surface reactions and mutual interactions of adjacent crystal planes on average surface properties of particles. We analyse inner surface potential (obtained by single-crystal electrode) and zeta-potential data (obtained by streaming potential measurements) that were obtained on identical samples. Among the systems for which comparable surface and zetapotentials are available, measured inner surface potential data for sapphire (0001), haematite (0001) and rutile (110) show the expected behaviour based on the face-specific surface chemistry model, whereas the slopes for rutile (110) and quartz (0001) do not. Isoelectric points for sapphire (0001), haematite (0001) and rutile (100) are in conflict with the standard model that implies consistent behaviour of surface potential and diffuse layer potential. For the two former systems, previous results from the literature suggest that the charge of interfacial water can explain the discrepancy. The water layer could also play a role for quartz (0001), but in this case, the discrepancy would simply not be noticed, because both point of zero potential and isoelectric point are low. Along with data on silver halides, it can be concluded that six-ring water structures on solids may generate the electrokinetic behaviour that is typical of inert surfaces like Teflon.

Interactions between silica particles in the presence of multivalent coions.

Forces between charged silica particles in solutions of multivalent coions are measured with colloidal probe technique based on atomic force microscopy. The concentration of 1 : z electrolytes is systematically varied to understand the behavior of electrostatic interactions and double-layer properties in these systems. Although the coions are multivalent the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory perfectly describes the measured force profiles. The diffuse-layer potentials and regulation properties are extracted from the forces profiles by using the DLVO theory. The dependencies of the diffuse-layer potential and regulation parameter shift to lower concentration with increasing coion valence when plotted as a function of concentration of 1 : z salt. Interestingly, these profiles collapse to a master curve if plotted as a function of monovalent counterion concentration.

Long-range interaction forces between 1,3,5-cyclohexanetrisamide fibers in crossed-cylinder geometry

Abstract We report on direct force measurements between single melt-electrospun 1,3,5-cyclohexanetrisamide (CTA) fibers in crossed-cylinder geometry. The two CTA compounds selected for this study differ in their peripheral substituents: aliphatic (-C 10 H 21 ) and fluorinated chains (-CH 2 C 6 F 13 ), respectively. Melt-electrospinning of the CTAs results in smooth and circular fibers with diameters of about 5 μm. Individual segments of these fibers were attached to tipless atomic force microscope (AFM) cantilevers and used to measure long-range interaction forces versus a second fiber from the same compound in crossed-cylinder geometry. This geometry is well-known from the surface force apparatus and allows for the normalization of forces according to the Derjaguin approximation. From symmetrical measurements, i.e. measurements between fibers from the same type of CTA, we quantify the diffuse layer properties in aqueous electrolyte solutions within the framework of the Derjaguin, Landau, Verwey and Overbeek (DLVO) theory. Apparent diffuse layer potentials resulting from the fits to the full solutions of the Poisson–Boltzmann equation show that the fiber surfaces bear a negative surface charge. Most likely, the origin of charging is the adsorption of hydroxyl ions as residual charges from the electrospining process would be compensated upon the immersion in the electrolyte solutions. Such ion adsorption processes are well-known for other hydrophobic surfaces such as aliphatic and fluorinated self-assembled monolayers (SAMs) (terminating with CH 3 and CF 3 groups). The apparent diffuse layer potentials for CTA fibers are comparable to the values reported for these SAMs.

The influence of surface energetic heterogeneity on electrofluidic gating of a metal oxide surfaces

We developed a theoretical model which describes the influence of the applied potential to the wall of an oxide nanochannel on the diffuse layer potential in the solution filling the nanopore. It was assumed that the surface of oxide is energetically heterogeneous and electrolyte ions from the solution can adsorb on channel walls. We performed calculations for two oxides: SiO2 and Al2O3. It was found that energetically heterogeneous oxide surfaces strongly suppress gating potential. Moreover, taking into account ion adsorption considerably increased the electrokinetic potential and reduced the influence of applied potential on the electric double layer in the solution. The density of surface sites is the key parameter in the modeling of oxide nanochannels. Low density of surface hydroxyl groups significantly increases susceptibility on electrofluidic gating.

Electric double-layer potentials and surface regulation properties measured by colloidal-probe atomic force microscopy.

We show how the colloidal-probe technique, which is based on force measurements made with the atomic force microscope, can be used to accurately determine the charging parameters of water-solid interfaces. Besides yielding accurate values of the double-layer or diffuse-layer potential, the method also allows reliable determination of the charge regulation properties of the surfaces. The latter can be quantified with a regulation parameter, which is essential to properly describe forces between interfaces, especially in asymmetric situations when one of the interfaces is charged and the other one is close to neutral. The technique relies on a highly charged probe particle, for which the charging properties are accurately determined by interpreting the double-layer contribution of the measured force profiles in the symmetric sphere-sphere geometry with Poisson-Boltzmann (PB) theory. Once the probe particle is calibrated, this particle is used to measure the force profile between an unknown substrate in the asymmetric sphere-sphere or sphere-plane geometry. From this profile, the diffuse-layer potential and regulation parameter of the substrate can be again determined with PB theory. The technique is highly versatile, as it can be used for a wide variety of substrates, including colloidal particles and planar substrates. The technique is also applicable in salt solutions containing multivalent ions. The current drawbacks of the technique are that it can only be applied up to moderately high salt levels, typically to 10 mM, and only for relatively large particles, typically down to about 1 μm in diameter. How the technique could be extended to higher salt levels and smaller particle size is also briefly discussed.

Study of ionic transport through metalized nanoporous membranes functionalized with self-assembled monolayers

Ionic transport through synthetic nanoporous membranes has received great attention in applications related to biosensing, fuel cell, and desalination. Past work has demonstrated that charge selectivity can be achieved by applying a potential across a metallized conductive membrane. However, challenges arise for improving charge selectivity as a result of irreversibility of the system from the anion adsorption at the membrane surface. This study demonstrates how charge selectivity can be improved with the presence of a well grown self-assembled monolayer (SAM), which can aid in applications that use chemical separation processes based on the surface charge of the nanopore.In this work, the transport and selectivity properties of gold-coated conductive nano-capillary-array-membranes (NCAMs) are studied using charged species methyl viologen paraquat, (MV2+) and napathalenedisulfonate disodium salt (NDS2−). The selectivity coefficients for MV2+ and NDS2− increased with the functionalization of undecanethiol on the gold-coated NCAM surface. With the presence of a SAM, the selectivity coefficients increased by 44% for MV2+ and 200% for NDS2−. The influence of ionic transport from the diffuse layer potential at the walls and surface of the nanopore is also discussed.

Which mechanism operates in the electron-transfer process at liquid/liquid interfaces?

We present a more general expression for the relationship of potential dependence, which implies that a change in the interfacial drop across the interface has little effect on the free energy of the reaction, but mainly affects the surface concentration of reactant in each phase. Abundant experimental results from several well-known groups are analyzed in great detail to confirm our conclusion. At the same time, we define a new parameter named Frumkin correction factor to describe this relationship of potential dependence, which expresses the thermodynamic effect of double diffuse layers within both phases in contrast with the so often suggested kinetic electron-transfer (ET) coefficient; we also find that it depends on two intimately related aspects: the charges of reactive species and the ratio of the diffuse layer potential to the total potential within each phase, so it is quite arbitrary to ignore the diffuse layer effect in the aqueous phase just because of its relatively small values. In addition, a fascinating question on the inverted region at liquid/liquid interfaces has been successfully interpreted by an opposite surface concentration effect, which was often considered as a kinetic Marcus inverse by most groups.

The Hofmeister effect in zeta potentials of CTAB-stabilised toluene-in-water emulsions

In this paper, we describe an experimental verification of the hypothesis of ion-specificity in counterion co-adsorption for cetyltrimethylammonium bromide (CTAB) at toluene–water interface (Hofmeister effect). For this purpose, toluene-in-water emulsions stabilised with CTAB in the absence and presence of inorganic electrolytes (NaBr, NaNO 3, NaF and NaClO 4), were used. Zeta potential measurements of the emulsions confirm both charging of the interface with surface-active cetyltrimethylammonium cation (CTA +), and anion dependence of the zeta potential. Electrokinetic measurements as a probe of diffuse layer potential show little effect of interfacial ion-specificity.

The voltammetric responses of nanometer-sized electrodes in weakly supported electrolyte: A theoretical study

The effect of the supporting electrolyte concentration on the interfacial profiles and voltammetric responses of nanometer-sized disk electrodes have been investigated theoretically by combining the Poisson–Nernst–Planck (PNP) theory and Butler–Volmer (BV) equation. The PNP-theory is used to treat the nonlinear couplings of electric field, concentration field and dielectric field at electrochemical interface without the electroneutrality assumption that has been long adopted in various voltammetric theories for macro/microelectrodes. The BV equation is modified by using the Frumkin correction to account for the effect of the diffuse double layer potential on interfacial electron-transfer (ET) rate and by including a distance-dependent ET probability in the expression of rate constant to describe the radial heterogeneity of the ET rate constant at nanometer-sized disk electrodes. The computed voltammetric responses for disk electrodes larger than 200 nm in radii in the absence of the excess of the supporting electrolyte using the present theoretical scheme show reasonable agreements with the predications of the conventional microelectrode voltammetric theory which uses the combined Nernst–Planck equation and electroneutrality equation to describe the mixed electromigration-diffusion mass transport without including the possible effects of the diffuse double layer (Amatore et al. [25]). For electrodes smaller than 200 nm, however, the voltammetric responses predicated by the present theory exhibit significant deviation from the microelectrode theory. It is shown that the deviations are mainly resulted from the overlap between the diffuse double layer and the concentration depletion layer (CDL) at nanoscale electrochemical interfaces in weakly supported media, which will result in the invalidation of the electroneutrality condition in CDL, and from the radial inhomogeneity of ET probability at nanometer-sized disk electrodes.

On the origin of electrostatic and steric repulsion in oil-in-water emulsion films from PEO-PPO-PEO triblock copolymers

Oil-in-water emulsion films were used to investigate the origin of electrostatic and steric surface forces between two oil droplets in aqueous solution of nonionic polymeric surfactants. The Thin Liquid Film–Pressure Balance Technique was used. Equivalent thickness of oil-in-water emulsion films stabilized by PEO-PPO-PEO triblock copolymers (Pluronic ® F108 and P104) vs. pH was measured at constant capillary pressure and ionic strength. The isoelectric point at the negatively charged film interfaces, corresponding to zero diffuse double layer potential was found. This demonstrates that the origin of the electrostatic repulsion in the emulsion films studied is associated to preferential adsorption of OH − ions. Disjoining pressure isotherms for the emulsion films obtained at different pH were fitted to de Gennes’ scaling theory for steric interaction between polymer ‘brush’ layers with the ‘brush’ thickness as a fitting parameter. The fit obtained was satisfying and yielded PEO-‘brush’ thickness of 9.6 nm. These results allowed the conclusion that in absence of diffuse double layer forces the stabilization of oil-in-water emulsion films from PEO-PPO-PEO triblock copolymers was due to ‘brush-to-brush’ steric repulsion.

The double layer potentials at the toluene–aqueous interface in the presence of CTAB/NaBr. Implications for Ion-Selective Electrodes

The interfacial tension isotherms for cetyltrimethylammnonium bromide (CTAB) in the presence of sodium bromide at the aqueous–toluene interface are discussed. In accordance with previous observations for an aqueous–air interface, the presence of a non-surface active electrolyte (NaBr) has strong influence on the interfacial activity of CTAB at the aqueous–toluene interface. The results were analysed within the framework of the Surface quasi-Two Dimensional Electrolyte model (STDE), assuming that the non-surface active bromide counterions partially penetrate the Stern layer formed by cetyltrimethylammonium cations adsorbed at the interface. This analysis allowed for calculation of the electrical double layer (EDL) potentials (Stern potential and the diffuse double layer potential). The calculated EDL potentials were compared with the membrane potentials generated in the Ion-Selective Electrodes (ISE) containing neither ionophore nor ion-exchanger, when exposed to aqueous solutions of CTAB.