Faradaic double layer depolarization in electrokinetics: Onsager relations and substrate limitations

More often than not, the measurement of interfacial potentials by means of electrokinetic techniques is affected by interfering processes that may relax or even annihilate their primary response function. Among these processes are faradaic ones, provided that the substrate is sufficiently conducting and a redox function is available, and non-faradaic ones, if geometrical constraints are in effect. Ample experimental evidence is available, e.g., in the collapse of streaming potentials generated by metal/electrolyte solution interfaces, the bipolar microelectrodic redox processes in fluidized beds of metallic particles, and the "superfast" electrophoresis of dispersed ion exchanger particles and electron-conducting particles. Common feature of these apparently disparate phenomena is that the lateral electric field is affected by coupling with transversal depolarization fields, or by conductance gradients due to Donnan effects. Recent work has rigorously analyzed the deformation of the lateral electric field in a (streaming potential) slit cell by electron transfer reactions at the interface, taking into account both convective diffusion of the electroactive species and kinetics of the interfacial electron transfer reaction. Here a common, generic basis for faradaic and non-faradaic double layer depolarization is formulated along the lines set by Onsager, and methodologies for retrieving the underlying electrokinetic parameters from experimental data are evaluated. Particular attention is paid to the limitations of double layer polarization, as posed by the substrate.     

Faradaic depolarization in the electrokinetics of the metal-electrolyte solution interface

Streaming potentials (E(str)) have been measured in a flat thin-layer cell with gold and aluminum surfaces. The conventional relation between E(str) and the zeta-potential is shown to be applicable only as long as charge transfer reactions at the metal-electrolyte solution interface are insignificant in terms of the ensuing contribution to the overall cell conductivity. Owing to the irreversibility of the reduction/oxidation of water at most metal surfaces, streaming potentials can be obtained over a very broad range of pressure gradients for metallic substrates in electrolytes such as KNO3. The situation changes drastically in the presence of a reversible redox couple like Fe(CN)(6)3-/Fe(CN)(6)4-. Even small streaming potentials are then greatly diminished due to the extensive conduction that results from the bipolar electrolysis at the metal surface. For gold and aluminum in the presence of various electroinactive and electroactive electrolytes, the measured values for E(str) are shown to be consistent with their conventional voltammetric characteristics.     

Probing of polyelectrolyte monolayers by zeta potential and wettability measurements

Detection of the very first step of polyelectrolyte adsorption onto a solid support is of great importance for understanding mechanisms of solid surface modification. It was shown that streaming potential and contact angle measurements can be successfully used for polyelectrolyte (PE) adsorption characterization in a broad range of surface coverage. Cationic polyallylamine hydrochloride (PAH) was used for the formation of the layer. The electrokinetic characteristics of the substrate covered by the PAH layer were compared with contact angles measured under wet (captive air bubble/substrate in water) and dry (sessile water droplet/dried substrate) conditions. It has been demonstrated that contact angle values determined under both conditions are in good agreement. The observed rapid increase in the contact angle from zero for the bare mica surface to the value close to one characteristic of the PAH monolayer appears in the same PAH coverage range as zeta potential value changes due to adsorption. These results show that wettability can be as sensitive to the presence of small amounts of adsorbed species as electrokinetic measurements.     

Polyelectrolyte adsorption layers studied by streaming potential and particle deposition

Adsorption of a cationic polyelectrolyte, polyallylamine hydrochloride (PAH), having a molecular weight of 70,000 on mica was characterized by the streaming potential method and by deposition of negative polystyrene latex particles. Formation of PAH layers was followed by determining the apparent zeta potential of surface zeta as function of bulk PAH concentration. The zeta potential was calculated from the streaming potential measured in the parallel-plate channel formed by two mica plates precovered by the polyelectrolyte. The experimental data were expressed as the dependence of the reduced zeta potential zeta/zeta0 on the PAH coverage Theta(PAH), calculated using the convective diffusion theory. It was found that for the ionic strength of 10(-2) M, the dependence of zeta/zeta0 on Theta(PAH) can be reflected by the theoretical model formulated previously for surfaces covered by colloid particles. The electrokinetic measurements were complemented by particle deposition experiments on PAH-covered mica surfaces. A direct correlation between the polymer coverage and the initial deposition rate of particles, as well as the jamming coverage, was found. For ThetaPAH > 0.3 the initial deposition rate attained the value predicted from the convective diffusion theory for homogeneous surfaces. The initial deposition rates for surfaces modified by PAH were compared with previous experimental and theoretical results obtained for heterogeneous surfaces formed by preadsorption of colloid particles. It was revealed that negative latex deposition occurred at surfaces exhibiting negative apparent zeta potential, which explained the anomalous deposition of particles observed in previous works. It was suggested that the combined electrokinetic and particle deposition methods can be used for detecting adsorbed polyelectrolytes at surfaces for coverage range of a percent. This enables one to measure bulk polyelectrolyte concentrations at the level of 0.05 ppm.     

Problems and results of zeta-potential measurements on fibers

A survey is given on both theoretical background and methodical details of zeta-potential measurements on fibers. Electro-osmosis and streaming potential/streaming current measurements can be used in order to obtain correct zeta-potentials. Both measuring principles yield the same values for zeta-potential if the errors due to resistance measurements are avoided. This agreement as well as the independence of zeta-potential of applied voltage (in the case of electro-osmosis) and hydrostatic pressure (in the case of streaming potential/streaming current) point out that the Stern-potential at the boundary immobile/diffuse layer can be determined. Electrophoresis and measurement of other electrokinetic phenomena give values related to but not identical with the zeta-potential. Applications of electrokinetic measurements for investigating fiber problems in production, processing and finishing are reviewed. Parameters determining the zeta-potential of fibers are discussed.Dedicated to Prof. Dr. E. R. Schwarzl with congratulations for his 60th birthday.     

Characterization of poly(ethylene imine) layers on mica by the streaming potential and particle deposition methods

Deposition kinetics of polystyrene latex (averaged particle size of 0.66 microm) on mica covered by poly(ethylene imine) (PEI), a cationic polyelectrolyte having an average molecular mass of 75,000 g mol(-1), was studied using the impinging-jet method. The hydrodynamic radius of PEI, determined by PCS measurements, was 5.3 nm. The electrophoretic mobility of PEI was measured as a function of pH for ionic strengths of 10(-3) and 10 (-2) M, which made it possible one to determine the amount of electrokinetic charge of the molecule and its zeta potential. Formation of the polyelectrolyte layer on mica was followed by measuring the streaming potential in the parallel-plate channel. From these measurements, the dependence of the apparent zeta potential of mica on the surface coverage of PEI was determined. The amount of adsorbed PEI on mica was calculated from the convective diffusion theory. These results were quantitatively interpreted in terms of the theoretical model postulating a particle-like adsorption mechanism for PEI with not too significant shape deformation upon adsorption. On the other hand, the Gouy-Chapman model postulating the adsorption in the form of flat disks was proved inappropriate. After the surface was fully characterized, particle deposition experiments were carried out with the aim of finding the correlation between the polymer coverage and the initial rate of latex particle deposition. In the range of small polyelectrolyte coverage, a monotonic relation between the polymer coverage and the initial deposition rate of particles, as well as the jamming coverage, was found. For Theta(PEI)>0.25, the initial particle deposition rate attained the value predicted from the convective diffusion theory for homogeneous surfaces. These results were interpreted theoretically by postulating that an effective immobilization of colloid particles occurred on local polyelectrolyte assemblages containing between two and three PEI molecules.     

Theoretical study of the electrokinetic and electrochemical behaviors of two-layer composite membranes

A theoretical study concerning the effect of structure (porosity, pore radius and layer thickness) and surface characteristics (zeta potential) of two-layer composite membranes on global streaming potential (SP_g), membrane potential (Em_g) and membrane conductivity (λ_g) is presented. To this end, each layer of the composite membrane (composed of a support layer and a filtering layer) was modeled as a bundle of identical capillary tubes with connections between pores of the two layers (the pores in the filtering layer being smaller than those of the support layer). The global parameters SP_g, Em_g and λ_g were calculated by using the theory of thermodynamics of irreversible processes and a space charge model. SP_g, Em_g and λ_g were expressed as a function of the individual parameters of each layer SP⁽ⁱ⁾, Em⁽ⁱ⁾ and λ⁽ⁱ⁾, respectively, the length fraction of the support layer, the porosity and pore radius ratios. It was shown that the electrokinetic (streaming potential and membrane conductivity) and electrochemical (membrane potential) behaviors of such composite membranes vary between that of single layers. For streaming potential, the results indicate that the contribution of the filtering layer to the global streaming potential is very little influenced by zeta potentials of both types of pores. It appears that the individual streaming potential of the filtering layer greatly dominates the global streaming potential. This is due to the fact that the streaming potential of the filtering layer is weighted by the pore radius ratio which is a predominant parameter in determining the global streaming potential. In contrast to the streaming potential, the contribution of the filtering layer to the global membrane potential (Em_g) or membrane conductivity (λ_g) depends more or less on the zeta potentials of both kinds of pores and the corresponding electrokinetic radii as well. As to the membrane potential, the contribution of the filtering layer to Em_g is all the more sensitive to the zeta potentials than the electrokinetic radii are small. The filtering layer greatly dominates the global membrane potential when its pores are narrow (with regard to the Debye length) and strongly charged. For the electrolyte conductivity inside pores, the smaller pores (inside the filtering layer) have an effect all the more dominant on the apparent membrane conductivity than their zeta potential is low and that of larger pores (inside the support layer) is high.     

The history of electrokinetic phenomena

Electrokinetic phenomena comprise the phenomena where a liquid moves tangentially to a charged surface. Well-known phenomena of this kind are electrophoresis, electro-osmosis, streaming potential and sedimentation potential. A historical review is given here, starting with their discovery by F.F. Reuss in 1808 and continuing with the early investigators including G. Wiedemann, G.Quincke, E. Dorn and U. Saxén. It is also discussed how electrokinetic phenomena gave rise to the concept electrical double layer in colloid science. The development of the theory starting with H. Helmholtz, continuing with M. Smoluchowski is described. Extension of the theory including relaxation and surface conduction is included. Finally the history of other kinds of electrokinetic phenomena such as electroacoustics and diffusiophoresis is treated.     

Electrokinetic flow in a planar slit covered by an ion-penetrable charged membrane

The electrokinetic flow of an electrolyte solution in a planar slit covered by an ion-penetrable charged membrane layer is analyzed theoretically. An approximate analytical expression for the spatial variation in the electrical potential is derived, and the electroosmotic velocity, the total electric current, and the streaming potential of the system under consideration are evaluated. The effects of epsilon' (relative permittivity of liquid phase/relative permittivity of membrane layer), eta' (viscosity of liquid phase/viscosity of membrane layer) and the valence of anions (coions) on the volumetric flow rate and total current are examined. We show that the effect of the valence of cations (counterions) on the volumetric flow rate is less significant than that of epsilon' and that of eta'. However, the effect of epsilon' on the total current is less significant than that of the valence of cations and that of eta'. The variation of total current as a function of ionic strength is found to have a local minimum, regardless of whether a pressure gradient is applied or not. The absolute streaming potential has a local maximum as the concentration of fixed charge varies, which was not found in previous studies.     

Analysis of effect of electrolyte types on electrokinetic energy conversion in nanoscale capillaries

An analytical study on the effect of electrolyte types on the electrokinetic energy conversion is presented using nanoscale cylindrical capillary, which is either positively or negatively charged. The sign of surface charge determines the role and concentration magnitude of ions in the capillary and the energy conversion performance. Our study shows that the electrokinetic energy conversion performance (maximum efficiency, pressure rise and streaming potential) are approximately identical for 1:1 (KCl), 2:1 (CaCl₂) and 3:1 (LaCl₃) electrolytes when capillary is positively charged. For negatively charged capillary, energy conversion performance degrades significantly with the increase of counter‐ion valence. For both positively and negatively charged capillaries, higher maximum efficiency can be resulted in low bulk concentration and surface charge density regimes. However, high maximum pressure rise generation for the pumping is found in the low bulk concentration and high surface charge density regimes. For the electric power generation, higher maximum streaming potential is found when both bulk concentration and surface charge density are low.     

On the behavior of electrokinetic streaming potential during protein filtration with fully and partially retentive nanopores

An experimental investigation of the electrokinetic streaming potentials of both fully and partially retentive nanopores as compared with the filtration progress of dilute globular protein solution under different surface charge conditions was performed using hollow fibers. The streaming potential is generated by the electrokinetic flow effect within the electric double layer of the charged surface. Depending on the solution pH, both the protein and the pore wall can be either repulsive or attractive due to the long-range electrostatic interaction. The repulsive electrostatic interaction allows the protein particles to stay in a suspended state above the outer surface of hollow fibers instead of being deposited. The apparent streaming potential value at partially retentive pores is larger than that at fully retentive pores for the oppositely charged case; however, the opposite behavior is shown for the same-charged case. The axial-position-dependent streaming potential was also observed in order to explore the development of a concentration polarization layer during the cross-flow filtration. The time evolution of the streaming potential during the filtration of protein particles is related to the filtrate flux, from which it can be found to provide useful real-time information on particle deposition onto the outer surfaces of hollow fibers.     

Zeta potential of particle bilayers on mica: a streaming potential study

The streaming potential of mica covered by bilayers of latex particles was measured using the parallel-plate channel cell. The size of the first latex (A500) bearing amidine charged groups was 503 nm and the second latex (L800) bearing sulfonate groups was 810 nm (at pH 5.5 and an ionic strength of 10(-2)M). The A500 latex exhibited an isoelectric point at pH 10.5, whereas the L800 latex was strongly negative at all pH. Mica sheets were precovered first by the A500 latex particles under diffusion transport conditions. The coverage of this supporting layer was regulated between 0.02 and 0.5 by changing the bulk concentration of latex and the deposition time. Then, the second layer of the L800 latex of regulated coverage up to 0.55 was deposited under the diffusion transport. The coverage of particles and their distributions in both layers were determined by a direct enumeration of particles by optical microscopy under wet conditions and by AFM. It was shown that the structure of the L800 particle layers and the maximum coverage were in accordance with theoretical simulations performed according to the random sequential adsorption (RSA) model. After forming bilayers of desired composition and structure, streaming potential measurements were carried out. The influence of the mica substrate, the supporting layer coverage, and its zeta potential on the apparent zeta potential of bilayers was systematically studied. It was established that for a bilayer coverage exceeding 0.20, the net zeta potential became independent of the substrate and the supporting layer zeta potentials. Then, the asymptotic values of the zeta potential of the bilayer approach 1/√2=0.71 of the bulk zeta potential of the particles forming the external (second) layer. This behavior was interpreted theoretically in terms of the electrokinetic model derived previously for monolayers. It was also concluded that results obtained in this work can be exploited for interpretation of polyelectrolyte film formation in the layer by layer (LbL) processes and protein adsorption pertinent to the antigen/antibody interactions.     

Analysis of the pressure-induced potential arising through composite membranes with selective surface layers

When a pressure gradient is applied through a charged selective membrane, the transmembrane electrical potential difference, called the filtration potential, results from both the applied pressure and induced concentration difference across the membrane. In this work we investigate the electrokinetic properties relative to both active and support layers of a composite ceramic membrane close to the nanofiltration range. First, the volume charge density of the active layer is obtained by fitting a transport model to experimental rejection rates (which are controlled by the active layer only). Next, the value of the volume charge density is used to compute the theoretical filtration potential through the active layer. For sufficiently high permeate volume fluxes, the concentration difference across the active layer becomes constant, which allows assessing the membrane potential of the active layer. Experimental measurements of the overall filtration potential arising through the whole membrane are performed. The contribution of the support layer to this overall filtration potential is put in evidence. That implies that the membrane potential of the active layer cannot be deduced directly from the overall filtration potential measurements. Finally, the contribution of the support layer is singled out by subtracting the theoretical filtration potential of the active layer from the experimental filtration potential measured across the whole membrane (i.e., support + active layers). The amphoteric behavior of both layers is put in evidence, which is confirmed by electrophoretic measurements carried out with the powdered support layer and by recently reported tangential streaming potential measurements.     

Determination of the electrokinetic potential of dispersed and macromolecular colloids by means of streaming potential measurements. II.

A principle for determining the electrokinetic potential, based on the measurement of the streaming potential has been developed for the investigation of dispersions of low concentration (10–100 ppm) and ultrafiltrable macromolecular solutions. An ultrafiltration apparatus operating with a permanent pressure difference was constructed, in which the streaming potential E produced on the filter layer and the filtration rate W were measured simultaneously on an XY recorder. The so-called apparent electrokinetic potential was calculated from the axial intercept E_∞ obtained by the extrapolation of the E vs. W curves. It was pointed out that the filtration mechanism which depended on the relation between the pore size of the filter and the dispersity of the colloid played a basic role in the e.k.p. measurement mentioned above.Simultaneously with our method comparative measurements were carried out on Nabentonite by electrophoresis. The difference between the electrokinetic potential data obtained by the two different methods was considered to be a consequence of the surface conductivity of the particles. On the basis of our investigations performed on agar solutions it is expected that the electrokinetic potential measuring method based on ultrafiltration is suitable for the investigation of macromolecular colloid solutions.     

Electrokinetic characterization of porous plugs from streaming potential coupled with electrical resistance measurements

The zeta potential of mixed nickel-iron oxide particles is evaluated by a new laboratory instrument. This latter allows the measurement of streaming potential together with the electrical resistance of porous plugs. The conductivity of electrolyte inside plug (pore conductivity) is deduced from electrical resistance measurements and is used together with streaming potential to evaluate the zeta potential by accounting for the surface conduction phenomenon. It is shown that neglecting the surface conduction phenomenon leads to a substantial underestimation of the zeta potential. The coupled measurements of streaming potential and plug electrical resistance yield zeta potential values that are in very good agreement with those obtained by electrophoresis. The densification of the porous plug with increasing pressure increments is put in evidence by the decrease in measured streaming potentials. Electrical resistance measurements make it possible to account for the increase in surface conductivity resulting from the more compacted structure of the plug. By doing so, the calculated zeta potential is found to be virtually independent of the pressure difference involved in streaming potential experiments, whereas the negligence of surface conduction phenomenon leads to a decrease in the apparent zeta potential with increasing pressure level.     

Clean and doped surface electronic structure in angle-resolved and resonant photoemission study

The paper presents the experimental results of the electronic band structure study of the semiconductor crystal clean surface and this surface doped by transition metal or rare earth metal atoms. For clean surfaces of the CdTe crystal the two-dimensional electronic band structure E(k) dependence was determined for surface states located in the valence band energy region. The doping of the clean surface of CdTe was performed by the controlled, sequential deposition of metal atoms (Fe, Gd or Yb) on the surface. After each deposition the synchrotron radiation was used to measure the resonant photoemission spectra (energy distribution curve – EDC, constant initial states – CIS and constant finale states – CFS). The results of the study showed that in the first stages of the metal atoms' deposition in the range of thickness equal to about 0.5 ML the effect of the crystal clean surface doping occurs. For bigger metal layer deposition the metallic islands electronic structure gave the contribution to the measured spectra. Heating of the sample surface covered by metal atoms leads to the diffusion of the atoms into the sample and results in an increase of the crystal doping and decrease of the metallic islands contribution to the measured spectra.     

Remarkable influence of surface composition and structure of oxidized iron layer on orange I decomposition mechanisms

Although the decomposition of water pollutants in the presence of metallic iron is known, the reaction pathways and mechanisms of the decomposition of azo-dyes have been meagerly investigated. The interface phenomena taking place during orange I decomposition have been investigated with the use of infrared external reflection spectroscopy, X-ray photoelectron spectroscopy, and scanning electron microscopy. The studies presented in this paper establish that there are close relationships between the composition and structure of the iron surface oxidized layers and the kinetics and reaction pathway of orange decomposition. The influence of the molecular structure of azo-dye on the produced intermediates was also studied. There are remarkable differences in orange I decomposition between pH 3 and pH 5 at 30 degrees C. Decomposition at pH 3 is very fast with pseudo-first-order kinetics, whereas at pH 5 the reaction is slower with pseudo-zero-order kinetics. At pH 3, only one amine, namely 1-amino-4-naphthol, was identified as an intermediate that undergoes future decomposition. Sulfanilic acid, the second harmful reduction product, was not found in our studies. At pH 3, the iron surface is covered only by a very thin layer of polymeric Fe(OH)(2) mixed with FeO that ensures orange reduction by a combination of an electron transfer reaction and a catalytic hydrogenation reaction. At pH 5, the iron surface is covered up to a few micrometers thick, with a very spongy and porous layer of lepidocrocite enriched in Fe(2+) ions, which slows the electron transfer process. The fastest decomposition reaction was found at a potential near -300 mV (standard hydrogen electrode). An addition of Fe(2+) ions to solution, iron preoxidation in water, or an increase of temperature all result in an increasing decomposition rate. There is no single surface product that would inhibit the decomposition of orange. This information is crucial to perform efficient, clean and low cost waste water treatment. The findings presented here make the treatment of wastewater in the presence of metallic iron a very promising solution.     

Characterisation of the electrokinetic properties of plane inorganic membranes using streaming potential measurements

We present and test a device designed to measure the streaming potential of plane inorganic membrane during filtration.Two kinds of microporous membranes (a membrane made of a mixture of alumina-titania and this same type of membrane covered with an additional titania layer) are studied with different pH, ionic strength and electrolyte nature. The modification of the surface acid-basic equilibriums is analysed from the streaming potential measurements. The pores size of the studied membranes is large enough to avoid overlapping of the double layers. Streaming potential measurements are used to determine the zeta potential of the membranes from the Helmholtz-Smoluchowski relationship, corrected for the lowest ionic strengths studied. The shifting of the isoelectric point of the membranes studied with CaCl₂ and Na₂SO₄ solutions shows specific adsorption of calcium and sulfate ions onto the surface. The additional titania layer on the alumina-titania support does not seem to modify the electrokinetic properties of the membrane.The interactions of the alumina-titania membrane with the H⁺ and OH⁻ ions are analysed by studying the variations of pH between permeate and retentate compartments. These variations allow determining the isoelectric point of the membrane with a reasonable precision.     

Electrokinetic flow in an elliptic microchannel covered by ion-penetrable membrane

The electrokinetic flow of an electrolyte solution in an elliptical microchannel covered by an ion-penetrable, charged membrane layer is examined theoretically. The present analysis extends previous results in that a two-dimensional problem is considered, and the system under consideration simulates the flow of a fluid, for example, in a microchannel of biological nature such as vein. The electroosmostic volumetric flow rate, the total electric current, the streaming potential, and the electroviscous effect of the system under consideration are evaluated. We show that, for a constant hydraulic diameter, the variations of these quantities as a function of the aspect ratio of a microchannel may have a local minimum or a local maximum at a medium level of ionic strength, which depends on the thickness of the membrane layer. For a constant cross-sectional area, the electroosmostic volumetric flow rate, the total electric current, and the streaming potential increase monotonically with the increase in the aspect ratio, but the reverse is true for the electroviscous effect.