Measurement of the streaming potential and streaming current near a rotating disk to determine its zeta potential

Methodology for determining the zeta potential of a disk-shaped sample by both streaming potential and streaming current measurements is presented. Integration of Laplace's equation within one radius of the disk surface revealed that the streaming potential decreased strongly in the surface normal direction. With this solution, the zeta potential can be calculated from measurements of the streaming potential near the surface of the disk provided the position of the working electrode near the disk surface is known. Determining the zeta potential of a disk-shaped sample by means of streaming current measurements required determination of a current collection efficiency because not all the streaming current from a disk flows through the auxiliary electronic current path. While the working electrode near the disk should be pointlike, several possible variants on counter electrode shape and size were explored. Although the current collection efficiency was only a few percent in each case, the measured current was of 10 nA order. The current collection efficiency depended only on system geometry and was independent of a disk's zeta potential and solution concentration. Streaming current measurements of zeta potential on silicon wafers in potassium chloride solutions up to 10 mM agreed well with published values.     

Influence of roughness and capillary size on the zeta potential values obtained by streaming potential measurements

Streaming potential measurements are performed to determine the zeta potential of flat surfaces, particles, or fibers. Although the zeta potential is a well-defined property of solid surfaces in a liquid, there are indications that the absolute values of the zeta potential calculated using the Helmholtz-Smoluchowski equation are affected by surface roughness and—in case of particle or fiber assemblies—their packing density. The study at hand investigates these influences using flat polymer surfaces with different roughness and topography and assemblies of basalt spheres. It was found that increasing roughness of the flat surface and larger size or smaller number of particles in particle assemblies result in flatter slopes of the streaming potential versus pressure and thus lower apparent absolute values of the zeta potential. The interpretation of streaming potential measurements should therefore not focus on absolute zeta potential values but on trends in pH- and concentration-dependent measurements.     

In situ particle zeta potential evaluation in electroosmotic flows from time-resolved microPIV measurements

A time-resolved microPIV method is presented to measure in an EOF the particles zeta potential in situ during the transient start-up of a microdevice. The method resolves the electrophoretic velocity of fluoro-spheres used as tracer particles in microPIV. This approach exploits the short transient regime of the EOF generated after a potential drop is imposed across a microchannel and before reaching quasisteady state. During the starting of the transient regime, the electrophoretic effect is dominant in the center of the channel and the EOF is negligible. By measuring the velocity of the tracer particles with a microPIV system during that starting period, their electrophoretic velocity is obtained. The technique also resolves the temporal evolution of the EOF with three regions identified. The first region occurs before the electroosmotic effect reaches the center of the channel, the second region extends until the EOF reaches steady state, and thereafter is the third region. The two time constants separating these regions are also obtained and compared to the theory. The zeta potential of 860 nm diameter polystyrene particles is calculated for different solutions including borate buffer, sodium chloride, and deionized water. Results show that the magnitudes of the electrophoretic and electroosmotic velocities are in the range of |300| to |700| μm/s for these measurements. The zeta potential values are compared to the well-established closed cell technique showing improved accuracy. The method also resolves the characteristic response time of the EOF, showing small but important deviations from current analytical predictions. Additionally, the measurements can be performed in situ in microfluidic devices under actual working EOF conditions and without the need for calibrations.     

Estimation of the zeta potential and the dielectric constant using velocity measurements in the electroosmotic flows

In this paper we develop a method for the determination of the zeta potential zeta and the dielectric constant epsilon by exploiting velocity measurements of the electroosmotic flow in microchannels. The inverse problem is solved through the minimization of a performance function utilizing the conjugate gradient method. The present method is found to estimate zeta and epsilon with reasonable accuracy even with noisy velocity measurements.     

On the streaming potential across a cation-exchange membrane

Electrical potentials developed during streaming of methanol, water and their mixtures through a Zeokarb 225 (Al⁺⁺⁺ form) membrane have been investigated. Build-up of streaming potential with time has been examined and discussed. Results indicate that dependence of streaming potential on applied pressure difference is non-linear and shows sign reversals. An attempt has been made to explain the results in terms of changes in the structure of electrical double layer at the membrane-permeant interface under the action of streaming pressure.With 4 figures     

Tangential flow streaming potential measurements: Hydrodynamic cell characterization and zeta potentials of carboxylated polysulfone membranes

Computational fluid dynamics calculations were carried out to ensure that a self-made tangential flow mode streaming potential measurement cell meets the hydrodynamic stipulations of laminar, steady and established electrolyte flow necessary for reproducible electrokinetic measurements. The calculations show that the cell design meets all of these conditions.Six carboxylated polysulfones with a range of different degrees of substitution (DS) from 0.26 to 1.74 carboxyl groups per polymer repeat unit were synthesized in a two-stage process of lithiation and carboxylation. Ultrafiltration membranes were made from both the unmodified polysulfone and these hydrophilic materials. The zeta potentials of these membrane surfaces were determined in 0.001 M KCl solution as a function of pH. The curves show the theoretically expected profiles for non-ionic and weakly acidic materials. The growing influence of the COOH dissociation on the surface charge formation is indicated by the flattening of the curves at low pH values. The magnitude of the negative zeta potentials plateau values ranged from −52 to −20 mV. While unmodified PSU has a plateau value of −52 mV this value decreases continuously with increasing DS to −20 mV for the PSU-COOH 1.74 material. It is suggested that this arises from a shift of the electrokinetic shear plane into the bulk electrolyte solution due to an extended swelling layer reflecting the enhanced hydrophilicity of these membrane surfaces.     

Direct determination of the oriented sample nmr spectrum from the powder spectrum for systems with local axial symmetry

A procedure is described for extracting the nuclear magnetic resonance spectrum of an oriented system from the spectrum of a superposition of randomly oriented domains. The procedure is applicable to dipolar, quadrupolar and anisotropic chemical shift interactions in systems having local axial symmetry and is illustrated using simulated and experimental spectra.     

On the electrophoretic mobility and zeta potential of montmorillonite in non-aqueous media

Experimental results on the electrophoretic velocity and mobility of Ca-montmorillonite in 2-propanol are reported. The variation of the electrophoretic velocity with the externally applied electric field and the particle size range, at constant volume fraction and temperature, is considered. Given the difficulties for determining the types and concentrations of ions present in these liquid media, two methods are discussed for the estimation of the double layer thickness and hence the product, necessary for the determination of the zeta potential () of the interface. Although both methods of calculation yield different values of, the results for the zeta potential are very similar in the regions of and characteristic of our systems. The application to the experimental data of three theoretical relations between electrophoretic mobility and zeta potential is also discussed.     

Estimation of zeta potential by electrokinetic analysis of ionic fluid flows through a divergent microchannel

The streaming potential is generated by the electrokinetic flow effect within the electrical double layer of a charged solid surface. Surface charge properties are commonly quantified in terms of the zeta potential obtained by computation with the Helmholtz-Smoluchowski (H-S) equation following experimental measurement of streaming potential. In order to estimate a rigorous zeta potential for cone-shaped microchannel, the correct H-S equation is derived by applying the Debye-Hückel approximation and the fluid velocity of diverging flow on the specified position. The present computation provides a correction ratio relative to the H-S equation for straight cylindrical channel and enables us to interpret the effects of the channel geometry and the electrostatic interaction. The correction ratio decreases with increasing of diverging angle, which implies that smaller zeta potential is generated for larger diverging angle. The increase of Debye length also reduces the correction ratio due to the overlapping of the Debye length inside of the channel. It is evident that as the diverging angle of the channel goes to nearly zero, the correction ratio converges to the previous results for straight cylindrical channel.     

Zeta potential determination by streaming current modelization and measurement in electrophoretic microfluidic systems

Electrophoresis in capillary and microfluidic systems, used in analytical chemistry to separate charged species, are quite sensitive to surface phenomena in terms of separation performances. In order to improve theses performances, new surface functionalization techniques are required. There is a need for methods to provide fast and accurate quantification about surface charges at liquid/solid interfaces. We present a fast, simple, and low-cost technique for the measurement of the zeta-potential, via the modelization and the measurement of streaming currents. Due to the small channel cross section in microfluidic devices, the streaming current modelization is easier than the streaming potential measurement. The modelization combines microfluidic simulations based on the Navier-Stokes equation and charge repartition simulations based on the Poisson-Boltzmann equation. This method has been validated with square and circular cross section shape fused-silica capillaries and can be easily transposed to any lab-on-chip microsystems.     

Modeling electroosmotic and pressure-driven flows in porous microfluidic devices: zeta potential and porosity changes near the channel walls

This work presents analytical solutions for both pressure-driven and electroosmotic flows in microchannels incorporating porous media. Solutions are based on a volume-averaged flow model using a scaling of the Navier-Stokes equations for fluid flow. The general model allows analysis of fluid flow in channels with porous regions bordering open regions and includes viscous forces, permitting consideration of porosity and zeta potential variations near channel walls. To obtain analytical solutions problems are constrained to the linearized Poisson-Boltzmann equation and a variation of Brinkman's equation [Appl. Sci. Res., Sect. A 1, 27 (1947); 1, 81 (1947)]. Cases include one continuous porous medium, two adjacent regions of different porosities, or one open channel adjacent to a porous region, and the porous material may have a different zeta potential than that of the channel walls. Solutions are described for two geometries, including flow between two parallel plates or in a cylinder. The model illustrates the relative importance of porosity and zeta potential in different regions of each channel.     

Melt-processable oligoamides having internal acetylene groups in the backbone,and thermally stable polyamides therefrom

Aromatic oligoamides of DP = 5 and 11 that have all meta-phenylene linkages were prepared by controlling the ratio of isophthaloyl chloride and diamines [m-phenylenediamine and bis(3-aminophenyl)acetylene], and then end-capped with aniline or 2-aminobiphenylene. Aromatic oligoamides having para-phenylene linkages were also prepared similarly using terephthaloyl chloride as a monomer. The oligoamides that have all m-phenylene linkages were soluble in organic solvents such as N-methyl-2-pyrrolidone and N,N-dimethylacetamide, though the oligoamides having p-phenylene linkages were much less soluble. The oligoamides having acetylene units in the backbone showed exotherm due to crosslinking. The onset of the exotherm appeared at 310-340°C for the oligoamides having all m-phenylene linkages, and 330-370°C for the oligoamides having p-phenylene linkages. They were melt-processed at 350 or 380°C for 1 h, giving tough and insoluble films from oligoamides having all m-phenylene linkages and brittle films from oligoamides having p-phenylene linkages. The films showed excellent thermal properties. For example, viscoelastic analyses showed little decrease of mechanical property up to 370°C, and T_g was not observed below the temperature. Thermogravimetric analyses also showed that thermal stability of the melt-processed films were excellent. © 1992 John Wiley & Sons, Inc.     

On an unexpected symmetry of the Coulomb potential in the Debye-Smoluchowski equation

It is pointed out that the symmetry of the Coulomb potential noted by Clifford et al. is valid only when the Smoluchowski boundary condition is used.     

Modified Booth equation for the calculation of zeta potential

 An easy-to-use computer program based on the modified Booth equation (MBE) is developed to calculate the zeta potential of a spherical nonconducting particle from knowledge of the electrophoretic mobility, particle size, and the type and concentration of ions present in the solution. The program is applied to five sets of previously published literature data and the resulting zeta potentials are compared with the values given by the Henry equation to illustrate the extent of the relaxation effect in each case. In four cases, the output zeta potential data are compared with the corresponding values obtained from the rigorous numerical solution of O’Brien and White. Results indicate that the computer program developed here gives a reliable estimate of the zeta potential. The main advantage in using the MBE lies in its capability of calculating the zeta potential even for cases where the experimentally measured mobility exceeds the maximum theoretical mobility predicted by the O’Brien and White solution. Received: 16 June 1997 Accepted: 11 September 1997     

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.     

Improvement of the spinning electrophorometer for zeta potential measurements

In this study, bubbles are held by centripetal force at the center of a rotating cylinder filled with an aqueous solution. Their velocities along the axe of rotation, after application of an electrophoretic force, are used for the calculation of the so-called electrokinetic potential. But this process necessitates the elimination of the electro-osmosis which occurs on the interior sides of the glass cylinder by superposing a concurrent force on the bubble. Efficiency of DEAE-Dextran reticulated with 1,4 Butanediol Diglycidyl Ether can be tested by the observation of a cloud of latex microspheres injected in the interior of the tube and allowed to move in respect with the application of an electric field. The experimental control of these velocity profiles proves the adequacy of the polymer for many cases such as surfactant solutions, presence of electrolytes, utilization with moderate pH.The dynamic interpretation of the electrophoretic motion of bubbles is possible by considering that small ones behave like rigid spheres moving in a rotating fluid. In the second part of this paper and in a previous publication, we have experimentally proved that the use of the theoretical expressions of the forces involved for rigid spheres is justified for small bubbles. So, the electrokinetic potential can be expressed versus the velocity, leading to possible interpretations of the adsorption on gas-water interfaces.     

Characterization of polyelectrolyte multilayers by the streaming potential method

Polyelectrolyte multilayer adsorption on mica was studied by the streaming potential method in the parallel-plate channel setup. The technique was calibrated by performing model measurements of streaming potential by using monodisperse latex particles. Two types of polyelectrolytes were used in our studies: poly(allylamine) hydrochloride (PAH), of a cationic type, and poly(sodium 4-styrenesulfonate) (PSS) of an anionic type, both having molecular weight of 70,000. The bulk characteristics of polymers were determined by measuring the specific density, diffusion coefficient for various ionic strengths, and zeta potential. These measurements as well as molecular dynamic simulations of chain shape and configurations suggested that the molecules assume an extended, wormlike shape in the bulk. Accordingly, the diffusion coefficient was interpreted in terms of a simple hydrodynamic model pertinent to flexible rods. These data allowed a proper interpretation of polyelectrolyte multilayer adsorption from NaCl solutions of various concentrations or from 10(-3) M Tris buffer. After completing a bilayer, periodic variations in the apparent zeta potential between positive and negative values were observed for multilayers terminated by PAH and PSS, respectively. These limiting zeta potential values correlated quite well with the zeta potential of the polymers in the bulk. The stability of polyelectrolyte films against prolonged washing (reaching 26 h) also was determined using the streaming potential method. It was demonstrated that the PSS layer was considerably more resistant to washing, compared to the PAH layer. It was concluded that the experimental data were consistent with the model postulating particle-like adsorption of polyelectrolytes with little chain interpenetration. It also was concluded that due to high sensitivity, the electrokinetic method applied can be effectively used for quantitative studies of polyelectrolyte adsorption, desorption, and reconformation.     

Calculation of the streaming potential near a rotating disk

A corrected theory of the streaming potential in the vicinity of a disk-shaped sample rotating in an electrolytic solution is presented. When streaming-potential measurements on a variety of materials were reduced to a zeta potential according to a prior theory, the results exceeded expected values by a factor of approximately 2, even though other aspects of the same experiments seemed to confirm the theory. Investigation of the source of the discrepancy revealed a flaw in the prior theory. The crucial understanding is that the surface current produced by the rotation of the disk emerges from the diffuse layer and enters the bulk solution at the periphery of the disk. The new treatment accounts entirely for the discrepancy between literature data and results based on the prior theory.