Constant Surface Potential Research Articles

Concept of Ideal Adsorbed Solution using Gibbsian Surface Excess Framework

ABSTRACT A concept of creating an ideal multi-component- gas adsorbed phase by mixing pure gas adsorbed phases of the components at constant surface potential and temperature using the Gibbsian Surface Excess (GSE) framework of adsorption is proposed. The GSE provides the only unambiguously measured experimental quantity to describe the extent of adsorption. The actual amounts adsorbed can be estimated from the GSE only by making extraordinary assumptions about the volume and structure of the adsorbed phase. The correlations between the multi-component and pure gas GSE isotherms generated by the proposed concept closely resemble those for the classic IAST, which was developed by using the actual amounts adsorbed as the primary variables. The proposed correlations can be obtained by simply substituting the actual amount adsorbed of components in the corresponding IAST correlations by the GSE of the components. All pure and multi-component gas adsorption data published in the literature are GSE, and they ar...

Geometric effects on electrocapillarity in nanochannels with an overlapped electric double layer.

Unsteady filling of electrolyte solution inside a nanochannel by the electrocapillarity effect is studied. The filling rate is predicted as a function of the bulk concentration of the electrolyte, the surface potential (or surface charge density), and the cross sectional shape of the channel. For a nanochannel, the average outward normal stress exerted on the cross section of a channel (P[over ¯]_{zz}^{}) can be regarded as a measure of electrocapillarity and it is the driving force of the flow. This electrocapillarity measure is first analyzed by using the solution of the Poisson-Boltzmann equation. From the analysis, it is found that the results for many different cross sectional shapes can be unified with good accuracy if the hydraulic radius is adopted as the characteristic length scale of the problem. Especially in the case of constant surface potential, for both limits of κh→0 and κh→∞, it can be shown theoretically that the electrocapillarity is independent of the cross sectional shape if the hydraulic radius is the same. In order to analyze the geometric effects more systematically, we consider the regular N-polygons with the same hydraulic radius and the rectangles of different aspect ratios. Washburn's approach is then adopted to predict the filling rate of electrolyte solution inside a nanochannel. It is found that the average filling velocity decreases as N increases in the case of regular N-polygons with the same hydraulic radius. This is because the regular N-polygons of the same hydraulic radius share the same inscribing circle.

Electroosmotic Flow through a Tubular Channel

In this study, the electroosmotic flow in a charge-regulated tubular channel is considered at low potential and arbitrary double layer thickness. Analytical expressions for the flow velocity and the corresponding asymptotic results for thick double layers that are readily applicable to experimentalists are recovered. For the range of salt concentration usually encountered in practice, the mean flow velocity for the case of constant surface potential differs both quantitatively and qualitatively from that for the case of constant surface charge density. Since this difference is both quantitative and qualitative, the true charged conditions on a channel wall can be inferred by appropriately designed experiments. Using an equivalent circular channel to simulate an elliptic one is inappropriate; in general, neither is assuming electroneutrality on the channel axis even when double layer is ca. 1/3 of the equivalent channel radius.

Theoretical study of electrolyte transport in nanofiltration membranes with constant surface potential/charge density

The pressure–driven electrolyte transport through nanofiltration membrane pores with constant surface potential or charge density is investigated theoretically. Two approaches are employed in the study. The first one is based on one–dimensional Nernst–Planck equation coupled with electroneutrality, zero current, and Donnan equilibrium conditions. This model is extended to account for interfacial effects by using a smooth approximation of step function for the volume charge density. The second approach is based on two–dimensional Nernst–Planck, Poisson, and Navier–Stokes equations, which are solved in a high aspect ratio nanopore connecting two reservoirs with much larger diameter. The modification of equations on the basis of Slotboom transformation is employed to speed up the convergence rate. The distributions of potential, pressure, ion concentrations and fluxes due to convection, diffusion, and migration in the nanopore and reservoirs are discussed and analyzed. It is found that for constant surface charge density, the convective flux of counter–ions in the nanopore is almost completely balanced by the opposite migration flux, while for constant surface potential, the convective flux is balanced by the opposite diffusion and migration fluxes. The co–ions in the nanopore are mainly transported by diffusion. A particular attention is focused on describing the interfacial effects at the nanopore entrance/exit. Detailed comparison between one– and two–dimensional models is performed in terms of rejection, pressure drop, and membrane potential dependence on the surface potential/charge density, volume flux, ion concentration, and pore radius. A good agreement between these models is found when the Debye length is smaller than the pore radius and the surface potential or charge density are sufficiently low.

Measurement of surface potential of non-uniformly charged insulating materials using a non-contact electrostatic voltmeter

Non-contact measurements performed with the auto-compensated electrostatic induction probe of an electrostatic voltmeter are often employed to characterize the charging state of insulating materials, such as films or non-woven media. The aim of the paper is double: (i) describe a simple method for assessing the resolution of such a probe; (ii) discuss the significance that can be attributed to the value displayed by the electrostatic voltmeter when the charge is non-uniformly distributed at the surface of the bodies examined by the probe and no constant surface potential can be defined. The measurements were performed for some simple experimental models that simulate surface potential non-uniformity of constant-charge insulating bodies. By examining the different surface potential distribution curves that were obtained for each of the situations under study, it is possible to estimate the resolution of the probe. A commercial computer program based on the superficial charge simulation method was employed for the numerical analysis of the electric field in a simplified 2-D representation of the geometric system formed by the probe, the experimental model, and the grounded plate. The potential that anneals the electric field at the surface of the probe (to simulate its principle of operation) was calculated by an iterative method. A good agreement was found between the results of the numerical simulations and the experimental data. The errors that can be made in the interpretation of the results of surface potential measurements are illustrated by the case of a non-uniformly-charged non-woven polypropylene fabric.

Accurate Doping Density Determination in SiC with Constant Surface Potential Corona Charging; Industry Ready Alternative to Hg-CV

We present a refined non-contact doping density determination in silicon carbide that incorporates 3 novel features: (1) constant surface potential method of corona charging into depletion; (2) vibrating Kelvin probe measurement of depletion surface voltage and voltage compensation maintaining constant surface potential, and (3) a unique self-consistent procedure for data analysis. The results obtained on epitaxial SiC demonstrate up to 3 times improved accuracy and enhanced repeatability giving 1σ in 10 repeats of 0.05% and 0.1% for doping in e15cm-3 and e19cm-3 range, respectively. An enhanced charging range enables measurement of high doping density in the e19cm-3 range and to achieve larger depth in doping profiling. With these refinements, a non-contact doping metrology for SiC represents an industry ready alternative to Hg-CV.

Alternating strings and clusters in suspensions of charged colloids.

We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects under the assumption of a constant surface potential, and consider their repercussions on the two-particle interaction potential. We find that the formation of induced dipoles close to a charge-reversed state may explain the formation of these structures. Finally, we will touch upon the formation of dumbbells and small clusters in a one-component system, where the effective electrostatic interaction is always repulsive.

Correlation equations for average deposition rate coefficients of nanoparticles in a cylindrical pore

AbstractNanoparticle deposition behavior observed at the Darcy scale represents an average of the processes occurring at the pore scale. Hence, the effect of various pore‐scale parameters on nanoparticle deposition can be understood by studying nanoparticle transport at pore scale and upscaling the results to the Darcy scale. In this work, correlation equations for the deposition rate coefficients of nanoparticles in a cylindrical pore are developed as a function of nine pore‐scale parameters: the pore radius, nanoparticle radius, mean flow velocity, solution ionic strength, viscosity, temperature, solution dielectric constant, and nanoparticle and collector surface potentials. Based on dominant processes, the pore space is divided into three different regions, namely, bulk, diffusion, and potential regions. Advection‐diffusion equations for nanoparticle transport are prescribed for the bulk and diffusion regions, while the interaction between the diffusion and potential regions is included as a boundary condition. This interaction is modeled as a first‐order reversible kinetic adsorption. The expressions for the mass transfer rate coefficients between the diffusion and the potential regions are derived in terms of the interaction energy profile. Among other effects, we account for nanoparticle‐collector interaction forces on nanoparticle deposition. The resulting equations are solved numerically for a range of values of pore‐scale parameters. The nanoparticle concentration profile obtained for the cylindrical pore is averaged over a moving averaging volume within the pore in order to get the 1‐D concentration field. The latter is fitted to the 1‐D advection‐dispersion equation with an equilibrium or kinetic adsorption model to determine the values of the average deposition rate coefficients. In this study, pore‐scale simulations are performed for three values of Péclet number, Pe = 0.05, 5, and 50. We find that under unfavorable conditions, the nanoparticle deposition at pore scale is best described by an equilibrium model at low Péclet numbers (Pe = 0.05) and by a kinetic model at high Péclet numbers (Pe = 50). But, at an intermediate Pe (e.g., near Pe = 5), both equilibrium and kinetic models fit the 1‐D concentration field. Correlation equations for the pore‐averaged nanoparticle deposition rate coefficients under unfavorable conditions are derived by performing a multiple‐linear regression analysis between the estimated deposition rate coefficients for a single pore and various pore‐scale parameters. The correlation equations, which follow a power law relation with nine pore‐scale parameters, are found to be consistent with the column‐scale and pore‐scale experimental results, and qualitatively agree with the colloid filtration theory. These equations can be incorporated into pore network models to study the effect of pore‐scale parameters on nanoparticle deposition at larger length scales such as Darcy scale.

Effect of eccentricity on the electroosmotic flow in an elliptic channel

The electroosmotic flow in an elliptic channel having constant surface potential (CSP) or charge density (CSCD) is considered at low potential and arbitrary double layer thickness. Analytical expressions for the flow velocity and the corresponding asymptotic results for thick double layers that are readily applicable to experimentalists are recovered. For the range of salt concentration usually encountered in practice, the mean flow velocity for the case of CSP differs both quantitatively and qualitatively from that for the case of CSCD. Using an equivalent circular channel to simulate an elliptic one is inappropriate, in general, neither is assuming electroneutrality on the channel axis even when double layer is ca. 1/3 of the equivalent channel radius.

Electrophoresis of two spheres: Influence of double layer and van der Waals interactions

Considering recent applications of electrophoresis conduced in nanoscaled devices, where particle–particle interaction can play a role, we studied for the first time the electrophoresis of two rigid spheres along their center line, taking account of the hydrodynamic, electric, and van der Waals interactions between them. Under the conditions of constant surface potential and surface charge density, the influences of the level of surface potential/charge density, the bulk salt concentration, and the particle–particle distance on their electrokinetic behaviors are examined. Numerical simulation reveals that these behaviors are much more complicated and interesting than those of isolated particles. In particular, we show that care must be taken in choosing an appropriate particle concentration in relevant experiment to avoid obtaining unreliable mobility data.

Combined electroosmosis-pressure driven flow and mixing in a microchannel with surface heterogeneity

We investigate the combined pressure-driven electroosmotic flow near a wall roughness in the form of a rectangular block mounted on one wall of an infinitely long microchannel. The insulated rectangular block has a constant surface potential which is different from the surface potential of the remaining part of the channel walls. The characteristics for the electrokinetic flow are obtained by numerically solving the Navier–Stokes equations coupled with the Nernst–Planck equation for ion transport and the Poisson equation for electric field. Vortical flow develops above the block when the surface potential of the block is in opposite sign to that of the surface potential of the channel. The strength of the re-circulating vortex grows as the surface potential of the block increases. Vortical flow also depends on the Debye length when it is in the order of the channel height. The combined effects due to the geometrical modulation of the channel wall and heterogeneity in surface potential is found to produce a stronger vortex and hence a stronger mixing, as compared with the effect of either of these. The recirculating vortex, which appears on the upper face of the block, grows and the average electroosmotic velocity increases with the increase of the electrolyte concentration. The recirculating vortex does not appear when EDL is thick and the effect of over-potential of the block on electroosmosis is negligible. The loss of momentum near the obstacle is compensated by the electrostatic force near the EDL, which prevents flow separation upstream or downstream of the obstacle. The mixing performance of the present configuration is compared with several other cases of surface modulation. The impact of the imposed pressure gradient on the vortical flow due to surface heterogeneity is analyzed.

Non‐contact high precision alternative to Hg‐probe for dopant profiling in SiC

AbstractThe silicon carbide industry has been expanding in the recent years, producing a search for SiC non‐contact electrical characterization methods capable of replacing the commonly used Hg‐probe technique. In this work we present doping metrology based on the corona‐Kelvin method, which was originally developed and used for silicon IC dielectric and interface characterization. The method employs corona discharge in air to deposit precise doses of charge on the SiC surface. The corresponding depletion voltage is then measured with a Kelvin probe enabling non‐contact determination of the static charge‐voltage and capacitance‐voltage characteristics. The approach incorporates three novel elements: 1. corona charging of SiC to high depletion voltage with constant surface potential method; 2. the derivative charge‐voltage measurements for d(1/C2)/dV analysis and doping profiling; 3. surface charge neutralization with appropriate SiC illumination for repeated measurements. We demonstrate excellent repeatability and accuracy of the novel approach for n and p‐type SiC doping measurements in a range from 1014cm‐3 to mid 1018cm‐3 and excellent correlation with results obtained with mercury‐probe C‐V. Using multi‐layer epitaxial SiC structures, we further demonstrate the effectiveness of novel non‐contact depth profiling. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electrophoresis of pH‐regulated particles in the presence of multiple ionic species

An electrophoresis model taking account of the pH‐regulated nature of particles and the presence of multiple ionic species is proposed for arbitrary surface potential and double‐layer thickness. It successfully simulated the electrophoretic behavior of Fe3O4 nanoparticles in an aqueous NaCl solution with pH adjusted by HCl and NaOH. The estimated zeta potential is compared with those from the conventional models, Smoluchowski's, Hückel's, and Henry's formulas. Due to the violation of the assumption of low and constant surface potential, these formulas yielded appreciable deviations (e.g., 23–30 mV at pH 9). With the surface charge density measured by titration and the zeta potential by electrophoresis, the true surface potential is estimated through a triple‐layer model. The estimated true potential is typically 1.5–10 times larger than the zeta potential, implying that using the latter in relevant calculations (e.g., stability and critical coagulation concentration) might yield appreciable deviation. © 2013 American Institute of Chemical Engineers AIChE J 60: 451–458, 2014

Analytical solution to Poisson-Boltzmann equation for two interacting parallel identical plates with constant surface potential

In this paper, we suggest an analytical solution to Poisson-Boltzmann equation for the calculation of potential distributions between two identical plates with high constant surface potential. Our expression fits well to the exact values of the potential between two parallel plates. Numerical results indicate that this analytical solution provides accurate description for the dimensionless distance ≤ 2. The suggested solution can be successfully applied in calculating the potential for identical plates with high or moderate surface potentials. A simple analytical expression for the energy of interactions between two identical plates with constantly high surface potential is also given. The solutions in analytical, exact and numerical forms become indistinguishable when y0 ≥ 3, κx ≤ 4 and y0 = 2.0, κx ≤ 3, respectively. When y0 = 2.0, κx ≤ 1.2, the approximate solution is in close agreement with the exact solution.

Analytical Solution to Poisson–Boltzmann Equation for Two Interacting Parallel Identical Plates with Constant Surface Potential

Analytical Solution to Poisson–Boltzmann Equation for Two Interacting Parallel Identical Plates with Constant Surface Potential

Comment on “Ocean mass from GRACE and glacial isostatic adjustment” by D. P. Chambers et al.

The modern global theory of the glacial isostatic adjustment (GIA) process is a theory that directly addresses the extent to which the geoid of classical geodesy is impacted by this phenomenon. Because the geoid is, by conventional definition, the surface of constant potential that overlaps the surface of the sea in the absence of currents and tides, we may determine the impact of the GIA process upon it only by explicit analysis of the manner in which mass is redistributed among the ocean basins and the level of the sea is thereby influenced. Although the dominant contribution to GIA is that associated with the transfer of mass between the oceans and the continents, there is an additional influence due to the variations in Earth's rotational state. This influence “feeds‐back” onto the geoid. In the recent paper by Chambers et al. (2010), several arguments were presented that question earlier attempts to discuss the consequences of this feedback. These arguments are interesting and we address them in what follows.

Electrokinetic Flow and Electric Current in a Fibrous Porous Medium

An analytical study is presented for the steady electrokinetic flow of electrolyte solutions in the fibrous medium constructed by an ordered array of identical, parallel, charged, circular cylinders. The electric field and/or pressure gradient are applied uniformly in the direction along the axes of the cylinders. The dielectric cylinders may have either a constant surface potential or a constant surface charge density of an arbitrary value. The electric double layer surrounding each cylinder may have an arbitrary thickness relative to the radius of the cylinder. A unit cell model, which allows for the overlap of the double layers of adjacent cylinders, is employed to account for the effect of fiber interactions. The electrostatic potential distribution in the fluid phase is determined by solving the Poisson-Boltzmann equation, and the fluid velocity profile is obtained as the analytical solution of a modified Navier-Stokes equation. Explicit formulas for the flow rate, electroosmotic velocity, electric current, effective electric conductivity, and streaming potential are derived as functions of the porosity of the fiber matrix and other characteristics of the system. The effect of interactions among the cylinders on the fluid velocity and effective conductivity is interesting and can be significant under appropriate conditions.

Analytical expressions for pH-regulated electroosmotic flow in microchannels

We derived analytical expressions for the pH-regulated electroosmotic flow in a microchannel for arbitrary level of surface potential and type of electrolyte solution; previous results are almost always based on the conditions of low, constant surface potential, which are inaccurate and unrealistic. In addition, an analytical expression for the dependence of the surface potential on the electrolyte concentration and solution pH is obtained, which is capable of explaining the behavior of the empirical relation used in the literature. The analytical results derived are readily applicable to further electrokinetic analyses, and to interpret experimental observations and/or design devices involving electroosmosis such as biosensors and lab-on-a-chip.

Importance of Temperature Effect on the Electrophoretic Behavior of Charge-Regulated Particles

The Joule heating effect is inevitable in electrophoresis operations. To assess its influence on the performance of electrophoresis, we consider the case of a charge-regulated particle in a solution containing multiple ionic species at temperatures ranging from 298 to 308 K. Using an aqueous SiO(2) dispersion as an example, we show that an increase in the temperature leads to a decrease in both the dielectric constant and the viscosity of the liquid phase, and an increase in both the diffusivity of ions and the particle surface potential. For a particle having a constant surface potential, its electrophoretic mobility is most influenced by the variation in the liquid viscosity as the temperature varies, but for a charged-regulated particle both the liquid viscosity and the surface potential can play an important role. Depending upon the level of pH, the degree of increase in the mobility can be on the order of 40% for a 5 K increase in the temperature. The presence of double-layer polarization, which is significant when the surface potential is sufficiently high, has the effect of inhibiting that increase in the mobility. This implies that the influence of the temperature on the mobility of the particle is most significant when the pH is close to the point of zero charge.

Influence of membrane layer properties on the electrophoretic behavior of a soft particle

The influence of the physical properties of the membrane layer of a soft particle, which comprises a rigid core and a porous membrane layer, on its electrophoretic behavior, is investigated. Because that influence was almost always neglected in the previous studies, the corresponding results can be unrealistic. The applicability of the model proposed is verified by the available theoretical and experimental results. The electrophoretic mobility of the particle under various conditions is simulated through varying the dielectric constant, the thickness, and the drag coefficient of the membrane layer, and the bulk ionic concentration. We show that under typical conditions, the deviation in the electrophoretic mobility arising from assuming that the dielectric constant of the membrane layer is the same as that of the bulk liquid phase can be in the order of 50%. In addition, the thicker the membrane layer and/or the higher the bulk ionic concentration, the larger the deviation. If the surface of the core of the particle is charged, as in the case of inorganic particles covered by an artificial membrane layer, the deviation at constant core surface potential is larger than that under other types of charged conditions. However, if the surface of the core is uncharged, as in the case of biocolloids, then that deviation becomes negligible. These findings are of fundamental significance to theoreticians in their analysis on the electrokinetic behaviors of soft particles, and to experimentalists in the interpretation of their data.