Nernst Layer Research Articles

Voltammetry under a Controlled Temperature Gradient

Electrochemical measurements are generally done under isothermal conditions. Here we report on the application of a controlled temperature gradient between the working electrode surface and the solution. Using electrochemical sensors prepared on ceramic materials with extremely high specific heat conductivity, the temperature gradient between the electrode and solution was applied here as a second driving force. This application of the Soret phenomenon increases the mass transfer in the Nernst layer and enables more accurate control of the electrode response enhancement by a combination of diffusion and thermal diffusion. We have thus studied the effect of Soret phenomenon by cyclic voltammetry measurements in ferro/ferricyanide. The time dependence of sensor response disappears when applying the Soret phenomenon, and the complicated shape of the cyclic voltammogram is replaced by a simple exponential curve. We have derived the Cotrell-Soret equation describing the steady-state response with an applied temperature difference.

Diffusion controlled analytical performances of hydrogen peroxide sensors: Towards the sensor with the largest dynamic range

Analytical performances of chronoamperometric sensors are limited by mass transport of analyte, specifically by its diffusion within Nernst's layer. Limiting performance characteristics of hydrogen peroxide sensors are achieved using the most advantageous electrocatalyst for its reduction – Prussian Blue. We report on improvement of sensitivity and detection limits of H 2O 2 sensors by substituting conventional electrode with ultramicroelectrode and with nano-electrode array. Prussian Blue based microelectrodes displayed improved sensitivity in hydrogen peroxide detection, which is close to be inversely proportional to electrode radius. To form nano-electrode arrays we used nano-structuring of the electrocatalyst on inert electrode support. Hydrogen peroxide sensor made by deposition of Prussian Blue through sol template based on vinyltriethoxysilane (nano-structuring was confirmed by AFM) displayed linear calibration range prolonged over seven orders of magnitude of H 2O 2 concentration, which is record in electroanalysis. The two to three orders of magnitude prolonged linear calibration range without loss of sensitivity seems to be at the limiting level for sensor improvement by forming micro- or nano-electrode arrays.

The simple model and linear stability analysis of the electrode process with the NDR region caused by the potential-dependent convective transport

In our earlier report on the experimental studies of convection coupled with electrochemical processes of Hg ions at the mercury electrode we showed that the potential-dependent onset and decay of this convection can give rise to the N-shaped negative differential resistance (NNDR) in the current–potential characteristics. As a consequence, the presence of appropriate serial ohmic resistance in the electric circuit caused bistability. Since the rather poorly reproducible nature of this convection makes the precise experimental studies difficult, we elaborated the simple model which extracts the basic dynamical properties of the system under study. The model involves the electrode potential and the Nernst layer thickness for the convective diffusion as the dynamical variables. Using linear stability analysis we derived the stability criteria and constructed the bifurcation diagram, showing bistability, in accordance with the experimental data, but not predicting the oscillatory behavior.

Water vapour pressure influence on the kinetics of the superconducting YBCO thin films epitaxic growth by the TFA–MOD method

We have found two different regimes in the kinetics of the YBCO formation depending on the water partial pressure at a constant temperature and total flow rate of the carrier gas. The first regime at low partial water pressure shows continual kinetics curves until the end of YBCO growth and the reaction is controlled chemically. The second regime at high partial water pressure shows irreproducible steps in the kinetics curves during the thin films YBCO growth. In this work we suggest that there is formation of a boundary layer of water (Nernst layer) when the partial water pressure is higher than 20hPa at 795°C for a total gas flow rate lower than 2.4×10−2ms−1. These irreproducible steps dues probably to a water boundary layer formation can be eliminated by increasing the stirring rate of the carrier gas. The reaction order of YBa2Cu3O7−x formation respect to the water pressure is n=0.5 when the water boundary layer is not formed, but the apparent reaction order respect to the partial water pressure is zero or negative when the gas flow rate of the carrier gas is not big enough for the elimination of this water layer. This work also evidences that there is an intermediate step in the kinetics curves before the formation of YBCO. This step, which starts at low temperature during the heating ramp (∼400°C) is attributed to the partial elimination of F from the BaF2 precursor to form oxyfluoride compounds. So, at low total flow gas rates and low partial water pressures, the reaction is controlled by diffusion mechanism due to the formation of a HF boundary layer (Nernst layer), because the apparent order of YBCO formation is one respect to the stirring rate. Nevertheless, at high flow gas rates and low partial water pressures, the YBCO formation is controlled chemically, then the apparent order respect to the stirring rate is zero and the HF Nernst layer is eliminated. The apparent Ea for the oxyfluoride formation at low temperatures is only ∼18Kj/mol indicating that this intermediate reaction is controlled by diffusion mechanism even at high stirring rate and relatively low partial water pressure. The apparent Ea for the YBCO formation at partial water pressures higher than 20hPa for a total flow rate of 2.4×10−2ms−1 is only ∼32Kj/mol, indicating that the reaction control is mainly diffusive or mixed (diffusive and chemist).

Aspects of ionic diffusion through thick matrices of charged particles

A review of the literature on ionic diffusion through matrices of charged particles shows that many workers have reported higher diffusivity of co-ions than of counterions. If these observations are correct then the requirement of electroneutrality of bulk solutions is violated. In those experiments other, not looked for, ions must have been taking part. It therefore appears that complete chemical analyses of solutions of both up- and downstream sides should be carried out, otherwise misleading inferences may be drawn, with practical consequences. Some researchers have studied transport of water under osmotic pressure differentials across clay membranes. However, a diffusing ion, during its transport from higher concentration to lower concentration, always carries its water of hydration. This second water transport process has not received attention. This suggests that at a critical concentration two transport processes will cancel each other. Attention has been drawn to this second type of water flow and its consequences. In ionic diffusion, each side of the membrane–outside solution interface is subject to the effects of the Nernst layer and Donnan zone. However, these layers and zones are seldom treated quantitatively. This has been carried out in this paper by two different methods. Both methods give identical thicknesses of the Nernst layer and Donnan zone. Finally, the effects of the presence of soluble bivalent salts on the diffusivity of different types of ions have been commented up on. In these cases some of the co-ions diffuse to the upstream side.

Boundary-layer exchange by bubble: A novel method for generating transient nanofluidic layers

Unstirred layers (i.e., Nernst boundary layers) occur on every dynamic solid-liquid interface, constituting a diffusion barrier, since the velocity of a moving liquid approaches zero at the surface (no slip). If a macromolecule-surface reaction rate is higher than the diffusion rate, the Nernst layer is solute depleted and the reaction rate becomes mass-transport limited. The thickness of a Nernst boundary layer (δN) generally lies between 5 and 50μm. In an evanescent wave rheometer, measuring fibrinogen adsorption to fused silica, we made the fundamental observation that an air bubble preceding the sample through the flow cell abolishes the mass-transport limitation of the Nernst diffusion layer. Instead exponential kinetics are found. Experimental and simulation studies strongly indicate that these results are due to the elimination of the Nernst diffusion layer and its replacement by a dynamic nanofluidic layer (δν) maximally 200–300nm thick. It is suggested that the air bubble leads to a transient boundary-layer separation into a novel nanoboundary layer on the surface and the bulk fluid velocity profile separated by a vortex sheet with an estimated lifetime of 30–60s. A bubble-induced boundary-layer exchange from the Nernst to the nanoboundary layer and back is obtained, giving sufficient time for the measurement of unbiased exponential surface kinetics. Noteworthy is that the nanolayer can exist at all and displays properties such as (i) a long persistence and resistance to dissipation by the bulk liquid (boundary-layer-exchange-hysteresis) and (ii) a lack of solute depletion in spite of boundary-layer separation. The boundary-layer-exchange by bubble (BLEB) method therefore appears ideal for enhancing the rates of all types of diffusion-limited macromolecular reactions on surfaces with contact angles between 0° and 90° and only appears limited by slippage due to nanobubbles or an air gap beneath the nanofluidic layer on very hydrophobic surfaces. The possibility of producing nanoboundary layers without any nanostructuring or nanomachining should also be useful for fundamental physical studies in nanofluidics.

Modelación del transporte de cobre en la capa límite en una celda de electrodiálisis

A semi empirical model was developed to characterize the transport of cupric ions within the Nernst layer generated between electrolyte bulk and the membrane surface in an electrodialysis cell. The model was derived from fundamental equations and was reduced to a linear expression incorporating the cupric ion transport number in the Nernst layer (t + BL ) and in the membrane (t + M ). The model critical condition is t + BL + M . The model correctly fits the experimental data when t + BL is 0.02. The model was validated with experimental results previously published by the authors and it accounts for a linear concentration gradient within the Nernst layer.

Mapping concentration profiles within the diffusion layer of an electrode: Part II. Potentiometric measurements with an ultramicroelectrode

A platinum-disk ultramicroelectrode is used to monitor electrochemical potential variations inside the steady-state diffusion layer created by a larger electrode. The experimental potential variations result from combination of a pure electrochemical component (viz., as given by the Nernst law) with a smaller ohmic drop contribution, which varies linearly with the distance from the working electrode surface so that it can be readily eliminated. From the ensuing corrected potential variations, the concentration profiles of the electroactive species present within the diffusion layer can be reconstructed by application of the Nernst law. The validity and great interest of the method are demonstrated experimentally by the study of the one-electron reversible oxidation of the Fe(CN) 6 3−/Fe(CN) 6 4− couple in aqueous KCl solutions. As a correlation, this demonstrates also for the first time the validity of the Nernst layer approximation. The method is then applied to examine the specific structure of the diffusion layers, which result from the involvement of a conproportionation reaction during the second reduction of tetracyanoquinodimethane (TCNQ) in DMF.

Asymptotic behaviour in the pressure-driven separations of ions of different mobilities in charged porous membranes

The pressure-driven transport of electrolyte mixtures with common coion through charged porous membranes has been studied theoretically. The mode of exponential increase of rejection of more mobile counterions with increasing transmembrane volume flow previously predicted in the approximation of one dominant salt has been found to occur at quite noticeable feed mole fractions of more mobile counterions, too. That is caused by their dynamic exclusion from the membrane phase by the electric field of filtration potential. The rejection of less mobile counterions may become strongly negative at larger transmembrane volume flows. The exponential increase in the rejection of more mobile counterions accompanied by negative rejections of less mobile ones corresponds to their strong separation. Concentrational polarisation has been accounted for within the scope of model of unstirred Nernst layer. Moderate concentrational polarisation does not suppress the exponential mode, and the separation remains quite strong whereas a stronger concentrational polarisation suppresses it completely. Criteria of acceptable concentrational polarisation have been formulated. Some of predicted qualitative features of rejection of counterions of different mobilities by charged porous membranes have been confirmed by experimental data found in the literature.

Mechanism and Kinetics of Copper(II) Transport through Diaza-crown Ether−Fatty Acid-Supported Liquid Membrane

The mechanism of macrocycle-mediated Cu(II) transport through a supported liquid membrane containing 1,10-didecyl-1,10-diaza-18-crown-6 ether−fatty acid in toluene/phenylhexane solvent mixture has been investigated. The mechanism was elucidated by studying the effects of parameters such as stirring speed, membrane thickness, and temperature on Cu(II) flux. The results showed that a countercation transport is controlled by a sodium gradient. The rate-limiting step of Cu(II) transport in the system has been found to be diffusion of metal−carrier complex in the membrane. But, depending on the hydrodynamic conditions and cell geometry, diffusion of metal in the stagnant aqueous Nernst layer is found to be rate limiting. In addition, a linear Cu(II) gradient in the membrane was found by performing Cu(II) transport experiments in a stack of eight membranes and analyzing the copper(II) concentration in each of the membranes separately, supporting diffusion-limited steady-state transport. Comparative studies at optimum operational conditions have been done with two types of supports, Celgard 2500 and Accurel, differing in their pore size and porosity. From lag time measurements, the effective diffusion coefficient, D̄m, of the metal−carrier complex in the membrane was evaluated and the values were found to be 5.2 × 10-8 and 2.55 × 10-7 cm2 s-1 for Celgard and Accurel membranes, respectively. These differences in D̄m between the two membranes has been interpreted in terms of molecular diffusion of the complex in the solvent, Dm, and of the equilibrium constant for its adsorption on the pore wall of the membrane.

Speciation modelling of the electroprecipitation of rare-earth cuprate and nickelate materials Speciation of aqueous solutions not at equilibrium

Films of insoluble metal hydroxide have been obtained by cathodic electroprecipitation from aqueous solutions containing the nitrate salts of a lanthanide (La3+ or Nd3+) and a transition-metal cation (Ni2+ or Cu2+). Manipulation of deposition parameters, such as deposition voltage, Va and solution composition, allows for extensive variation in mole fractions, x, of each metal in the final bimetallic hydroxide product. The variations in x are attributed to changes in the chemical environment within the Nernst layer at the electrode/solution interface, occurring in tandem with differences in the solution- and solid-phase speciation characteristics of the two metals and their hydroxides.The experimentally obtained compositions of the deposited solid oxyhydroxide have been correlated with thermodynamically derived overall formation constants, β, and calculations of concentration obtained using a full speciation analysis. This model can be used to correctly predict compositions, which is taken to verify the model of electroprecipitation used.

Chronopotentiometric response of an ion-exchange membrane in the underlimiting current-range. Transport phenomena within the diffusion layers

The chronopotentiometric response of a cation exchange membrane in contact with a symmetrical 0.01 M NaCl solution was investigated as a function of the applied current density below the limiting one. Taking into account classical assumptions such as the variation of concentrations associated to the Teorell-Meyer-Sievers (TMS) segmentation model, the concept of the Nernst layer model, the quasi-electroneutrality condition within the diffusion boundary layers (DBL) and the validity of the Donnan equation at the solution-membrane boundaries, theoretical values of the transmembrane potential difference were obtained which fit very well the experimental V− t responses. Moreover, this method allows the calculation of the DBL thickness. In addition, a decrease of the DBL thickness was observed when the current density increases. This result was attributed to the occurrence of convection effects inside the DBL.

A hollow fibre supported liquid membrane system for metal speciation and preconcentration: calculation of the response time

We report a method for calculating the response time of a hollow fibre supported liquid membrane (SLM) for metal preconcentration. The SLM system is composed of three distinct compartments: an internal stripping solution (filling the hollow fibre lumen), a hydrophobic liquid membrane (adsorbed in the hollow fibre pores), and an external source solution (containing the analyte). The calculation consists of resolving the diffusion equation which describes the evolution of the concentration of the metal ion in the system. The Laplace transform method is used for this purpose, and the inverse Laplace transformation is performed using discrete Fourier transforms. Variation in the concentration of the strip solution with time, after a given change in concentration of the source solution, can be predicted from these calculations. The numerical results obtained by considering various geometrical (membrane thickness, lumen diameter), hydrodynamic (Nernst layer thickness) and chemical (diffusion and partitioning constants) conditions, are presented in order to allow optimization of the system, i.e. reproducibility, fast response time, and high metal preconcentration.

Dissolution kinetics of human enamel powder: II. A model based on the formation of a self-inhibiting surface layer

A model describing the dissolution kinetics of human enamel powder (HEP) is presented. It is based on five main experimental observations obtained in pH-stat and nonsaturated conditions at 37°C. • —The dissolution rate is initially rapid, then gradually decreases, falls to a very low level, and continues for a long period until bulk concentration is close to saturation. • —At low stirring speed, the dissolution rate is stirring dependent and controlled by the diffusion of calcium and/or phosphate ions in the stagnant Nernst layer due to the effect of a low concentration gradient. • —At high stirring speed, the dissolution rate becomes stirring independent and appears to be a surface layer-controlled process. • —In both cases, diffusion is the controlling process and is determined by the interfacial calcium and/ or phosphate ion gradients. • —In both cases, a tendency toward interfacial calcium accumulation is observed in parallel with a progressive decrease of the dissolution rates. These facts suggest that for any pH, during the early stages of attack, the enamel surface is rapidly covered by a surface layer which considerably reduces the dissolution rate. An analytical kinetic expression taking into account the surface area decrease, the approach to the equilibrium, and the layer formation is proposed. This expression describes the experimental kinetics very well. Depending on the stirring speed, the surface layer or the Nernst layer (adjacent to it) is the rate-controlling medium. The surface layer is characterized by the D Ca δ cc ratio, where D Ca is the apparent diffusion coefficient of calcium in the layer and δ ∞ its thickness attained at equilibrium, D Ca δ∞ is found to be pH independent. With an estimated value of 1 μm for δ ∞ values of l.3 × 1O −7 and 9.7 × 1O −8 cm 2 · s −1 are obtained at l860 rpm with respectively dry or equilibrated HEP for D Ca in the layer. This model is believed to be of particular interest in explaining the mode of action of inhibiting substances which strengthen the surface layer and may promote the remineralization process.

Dissolution kinetics of human enamel powder: I. Stirring effects and surface calcium accumulation

The kinetics of dissolution of human enamel powder were studied at 37°C and constant pH in the range 3.7–6.5 by continuous recording of proton uptake and calcium release. The effects of stirring and the behavior of the enamel powder during the first stages of dissolution were analyzed. It was shown that the dissolution rate was controlled at low stirring speed by a diffusive process which became a solid-like controlled process at higher stirring speed. Moreover, in any case, a tendency of interfacial calcium accumulation was observed in parallel with a progressive slowing of the dissolution rate. The higher the pH, the more important the accumulation. These observations suggest that an interfacial calcium-and/ or phosphate-rich layer is rapidly formed on the crystal surface. This “by-product” layer reduces considerably the rate of dissolution of hydroxyapatite. At high stirring, the dissolution rate is limited by the diffusion of calcium and/or phosphate ions through this layer, whereas at low stirring, the rate is limited by the diffusion of calcium or phosphate in the Nernst layer adjacent to the surface deposited layer.

Influence of hydrogen on the carburizing of steel in nitrogen-hydrogen mixtures with the addition of pure methane

1. An increase in hydrogen partial pressure in an N2−H2−CH4 gaseous mixture promotes an increase in the flow of carbon into the steel as a result of the increase in the diffusion mobility of methane in the Nernst layer. 2. The effective diffusion coefficient of carbon in unalloyed austenite in carburzing of steels in nitrogen-hydrogen mixtures with pure methane significantly exceeds the actual diffusion coefficient of it and increases with an increase in the partial pressures of hydrogen and methane. 3. In carburizing in an N2−H2−CH4 mixture there is observed the mutual influence of carbon and hydrogen on the kinetics of establishment of equilibrium with the steel with respect to hydrogen, which is probably caused by the existence of C−H complexes. 4. Carburizing in nitrogen-hydrogen mixtures with additions of pure methane may be intensified by increasing the partial pressures of methane and hydrogen and also by increasing the frequency of change as the result of the use of higher capacity centrifugal blowers.

The film model for determining the effect of ionic migration in electrochemical systems

The film model is used to examine the effect of ionic migration on the concentration of ionic species and on the electrolyte potential profiles inside the Nernst layer.

The Kinetics and mechanism of caffeine infusion from coffee: Hydrodynamic aspects

AbstractHydrodynamic flow conditions were controlled by means of large horizontal rotating discs. These were coated with ground and sieved Kenyan Arabica coffee, and rotated at various speeds in distilled water at 25°C. The rate of extraction of caffeine was measured in each experiment. At a constant rotation speed, the first order rate constant rose steeply with decreasing size of coffee particle and was found to be inversely proportional to the square of the particle radius. For a given particle size, however, the rate constants were independent of the rotation speed. These two findings show that the rate‐determining step for extraction from coffee‐coated discs was the diffusion of caffeine through the bean particle and not its diffusion through the Nernst layer. The same mechanistic conclusion can be drawn for stirred coffee suspensions by applying the hydrodynamics of turbulent flow.

Effect of concentration polarization upon the valency-induced counterion selectivity of ion-exchange membranes

The paper contains a theoretical study of the variation of steady-state membrane selectivity for counterions of different valencies in the course of concentration polarization. The computations show that the system loses most of its counterion selectivity before the concentration polarization results in a pronounced deviation from the linear ohmic voltage against current dependence. This is explained by the enhanced depletion of the Nernst layer of the preferred counterion, resulting in the relative inpoverishment of the membrane in the latter, under conditions at which the membrane still controls the counterion selectivity. At higher currents, when a strong concentration polarization sets in and the limiting stage of counterion transfer shifts to the Nernst layer, the selectivity is almost totally lost, except for a small residual effect, due to a different contribution of migration into the limiting ionic fluxes for species of different valencies.

Colloidal catalysis. Transport versus surface control

It has been shown that the flux of material diffusing to the surface of a colloidal particle is greater than to a plane surface of the same area and diffusion layer thickness (δ). Around a small sphere of radius R the effective Nernst layer thickness δeff is given by 1//δeff=1//R+1//δ. The dependence of δ on radius was established by applying the hydrodynamic theory of Acrivos and Taylor at both large and small Péclet numbers, with a graphical treatment for the intermediate range. At very small radii δ was found to be proportional to R7/6 and at large radii to R3/2. It follows that the total flux or mass flow varies inversely with R2+α(0 ⩽α < 0.17) over the whole range.