Transport nernst equation

Mass transport Nernst equation, drag coefficient, or Stefan-Maxwell equation... 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

When paint films are immersed in water or solutions of electrolytes they acquire a charge. The existence of this charge is based on the following evidence. In a junction between two solutions of potassium chloride, 0 -1 N and 0 01 N, there will be no diffusion potential, because the transport numbers of both the and the Cl" ions are almost 0-5. If the solutions are separated by a membrane equally permeable to both ions, there will still be no diffusion potential, but if the membrane is more permeable to one ion than to the other a diffusion potential will arise it can be calculated from the Nernst equation that when the membrane is permeable to only one ion, the potential will have the value of 56 mV. 

The Nernst equation written in terms of the transport overpotential of a cathode is... 

As reversible ion transfer reactions are diffusion controlled, the mass transport to the interface is given by Fick s second law, which may be directly integrated with the Nernst equation as a boundary condition (see, for instance. Ref. 230 232). A solution for the interfacial concentrations may be obtained, and the maximum forward peak may then be expressed as a function of the interfacial area A, of the potential scan rate v, of the bulk concentration of the ion under study Cj and of its diffusion coefficient D". This leads to the Randles Sevcik equation [233] ... 

Movement of Ions and Molecules Across Membranes Transport Across Membranes The Nernst Equation... 

Barry, P. H. (1998). Derivation of unstirred-layer transport number equations from the Nernst-Planck flux equations, Biophys. J., 74, 2903-2905. 

ET much faster than transport (transport control). Electrochemical equilibrium is attained at the electrode surface at all times and defined by the electrode potential E. The concentrations Cox and Cred of oxidized and reduced forms of the redox couple, respectively, follow the Nernst equation (1) (reversible ET)... 

The behavior of an ion type is described quantitatively by the Nernst equation (3). A /g is the membrane potential (in volts, V) at which there is no net transport of the ion concerned across the membrane (equilibrium potential). The factor RT/Fn has a value of 0.026 V for monovalent ions at 25 °C. Thus, for K, the table (2) gives an equilibrium potential of ca. -0.09 V—i. e., a value more or less the same as that of the resting potential. By contrast, for Na ions, A /g is much higher than the resting potential, at +0.07 V. Na" ions therefore immediately flow into the cell when Na channels open (see p. 350). The disequilibrium between Na" and IC ions is... 

Thus the electrolysis process is controlled by a combination of (1) mass transport of O to the edge of the stagnant layer by the laminar flow, and (2) subsequent diffusion of O across the stagnant layer under the influence of the concentration gradient (caused by electrolysis of O to R at the electrode surface) to satisfy the Nernst equation. 

Note that the mass transport coefficients r and mo are different and that the concentration gradient is reversed, hence the minus sign. As we have specified above, the electrochemical reaction is very fast, which means that the Nernst equation (5.20b) is satisfied for all values of the surface concentrations of O and R. Thus,... 

Fick s first and second laws (Equations 6.15 and 6.18), together with Equation 6.17, the Nernst equation (Equation 6.7) and the Butler-Volmer equation (Equation 6.12), constitute the basis for the mathematical description of a simple electron transfer process, such as that in Equation 6.6, under conditions where the mass transport is limited to linear semi-infinite diffusion, i.e. diffusion to and from a planar working electrode. The term semi-infinite indicates that the electrode is considered to be a non-permeable boundary and that the distance between the electrode surface and the wall of the cell is larger than the thickness, 5, of the diffusion layer defined as Equation 6.19 [1, 33] ... 

Measurements can be done using the technique of redox potentiometry. In experiments of this type, mitochondria are incubated anaerobically in the presence of a reference electrode [for example, a hydrogen electrode (Chap. 10)] and a platinum electrode and with secondary redox mediators. These mediators form redox pairs with Ea values intermediate between the reference electrode and the electron-transport-chain component of interest they permit rapid equilibration of electrons between the electrode and the electron-transport-chain component. The experimental system is allowed to reach equilibrium at a particular E value. This value can then be changed by addition of a reducing agent (such as reduced ascorbate or NADH), and the relationship between E and the levels of oxidized and reduced electron-transport-chain components is measured. The 0 values can then be calculated using the Nernst equation (Chap. 10) ... 

The O2- ions are transported through the -> solid electrolyte (and also -> stabilized zirconia) at elevated temperature (above 400 °C). The measured potential of the sensor is then given by the -> Nernst equation ... 

As noted in Section 2, when the electron-transfer kinetics are slow relative to mass transport (rate determining), the process is no longer in equilibrium and does not therefore obey the Nernst equation. As a result of the departure from equilibrium, the kinetics of electron transfer at the electrode surface have to be considered when discussing the voltammetry of non-reversible systems. This is achieved by replacement of the Nernstian thermodynamic condition by a kinetic boundary condition (36). 

A reversible one-electron transfer process (19) is initially examined. For all forms of hydrodynamic electrode, material reaches the electrode via diffusion and convection. In the cases of the RDE and ChE under steady-state conditions, solutions to the mass transport equations are combined with the Nernst equation to obtain the reversible response shown in Fig. 26. A sigmoidal-shaped voltammogram is obtained, in contrast to the peak-shaped voltammetric response obtained in cyclic voltammetry. 

In voltaic cells, it is possible to carry out the oxidation and reduction halfreactions in different places when suitable provision is made for transporting the electrons over a wire from one half-reaction to the other and to transport ions from each half-reaction to the other in order to preserve electrical neutrality. The chemical reaction produces an electric current in the process. Voltaic cells, also called galvanic cells, are introduced in Section 17.1. The tendency for oxidizing agents and reducing agents to react with each other is measured by their standard cell potentials, presented in Section 17.2. In Section 17.3, the Nernst equation is introduced to allow calculation of potentials of cells that are not in their standard states. 

The current at any point in the voltammetry experiment described in Figure 23-5 is determined by a combination of (1) the rate of mass transport of A to the edge of the Nemst diffusion layer by convection and (2) the rate of transport of A from the outer edge of the diffusion layer to the electrode surface. Because the product of the electrolysis P diffuses away from the surface and i.s ultimately swept away by convection, a continuous current is required to maintain the surface concentrations demanded by the Nernst equation. Convection, however, maintains a constant supply of A at the outer edge of the diffusion layer. Thus, a steady-state cuirent results that is determined by the applied potential. 

The relation between the interfacial and bulk concentrations depends on mass transport, most often by diffusion (i.e., thermal motion) and/or convection (mechanical stirring). Often a stationary state is reached, in which the concentrations near the electrode can be described approximately by a diffusion layer of thickness 8. For a constant diffusion layer thickness the Nernst equation takes the form... 

In addition to being an indirect measurement of the formation constant (Ki) of the iron complex, the reduction potential of the ferric siderophore complex is an important factor in developing the iron-release mechanism for siderophore-mediated iron transport. Under standard conditions, the reduction potentials for most known siderophores (ferric enterobactin —750 mV NHE V" ferriferrioxamine B 450mV NHE ) seem to preclude the use of biological reduc-tants (NAD(P)H/NAD(P)+ —324mV NHE ) to reduce the ferric ion to the ferrous ion and therefore prompt release of the ion from the siderophore. However, this potential is highly sensitive to the ratio of [Fe +]/[Fe +], as predicted by the Nernst equation. 

Air, O2, N2 and H2 were used as gas 1 or gas 2, in wet or dry states. The relevant ionic transport number is then obtained by comparing the measured emf with the predicted emf from the Nernst equation. 

When the UME is moved close to an insulating surface, the current drops to a lower value Ij because the surface and the insulating sheath of the UME block transport of active species O. This effect is sometimes called negative feedback and is further enhanced by the fact that no reoxidation of R can occur at insulating parts of the surface. Approaching a conductive surface kept at an electrode potential where reoxidation of R is possible causes an opposite effect (positive feedback) and Ij is enhanced with a closer distance. Both possibilities are schematically depicted in Fig. 7.11. A similar effect may be observed with an unbiased (not kept at any specific potential, but instead at open circuit) surface. Because the large surface area is in contact with the solution containing a supply of O, the surface electrode potential is essentially controlled by the Nernst equation. At the potential established by the concentration of O, the reduced species R created at the UME will be reoxidized, whereas further O is reduced elsewhere on the surface. 

In the given form, the Butler-Volmer equation is applicable rather broadly, for flat model electrodes, as well as for heterogeneous fuel cell electrodes. In the latter case, concentrations in Eq. (2.13) are local concentrations, established by mass transport and reaction in the random composite structure. At equilibrium,/f = 0, concentrations are uniform. These externally controlled equilibrium concentrations serve as the reference (superscript ref) for defining the equilibrium electrode potential via the Nernst equation. 

Assuming the kinetics of the electron transfer are fast relative to the rate of mass transport, Nernstian equUibrinm is attained at the electrode surface throughout the potential scan, and the Nernst equation therefore relates... 

Nemst s law (Eq. II. 1.7, which is simply the Nernst equation written in the exponential form) defines the surface concentrations of the oxidised, [A]jc=o. and die reduced form, [B] =o. of the redox reagents for a reduction process A + n e B as a function of E t) and, the applied and the formal reversible potential [4], respectively, where t is time, n is the number of electrons transferred per molecule of A reacting at the electrode surface, F, the Faraday constant, R, the constant for an ideal gas, and T, the absolute temperature. Pick s second law of diffusion (Eq. II. 1.6) governs the mass transport process towards the electrode where D is the diffusion coefficient. The parameter x denotes the distance from the electrode surface. 

It ould also be noted that, in practice, it is not always possible to estimate kinetic parameters from I-E data. Some redox couples 0/R have kinetic parameters such that the rate of electron transfer is, under all experimental conditions, fast compared with the prevailing rate of mass transport in such circumstances the electron transfer at the surface will appear to be in equilibrium and the ratio of surface concentrations can be calculated from the Nernst equation. Such... 

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