Nemst diffusion-layer model

The diffusion-layer thickness S is defined by the Nemst diffusion layer model illustrated in Fig. 6. This model assumes that the concentration of M " " ions has a bulk concentration q, up to a distance 5 from the electrode surface and then falls off linearly to Cx= at the electrode surface. 

Figure 2.8 depicts the Nemst diffusion layer model which shows that beyond the critical distance, <5, the solution is well mixed such that the concentration of the electroactive species is maintained at a constant bulk value. In this vicinity, the mixing of the solution to even out inhomogeneities is due to natural convection induced by density differences. Additionally, if the electrochemical arrangement is not sufficiently thermostated, slight variation throughout the bulk of the solution can provide a driving force for natural convection. 

Fig. 15 Two of the simplest theories for the dissolution of solids (A) the interfacial barrier model, and (B) the diffusion layer model, in the simple form of Nemst [105] and Brunner [106] (dashed trace) and in the more exact form of Levich [104] (solid trace). c is the concentration of the dissolving solid, cs is the solubility, cb is the concentration in the bulk solution, and x is the distance from the solid-liquid interface of thickness h or 8, depending on how it is defined. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., from Ref. 1, p. 478.)...

A Nemst stagnant-diffusion-layer model was used to accovmt for the diffusion impedance. This model is often used to account for mass transfer in convective systems, even though it is well known that this model caimot ac-coimt accurately for the convective diffusion associated with a rotating disk electrode. 

To predict the current response versus applied potential, the simplified diffusion-layer model may be combined wi the Nemst equation (for a reversible system) to yield the familiar hydrodynamic voltammogram. The latter relationship states that the potential of the electrode is determined by the concentration activity ratio of the oxidized and reduced forms of the redox couple at the electrode surface (Fig. 9A). ... 

However, this is an important issue in the determination of a diffusion coefficient from experimental data. It seems that the charge transfer resistance, necessary to determine the reaction kinetics, is less affected by a 2D current distribution, and so a simpler model might be used in the kinetic studies. Even simple models based on the Nemst diffusion layer are often used in kinetic studies [180] because of their simplicity. 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

In addition to this, the three-dimensional mathematical model of heat and mass transfer [3, 4] has been developed. Stephan-Maxwell equation was used for mass transport calculations in gas channels and gas diffusion layers. Proton transport in membrane and electrocatalytic layer was described by Nemst-Planck equation. The diffusion and electroosmosis of water were taken into account for membrane potential distribution. 

Figure 16. FEM meshing for the Nemst-Planck s model. Compared to Fig. 10 an interfacial domain has been introduced to mimic pseudo-diffusion layer, where both diffusion and migration of species are possible.

This point can be appreciated more quantitatively after consideration of an important (but simple) model of transport-controlled adsorption kinetics, the film diffusion process.34 35 This process involves the movement of an adsorptive species from a bulk aqueous-solution phase through a quiescent boundary layer ( Nemst film ) to an adsorbent surface. The thickness of the boundary layer, 5, will be largest for adsorbents that adsorb water strongly and smallest for aqueous solution phases that are well stirred. If j is the rate at which an... 

Process models Nemst dielectrics (1894) Warburg diffusion (1901) Finkelstein Solid film (1902) Randles double layer and diffusion impedance (1947) Gerischer two heterogeneous steps with adsorbed intermediate (1955) De Levie porous electrodes (1967) Schuhmann homogeneous reactions and diffusion (1964) Gabrielli generalized impedance (1977) Isaacs LEIS (1992)... 

A very simplified model of the convective diffusion was introduced in electrochemistry by Nemst (1904), which is based on the hypothesis of the formation, at the electrode surface, of a motionless limiting layer with a thickness 5n where diffusion occurs. 

The contribution of electric field to lithium transport has been considered by a few authors. Pyun et al argued on the basis of the Armand s model for the intercalation electrode that lithium deintercalation from the LiCoO composite electrode was retarded by the electric field due to the formation of an electron-depleted space charge layer beneath the electrode/electrolyte interface. Nichina et al. estimated the chemical diffusivity of lithium in the LiCo02 film electrode from the current-time relation derived from the Nemst-Planck equation for combined lithium migration and diffusion within the electrode. 

To determine the flux, Nemst model of stationary diffusion with linear distribution of the concentration across the layers of the constant thickness is used, and the concentration of the intermediate is assumed to be zero, i.e. the anode discharge proceeds at limit current condition. Then... 

One of the early mechanistic models for a PEM fuel cell was the pioneering work of Bemardi and Verbrugge [45, 46]. They developed a one-dimensional, steady state, isothermal model which described water transport, reactant species transport, as well as ohmic and activation overpotentials. Their model assumed a fully hydrated membrane at all times, and thus calculated the water input and removal requirements to maintain full hydration of the membrane. The model was based on the Stefan Maxwell equations to describe gas phase diffusion in the electrode regions, the Nemst-Planck equation to describe dissolved species fluxes in the membrane and catalyst layers, the Butler Volmer equation to describe electrode rate kinetics and Schlogl s equation for liquid water transport. 

Very often, transport in a liquid near the interface is modelled as a purely diffusive process in a stagnant layer of some thickness S. Generally this thickness has different values S/i and 6b in phases A and B. The concept of stagnant layer was introduced by Nemst at the beginning of this century and it constituted the basis of the two-film theory proposed by Whitman [9]. The parameter 6 represents the... 

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