Faradaic current density

When the area A of the eleetrode/solution interface with a redox system in the solution varies (e.g. when using a streaming mercury electrode), the double layer capacity which is proportional to A, varies too. The corresponding double layer eharging current has to be supplied at open eireuit eonditions by the Faradaic current of the redox reaction. The associated overpotential can be measured with respect to a reference electrode. By measuring the overpotential at different capaeitive eurrent densities (i.e. Faradaic current densities) the current density vs. eleetrode potential relationship can be determined, subsequently kinetic data can be obtained [65Del3]. (Data obtained with this method are labelled OC.)... 

The charge propagates in the film by electron hopping between the polymer Red/Ox couples. This is controlled by the electrode potential only in a close proximity of the electrode in more distant sites, the charge transport is driven by a concentration gradient of reduced or oxidized mediators. The observed faradaic current density, jF, is a superposition of... 

Transport properties of hydrated PFSA membranes strongly depend on nanophase-segregated morphology, water content, and state of water. In an operational fuel cell, these characteristics are indirectly determined by the humidity level of the reactant streams and Faradaic current densities generated in electrodes, as well as the transport properhes of catalyst layers, gas diffusion layers, and flow... 

Naturally, the mathematics of a mechanism will always yield the net rate, v, of the reaction O + n e = R and, by convention, the faradaic current density, jF, is... 

The two interfacial processes, charge transfer and double-layer charging, proceed in parallel and so the total current density is the sum of the faradaic and the charging (sometimes called non-faradaic) current densities... 

The current density, will be the sum of the faradaic current density, jF, and the charging current density, c, cf. eqn. (8). The latter is related to the interfacial potential indicated in an implicit way by eqn. (20). The theory of the electrical double layer provides no analytical expression for the relation between E and qM and so, rigorously, this part of the problem would have to be solved numerically using the empirical relationship, which is known for many commonly used indifferent electrolytes. If Cd = dqM/dE is the differential double-layer capacity, we have... 

The potential E is also related to the faradaic current density by eqn. (18). Evidently, it is required to eliminate the surface concentrations, i.e. to find the solution of eqns. (19) for x = 0. Without derivation, we now give this solution, which is of the form of an implicit integral equation [28]. 

Two electrochemical techniques are directly based on the expression for the faradaic current density jF, namely chronoamperometry and normal pulse polarography. A third technique, named chronocoulometry, deals with the integral of jF, giving the charge transferred per unit area via the faradaic process as a function of time. The general expression obtained... 

Although being of great fundamental importance, it should not be ignored that practical application of the semi-integral analysis requires separation of the faradaic current density jF, i.e. subtraction of the charging current density jc, from the overall current density, j, as well as perfect instrumental compensation or numerical subtraction of the ohmic potential drop jARn in order to obtain the interfacial potential E. 

This is a case where two faradaic current densities are involved jr F,i for reaction Re,i and P 2 for reaction RE2 (see Sect. 7.1.6). The species involved in a chemical conversion are Z and X. The four surface concentrations are given by... 

From the foregoing, it follows that the presence of a coupled chemical reaction manifests itself in the relation between the faradaic current density and the surface concentration of the electroactive species, in terms of the parameters Kt and fe, (see Table 8). The equilibrium constant, Kh may be known from a separate (e.g. potentiometric or spectrophoto-metric) experiment. 

Here C is the specific differential double layer capacitance. The two terms on the left side of Eq. (4) describe the capacitive and faradaic current densities at a position r at the electrode electrolyte interface. The sum of these two terms is equal to the current density due to all fluxes of charged species that flow into the double layer from the electrolyte side, z ei,z (r, z = WE), where z is the direction perpendicular to the electrode, and z = WE is at the working electrode, more precisely, at the transition from the charged double layer region to the electroneutral electrolyte. 4i,z is composed of diffusion and migration fluxes, which, in the Nernst-Planck approximation, are given by... 

Figure 7.3 Schematic representation of an electrode interface demonstrating the contribution of charging and Faradaic current densities.

The Faradaic current density for a linear system can be expressed as... 

The Faradaic current density is expressed as a function of interfacial concentration as... 

For minor species, in the presence of supporting electrol3rte and with neglect of double-layer adsorption of these minor species, the concentration gradient is related to the Faradaic current density by... 

AJ amplitude of sinusoidal current signal, see, e.g., equation (4.7), A if Faradaic current density, mA/cm ... 

At the electrode, the current flux at a certain position is given by the sum of capacitive and faradaic current densities. A thorough mathematical analysis of this problem was carried out by Christoph et The... 

Fundamentals of Electrode Processes 2.3.1. Faradaic Current Density... 

An effective Tafel equation can be written for the Faradaic current density generated by a single agglomerate, which includes the effectiveness factor... 

The effective law of current generation in single agglomerates, Eq. (2.53), can be incorporated into macroscopic models of CCL operation in Section 2.6, viz. as an effective Faradaic current density in REVs in Eq. (2.73). In that context, the surface values rj p = 1) and co p = 1) have to be considered as functions of the position z within the CCL. 

Internal wetted pore fraction (nomalized) Volumetric Faradaic current density Effective Volumetric Faradaic current density including effectiveness factor of agglomerates... 

Faradaic current density Effective and generic exchange current density... 

FIGURE 6.15. Partition of a cyclic voltammogram into capacitive and faradaic currents densities at a scan rate of 20mVs [Reprinted with permission from T. Yeu, V. Nguyen, and R. E. White, J. Electrochem. Soc. 138, 2869 (1991).]... 

The electrochemistry of the SOFC can be modeled at the mesoscale in cell- and electrode-level models. In these models, the electrochemistry is calculated based on the local conditions within the SOFC tri-layer and the local Faradaic current density is resolved through the thickness of the cell. In mesoscale electrochemistry, both the local electrochemistry and the global electrochemistry are considered. The local electrochemistry is the local reactions within the electrodes which produce a local Faradaic current density the global electrochemistry is the integral of the local electrochemistry over the tri-layer and produces the common I-Vcurves that are used to describe the performance of the SOFC. 

There are two approaches to modeling the SOFC electrochemistry at the mesoscale an elementary kinetics-based model and a modified Butler-Volmer model. In the elementary kinetics-based model, the electrochemical reactions of the SOFC are modeled exactly, whereas in the modified Butler-Volmer model, the phenomenological Butler-Volmer equation is solved based on the local Faradaic current density. 

The local Faradaic current density of the SOFC is formulated from the electrochemical reactions, Eqs. (26.14-26.17), as [27]... 

Many SOFC models chose not to model explicitly the electrochemical reactions. Instead, a modified Butler-Vohner relation based on the local conditions within the tri-layer can be used to solve for the current density of the fuel cell in a mesoscale electrochemistry approach [25]. The local Faradaic current density can be calculated from the modified Butler-Vohner relation as [31]... 

Figure 26.10 Local Faradaic current density through the tri-layer for several optimization cases. The table inset gives the overall cell current density for each case. Note that Case 3 is not shown in the plot as it overlaps Case 2 [55].

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