Diffusion limited current density Diffusivity

Therefore, in tire limiting case—tire surface concentration of tire reacting species is zero as all tire arriving ions immediately react—tire current density becomes voltage independent and depends only on diffusion, specifically, on tire widtli of tire Nerstian diffusion layer S, and of course tire diffusion coefficient and tire bulk concentration of anions (c). The limiting current density (/ ) is tlien given by... 

In Section 1.4 see Fig. 1.31h) it has been shown that when a corrosion reaction is controlled by the rate of oxygen diffusion, both the rate of corrosion and the corrosion potential increase with / l. the limiting current density, i.e. 

The limiting current density in equation 20.77 has been derived on the assumption that transport is solely by diffusion, but if migration also occurs then for a cathodic process... 

The basic theory of mass transfer to a RHSE is similar to that of a RDE. In laminar flow, the limiting current densities on both electrodes are proportional to the square-root of rotational speed they differ only in the numerical values of a proportional constant in the mass transfer equations. Thus, the methods of application of a RHSE for electrochemical studies are identical to those of the RDE. The basic procedure involves a potential sweep measurement to determine a series of current density vs. electrode potential curves at various rotational speeds. The portion of the curves in the limiting current regime where the current is independent of the potential, may be used to determine the diffusivity or concentration of a diffusing ion in the electrolyte. The current-potential curves below the limiting current potentials are used for evaluating kinetic information of the electrode reaction. 

The dependence of the limiting current density on the rate of stirring was first established in 1904 by Nernst (N2) and Brunner (Blla). They interpreted this dependence using the stagnant layer concept first proposed by Noyes and Whitney. The thickness of this layer ( Nernst diffusion layer thickness ) was correlated simply with the speed of the stirring impeller or rotated electrode tip. 

Drake [35] has measured the thickness of the diffusion layer during the electrodeposition of copper from an acidic-sulphate system. He obtained a value of approximately 200 pm for the silent system and values of 34 pm and 3.4 pm for ultrasonic frequencies of 1.2 MHz and 20 kHz respectively. The corresponding values of the limiting-current density were from 8 Am (silent) to 50 A m (1.2 MHz) to 500 A m (20 kHz), indicating a significant increase in the rate of deposition. 

The last part of the polarization curve is dominated by mass-transfer limitations (i.e., concentration overpotential). These limitations arise from conditions wherein the necessary reactants (products) cannot reach (leave) the electrocatalytic site. Thus, for fuel cells, these limitations arise either from diffusive resistances that do not allow hydrogen and oxygen to reach the sites or from conductive resistances that do not allow protons or electrons to reach or leave the sites. For general models, a limiting current density can be used to describe the mass-transport limitations. For this review, the limiting current density is defined as the current density at which a reactant concentration becomes zero at the diffusion medium/catalyst layer interface. 

Example 6.2. Calculate the diffusion limiting current density for the deposition of a metal ion at a cathode in a quiescent (unstirred) solution assuming a diffusion layer thickness 8 of 0.05 cm. The concentration of ions in the bulk (cj,) is 10 moEL (10 moEcm ), the same as in Example 6.1. The diffusion coefficient D of in the unstirred solution is 2 X lO cm /s. Using Eq. (6.83), we calculate that the limiting diffusion current density for this case is... 

Using the rotating disk electrode, Seliv-anov et al. [214] have investigated the zinc electrodeposition from zincate electrolyte containing polyethylene polyamine. The limiting current density of [Zn(OH)4] ion diffusion through a film of zinc oxides and hydroxides is shown to be responsible for the formation of dark zinc deposits in the potential range from —1.33 to —1.47 V. 

It is shown elsewhere (Section 7.9.2) that an approximate numerical formula for this limiting diffusion current iL is iL = 0.02 nc, where n is the number of electrons used in one step of the overall reaction in the electrode and c is the concentration of the reactant in moles liter-1. Hence, at 0.01 M, and n = 2, say, iL = 0.4 mA cm-2—a current density less than may be desirable for many purposes. The problem is how to increase this diffusion-controlled limiting current density and obtain data on the interfacial reaction free of interference by transport at increasingly high current densities. 

Influence of Rotating Disk Electrode Condition (Stationary or Rotating) on the Diffusion-Layer Thickness and the Limiting Current Density for the Reaction... 

It is seen from Eq. (7237) that the current density i is always greater than in the case of pure diffusion [Eq. (7.202)], in which case tA = 0 and Eq. (7.237) reduces to (7.202). Similarly, the limiting current density must be greater for migration plus diffusion than for pure diffusion [Eq. (7.206)] and is given by... 

Using Levich s equation we can determine the diffusion coefficients for the reactant species by measuring the limiting current densities at known angular velocities. 

Such a consideration, then, turns attention to the time dependence of iL. Would there be a time domain in which iL is very large The basis of an answer to this question has been given in Section 7.9.10, where discussion shows two time regions in which iL is to be considered. To understand the first of these, one must recall Eq. (7.206), the relation between the limiting current density, iL, and the diffusion layer thickness, 8. It is... 

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