Diffusion current, limiting

For many cooling waters, including seawater and also drinking water, where corrosion rates are 70 to 100% of the limiting diffusion current, the use of dimensionless group analysis can then be applied. 

Using the expression for the limiting diffusion current density, we can rewrite the surface concentration as... 

In many cases the concentration of a substance can be determined by measuring its steady-state limiting diffusion current. This method can be used when the concentration of the substance being examined is not very low, and other substances able to react in the working potential range are not present in the solution. 

Polarograms are sometimes distorted by polarographic maxima, where the current in individual segments of the I vs. E curves is much higher (several times) than the limiting diffusion current. A number of reasons exist for the development of these maxima. 

Together with the boundary condition (5.4.5) and relationship (5.4.6), this yields the partial differential equation (2.5.3) for linear diffusion and Eq. (2.7.16) for convective diffusion to a growing sphere, where D = D0x and = Cqx/[1 + A(D0x/T>Red)12]- As for linear diffusion, the limiting diffusion current density is given by the Cottrell equation... 

The properties of the voltammetric ultramicroelectrode (UME) were discussed in Sections 2.5.1 and 5.5.1 (Fig. 5.19). The steady-state limiting diffusion current to a spherical UME is... 

If all the constants in the expression for the limiting diffusion current are known, including the diffusion coefficient, then the number of electrons consumed in the reaction can be found from the limiting current data. However, this condition is often not fulfilled, or the limiting diffusion... 

Fig. 4. Migration contribution to the limiting current in acidified CuS04 solutions, expressed as the ratio of limiting current (iL) to limiting diffusion current (i ) r = h,so4/(( h,so, + cCuS(>4). "Sulfate refers to complete dissociation of HS04 ions. "bisulfate" to undissociated HS04 ions. Forced convection" refers to steady-state laminar boundary layers, as at a rotating disk or flat plate free convection refers to laminar free convection at a vertical electrode penetration to unsteady-state diffusion in a stagnant solution. [F rom Selman (S8).]...

Polarography is the classical name for LSV with a DME. With DME as the working electrode, the surface area increases until the drop falls off. This process produces an oscillating current synchronized with the growth of the Hg-drop. A typical polarogram is shown in Fig. 18b. 10a. The plateau current (limiting diffusion current as discussed earlier) is given by the Ilkovic equation... 

Fig. 8-10. Anodic reaction current vs. potential curve for a redox electron transfer of hydrated redox particles at a metal electrode iibi = limiting diffusion current of redox particles 1/3 = potential at which reaction current is half the limiting diffusion current ( = 0.6iiin). [From Bard-Paulkner, 1980.]...

As the polarization (the overvoltage t) ) increases of a redox reaction that requires the transport of minority charge carriers towards the electrode interface (anodic hole transfer at n-type and cathodic electron transfer at p-type electrodes), the transport overvoltage, t)t, increases from zero at low reaction currents to infinity at high reaction current at this condition the reaction current is controlled by the limiting diffusion current (iu.)tm or ip.um) of minority charge carriers as shown in Fig. 8-25. 

The holes injected by a cathodic redox reaction (Eqn. 10-47) diffuse toward the electrode interior and recombine with electrons of the m ority charge carriers in the same way as photogenerated holes, thereby producing a cathodic current inc, which is equivalent to the rate of recombination of holes. The cathodic current i actually observed is the sum of the current of recombination inc and the limiting diffusion current of holes ip.um as shown in Eqn. 10-48 ... 

At 60 minutes only, dc potentiodynamic curves were determined from which the corrosion current was obtained by extrapolation of the anodic Tafel slope to the corrosion potential. The anodic Tafel slope b was generally between 70 to 80 mV whereas the cathodic curve continuously increased to a limiting diffusion current. The curves supported impedance data in indicating the presence of charge transfer and mass transfer control processes. The measurements at 60 minutes indicated a linear relationship between and 0 of slope 21mV. This confirmed that charge transfer impedance could be used to provide a measure of the corrosion rate at intermediate exposure times and these values are summarised in Table 1. 

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... 

As already stated, when metal electrodes are used in electrochemical reactions and one speaks of a limiting diffusion current, one is referring to ionic charge carriers... 

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. 

However, advantageous applications of micro- and ultramicroelectrodes are not limited to fundamental investigations. Such electrodes open up possibilities for work in very low concentrations of solute. Whatever can be done at a planar electrode can be done at a concentration about a thousand times lower by using an ultramicroelectrode without reaching the limiting diffusion current. This means that one could even obtain responses from solutes of 1 ppb (assuming a measured current density of 1 pA cm-2). 

Another advantage in the use of microelectrodes is that the limiting diffusion current is independent of disturbances in the solution. Thus, for a planar electrode, the... 

For a more complex (more usual) reaction involving surface intermediates, it is possible that their adjustment to steady-state value may lengthen the time at which the potentiostated current density reaches constancy, even at current densities well below the limiting diffusion-current density. 

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