Nonuniformly accessible electrode

The diffusion layer thickness also varies with, which from Eq. (9) means that the mass transport-limited flux across the CE varies with, so that the electrode is nonuniformly accessible. An analogous Levich equation to the TE has been derived analytically for the CE. This gives the mass transport-limited current for fast flow (where as with the TE, diffusion in the direction of convective flow can be considered to be negligible and where convection is so efficient that the concentration gradient of reactive species near the electrode can be linearized [53]) and for short electrodes (in which the diffusion layer can be considered to be thin compared to the height of the channel) as... 

For example, a cell of 1-cm width, 50-micrometer half height, a diffusion coefficient of 10 m s a volume flow of 20 microLmin, and the length of the electrode x = 1.6 mm, the average diffusion layer thickness is approximately hdiffusion = 50 micrometer (note that here the nonuniformly accessible diffusion layer increases toward the trailing edge). 

This equation is applicable to ET at the metal/solution interface and to IT at the nano-TTIES if the diffusion inside the pipette shaft does not have to be taken into account. In the former case, 6=l+exp[nF(E-E° )/RT mo/mR and K=k°exp[-anF(E-Ey)/RT]/nio for the reduction reaction, where mg and represent mass-transfer coefficients of oxidized and reduced species, respectively, E is the electrode potential, and E° is the formal potential of the redox couple and and a are the standard rate constant and the transfer coefficient, respectively. For IT from the external organic solution (phase 2) to the aqueous solution (phase 1), Q = 1 + exp[(A and A (p are the Galvani potential difference across the ITIES and its standard value for the given IT, respectively, and m2 is the mass-transfer coefficient in the outer solution. Conceptually similar equations were derived for a nonuniformly accessible disk-shaped interface and SECM. ... 

The geometry of the microelectrodes is critically important not only from the point of view of the mathematical treatment, but also their performance. Thus, the diffusion equations for spherical microelectrodes can be solved exactly because the radial coordinates for this electrode can be reduced to the point at r = 0. On the other hand, a microelectrode with any other geometry does not have a closed mathematical solution. It would be advantageous if a microdisc electrode, which is easier to fabricate, would behave identically to a microsphere electrode. This is not so, because the center of the disc is less accessible to the diffusing electroactive species than its periphery. As a result, the current density at this electrode is nonuniform. 

Some issues pertaining to mass transfer to electrodes are described in Section 5.6, and the associated issues for cell design are considered further in Section 8.1.2. In many cases, a uniformly accessible electrode cannot be used. The time-constant dispersion that can arise as a result of nonuniform mass transfer is discussed in Section 13.2. 

In the intermediate and late time regimes, the current density at a UME disk is intrinsically nonuniform because the edges of the electrode are more accessible geometrically to the diffusing electroreactant (17). This non-uniformity affects the interpretation of phenomena that depend on local current density, such as heterogeneous electron-transfer kinetics or the kinetics of second-order reactions involving electroactive species in the diffusion layer. 

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