Ilkovid equation

These are both forms of the Ilkovid equation. The first has been shown experimentally to be only reasonably correct in terms of time dependence however, the expression for the average current is substantially correct. The principal defect of this derivation is that it takes no account of electrode curvature. 

In polarography, not enough time is available for the diffusion layer to reach its stationary thickness. Instead, the current per unit electrode area decreases with the square root of time, the signature time-dependence for diffusion. On the other hand, the area of the growing drop expands, proportional to the two-thirds power of drop age r (i.e., time elapsed since the previous mercury drop fell off). These two counteracting effects, diffusion currents per area proportional to r 1/2, and area growth as t2/3, combine to yield polarographic current-time curves with a time dependence of t-1/2 X t2/3 = t1/6, as expressed in the Ilkovid equation. 

The current is proportional to the rate at which X diffuses to the cathode, a function which can be expressed mathematically for a spherical electrode on which X converges from all directions. The situation is complicated by two factors. Because the mercury drop is steadily expanding, the surface area increases gradually and also the surface moves relative to the solution against the concentration gradient. The diffusion current at any time t during the life of the drop is given by an equation first derived by Ilkovid ... 

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