Ilkovic differential equation

Substitution into Eq. (2.7.5) respecting only changes along the x coordinate yields the Ilkovic differential equation... 

The other factor that can show the influence of kinetic, catalytic, and adsorption effects on a diffusion-controlled process is the temperature coefficient.10 The effect of temperature on a diffusion current can be described by differentiating the Ilkovic equation [Eq. (3.11)] with respect to temperature. The resulting coefficient is described as [In (id,2/id,iV(T2 — T,)], which has a value of. +0.013 deg-1. Thus, the diffusion current increases about 1.3% for a one-degree rise in temperature. Values that range from 1.1 to 1.6% °C 1, have been observed experimentally. If the current is controlled by a chemical reaction the values of the temperature coefficient can be much higher (the Arrhenius equation predicts a two- to threefold increase in the reaction rate for a 10-degree rise in temperature). If the temperature coefficient is much larger than 2% °C-1, the current is probably limited by kinetic or catalytic processes. 

Those of you who wish can differentiate the Heyrovsky-Ilkovic equation (l-5j) to obtain df/d/and then invert this to give d//d . Then put / = /(j/2, when E = Ei and show that ... 

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