Randles-Sevcik equation derivation

Sevcik, Augustin — (1926-2006) Research student of -> Heyrovsky, /. In his dissertation he derived an equa-tionfor diffusion-controlledvoltammetric curves [i],independently of - Randles. See also - Randles-Sevcik equation. 

J.E.B. RANDLES (1912-1998) develops linear sweep voltammetry and gives the equation for the peak current of hnear sweep voltammetry known as the Randles-Sevcik equation (1948) Trans Faraday Soc 44 327. A. SEVCIK (1926-2006) derives a similar equation independently (1948) CoU Czech Chem Commun 13 349... 

This integral equation is essentially similar in form to that derived many years ago by Nicholson and Shain and others " for the linear potential sweep response of redox-active molecules in homogeneous media. Methods developed by these researchers (numerical or analytic) can be used to evaluate the integral in Eqn. 322. We do not do this here but simply note that the peak current can be given by the Randles-Sevcik equation, which is... 

As soon as the growing diffusion layer is reaching a critical value with decreasing scan rate, it will no longer be small compared to the wire radius. It cannot be considered to be planar, but from this moment it will change more and more to a curved, i.e. cylindric, character. Start of cylindric diffusion can be detected by analysing the value of the apparent diffusion coefficient )obt=/(log v). If the classic equation (5.5) will dehver an exotic value of )obt> far from reality, obviously cylindric diffusion is predominant. For cylindric diffusion, a modified form of the Randles-Sevcik equation has been derived [7] ... 

Regarding the electrochemical method, the generalized forms of the Cottrell relation and the Randles-Sevcik relation were theoretically derived from the analytical solutions to the generalized diffusion equation involving a fractional derivative operator under diffusion-controlled constraints and these are useful in to determining the surface fractal dimension. It is noted that ionic diffusion towards self-affine fractal electrode should be described in terms of the apparent self-similar fractal dimension rather than the self-affine fractal dimension. This means the fractal dimension determined by using the diffusion-limited electrochemical method is the self-similar fractal dimension irrespective of the surface scaling property. 

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