Reactions of Dissolved Species on Spherical Electrodes and Microelectrodes

2 Reactions of Dissolved Species on Spherical Electrodes and Microelectrodes 

On a stationary spherical electrode, the reaction (1.1) can be mathematically represented by the following system of differential equations and boundary conditions  

The application of (2.17)-(2.20) is shown in Fig. 2.18. The response depends on the sphericity parameter p = VD/rov7 [27]. Under the influence of increasing parameter p, the minimum of the forward component and the maximum of the backward component gradually vanish and both components acquire the form of a polarographic wave. At potentials much lower than the half-wave potential, both currents tend to the limiting value which is equal to —p. The net peak potential is equal to the reversible half-wave potential and independent of the sphericity parameter, but the dimensionless net peak current is a linear function of the parameter p. If n sw = 50 mV and uAE = -5 mV, this relationship is  

This is shown in Fig. 2.19. The relationships between A fJ, and nE v, and nIEE do not depend on electrode size [28-30]. So, if nE vi = 25 mV and nAF, = —5 mV, the relationship (2.21) is AWp = 0.465 + 0.45p [26]. If the frequency is high and a hanging mercury drop electrode is used, the spherical effect is usually negh-gible (p 10 ). However, the influence of sphericity must be taken into consideration under most other conditions, and generally at microelectrodes. The net peak current is a linear function of the square-root of frequency Alp/nFAc QD I = 

Theoretically, if an extremely small electrode is used and low frequency is applied, so thatro/ / 2 a steady-state, frequency-independent net peak current should appear A/p ss = 4.706n co ro. 

At an inlaid microdisk electrode, the dependence of the dimensionless net peak current on the sphericity parameter is given by the following equation [31]  

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