Microelectrode current-time dependence

The current-time dependence of a cyclic voltammogram at a microelectrode for diffusion-controlled conditions is given by the equation... 

Advantages are also found with microelectrodes used at short time scales where time-dependent currents are obtained, as the example in Figure 12.4 shows [56]. Time-dependent currents are proportional to the electrode area. Thus, for the case of a sphere, combination of the expression for the time-dependent current with the resistance shows that the ohmic drop is directly proportional to the radius. Thus, ohmic drop is always minimized by the use of a smaller electrode. 

Here, r0 is the radius of the hemispherical electrode A = Anr for a sphere and A = 27t/q for a hemisphere. The first term on the right-hand side of (7.18) is the Cottrell term (7.17) and the second is the correction for radial diffusion to the microelectrode. With time, the first term becomes negligible compared to the second. The time te required for the current to reach the steady-state value depends on the desired accuracy (e%) and on the diameter of the electrode d = 2ro (in Am). It can be estimated by making the first term in (7.18) negligible against the second term, according to the formula... 

In the case of microcyclinders and microbands, fG,micro is time dependent (Table 2.3) and only a pseudo-stationary response can be achieved. This is because all the microelectrode dimensions have to fall in the range of the microns to attain a true steady state. The expressions for the pseudo-stationary current-potential responses when the diffusion coefficients of species O and R fulfills Dq = Dr are ... 

The diffusion-limited current at spherical and hemispherical microelectrodes follows directly from (5.23). We consider a hemispherical electrode as shown in Fig. 5.8. After a certain time, depending on the electrode size, a steady-state is reached, and the current is... 

Early two-dimensional simulations focused on the evaluation of the current distribution at microdisc electrodes [107, 108] and simulations of a variety of electrode geometries [109-111] including the influence of recessed microelectrode configurations [112]. Work has been also extended to cases involving coupled homogeneous kinetics, adsorption [113], and time-dependent redox polymer electrochemistry [114]. 

Note that if r > 5, which occurs at short times, the 1/6 term predominates, and Equation 2S-22 reduces to an equation analogous to Equation 25-5. If r 6, which occurs at long times, the 1/r term predominates, the electron-transfer process reaches a steady state, and the steady-state current then depends only on the size of the electrode. This means that if the size of the electrode is small compared to the thickness of the Nernst diffusion layer, steady state is achieved very rapidly, and a constant current is produced. Because the current is proportional to the area of the electrode, it also means that microelectrodes produce tiny currents. Expressions similar in form to Equation 25-22 may be formulated for other geometries, and they all have in common the characteristic that the smaller the electrode, the more rapidly steady-state current is achieved. 

Cyclic voltammetry is one such electrochemical technique which has found considerable favour amongst coordination chemists. It allows the study of the solution electron-transfer chemistry of a compound on the sub-millisecond to second timescale it has a well developed theoretical basis and is relatively simple and inexpensive. Cyclic voltammetry is a controlled potential technique it is performed at a stationary microelectrode which is in contact with an electrolyte solution containing the species of interest. The potential, E, at the microelectrode is varied linearly with time, t, and at some pre-determined value of E the scan direction is reversed. The current which flows through the cell is measured continuously during the forward and reverse scans and it is the analysis of the resulting i—E response, and its dependence on the scan rate dE/dt, which provides a considerable amount of information. Consider, for example, the idealized behaviour of a compound, M, in an inert electrolyte at an inert microelectrode (Scheme 1). 

The current-potential relationship of the totally - irreversible electrode reaction Ox + ne - Red in the techniques mentioned above is I = IiKexp(-af)/ (1+ Kexp(-asteady-state voltammetry, a. is a - transfer coefficient, ks is -> standard rate constant, t is a drop life-time, S is a -> diffusion layer thickness, and

logarithmic analysis of this wave is also a straight line E = Eff + 2.303 x (RT/anF) logzc + 2.303 x (RT/anF) log [(fi, - I) /I -The slope of this line is 0.059/a V. It can be used for the determination of transfer coefficients, if the number of electrons is known. The half-wave potential depends on the drop life-time, or the rotation rate, or the microelectrode radius, and this relationship can be used for the determination of the standard rate constant, if the formal potential is known. 

In this case, the coverage by the bubbles is complete and they can attain the radius R irrespective of the current density. The dependence of the radius of the bubble with time was followed in the case of vertical microelectrodes in an unstirred solution in Ref. [84], The electrochemical evolution of the hydrogen on the platinum in 1 M sulfuric solution can be related by the following equation that correlates the radius of the bubble with the current that is exclusively related to the gas evolution ... 

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