Cottrell plot

FIGURE 4-29 Cottrell plot of the chronoamperometric response for 1 x 1(T3M Ru(NH3)63 + at a Kel-F/gold composite electrode. Points are experimental data, the solid line is the least-squares fit to theory. Dashed lines are theoretical Cottrell plots for a macroelectrode with active area equal to the active area of the composite (curve a) and to the geometric area of the composite (curve b). (Reproduced with permission from reference 87.)... 

Additionally, it can often, however, be a good idea to perform chronoamperometric transients over a wide range of times and voltages to ascertain those experimental conditions which do indeed yield a linear Cottrell plot that passes through the origin, i.e. to ascertain those experimental conditions over which diffusion is indeed the sole form of mass transport. 

When determining a diffusion coefficient D from a Cottrell plot, it is important to determine the current for as long a time as possible, in order to ensure reliability. With suitable precautions, as much as 10 s may be possible. Certainly, 4 or 5 s should be attempted as a minimum and, in practice, data are best obtained over a range of, say, 1 ms to 5 s. 

Figure 1. Cottrell plots obtained from oxidation of (+ ) Pt/Nafion-GOD-DMAFc, ( O ) Pt/Nafion-GOD-ClFc+ and ( ) Pt/Nafion-GOD-C6Fc+ in 0.1M phosphate buffer. DMAFc, CiFc+ and C6Fc+ were incorporated into the Nafion-GOD films from a 0.5 mM solution.

Finite diffusion — Finite (sometimes also called -> limited) diffusion situation arises when the -> diffusion layer, which otherwise might be expanded infinitely at long-term electrolysis, is restricted to a given distance, e.g., in the case of extensive stirring (- rotating disc electrode). It is the case at a thin film, in a thin layer cell, and a thin cell sandwiched with an anode and a cathode. Finite diffusion causes a decrease of the current to zero at long times in the - Cottrell plot (-> Cottrell equation, and - chronoamperometry) or for voltammetric waves (see also - electrochemical impedance spectroscopy). Finite diffusion generally occurs at -> hydrodynamic electrodes. 

The electrochemistry of [M(TRPyP)]X4 modified electrodes exhibited several redox waves in nonaqueous media. However, in aqueous solution, only a characteristic pair of sine-shaped waves is found at = 0.92 and = 0.99 V (20 mV s ) in the CVs (121,122,250) associated with the Ru(lll/ll) redox couple (Fig. 32). The conductivity of such molecular films is associated with an electron-hoping mechanism, reaching a maximum at the redox potential. The charge-diffusion constant was estimated to be d] C= 1.0 x 10 molcm s from the linear portion of the Cottrell plots. 

This indicates that, under these conditions, there is a linear relationship between the current and the 1/square root of time. A plot of i vs. t V is often referred to as the Cottrell plot. 

The slope and intercept of the Cottrell plot can be measured. Since the slope is determined by n, A, C, and D, one of these parameters can be calculated, provided the other three are knovm. 

The rate of charge transfer has been represented by an apparent diffusion coefficient of the charges (App), which is obtained from the slope of a conventional Cottrell plot (Eq. (14-11)) by chronoamperometry or chronospectrometry [47], where / is the current density, n the number of charges involved in the reaction, F Faraday s constant, c the redox-center concentration and t the reaction time. 

Linear Cottrell plots with zero intercepts were obtained for CA experiments for times up to 20 msec the slopes of which were used to evaluate the rate of... 

The modified electrodes are electrochemically active and present a pair of sine-shaped waves at pc = 0.92 and fpa = 0.99 V (20 mV s ), whose intensities are directly proportional to the scan rate, as expected for redox species immobilized on the electrode surface . A linear Cottrell plot has been obtained for the chronoamperometry data but with a negative deviation at longer times, where the charge propagation is not diffusion controlled. The estimated charge-... 

For thick films at not too high D values from the linear section of the Cottrell plot, D l c can be determined however, in the case of thin films this section might be too short to allow us to derive reliable D values. If the rate of charge transfer... 

FIGURE 1.47. Schematic of a Cottrell plot for an electroactive polymer film. The plot was... 

Hence we see that a plot of i versus is very diagnostic it is termed a Cottrell plot (see Fig. 1.47). The simple linearity implied in either Eqn. 259 or Eqn. 260 is valid only for short time periods. At longer time periods when t DdlL the concentration polarization in the film reaches the outer surface of the latter, and the diffusion-limited current falls below that given by the simple Cottrell expression due to the onset of the finite-diffusion terms outlined in the more complete expressions (see Eqns. 256-258). This fact is illustrated in Fig. 1.47. 

All that we can estimate from the slope of the Cottrell plot is the compound factor Darior Hence to be able to estimate Z>cr,... 

Note this plot is not expected to go through the origin, because of the decay to a constant value at a microelectrode, although the slope will be Cottrellian at short enough times. The limiting current value is not small enough compared to the current values reported in the table of data for the intercept of a Cottrell plot to be near zero. 

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