Chronoamperometry concentration profiles

Fig. 3 Chronoamperometry (a) typical excitation signal (b) current response and concentration profiles [(c) first step (d) second step educt solid lines, product dotted lines five...

Figure 6.3 Plots of concentration against distance from the electrode solution interface ( concentration profiles ) as a function of time during the chronoamperometry experiment for (a) the concentration of Tl (as reactant) remaining in solution (b) the concentration of Tl + (as product). Movement of the material through the solution is by diffusion, i.e. a convection-free situation.

Fig. 7.35. Development of diffusion concentration profiles in ensembles of microelectrodes. Concentration distortions at very short times during chronoamperometry or fast sweep rates during (a) cyclic voltammetry, (b) intermediate times or sweep rates, and (c) long times or slow sweep rates. Voltam-metric responses are shown schematically. (Reprinted from B. R. Scharifker, Microelectrode Techniques in Electrochemistry, in Modem Aspects of Electrochemistry, Vd. 22, J. O M. Bockris, B. E. Conway, and R. E. White, eds., Plenum, 1992, p. 505.)...

There is an important electrochemical technique called chronoamperometry (i.e., current measured as a function of time), where a vacancy is maintained at the surface (Chap. 3). The electrode potential is controlled at a value sufficient to immediately react any sample molecule that diffuses to the surface. This results in the sequence shown in Figure 2.9. The top drawings indicate consumption of the reactant at three times following the application of the potential. The corresponding concentration profiles are also shown. The bottom sequence indicates creation of product at the same three times. The sample molecules try their best to fill in the vacancy, but the electrode reaction prevents this. If the... 

Fig. 6.6 Relative concentration profiles for O (solid line) and R(dots) near a planar working electrode (a) at f = 0.5, 2 and 7 seconds, corresponding to a chronoamperometry experiment, and (b) at f = 10.5,12 and 17 seconds, corresponding to the second half of a double potential step chronoamperometry experiment.

Fig. 3.14 Single potential step chronoamperometry at large overpotentials, (a) Variation of the limiting current with time (b) concentration profiles at the end of the pulse. Planar electrode. / jrn (/)//ii , (t p) /d o"e (/)//d>1c"e ( p) f°r the two kinetic models considered. k° = 10-4 cm/s. Reproduced with permission of reference [30]. In this Figure X = A.

Dimensionless analysis — Use of dimensionless parameters (-> dimensionless parameters) to characterize the behavior of a system (- Buckinghams n-theorem and dimensional analysis). For example, the chronoampero-metric experiment (-> chronoamperometry) with semiinfinite linear geometry relates flux at x = 0 (fx=o, units moles cm-2 s-1), time (t, units s-1), diffusion coefficient (D, units cm2 s-1), and concentration at x = oo (coo, units moles cm-3). Only one dimensionless parameter can be created from these variables (-> Buckingham s n-theorem and dimensional analysis) and that is fx=o (t/D)1/2/c0C thereby predicting that fx=ot1 2 will be a constant proportional to D1/,2c0O) a conclusion reached without any additional mathematical analysis. Determining that the numerical value of fx=o (f/D) 2/coo is 1/7T1/2 or the concentration profile as a function of x and t does require mathematical analysis [i]. 

If charge diffusion is significantly slower so that the distance of charge transport, L, (=2(Dt) ) is clearly smaller than the thickness of the lamina, 5, the electrochemical response will be equivalent to that recorded when reactants freely diffuse from an infinite volume of solution to the electrode. This situation, often termed as thick-layer behavior, corresponds to semi-infinite boundary conditions, and concentration profiles such as that shown in Figure 2.5c are then predicted. Accordingly, Cottrell-type behavior is observed, for instance, in cyclic voltammetry (CV) and chronoamperometry (CA). In this last technique, a constant potential sufficiently cathodic for ensuring diffusion control in the reduction of Ox to Red is applied. The resulting current-time (i-t) curves should verify the Cottrell equation presented in the previous chapter (Equation (1.3)). 

Figure 5.5 Chronoamperometry, depletion of concentration at the electrode surface, and growth with time of concentration profiles into the electrolyte.

A simple analytical expression is also available for the complete concentration profile of species A in chronoamperometry ... 

Figure 4.18 shows, during a chronoamperometry experiment, typical concentration profiles, at different instants, of the species consumed at the left electrode with no interaction with the right electrode. A constant potential is imposed to an electrode over time and the result in a fast redox system is that the interfacial concentration of the consumed species (here at the left electrode) is fixedin such a case, the slope of the concentration profile at the interface, namely the current, changes over time . ... 

In this chronoamperometry experiment the thickness of the diffuse layer increases with time. One can gain a good order of magnitude for this thickness by looking at the intersection between the interfacial slope of the concentration profile and the initial flat profile VKDt I Even if this value is sometimes confused with the diffusion layer thickness, it is best still to distinguish between them for instance, at a distance equal to -sJnDt, the concentration is still 18% off from the initial concentration. The thickness of the diffusion layer is equal to 2.0 VnDt for an accuracy of 1% and 2.6 VnDt for an accuracy of 0.1%. 

Figure 4.18- Time evolution of the concentration profile of a species consumed in a chronoamperometry experiment...

Firstly, let us note the fact that shortly after the start of the experiment, the concentration profile follows the same pattern as that of chronoamperometry In seml-infinite geometric conditions (see figure4.18 in section 4.3.1.3). The specific condition of there being zero flux in the zone located far away from the left Interface leads to a constant... 

Explain why double potential step chronoamperometry is able to distinguish between the two mechanisms. Include a sketch of the concentration profiles immediately before the second step. 

Fig. 10.9 Chronoamperometry at a potential corresponding to Co(0,t) = 0 (a) perturbation signal (b) concentration profiles at increasing times (c) signal recorded i =f(t) according to Cottrell s equation normalization in (b) is performed by dividing Co(x,t) by Cq with respect to the bulk concentration, which is quite common practice...

The product D0 (dCo/dx)x=0 t is the flux or the number of moles of O diffusing per unit time to unit area of the electrode in units of mol/(cm2 s). (The reader should perform a dimensional analysis on the equations to justify the units used.) Since (3Co/3x)x=01 is the slope of the concentration-distance profile for species O at the electrode surface at time t, the expected behavior of the current during the chronoamperometry experiment can be determined from the behavior of the slope of the profiles shown in Figure 3. IB. Examination of the profiles for O at x = 0 reveals a decrease in the slope with time, which means a decrease in current. In fact, the current decays smoothly from an expected value of oo at t = 0 and approaches zero with increasing time as described by the Cottrell equation for a planar electrode,... 

The profiles in D correspond to a potential that is sufficiently negative of the formal electrode potential that the concentration of O is effectively zero at the electrode surface. The conditions for these profiles are analogous to those for chronoamperometry (Sec. II.A, Fig. 3.1). Once the potential has reached a value sufficient for a zero reactant-surface concentration, the potential and its rate of change become immaterial to the diffusion-controlled current. In other words, should the scan be stopped at the potential for D, the current will follow the same time course as if the scan had been continued. 

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