Chronoamperometric conditions

Deposition of mercury at boron-doped diamond (BDD) and platinum electrodes has also been studied [33]. Deposition and oxidation of mercury was performed by cyclic voltammetry from the solution of 1 mM Hg2 ( 104)2 in 1 M Na l04. In order to learn more about this deposition, it was carried out also under chronoamperometric conditions. The results obtained are shown in Fig. 2 in the form of dimensionless current-time transients. Experimental curves obtained at two different overpotentials were compared with the theoretical curves calculated for instantaneous and progressive nucleation. A good agreement of experimental plots with the instantaneous nucleation mechanism was... 

This equation is only approximate, due to the approximate nature of (7.12). However, it expresses the important characteristics of the experiment done under constant potential, that is, chronoamperometric conditions. 

Figure 2.62 Chronoamperometric conditioning of n-Si(l 11) in 0.1 M NH4F, pH 4 potentials A and C correspond to the respective light intensities in Figure 2.60 and indicate divalent and tetravalent dissolution,...

F(y), G(y), and H y) are shown in the figure. Around the center of the base of the cylinder, where the metal disk lies, the axial component of the solution velocity is most important, since the electroactive material is transported towards the surface in this direction only. Under chronoamperometric conditions, a diffusion layer develops at the electrode surface and extends as far into the solution as the flux at the surface is not equal to the rate of mass transport in the bulk of the solution. Under steady-state conditions and the laminar flow of the solution, the distance S depends on the electrode rotation rate 8 = where D is the diffu-... 

The diffusion equation including the delay of a concentration flux from the formation of a concentration gradient, called diffusion with memory, was formulated by Aoki and solved under chronoamperometric conditions (Aoki, 2006). A slower decay than predicted by the Cottrell equation was obtained. 

In general, for SECM dissolution, under the conditions outlined earlier, where the solution is initially saturated with respect to the solid material, the UME cunent approaches that for an inert surface as the rate constant decreases. On the other hand, the flux of material from the CTystal surface increases with the dissolution rate constant, increasing up to a point where the UME response is limited by mass transfer between the tip and the substrate, that is, the dissolution process becomes diffusion-controlled. Under these conditions, the kinetics are sufficiently fast to maintain the concentration at the substrate at the saturated solution value and the induced dissolution approach curve resanbles that for positive feedback. Under potential step chronoamperometric conditions, the time taken for the current to approach a steady value obviously decreases with increasing rate constant [50-52]. 

Given that, under the defined conditions, there is no interfacial kinetic barrier to transfer from phase 2 to phase 1, the concentrations immediately adjacent to each side of the interface may be considered to be in dynamic equilibrium throughout the course of a chronoamperometric measurement. For high values of Kg the target species in phase 2 is in considerable excess, so that the concentration in phase 1 at the target interface is maintained at a value close to the initial bulk value, with minimal depletion of Red in phase 2. Under these conditions, the response of the tip (Fig. 11, case (a)] is in agreement with that predicted for other SECM diffusion-controlled processes with no interfacial kinetic barrier, such as induced dissolution [12,14—16] and positive feedback [42,43]. A feature of this response is that the current rapidly attains a steady state, the value of which increases... 

Under conditions of nonlimiting interfacial kinetics the normalized steady-state current is governed primarily by the value of K y, which is the relative permeability of the solute in phase 2 compared to phase 1, rather than the actual value of or y. In contrast, the current time characteristics are found to be highly dependent on the individual K. and y values. Figure 16 illustrates the chronoamperometric behavior for K = 10, log(L) = —0.8 and for a fixed value of Kf.y = 2. It can be seen clearly from this plot that whereas the current-time behavior is sensitive to the value of Kg and y, in all cases the curves tend to be the same steady-state current in the long-time limit. This difference between the steady-state and chronoamperometric characteristics could, in principle, be exploited in determining the concentration and diffusion coefficient of a solute in a phase that is not in direct contact with the UME probe. 

The influence of an interfacial kinetic barrier on the transfer process is readily illustrated by fixing the concentrations and the diffusion coefficients of Red for the two phases and examining the current response of the UME as K is varied. For illustrative purposes, we arbitrarily set and y = 1, i.e., initially the equilibrium conditions are such that there are equal concentrations of the target solute in the two phases, and the solute diffusion coefficient is phase-independent. Figure 17 shows the chronoamperometric characteristics for several K values from zero up to 1000. Under the defined conditions, these values of K reflect the ease with which the transfer process can respond to a perturbation of the local concentration of Red in phase 1, due to electrolytic depletion. 

This is a case where another electrochemical technique, double potential step chronoamperometry, is more convenient than cyclic voltammetry in the sense that conditions may be defined in which the anodic response is only a function of the rate of the follow-up reaction, with no interference from the electron transfer step. The procedure to be followed is summarized in Figure 2.7. The inversion potential is chosen (Figure 2.7a) well beyond the cyclic voltammetric reduction peak so as to ensure that the condition (Ca) c=0 = 0 is fulfilled whatever the slowness of the electron transfer step. Similarly, the final potential (which is the same as the initial potential) is selected so as to ensure that Cb)x=0 = 0 at the end of the second potential step whatever the rate of electron transfer. The chronoamperometric response is recorded (Figure 2.7b). Figure 2.7c shows the variation of the ratio of the anodic-to-cathodic current for 2tR and tR, recast as Rdps, with the dimensionless parameter, 2, measuring the competition between diffusion and follow-up reaction (see Section 6.2.3) ... 

The simplest chronoamperometric technique is that defined as single potential step chronoamperometry. It consists of applying an appropriate potential to an electrode (under stationary conditions similar to those of cyclic voltammetry), which allows the electron transfer process under study (for instance Ox + ne — Red) to run instantaneously to completion (i.e. COx(0,0 —1 0). At the same time the decay of the generated current is monitored.20... 

As mentioned in the introduction to controlled potential electrolysis (Section 2.3), there are various indirect methods to calculate the number of electrons transferred in a redox process. One method which can be rapidly carried out, but can only be used for electrochemically reversible processes (or for processes not complicated by chemical reactions), compares the cyclic voltammetric response exhibited by a species with its chronoamperometric response obtained under the same experimental conditions.23 This is based on the fact that in cyclic voltammetry the peak current is given by the Randles-Sevcik equation ... 

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. 

It should be noted, however, that the changes in the voltammetric response are conditioned by the nature of the extent of the redox reaction across the solid. Thus, for organic solids in contact with aqueous electrolytes, and using the aforementioned model of Lovric, Scholz, Oldham, and co-workers [115-118], the propagation of the redox reaction should involve proton hopping coupled with electron hopping between adjacent immobile molecules [119-125]. Chronoamperometric data... 

Figure 3.31 illustrates the simplest example of LAPV at a stationary electrode. In this case we assume that the time delay td between pulses is such that the initial condition is restored. This implies that all concentration profiles are completely relaxed before the next pulse is applied and every pulse initiates a new chronoamperometric experiment. The length of td required to accomplish this will depend on the chemical reversibility of the system, being shorter for reversible reactions and longer for irreversible reactions. 

Several approaches to solving this expression for various boundary conditions have been reported [25,26]. The solutions are qualitatively similar to the results at a hemisphere at very short times (i.e., when (Dt),y4 rD), the Cottrell equation is followed, but at long times the current becomes steady-state. Simple analytical expressions analogous to the Cottrell equation for macroplanar electrodes or Equation 12.9 for spherical electrodes do not exist for disk electrodes. For the particular case of a disk electrode inlaid in an infinitely large, coplanar insulator, the chronoamperometric limiting current has been found to follow [27] ... 

Determination of morphine using chronoamperometric transduction may serve as an example of the competitive procedure presented above [25], The linear dynamic concentration range was 0.1-10 pg mL 1 morphine. Codeine played the role of an electroinactive competitor. Microorganism contamination was removed from the MIP film prior to morphine determination using an autoclave. Performance of this chemosensor was much improved with respect to those of traditional biosensors in terms of stability under extremely harsh chemical conditions and elevated temperature. 

Fig. 11.10 Parallel chronoamperometric screening of a 64-element, thin film electrocatalyst library for the oxidation of methanol. The library contained a diverse set of binary, ternary and quaternary electrocatalyst compositions consisting of Pt in combination with W, Ni, Co and Ru. The graph plots current vs. time and channel number. Conditions 1 M methanol, 0.5 M H2S04, room temperature, = + 450 mV/RHE, test time = 5 min. For clarity, channel numbers 2-4,10,12,19, 20, 23, 26-29, 42,45 and 57 are omitted. (Reproduced from [18]).

Fig. 11.17 Chronoamperometric screening results from the ternary catalyst library described in Figs. 11.15 and 11.16. Surface-area-normalized activity values of each individual composition are plotted as a function of composition. Color-coding indicates activity red = high, blue = low. The pt-Ru binary compositions are connected by a solid line to underscore the activity trends observed in this binary system. Conditions 1 M methanol, 0.5 M H2S04, 550 mV/RHE, 5 min.

Figure 2 Chronoamperometric and chronogravimetric data for a PBT film immersed in 0.1 mol dm 3 TEAPF. The potential was stepped from 0V to 1.05V held at 1.05V for 15s, then stepped back to 0V. Values of 5>pf6 were calculated according to equation [3]. Charge data are referred to tne initial condition at 0V.

The latest contribution to the theory of the EC processes in SECM was the modeling of the SG/TC situation by Martin and Unwin [86]. Both the tip and substrate chronoamperometric responses to the potential step applied to the substrate were calculated. From the tip current transient one can extract the value of the first-order homogeneous rate constant and (if necessary) determine the tip-substrate distance. However, according to the authors, this technique is unlikely to match the TG/SC mode with its high collection efficiency under steady-state conditions. 

Both chronoamperometric and steady-state responses were calculated by solving the related equations numerically. An analytical approach discussed in the previous section is equally applicable to the ErC2i mechanism under steady-state conditions. Equation (38) was verified using the data simulated from Ref. [22], and I T versus I s dependencies were plotted for different values of L [22]. Although for the ErC2i mechanism, the choice of k is less straightforward than for Ej-Cj, an acceptable fit for all the data points computed in Ref. [22] was obtained using k = c°k cd3/aD (Fig. 10b). This data was fit to Eq. (43) ... 

Fig. 10.15. Experimental (—) and theoretical (—) chronoamperometric response for the diffusion-limited oxidation of 2 x 10-3 mol dm-3 Fe(CN)S in 0.1 mol dm-3 KC1 at a rectangular electrode, 2.5 mm long and 6.25 mm wide, in a 0.5 mm high channel flow cell under channel stopped flow conditions. The initial volume flow rate of the solution was 0.197 cm3 s-1, which gave a limiting current at the channel electrode, defined as / . At time, f.top, solution flow was retarded (Evans et al., in preparation). The theoretical data has been simulated assuming Df (cn)2 = 6.5 x 10-6 cm2 s l.

If the chronoamperometric response of a - polymer-modified electrode is measured alone - in contact with inert - supporting electrolyte - Cottrell-type response can be obtained usually for thick films only, because at short times (f < 0.1-1 ms) the potential is not established while, at longer times (t > 10-100 ms), the finite diffusion conditions will prevail and / exponentially decreases with time. Another complication that may arise is the dependence of D on the potential in the case of - conducting polymer films [vi]. 

Figure 32. Amperometric response of rotating Cat/NiO modified GC electrode to H202, conditions -0.3 V constant potential, pH 7.0 and rotation speed is 2000 rpm, (A) successive addition of lOOpM and (B ) 1 liM insets plot of chronoamperometric current vs, H202 concentration and linear calibration curve for determination of KM. Reprinted from Biophysical Chemistry, 125, A.Salimi, E. Sharifi, A. NoorBakhash, S. Soltanian, Direct electrochemistry and electrocatalytic activity of catalase immobilized onto electrodeposited nano-scale islands of nickel-oxide, 546, Copyright( 2007), with permission from Elsevier.

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