Derivative Chronopotentiometry

In derivative chronopotentiometry, the potential response signal of a normal chronopotentiometry experiment is electronically differentiated, and this rate of change of potential with time, dE/dt, is recorded as a function of time, as shown in Figure 4.9 [12]. The minimum in a derivative chronopotentiogram is quantitatively related to the transition time. Thus for a reversible couple,... 

Figure 4.9 Derivative chronopotentiometry. (A) Current excitation signal. (B) Potential response signal. (C) Monitored response dE/dt.

Equation (7.116) indicates that the charge-potential curves for reversible processes are only dependent on the square wave amplitude Sw and are independent of the frequency / = 1 jh and the staircase amplitude AEs. As a consequence, they are superimposable on those obtained at any differential electrochemical technique, such as DSCVC, provided that the differences between the successive potential pulses coincide (AE = 2 sw)- Moreover, when this difference is much less than RT/F (i.e., less than 25 mV at T = 198 K), the responses obtained in Cyclic Voltammetry (CV), Alternating Current Voltammetry, Potentiometric Stripping Analysis (PSA) and also in any Reciprocal Derivative Chronopotentiometry (RDCP) fulfill [5, 74, 75] ... 

A frequently used method for determination of surfactants of various types is tensammetry, A large variety of nonionic surfactants was analyzed by means of derivative chronopotentiometry mainly for water purity determination in respect to fisheries[11]. The concentration range for most of the surfactants investigated is within the range of 1-200 mg 1. ... 

Chen L, Lv C, Chen J, Bi S (2013) Numerical simulation study on cyclic redpiocal derivative chronopotentiometry of reversible electrode reaction coupled with Langmuir adsorption. Electrochim Acta 93 222-229... 

Fekner Z (2008) Eligital simulation of cyclic chronopotentiometry turd reciprocal derivative chronopotentiometry for linear adsorption systems. Collect Czechoslov Chem Commun 73 201-228... 

HMDE has been mostly used [417]. For sensitive electroanalytical measurements, derivative chronopotentiometry was introduced [418, 419]. 

Analogously to eqn. 3.72 for stationary electrodes and a reversible redox couple of soluble ox and red, Kies derived for chronopotentiometry at a dme via insertion in the Nernst equation... 

Chronopotentiometry has also been used to determine chloride ions in seawater [31]. The chloride in the solution containing an inert electrolyte was deposited on a silver electrode (1.1 cm2) by the passage of an anodic current. The cell comprised a silver disc as working electrode, a symmetrical platinum-disc counter-electrode and a Ag-AgCl reference electrode to monitor the potential of the working electrode. This potential was displayed on one channel of a two-channel recorder, and its derivative was displayed on the other channel. The chronopotentiometric constant was determined over the chloride concentration range 0.5 to 10 mM, and the concentration of the unknown solution was determined by altering the value of the impressed current until the observed transition time was about equal to that used for the standard solution. 

Figure 6.20 Current-reversal chronopotentiometry with derivative output.

The mercury-pool electrode. Mercury pools of sufficient diameter to approach a planar configuration obey the equations derived for linear diffusion to a planar electrode. This has certain theoretical advantages because of the large number of equations that have been derived for the planar electrode geometry, especially in terms of constant-current chronopotentiometry and linear-potential sweep chronoamperometry. 

The oxidation potentials of substituted ferrocenes are, perhaps not unexpectedly, found to be a sensitive function of the number and type of ring substituents. The formal oxidation potentials of a considerable number of mono- and disubstituted ferrocene derivatives have been determined titrimetrically 19, 20, 31, 35, 38), as well as by chronopotentiometry 5, 25, 27, 28, 29, 62, 63) and polarography 2, 39, 56, 57, 58). The oxidation potentials of these substances appear to correlate rather well with disubstituted ferrocenes, although Nesmeyanov and his coworkers have more recently claimed 35) that a better correlation is obtained with the Taft constants 53, 54). 

Consider a chronopotentiometric experiment dealing with two components that are reversibly reduced in waves separated by 500 mV. Derive an expression for the second transition time in an experiment carried out in a thin-layer cell. Compare and contrast the properties of multicomponent systems in thin-layer chronopotentiometry with those of the semi-infinite method. 

Derive the limiting values of for chronopotentiometry with a following catalytic reaction... 

Derive the equation for the E-t curve for chronopotentiometry with a following catalytic reaction (Ei-C-). See (12.3.34) and (12.3.35). Show that as / -> 0, the E-t curve for a nemstian electrode reaction is approached. What is the limiting (KP) behavior as A oo Plot a curve showing how r/4 varies with A. 

Tomschik, M., Havran, L., Palecek, E., Heyrovsky, M. (2000). The presodium catalysis of electroreduction of hydrogen ions on mercury electrodes by metallothionein an investigation by constant current derivative stripping chronopotentiometry. Electroanalysis 12, 274-279. 

A different boundary condition is the Neumann condition or derivative boundary condition. An example is seen with chronopotentiometry. Equation sets (4 and 10). The procedure here is that a value of Co is computed such that it fits with the concentration profile (set of points C. .. Cn), so as to satisfy the gradient specification. Using the simple two-point approximation (33) and given a G value, this yields an expKcit expression for Co,... 

Figure 23 illustrates the form of the curve for the determination of Cd, Tl, and Pb by stripping chronopotentiometry. The normal potential - time curve (A) is compared with the second derivative (B). from which the transition times can be more simply and accurately obtained. A TMFE coated in situ is used for the accumulation. 

If we are simulating a reaction where Cq varies with time for all involved species then we would like to compute these accurately also. For simplicity, take again the case of chronopotentiometry, only one species being involved. The diffusion equation results, by the process described in Sect. 5.4.1, in system 5.129. To get Cq (which is needed to solve that system), we cannot simply add its diffusion-derived equation we need an anchor for it. This we get from the constant current or gradient G at U = 0. Again Eq. 5.124 is the key, expressed as Eq. 5.132. This yields Cq as a function of all other C and can then be substituted for in system 5.129. Then, Cq will adjust itself along with the whole profile. Without any special effort, Cq is found implicitly in the solution. This was developed by Pons (1981A). 

Several precautions and limitations should be mentioned upon the application of chronopotentiometry as an electrochemical method to analyze interface properties of layered-modified-electrodes, and, specifically, monolayer-function-alized-electrodes (1) The chronopotentiometric pulse results in a potential shift on the electrode after the transition-time, x, resulting in the discharge of the electrolyte. This potential shift often ruins the chemically functionalized layer on the electrode (e.g., thiolated monolayers on Au-electrodes). Thus, it is essential to terminate the chronopotentiometric pulse at shorter time-intervals than the transition time, X, in order to eliminate the destruction of the functionalized electrode. (2) The electrode resistance, R, values derived from the chronopotentiometric exper-... 

FIGURE 2.8 Chronopotentiometries at nil current for Pt deposits onto gold. Amounts of deposited Pt 10 mC. These Pt layers were previously charged with different amounts of charge. Electrolytic solution 0.1 mol.L" Nal in DMF. Saturation ratios are derived from theoretical values (a) 100%, (b) 85%, (c) 75%, and (d) 50%. Potentials are referred to SCE electrode (Cougnon, C., Ph.D. thesis, Universite de Rennes 1, 2002). 

Unlike cyclic voltammetry, the solution of Pick s diffusion equations [Eqs. (2.34) and (2.35)] for chronopotentiometry can be obtained as an exact expression by applying appropriate boundary conditions. For a reversible reduction of an electroactive species [Eq. (2.9)], the potential-time relationship has been derived by Delahay for the case where O and R are free to diffuse to and from the electrode surface, including the case where R diffuses into a mercury electrode. 

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