Potential-time curves, in constant-current

Potential-Time Curves in Constant-Current Electrolysis... 

POTENTIAL-TIME CURVES IN CONSTANT-CURRENT ELECTROLYSIS... 

Growth of isolated nuclei at an electrode surface is eventually limited when they start to coalesce due to their number and size and the size of the electrode area. Analysis of the overlap problem can be performed by use of the Avrami theorem [152] and leads to maxima in the current—time curves at constant potential. Potentiostatic conditions are convenient for the study of these phenomena because electrochemical rate coefficients and surface concentration conditions are well controlled. 

B. Chronopotentiometry (Formerly called Voltammetry at Constant Current). These terms were applied by Delahay et al (Refs 4 5) to measurements in which the course of polarization of an electrode (immersed in an unstirred soln) under forced constant current was followed potentiometrically as a function of time. The potential-time curve recorded in the presence of a depolarizer is characterized by a transition time, during which the rate of change of potential is relatively small. This... 

Potentiometric stripping analysis is carried out in several stages. After electrochemical generation of the mercury film on a graphite substrate, the elements to be determined are accumulated by electrolysis at constant potential. The next stage is the oxidation of the deposited elements by the oxidant present in the. solution. For this, the current circuit is disconnected. The deposited analytes are stripped in the order of their electrochemical jxitentials. Anodically deposited precipitates can similarly be stripped by chemical reduction. In all cases, potential - time curves with transition times proportional to concentration result [39]-[41]. 

A second approach to coulometry is to use a constant current in place of a constant potential (Figure 11.23). Controlled-current coulometry, also known as amperostatic coulometry or coulometric titrimetry, has two advantages over controlled-potential coulometry. First, using a constant current makes for a more rapid analysis since the current does not decrease over time. Thus, a typical analysis time for controlled-current coulometry is less than 10 min, as opposed to approximately 30-60 min for controlled-potential coulometry. Second, with a constant current the total charge is simply the product of current and time (equation 11.24). A method for integrating the current-time curve, therefore, is not necessary. 

Coulometry. If it can be assumed that kinetic nuances in the solution are unimportant and that destmction of the sample is not a problem, then the simplest action may be to apply a potential to a working electrode having a surface area of several cm and wait until the current decays to zero. The potential should be sufficiently removed from the EP of the analyte, ie, about 200 mV, that the electrolysis of an interferent is avoided. The integral under the current vs time curve is a charge equal to nFCl, where n is the number of electrons needed to electrolyze the molecule, C is the concentration of the analyte, 1 is the volume of the solution, and F is the Faraday constant. 

Curve 1 in Fig. 5 gives an example of the oscillation of membrane current observed with the liquid membrane system as in Eq. (3) by applying a constant AFwi-w2 of —0.48 V and measuring the time course of the current through the LM, /wi-w2- The cell used was the same as that used for the measurement of the potential oscillation, except a tetraphenyl-arsonium ion selective electrode [26,27], TPhAsE, was employed as a reference electrode in LM of NB ... 

In deriving theoretical equations of the current-potential (or time) curves of ion transfer of an acid we shall make essentially the same assumptions as the assumption 1-6 above. It is noted here that theoretical equations of the more general case, that is, of a dibasic acid, such as expressed by AH2 = AH + H, AH = A + H, can be derived [24], but are not included here, to save space. The formal formation constant, and formal dissociation constant,, in the a phase is defined by... 

The case of the prescribed material flux at the phase boundary, described in Section 2.5.1, corresponds to the constant current density at the electrode. The concentration of the oxidized form is given directly by Eq. (2.5.11), where K = —j/nF. The concentration of the reduced form at the electrode surface can be calculated from Eq. (5.4.6). The expressions for the concentration are then substituted into Eq. (5.2.24) or (5.4.5), yielding the equation for the dependence of the electrode potential on time (a chronopotentiometric curve). For a reversible electrode process, it follows from the definition of the transition time r (Eq. 2.5.13) for identical diffusion coefficients of the oxidized and reduced forms that... 

If the nonlinear character of the kinetic law is more pronounced, and/or if more data points than merely the peak are to be used, the following approach, illustrated in Figure 1.18, may be used. The current-time curves are first integrated so as to obtain the surface concentrations of the two reactants. The current and the surface concentrations are then combined to derive the forward and backward rate constants as functions of the electrode potential. Following this strategy, the form of the dependence of the rate constants on the potential need not be known a priori. It is rather an outcome of the cyclic voltammetric experiments and of their treatment. There is therefore no compulsory need, as often believed, to use for this purpose electrochemical techniques in which the electrode potential is independent of time, or nearly independent of time, as in potential step chronoamperometry and impedance measurements. This is another illustration of the equivalence of the various electrochemical techniques, provided that they are used in comparable time windows. 

The formation of pores during anodization of an initially flat silicon electrode in HF affects the I-V characteristics. While this effect is small for p-type and highly doped n-type samples, it becomes dramatic for moderate and low doped n-type substrates anodized in the dark. In the latter case a reproducible I-V curve in the common sense does not exist. If, for example, a constant potential is applied to the electrode the current density usually increases monotonically with anodization time (Thl, Th2]. Therefore the I-V characteristic, as shown in Fig. 8.9, is sensitive to scan speed. The reverse is true for application of a certain current density. In this case the potential jumps to values close to the breakdown bias for the flat electrode and decreases to much lower values for prolonged anodization. These transient effects are caused by formation of pores in the initially flat surface. The lowering of the breakdown bias at the pore tips leads to local breakdown either by tunneling or by avalanche multiplication. The prior case will be discussed in this section while the next section focuses on the latter. 

If a constant current i equal to 60% of the limiting current found for the most concentrated solution of precursor (i.e., i = 0.6 i,) is applied to the cell, then the ratio i/i, is 0.6 and is represented by line A of Figure 25.1. The potential of the electrode at the time the constant current is applied would be the potential at the intersection of line A with the curve. Now, consider a second precursor solution which is only 90% as concentrated as the first one. The new limiting current, i[, would be nine-tenths of the original limiting current, or ij = 0.9i,. However, in a constant-current experiment, the applied current would not change, so the new ratio, i/ij, is larger than the former ratio and can be calculated as... 

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