Controlled-Current Methods

Both the automatic coulometric titration of petroleum streams and the continuous monitoring of pesticides and sulfur-halogen compounds indicate that the coulometric titrator method is amenable to the automatic maintenance of the concentration of a component in a solution system. A manual version of this approach has been used to study the kinetics of hydrogenation of olefins as well as to determine the rate of hydrolysis of esters.12 The latter system is a pH-stat that is based on the principles of coulometric titrations. Equations (4.9)-(4.11) indicate how this approach is applied to the evaluation of the rate constants for ester hydrolysis. A similar approach could be used to develop procedures for kinetic studies that involve most of the electrochemical intermediates summarized in Table 4.1. The coulometric titration method provides a convenient means to extend the range of systems that can be subjected to kinetic study in solution. 

The principle of controlled current electrolysis has been known since the beginning of this century.21 However, the utilization of this form of electrochemistry remained dormant for 50 years until three groups of investigators illustrated its many advantages for analytical and physicochemical measurements.22 24 Several works describe this technique in detail,25 27 and other re- 

The point at which the sample ion is depleted in the vicinity of the working electrode is called the transition time r this quantity is related to a number of variables including the sample-ion concentration. In 1901 Sand21 derived the equation that describes the functional dependence of the transition time for a constant-current electrolysis of a diffusion-controlled process 

A = area of the working electrode D = diffusion coefficient of the electroactive species C = concentration of the electroactive species 

This relation can be expanded for a two-step electrolysis involving two sample species. Because the first species continues to diffuse to the electrode even after the first transition time, the expression is more complex than a simple additive relation  

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In contrast to the previous voltammetric methods at stationary electrodes, chronopotentiometry, which is based on interpretation of E-t curves, represents a controlled current method. 

Controlled potential methods have been successfully applied to ion-selective electrodes. The term voltammetric ion-selective electrode (VISE) was suggested by Cammann [60], Senda and coworkers called electrodes placed under constant potential conditions amperometric ion-selective electrodes (AISE) [61, 62], Similarly to controlled current methods potentiostatic techniques help to overcome two major drawbacks of classic potentiometry. First, ISEs have a logarithmic response function, which makes them less sensitive to the small change in activity of the detected analyte. Second, an increased charge of the detected ions leads to the reduction of the response slope and, therefore, to the loss of sensitivity, especially in the case of large polyionic molecules. Due to the underlying response mechanism voltammetric ISEs yield a linear response function that is not as sensitive to the charge of the ion. 

In electrogravimetry [19], the analyte, mostly metal ions, is electrolytically deposited quantitatively onto the working electrode and is determined by the difference in the mass of the electrode before and after the electrolysis. A platinum electrode is usually used as a working electrode. The electrolysis is carried out by the con-trolled-potential or the controlled-current method. The change in the current-potential relation during the process of metal deposition is shown in Fig. 5.33. The curves in Fig. 5.33 differ from those in Fig. 5.31 in that the potentials at i=0 (closed circles) are equal to the equilibrium potential of the M +/M system at each instant. In order that the curves in Fig. 5.33 apply to the case of a platinum working electrode, the electrode surface must be covered with at least a monolayer of metal M. Then, if the potential of the electrode is kept more positive than the equilibrium potential, the metal (M) on the electrode is oxidized and is dissolved into solution. On the other hand, if the potential of the electrode is kept more negative than the equilibrium potential, the metal ion (Mn+) in the solution is reduced and is deposited on the electrode. 

When metal ion M"+ is deposited by the controlled-current method, the electrode potential during the electrolysis changes in the order T, 2, 3, 4, 5, 6 in Fig. 5.33 and the next reduction process occurs near the end of the electrolysis. If the solution is acidic and the next reduction process is hydrogen generation, its influence on the metal deposition is not serious. However, if other metal is deposited in the next reduction process, metal M is contaminated with it. In order that two metal ions M"1+ and M "21 can be separated by the controlled-current method, the solution must be acidic and the reduction of hydrogen ion must occur at the potential between the reductions of the two metal ions. An example of such a case is the separation of Cu2+ and Zn2+ in acidic solutions. If two metal ions are reduced more easily than a hydrogen ion (e.g. Ag+ and Cu2+), they cannot be separated by the controlled-current method and the controlled-potential method must be used. 

There are three ways to control the concentration ratios at the electrode surface. One can control the current, the electrode potential, or the bulk concentrations of the oxidized and reduced forms of the main couple. The two forms of small-amplitude control and three methods of controlling the overall surface concentrations produce a total of six overall control methods examples of all six have appeared in the literature. When the small-amplitude current is controlled, the experimenter has only a very indirect influence on whether the small-amplitude limit is exceeded. In addition, the magnitude of the potential response is reciprocally related to the bulk concentration of the electroactive species. For these reasons, small-amplitude controlled-current methods are encountered very infrequently. Because of the problems associated with small-amplitude current-control methods, we will not consider them further. 

From these equations, it is seen that the experimental variables in a controlled-current coulometric experiment are current and time, and it is possible to identify the following components of an appropriate apparatus an electrolysis cell, a current source, a method of measuring elapsed time (or a method of measuring coulombs), and a switching arrangement to control experimental variables. Electrochemical experiments using controlled-current methods are widespread and include titrimetry, kinetic studies, process stream analysis, and others (see Chap. 4). 

ELECTROCHEMICAL TITRATIONS AND CONTROLLED-CURRENT METHODS reaction... 

A fundamental disadvantage of controlled-current techniques is that double-layer charging effects are frequently larger and occur throughout the experiment in such a way that correction for them is not straightforward. Treating data from multicomponent systems and stepwise reactions is also more complicated in controlled-current methods, and the waves observed in E-t transients are usually less well-defined than those of potential sweep i-E curves. 

Controlled-current methods can be of particular value when the process being studied is the background process, such as solvated electron formation in liquid ammonia or reduction of quaternary ammonium ion in an aprotic solvent. A simple method for determination of the thickness of metal films is by anodic stripping at constant current. Working with background processes in a controlled-potential mode is often difficult. 

General Theory of Controlled-Current Methods 307 Response... 

General Theory of Controlled-Current Methods 309 The inverse transform of this equation yields the expression for Co(x, t) ... 

The effect of double-layer charging is clearly most important at small r values (see equation 8.3.20). Problems with distorted E-t curves and the difficulty of obtaining corrected T values have discouraged the use of controlled-current methods as opposed to con-trolled-potential ones. 

Generally, except for the simpler apparatus involved, controlled-current electrolysis offers no advantages over controlled-potential methods. With the commercial availability of suitable potentiostats, controlled-current methods are being used less frequently in analysis and lab-scale preparative electrolysis. For large-scale electrosynthesis or separations involving very high currents, especially in flow systems where the reactants are... 

IR drop generated by the Ri of a voltage source compromises accurate potential control, particularly for high cell currents. This point led many early investigators to prefer controlled current methods. A real current source can be considered to consist of an ideal current source in parallel with an internal resistance (Fig. lb). Current passing through the parallel resistance... 

Different electrochemical techniques depend on whether they are bulk methods as in conductometry or interfacial methods. The latter may be static as in potentiometry or dynamic. Dynamic methods are classified on the basis of the current used. Conductometry uses a constant current but controlled current methods include voltametry, amperometry and coulometry. 

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