Current-concentration relationships, potential

This section introduces basic theory behind the potential waveform applied during CV and the current response that should enable readers to follow the practical explanations given as follows for the case studies eited. A rigorous treatment and derivation of the diffusion equations relating transport phenomena with reaction rate kinetics at the electrode surface are not presented here instead, these are only shown in their final form. There are many classical electrochemistry textbooks that cover these topics, and a trip to a nearby library or accessing an online collection is fully warranted here. However, where necessary, we cover important assumptions about the derivation of current-voltage/current-concentration relationships. 

Information is obtained with this type of electrochemical sensor from either the combined cur-rent/potential-concentration relationship (voltammetry) or from the current-concentration relationship alone (amperometry). 

The second strategy which may be used to learn about the kinetics of an electrode reaction is illustrated in Fig. 7. As before, a potential (constant or varying) is imposed on the cell and a current—time relationship is monitored. However, instead of assuming a particular kinetic law, one processes the experimental current by semi-integration (see Sects. 5.2 and 5.4), thus enabling the surface concentrations to be calculated directly. Hence, the kinetics can be elucidated by a study that involves only the... 

Stirred-solution voltammetry utilizes current-voltage relationships that are obtained at a stationary electrode immersed in a stirred solution. In order to understand this aspect of electrochemistry, it is extremely useful to consider a typical current-voltage curve (voltammogram) in terms of the concept of concentration-distance profiles presented in the preceding section. The discussion will consider the potential, rather than the current, as the controlled variable. 

Modern dynamic electrochemical techniques offer additional enhancement of the information acquisition process, including selectivity and detection limit. Instead of holding the potential of the working electrode at a constant value, the potential is varied in some specific way. In that approach, we have a choice of several nonsteady-state electrochemical techniques. They are all derived from the basic current-voltage concentration relationship (Section 5.1). A complete discussion of these electroanalytical techniques can be found in electrochemistry textbooks (Bard and Faulkner, 2001). 

The most popular electroanalytical technique used at solid electrodes is Cyclic Voltammetry (CV). In this technique, the applied potential is linearly cycled between two potentials, one below the standard potential of the species of interest and one above it (Fig. 7.12). In one half of the cycle the oxidized form of the species is reduced in the other half, it is reoxidized to its original form. The resulting current-voltage relationship (cyclic voltammogram) has a characteristic shape that depends on the kinetics of the electrochemical process, on the coupled chemical reactions, and on diffusion. The one shown in Fig. 7.12 corresponds to the reversible reduction of a soluble redox couple taking place at an electrode modified with a thick porous layer (Hurrell and Abruna, 1988). The peak current ip is directly proportional to the concentration of the electroactive species C (mM), to the volume V (pL) of the accumulation layer, and to the sweep rate v (mVs 1). 

A similar technique is used to study the concentration - chemical potential relationships in nonstoichio-metric solids. In this case, -> solid materials are to be equilibrated with a gas phase, resulting in adsorption or desorption of a component the determination of compositional changes in the solid is based on the gas coulo-metric titration. The relaxation curves may be used to calculate the -> exchange currents and -> diffusion coefficients (see also -> Diffusion determination in solids). 

Figure 7.6 Current-voltage relationship for passive channel models of Equations (7.27) and (7.28). Sodium concentrations typical for the squid giant axon are used [Na+ ] = 437 mM [Na J = 50 mM. The sodium equilibrium potential is VNa = 58.5 mV. Conductance g a is set to 0.01 mS-cm-2. The permeability for the GHK model of Equation (7.28) is set so that both models predict the same current density at AT = 0. Figure adapted from [108],...

Anodic behavior of sihcon can best be characterized by i-V curves. Neglecting the details associated with a silicon substrate such as doping, the current-potential relationship of silicon in aqueous solutions can be considered to be principally determined by the pH and HE concentration as illustrated in Pig. 5.1. In nonalkaline and nonfluoride aqueous solutions, silicon as an electrode is essentially inert, showing a very small current at anodic potential due to the presence of a thin oxide film. In alkaline solutions, silicon is also passivated by an oxide film at anodic potentials but is active below the passivation potential, Vp. In fluoride solutions, the silicon electrode is active in the whole anodic region as shown by the large anodic current. 

Current/Voltage Relationships for Irreversible Reactions Many voltammetric electrode processes, particularly those associated with organic systems, are partially or totally irreversible, which leads to drawn-out and less well defined waves. The quantitative description of such waves requires an additional term (involving the activation energy of the reaction) in Equation 23-11 to account for the kinetics of the electrode process. Although half-wave potentials for irreversible reactions ordinarily show some dependence on concentration, diffusion currents are usually still linearly related to concentration many irreversible processes can, therefore, be adapted to quantitative analysis. 

This section introduces you to the factors that determine the overall rate of an electrode reaction in a system which is not stirred. This allows predictions of the shape of the resulting current/WE potential curves for a system which is under diffusion control. The work of llkovic in 1934 in deriving the current/analyte concentration relationship for the DME is covered and the llkovic equation is stated and partially derived. The Heyrovsky-Ilkovic equation (1935) is then derived this provides an explanation of the shape of the current WE potential curve. This curve now becomes a polarogram and the half-wave potential is defined and related to the polarogram. Finally the question of the reversibility of the electrode reaction is discussed and tests for reversibility are given. 

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