Electrode surfaces reactant concentration

At the infinite distance from the electrode surface, the concentrations of the reactant and product do not change ... 

Within its working window, an electrode can be depolarized by electroactive substances which are dissolved in the electrolyte. The electrochemical reaction on the electrode surface causes concentration gradients perpendicular to the electrode surface. The current is proportional to these concentration gradients. This relationship depends on the electrode geometry, on the hydrodynamic conditions in the solution (whether it is stirred, or not) and on the voltammetric technique. However, in all cases, the current reaches a maximum, or a limiting value, which is proportional to the bulk concentration of the reactant. This is called the concentration polarization of the working electrode. It is the basis of all analytical applications of voltammetry. 

To visualize the concentration distribution near the electrode surface, Figure 2.7 shows several curves of Co(x,f) vs x at several different time periods, which are calculated according to Eqn (2.43). It can be seen that the reactant concentration is decreased with increasing reaction time due to the reaction consumption. The larger decrease in concentration can be seen at the region more close to the electrode surface. At the electrode surface, the concentration can be expressed as Eqn (2.45) by setting j = 0 in Eqn (2.43) ... 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

Design possibilities for electrolytic cells are numerous, and the design chosen for a particular electrochemical process depends on factors such as the need to separate anode and cathode reactants or products, the concentrations of feedstocks, desired subsequent chemical reactions of electrolysis products, transport of electroactive species to electrode surfaces, and electrode materials and shapes. Cells may be arranged in series and/or parallel circuits. Some cell design possibiUties for electrolytic cells are... 

At this second potential, the ratio of the products P1/P2 will clearly depend on the ratio of the reactant concentrations a large excess of Ri will favour the former route while a large excess of R2 will favour P2 smce the reaction between I2 diffusing away from the electrode and incoming R will ensure that the flux of R at the surface is zero and hence that no Ij will be formed. If the ratio of the reactant concentrations is of the order of unity, it can be shown that it is the ratio of the rate... 

In a similar way, electrochemistry may provide an atomic level control over the deposit, using electric potential (rather than temperature) to restrict deposition of elements. A surface electrochemical reaction limited in this manner is merely underpotential deposition (UPD see Sect. 4.3 for a detailed discussion). In ECALE, thin films of chemical compounds are formed, an atomic layer at a time, by using UPD, in a cycle thus, the formation of a binary compound involves the oxidative UPD of one element and the reductive UPD of another. The potential for the former should be negative of that used for the latter in order for the deposit to remain stable while the other component elements are being deposited. Practically, this sequential deposition is implemented by using a dual bath system or a flow cell, so as to alternately expose an electrode surface to different electrolytes. When conditions are well defined, the electrolytic layers are prone to grow two dimensionally rather than three dimensionally. ECALE requires the definition of precise experimental conditions, such as potentials, reactants, concentration, pH, charge-time, which are strictly dependent on the particular compound one wants to form, and the substrate as well. The problems with this technique are that the electrode is required to be rinsed after each UPD deposition, which may result in loss of potential control, deposit reproducibility problems, and waste of time and solution. Automated deposition systems have been developed as an attempt to overcome these problems. 

In electrochemical cells we often find convective transport of reaction components toward (or away from) the electrode surface. In this case the balance equation describing the supply and escape of the components should be written in the general form (1.38). However, this equation needs further explanation. At any current density during current flow, the migration and diffusion fluxes (or field strength and concentration gradients) will spontaneously settle at values such that condition (4.14) is satisfied. The convective flux, on the other hand, depends on the arbitrary values selected for the flow velocity v and for the component concentrations (i.e., is determined by factors independent of the values selected for the current density). Hence, in the balance equation (1.38), it is not the total convective flux that should appear, only the part that corresponds to the true consumption of reactants from the flux or true product release into the flux. This fraction is defined as tfie difference between the fluxes away from and to the electrode ... 

As an example, consider a simple reaction of the type (6.2) taking place under pure diffusion control. At all times the electrode potential, according to the Nemst equation, is determined by the reactant concentrations at the electrode surface. It was shown in Section 11.2.3 that periodic changes in the surface concentrations which can be described by Eq. (11.19) are produced by ac flow. We shall assume that the amplitude of these changes is small (i.e., that Ac electrode polarization. With this substitution and using Eq. (11.19), we obtain... 

Reactant concentrations Cyj in the bulk solution, as well as the Galvani potential between the electrode and the bulk solution (which is a constituent term in electrode potential E), appear in kinetic equations such as (6.8). However, the reacting particles are not those in the bulk solution but those close to the electrode surface, near the outer Helmholtz plane when there is no specific adsorption, and near the inner Helmholtz plane when there is specific adsorption. Both the particle concentrations and the potential differ between these regions and the bulk solution. It was first pointed out by Afexander N. Frumkin in 1933 that for this reason, the kinetics of electrochemical reactions should strongly depend on EDL structure at the electrode surface. 

Often, mnltistep reactions are enconntered where a reactant j first becomes adsorbed on the electrode, then is converted electrochemically (or chemically) to a desorbing prodnct. We shall consider the case where the electrochemical step involving adsorbed particles is rate determining. With a homogeneons electrode surface and without interaction forces between the adsorbed particles [i.e., in conditions when the Langmuir isotherm (10.14) can be apphed], the assumption can be made that the rate of this step is proportional not to the bulk concentration Cy j but to the surface concentration Aj or to the degree of surface coverage 0 hence. 

However, with an inhomogeneous electrode surface and adsorption energies that are different at different sites, the reaction rate constant and the related parameter will also assume different values for different sites. In this case the idea that the reaction rate might be proportional to surface concentration is no longer correct. It was shown by M. Temkin that when the logarithmic adsorption isotherm (10.15) is obeyed, the reaction rate will be an exponential function of the degree of surface coverage by the reactant ... 

Interelectrode Gap The relative electrolyte volume available per unit surface area of the electrodes is determined by the distance (gap) between the electrodes. This distance is between fractions of a millimeter and some 10 cm. The ohmic losses in the electrolyte increase with the distance between the electrodes. On the other hand, when the electrolyte volume is too small, the reactant concentrations will change rapidly. Often, the electrolyte volume in a reactor is increased by providing space for the electrolyte not only between the electrodes but also above or below the block of electrodes. Sometimes the electrolyte is pumped around in an external circuit, including an additional electrolyte vessel. 

The surface concentration Cq Ajc in general depends on the electrode potential, and this can affect significantly the form of the i E) curves. In some situations this dependence can be eliminated and the potential dependence of the probability of the elementary reaction act can be studied (called corrected Tafel plots). This is, for example, in the presence of excess concentration of supporting electrolyte when the /i potential is very small and the surface concentration is practically independent of E. However, the current is then rather high and the measurements in a broad potential range are impossible due to diffusion limitations. One of the possibilities to overcome this difficulty consists of the attachment of the reactants to a spacer film adsorbed at the electrode surface. The measurements in a broad potential range give dependences of the type shown in Fig. 34.4. 

Potentiostatic current sources, which allow application of a controlled overpotential to the working electrode, are used widely by electrochemists in surface kinetic studies and find increasing use in limiting-current measurements. A decrease in the reactant concentration at the electrode is directly related to the concentration overpotential, rj0 (Eq. 6), which, in principle, can be established directly by means of a potentiostat. However, the controlled overpotential is made up of several contributions, as indicated in Section III,C, and hence, the concentration overpotential is by no means defined when a given overpotential is applied its fraction of the total overpotential varies with the current in a complicated way. Only if the surface overpotential and ohmic potential drop are known to be negligible at the limiting current density can one assume that the reactant concentration at the electrode is controlled by the applied potential according to Eq. (6). 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

Cyclic voltammetry was used to monitor the mechanism for (TPP)Rh(R) formation according to Equation 3 where RX is a terminal alkyl halide. The current for reduction of electrogenerated (P)Rh(R) or (P)Rh(RX) species is a measure of the concentration of this product at the electrode surface, and hence a measure of its rate of formation. The current must be standardized for experimental factors such as scan rate, initial concentration of [(TPP)Rh(L)J+cr (or other initial Rh(III) species), electrode area, and concentration of the alkyl halide reactant. 

The rate of an electrode reaction is a function of three principle types of species charge carriers on the surface, active surface atoms and reactant species in the solution as illustrated in Figure 23. That is, r cc [h] [Siactive] [A]. Carrier concentration and reactant concentration do not, in general, depend on surface orientation while active surface atoms may be a function of surface orientation. Anisotropic effect occurs when the rate determining step depends on the active surface atoms that vary with crystal orientation of the surface. On the other hand, reactions are isotropic when the concentration of active surface atoms is not a function of surface orientation or when the rate determining step does not involve active surface atoms. 

How electron transfer kinetics may be investigated by means of an electrochemical method such as cyclic voltammetry is the question we address now, starting with the case where the reactants are immobilized on the electrode surface, as in the beginning of Section 1.2. The key equations are those that relate the surface concentrations rA and rB to the current. The first of these expresses the Faradaic consumption of A and production of B as the current flows ... 

The convolution treatment of the linear and semi-infinite diffusion reactant transport (Section 1.3.2) leads to the following relationship between the concentrations at the electrode surface and the current ... 

Electrochemistry is in many aspects directly comparable to the concepts known in heterogeneous catalysis. In electrochemistry, the main driving force for the electrochemical reaction is the difference between the electrode potential and the standard potential (E — E°), also called the overpotential. Large overpotentials, however, reduce the efficiency of the electrochemical process. Electrode optimization, therefore, aims to maximize the rate constant k, which is determined by the catalytic properties of the electrode surface, to maximize the surface area A, and, by minimization of transport losses, to result in maximum concentration of the reactants. 

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