Irreversible overpotentials

Resistance overpotential p and activation overpotential p are characteristic of irreversible reactions and are, therefore, termed irreversible overpotentials . Since deviations from the equilibrium potential due to changes in the concentrations of the reactants are largely reversible, concentration overpotential p is known as a reversible polarization . Crystallization overpotential p is more complicated. It can be caused either by reversible polarization or irreversible polarization . The details will be discussed later. 

The source term (Sj, W m ) in the energy equationrepresents the heat generation/consumption by chemical reactions or electrochemical reactions. In the porous anode, the heat source term comes from heat generated by a WGSR and heat consumption by a DIR reaction. The heat generatedby the electrochemical reaction, taking into accoimtthe irreversible overpotential losses, is applied evenly to the electrolyte. Therefore, the source term ST can be written as ... 

Thus, irrespective of r.ceii. a thermodynamic parameter, the rate will be controlled by the irreversibility of the reaction, which is reflected in the magnitudes of the anode and cathode overpotentials. 

As in chemical systems, however, the requirement that the reaction is thermodynamically favourable is not sufficient to ensure that it occurs at an appreciable rate. In consequence, since the electrode reactions of most organic compounds are irreversible, i.e. slow at the reversible potential, it is necessary to supply an overpotential, >] = E — E, in order to make the reaction proceed at a conveniently high rate. Thus, secondly, the potential of the working electrode determines the kinetics of the electron transfer process. 

Plotting the overpotential against the decadic logarithm of the absolute value of the current density yields the Tafel plot (see Fig. 5.3). Both branches of the resultant curve approach the asymptotes for r RT/F. When this condition is fulfilled, either the first or second exponential term on the right-hand side of Eq. (5.2.28) can be neglected. The electrode reaction then becomes irreversible (cf. page 257) and the polarization curve is given by the Tafel equation... 

Very often, the value of the formal electrode potential E 0 is not known for an irreversible electrode reaction. The overpotential f] cannot, therefore,... 

It is often useful to replace this equation by Eq. (5.2.24) modified for an irreversible process (occurring at large overpotentials), which has the following form for cathodic processes ... 

Useful work (electrical energy) is obtained from a fuel cell only when a reasonable current is drawn, but the actual cell potential is decreased from its equilibrium potential because of irreversible losses as shown in Figure 2-2". Several sources contribute to irreversible losses in a practical fuel cell. The losses, which are often called polarization, overpotential, or overvoltage (ri), originate primarily from three sources (1) activation polarization (r act), (2) ohmic polarization (rjohm), and (3) concentration polarization (ricoiic)- These losses result in a cell voltage (V) for a fuel cell that is less than its ideal potential, E (V = E - Losses). 

SO that the concentration of [Zn ] under the same conditions will be 10 g-molecule/L. With these ionic concentrations, the deposition potentials of copper and zinc in the absence of any polarization can each be calculated from Eq. (11.1) to be about —1.30 V. It should be mentioned here again that in practice, Eq. (11.1) refers to reversible equilibrium, a condition in which no net reaction takes place. In practice, electrode reactions are irreversible to an extent. This makes the potential of the anode more noble and the cathode potential less noble than their static potentials calculated from (11.1). The overvoltage is a measure of the degree of the irreversibility, and the electrode is said to be polarized or to exhibit overpotential hence, Eq. (11.2). 

Whereas Pt in an acidic solution saturated with H2 acquires the reversible potential of the hydrogen electrode, this is not the case for the same Pt electrode in an acidic solution saturated with O2. This is related to the high activation energies involved in breaking and forming chemical bonds. Thus the O2 reaction is known to be highly irreversible. In particular, a Pt electrode in 02-saturated solution acquires a potential 0.9V (SHE) rather than 1.23 V. Hence an overpotential of >0.3 V can already be expected from an analysis of the equilibrium conditions. 

However, the oxidation of NAD(P)H to NAD(P)+ at practical rates on most electrode materials proceeds only at high overpotentials [182] and often fouling of the electrode surface has been observed. This situation induces the search for suitable mediators or electrode modification processes to accelerate the highly irreversible oxidation of NAD(P)H. The stability of the reaction products in the presence of each other is also a necessary condition for usefulness. 

However, electrochemical reactions generally occur at t RT/F. Such reactions are called irreversible and the physical occurrences that govern the degree of overpotential that has to be developed to make a given i flow depend on the chemical physics of the interface—the work function of the electrode and the bond strength of its surface atoms, etc.82 (Chapter 9). 

These matters show up in terminology. For the physical electrochemist, there is the state of thermodynamic reversibility, the domain of the Nernst equation, and this state is the bedrock and the base from which he or she starts out. When a reaction departs from equilibrium in the cathodic and anodic direction, it has a degree of irreversibility in the thermodynamic sense. Thus, for overpotentials less than RT/b one refers to the linear region (i a It)I), where departure from reversibility is small enough to be measured in millivolts. If 11)1 > RT/F (about 26 mV at room temperature), the reaction is simply and straightforwardly irreversible the forward reaction has been made to become much faster than the back-reaction. 

In addition, electrode reactions are frequently characterized by an irreversible, i.e., slow, electron transfer. Therefore, overpotentials have to be applied in preparative-scale electrolyses to a smaller or larger extent. This means not only a higher energy consumption but also a loss in selectivity as other functions within the molecule can already be attacked. In the case of indirect electrolyses, no overpotentials are encountered as long as reversible redox systems are used as mediators. It is very exciting that not only overpotentials can be eliminated but frequently redox catalysts can be applied with potentials which are 600 mV or in some cases even up to 1 Volt lower than the electrode potentials of the substrates. These so-called redox reactions opposite to the standard potential gradient can take place in two different ways. In the first place, a thermodynamically unfavorable electron-transfer equilibrium (Eq. (3)) may be followed by a fast and irreversible step (Eq. (4)) which will shift the electron-transfer equilibrium to the product side. In this case the reaction rate (Eq. (5)) is not only controlled by the equilibrium constant K, i.e., by the standard potential difference be-... 

On the other hand, if the exchange current is very small and a large overpotential is needed for the current to flow, the electrode process is said to be irreversible. In some cases, the electrode process is reversible (the overpotential is small) for small current values but irreversible (the overpotential is large) for large current values. Such a process is said to be quasi-reversible. 

Logarithmic analysis is therefore possible and can be utilised in the determination of E /2 and (an) from quasi-reversible voltammetric waves [159]. For the totally irreversible case, when there is a significant overpotential, we obtain, for all electrodes for a cathodic process... 

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