Reference Work Entry

Encyclopedia of Applied Electrochemistry

pp 417-423

Date:

Electrocatalysis, Fundamentals - Electron Transfer Process; Current-Potential Relationship; Volcano Plots

  • Svetlana B. StrbacAffiliated withICTM-Institute of Electrochemistry, University of Belgrade Email author 
  • , Radoslav R. AdzicAffiliated withChemistry Department, Brookhaven National Laboratory

Introduction

Electrocatalysis is the science exploring the rates of electrochemical reactions as a function of the electrode surface properties. In these heterogeneous reactions, the electrode does not only accepts or supplies electrons (electron transfer), as in simple redox reactions, but affects the reaction rates interacting with reactants, intermediates, and reaction products, i.e., acts as a catalyst remaining unchanged upon its completion. The term electrocatalysis, an extension to electrochemistry of the term catalysis (Greek kata (down) and lyein (to let)), was apparently first used in 1934[1]. The beginning of intensive research in this area can be traced back to early 1960s in connection with the broadening fuel cell research. Many electrocatalytic reactions have great importance. These include hydrogen, oxygen, and chlorine evolution; oxygen reduction oxidation of small organic molecules suitable for energy conversion (methanol, ethanol, formic acid); and reactions of organic syntheses. The limitations of the operating temperature for aqueous solutions in electrocatalysis, compared those in catalysis, are compensated by the possibility to increase the reaction rates by applied potential. The rates of some reactions can be increased several orders of magnitude by small change of potential. Such an increase in the rate of chemical reaction would require very high temperatures. Important features of electrocatalytic reactions, facilitated by the application of the electrode potential, include (i) high reaction rates that can be achieved, (ii) high selectivity at defined potentials, and (iii) the unique direct energy conversion in fuel cells that are likely to become one of the major sources of clean energy. The main events in an electrocatalytic reaction are adsorption/desorption, electron transfer, and bond breaking/formation.

Electron Transfer Process

Electrochemical reactions are heterogeneous chemical reactions in which electrons are exchanged between the electrode and the molecules or ions in the electrolyte. The electrode is metal or other electronic conductive material, while the electrolyte is purely ionic conductor which includes water and nonaqueous solvents and melt or solid electrolytes. In the course of an electrochemical reaction, the electron transfer occurs through the electrode/electrolyte interface. Electrons can be transferred through the interface in both directions. Particle in the electrolyte becomes either reduced when it accepts an electron from the electrode or oxidized when it gives an electron to the electrode. Thus, the electrochemical reaction involves the passage of electrical current. Currents corresponding to the oxidation and reduction reactions are called a partial anodic and partial cathodic current, respectively. When the electrode potential is equal to the equilibrium potential, partial anodic and partial cathodic currents are equal, so that the total current is zero. However, when the imposed electrode potential is more positive or more negative than the equilibrium potential, the total current that passes through the electrode is the anodic or cathodic current, respectively. The corresponding electrodes are called anodes or cathodes.

The simplest electrochemical reactions are those in which the electron transfer causes only the change of the oxidation state of a reactant, no bond formation or splitting takes place. Much more common are cases in which the electron transfer is followed by or occurs simultaneously with the adsorption and/or chemical changes of a reactant, reaction intermediates, or products. Thus, the electrochemical reactions are divided into two classes: (i) outer-sphere one-electron transfer with the solution-phase electron donors or acceptors in the outer Helmholtz plane (OHP) of the electrical double layer where the electron transfer occurs and (ii) more complex processes where more than one electron may be transferred. Class 1 of electrochemical reactions involves a simple ionic redox process in which only the change of oxidation state of reactants positioned in the OHP is involved. Class 2 reactions often involve multiple steps, some can be chemical. When a reaction occurs in a series of consecutive steps, the overall reaction rate is determined by the rate of the slowest step, called the rate-determining step. All other preceding and following steps can be considered to be in equilibrium. If the slowest step in the reaction mechanism is the exchange of electron, then electrochemical reaction takes place under electrochemical or activation control. Many electrochemical reactions of organic molecules and reactions accompanied by gas evolution or dissolution are in a class 2.

Just as for chemical reactions in general, the charge transfer is controlled by the existence of the energy barrier between oxidized and reduced states. A unique feature of the electrode reactions is that the height of this barrier can be decreased or increased by changing the potential across the interface.

The Rate of Electron Transfer

Because of the heterogeneous nature of electrode reactions, the rate of charge transfer across the electrochemical interface depends not only on the potential but also on the double layer structure and the adsorption of reactants, intermediates and products, and other eventual solution phase species. Mass-transport limitations are not considered here. The expression relating current to the electrode potential can be obtained from the absolute rate theory applied to the electrochemical interface. For that electrochemical reaction case, the heights of the free energy barriers are functions of the potentials drop across the interface in accordance with the absolute rate theory.

In the simplest case of one-electron transfer reaction:
$$ O+e\Leftrightarrow R $$
(1)
A shift in the electrode potential from 0 to a value E causes the changes depicted in Fig. 1.
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Electrocatalysis, Fundamentals - Electron Transfer Process; Current-Potential Relationship; Volcano Plots, Fig. 1

Effect of electrode potential on the free energy versus coordinate curves for an electron reactant at two electrode potentials: E =Ee and E < Ee (broken line parabola)

The barrier for the oxidation ΔG is decreased by a fraction α of the energy change nFE, while the barrier for reduction is increased by (1 – α) nFE. Rate constants for the reduction and oxidation are k red and k ox , respectively. Assuming that there is an arbitrary amount of oksidant (O) and reductant (R) species in the solution, the total current flowing j is the sum of the partial cathodic j c , and partial anodic j a , currents:
$$ j={j}_c+{j}_a= nFA{k}_{red}{\left[O\right]}_o- nFA{k}_{ox}{\left[R\right]}_o $$
(2)
where A is the electrode area, F is the Faraday constant, n is the number of electrons transferred, and [O] 0 and [R] 0 are the surface concentrations of (O) and (R), respectively. According to the transition state theory from chemical kinetics, rate constants are related to the free energies of activation, which are related to the potential. From these relations the basic equation is derived, which describes how the overall current on an electrode depends on the applied potential.

Current–Potential Relationship

The equation which describes the fundamental relationship between the electrical current on an electrode and the electrode potential, assuming that both a cathodic and an anodic reaction occur on the same electrode, is called the Butler–Volmer equation:
$$ j={j}_0\left\{ \exp \left(\frac{\left(1-\alpha \right) nF\eta}{ RT}\right)- \exp \left(\frac{-\alpha nF\eta}{ RT}\right)\right\} $$
(3)
where j 0 is the exchange current density, T is absolute temperature, R is universal gas constant, α is so-called symmetry factor or charge transfer coefficient, and η is the overpotential. Overpotential is the extent to which the reaction is driven beyond the equilibrium potential, Eeq:
$$ \eta =E-{E}_{eq} $$
(4)
At high anodic overpotential, partial cathodic current can be excluded compared to the anodic, meaning that the Butler–Volmer Eq. (3) simplifies to
$$ j={j}_a={j}_0 \exp \left[\frac{\left(1-\alpha \right) nF\eta}{ RT}\right] $$
(5)
Partial anodic currents can be excluded from Butler–Volmer equation at high cathodic overpotential:
$$ j={j}_c=-{j}_0 \exp \left[-\frac{\alpha nF\eta}{ RT}\right] $$
(6)

From the Eqs. (5) and (6) for the high anodic or cathodic overpotential, the corresponding

Tafel equations can be derived:
$$ \begin{array}{ll} \eta =-2.303\frac{ RT}{\left(1-\alpha \right) nF} \log {j}_0+2.303 \\ \qquad \times \frac{ RT}{\left(1-\alpha \right) nF} \log {j}_a \end{array}$$
(7)
$$ \eta =2.303\frac{ RT}{\alpha nF} \log {j}_0-2.303\frac{ RT}{\alpha nF} \log {j}_c $$
(8)

Since the partial cathodic current is negative under the conventions and a logarithm of a negative number is undefined, it is assumed in Eq. (8) that value j c is in fact absolute value ∣ j c ∣.

Tafel Slope

Logarithmic dependence of η on j given by Eqs. (7) and (8) can be simplified to
$$ \eta =a+b \log j $$
(9)
where a and b are constants. In its graphical presentation (Fig. 2), the value of a is the intercept and b is a slope. From the intercept, one can calculate the exchange current density, j 0, by the extrapolation of the potential to the equilibrium potential. Slope b is called the Tafel slope. For anodic reaction Tafel slope is positive, while for the cathodic reaction it is negative. This value is important in electrochemical kinetics, because it allows the calculation of the symmetry factors for elementary reactions and makes it possible to predict the reaction mechanism of complex reactions. The linear dependence takes place at η ≈ 50–100 mV.
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Electrocatalysis, Fundamentals - Electron Transfer Process; Current-Potential Relationship; Volcano Plots, Fig. 2

Tafel plot

Tafel slope value also indicates the number of electrons exchanged in the electrochemical reaction. For a reaction, where the number of electrons exchanged equals 1 and the charge transfer coefficient is 0.5, the theoretical Tafel slope at 25 °C is ± 118 mV per decade. Thus, Tafel slopes provide valuable information regarding the mechanism of a reaction and indicate the identity of a rate-determining step of the overall reaction.

Theories of Charge Transfers

Theoretical reactions at electrodes as well as between redox couples in solutions can be interpreted in terms of electron tunneling. Microscopic aspects of the charge transfer in the phenomenological treatment are contained in the rate constants k and the transfer coefficient a.

Descriptions of charge transfer of charge transfer (electrons or protons) in electrochemical reactions, have been a subject of much interest since the work of Gurney [2] who suggested that electron transfer has two main approaches to the problem. In the first, which can be termed “molecular,” attention is focused on the behavior of one chemical bond that is modified in the interfacial reaction. The theory assumes that the energy of activation is determined by the distribution of thermal energy in the various internal modes of the reacting species but ignores the dynamic behavior and dielectric relaxation properties of the solvent [3, 4].

The second approach, referred to as a “continuum theory,” has been pursuit by theorists using classical or quantum statistical mechanics with the common focus on solvent dipole fluctuation as a major factor controlling the charge transfer [5, 6].

Volcano Plots

Electrocatalytic reactions involve the strong interactions of reactants and/or intermediates with the electrode surface. As a consequence, the rate of these reactions shows pronounced dependence on the nature of the electrode material. A good example is hydrogen evolution reaction, for which the rate of various metals varies by 11 orders of magnitude. The plots of the catalyst activity (reaction rate) against a descriptor of the adsorption properties such as the adsorption energies or adsorption bond strength of the reactant or reaction intermediates pass through a maximum. These are volcano plots that are generally based on the Sabatier principle [7], which states that the interactions between the catalyst and the adsorbate should be neither too strong nor too weak. If the interaction is too weak, the adsorbate will fail to bind to the catalyst and no reaction will take place. On the other hand, if the interaction is too strong, the catalyst gets blocked by adsorbate or product that fails to desorb. Volcano correlations are important for describing trends in reactivity that are helpful in designing new more active catalysts. Early treatments of volcano plots in catalysis are due to Balandin [8], in electrocatalysis Parsons [9], Gerischer[10], Krishtalik[11], Trasatti[12], and Appleby[13].

From the basic relationship between kinetic current, i, and potential, E, consistent with the Butler–Volmer approach, the rate expression for electrocatalytic reaction:
$$ A+e\to {B}^{-}\to C $$
(10)
can be written in the following form: ΔG
$$ \begin{array}{ll} I = const{C}_A\left(1-{\theta}_B\right) \exp \left(1-\Delta {G}^{\ne }/ \right. \\ \qquad \left.{RT-\alpha \Delta {G}_B^O}\alpha FE/ RT\right) \end{array}$$
(11)

Assuming formation of B to be the rate-determining step, if B is adsorbed on the electrode surface, it will form with a lower activation Gibbs energy than in the absence of adsorption. For the limiting cases when θB ∼ 0 and θB ∼ 1, Eq. (11) at constant potential, E, becomes ln i ∼ ΔG B or ln i ∼ ΔG B , respectively.

As illustrated schematically in Fig. 3, the logarithm of the reaction rate varies linearly with ΔG, increasing from weak adsorption (positive) to very strong adsorption (negative), which predicts a linear decrease of the reaction rate as result of the blocking effect.
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Electrocatalysis, Fundamentals - Electron Transfer Process; Current-Potential Relationship; Volcano Plots, Fig. 3

Schematics of a volcano curve in electrocatalysis with adsorption of B being the rate-determining step

As an example, volcano plot for the activity of different metal catalysts for oxygen reduction reaction (ORR) versus the respective metal–oxygen bond strength is shown in Fig. 4.
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Electrocatalysis, Fundamentals - Electron Transfer Process; Current-Potential Relationship; Volcano Plots, Fig. 4

Oxygen reduction activity plotted as a function of the oxygen binding energy [14]

Analogous two-dimensional plots can also be built against two different descriptors, such as the adsorption bond strength of the two intermediates. In that case the plot is generally shown as a contour plot and is called a volcano surface [14]. Figure 5 shows volcano surface for the activity of different metal catalysts for ORR versus both metal–O and metal–OH binding energies.
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Electrocatalysis, Fundamentals - Electron Transfer Process; Current-Potential Relationship; Volcano Plots, Fig. 5

Oxygen reduction activity plotted as a function of both the O and the OH binding energies [14]

Cross-References

Electrocatalysts​ for the Oxygen Reaction, Core-Shell Electrocatalysts​

Electrode

Hydrogen Evolution Reaction

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