Charge Transfer at the Electrode-Electrolyte Interface

The current, in general, is composed of a steady state or dc part determined by the mean dc potential E and the mean dc concentrations at the interface, Co and c , and an ac part, A/, determined by the ac perturbing potential A and the fluctuating concentrations Ac,. The faradic impedance is given by the ratio of the Laplace transforms of the ac parts of the voltage and current 

Because charge transfer is involved, the presence of an electric field at the interface affects the energies of the various species differently as they approach the interfadal region. In other words, the activation energy barrier for the reaction depends on the potential difference across the interface. It is convenient to express the potential dependence of the rate constants in the following manner  

Generally, we can express Aip as an expansion of the ac parts of the concentrations and electrode potential, 

Neglecting aU but the first-order terms (linearization) and solving for AE, 

The first term is the charge transfer resistance the second term contains the influence of the ac part of the mass transport on the impedance. Here Ac, / Aiy can be expressed as a solution of the diffusion equation. For example, for semiinfinite diffusion to a plane, we can use Eq. (126)  

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Figure 3.1 shows a typical equivalent circuit of an electrochemical cell. Rel represents the electrolyte resistance between the working electrode surface and the point of reference electrode Cd is a pure capacitor of the capacity associated with the double layer of the electrode/electrolyte interface and Zf refers to the Faradaic impedance, which corresponds to the impedance of the charge transfer at the electrode/electrolyte interface. The connection of X, and Cd in Figure 3.1 is in parallel. The impedance X, can be subdivided in two equivalent ways, as seen in Figure 3.1 b ... 

If the concentrations of the reactants and products at the electrode surface are the same as in the bulk solution, the overvoltage resulting from a potential change is called activation overvoltage or charge transfer overvoltage. It stems from the fact that the rate of charge transfer at the electrode-electrolyte interface is not... 

This section describes the electrode reactions that are limited by the rate of charge transfer at the electrode-electrolyte interface. In this case, the Butler-Volmer equation (B V equation) provides a functional relationship between the potential and the current... 

At high acid concentration, the reaction rate of protons is normally limited by charge transfer at the electrode-electrolyte interface (Sect. 4.2). In weakly acidic environments, however, the reaction rate may be limited by the rate of transport. The hydrodynamic conditions and the pH then determine the value of the limiting current. Neglecting migration effects its value is given by ... 

However, if the kinetics of charge transfer at the electrode/ electrolyte interface are so rapid that the electrochemical reactants and products stay in equilibrium at the electrode surface even though a current passes, the Nernst equation still applies to the surface concentrations. Such a process is said to be electrochemically reversible or Nernstian - sometimes written with a lower case n, a mark of distinction also accorded to the adjectives coulombic, ohmic and faradaic. 

There are two primary mechanisms of charge transfer at the electrode-electrolyte interface, illustrated in Fig. 1. One is a non-Faradaic reaction, where no electrons are... 

In this paper, some of the possibilities associated with the FREECE technique wil1 be described. Results referring to the charge distribution at the electrode-electrolyte interface and to charger-transfer reactions will be presented and briefly discussed. 

Since in the steady state, it is necessary to maintain a condition of electroneutrality in any macroscopic part of the system, the total charge flux through all cross-sections of the circuit must be the same. In particular, the rate of electron flow in the external circuit is equal to the rate of charge transfer at each electrode/electrolyte interface. 

While many of the standard electroanalytical techniques utilized with metal electrodes can be employed to characterize the semiconductor-electrolyte interface, one must be careful not to interpret the semiconductor response in terms of the standard diagnostics employed with metal electrodes. Fundamental to our understanding of the metal-electrolyte interface is the assumption that all potential applied to the back side of a metal electrode will appear at the metal electrode surface. That is, in the case of a metal electrode, a potential drop only appears on the solution side of the interface (i.e., via the electrode double layer and the bulk electrolyte resistance). This is not the case when a semiconductor is employed. If the semiconductor responds in an ideal manner, the potential applied to the back side of the electrode will be dropped across the internal electrode-electrolyte interface. This has two implications (1) the potential applied to a semiconducting electrode does not control the electrochemistry, and (2) in most cases there exists a built-in barrier to charge transfer at the semiconductor-electrolyte interface, so that, electrochemical reversible behavior can never exist. In order to understand the radically different response of a semiconductor to an applied external potential, one must explore the solid-state band structure of the semiconductor. This topic is treated at an introductory level in References 1 and 2. A more complete discussion can be found in References 3, 4, 5, and 6, along with a detailed review of the photoelectrochemical response of a wide variety of inorganic semiconducting materials. 

It is the aim of this chapter to explain the basic requirements for performing electrochemistry, such as equipment, electrodes, electrochemical cells and boundary conditions to be respected. The following chapter focuses on the basic theory of charge transfer at the electrode-electrolyte solution interface and at transport phenomena of the analyte towards the electrode surface. In Chapter3, a theoretical overview of the electrochemical methods applied in the work described in this book is given. 

Tafalla, D. and Salvador, P. 1987. Mechanisms of charge transfer at the semiconductor-electrolyte interface oxygen electroreduction at naked and platinized n-Ti02 electrodes. Ber. Bunsenges. Phys. Chem., 91,475M79. 

Charge-transfer resistance is the resistance that occurs when electrons transfer at the electrode/electrolyte interface. The charge-transfer resistance is dependent on the reaction, the electrode surface, and the electrode potential. In general, an increase in overpotential leads to a decrease in charge-transfer resistance. 

FF = 0.68, and rj = 11.7%. The improvement in the photoelectrochemical solar cell properties has been ascribed to the formation of n-CdSe/n-WOs heterojunctions, which enhances the charge transfer at the semiconductor/electrolyte interface. These results indicated for the first time the interesting effects of STA and PTA on chemically deposited CdSe films. This opens up a new method for fabricating mixed electrodes with improved physical properties and photoelectrochemical solar cell performances. 

The electrode reactions involve both mass and charge transfer at the metal-electrolyte interface as well as transport of mass (ions and molecules) in the solution to and from the interface. Above we have introduced activation polarization, where the mass or charge transfer across the interface is rate determining. In other cases, the mass transport within the solution may be rate determining, and in this case we have concentration polarization. This implies either that there is a shortage of reactants at the electrode surface, or that an accumulation of reaction products... 

Figure 6.27 Evolution of the potential profile during potentiostatic film growth controlled, respectively, by high field conduction (HFM) and by charge transfer at the film-electrolyte interface (IFM). When an anodic potential step is applied to a passive metal electrode, both mechanisms predict a decreasing growth rate with time.

In a carbon-supported metal electrocatalyst, the electronic interaction between metal and carbon support has a significant effect on its electrochemical performance [4], For carbon-supported Pt electrocatalyst, carbon could accelerate the electron transfer at the electrode-electrolyte interface, leading to an accelerated electrode process. Typically, the electrons are transferred from platinum clusters to the oxygen species on the surfece of a carbon support material and the chemical bond formation or the charge transfer process occurs at the contacting phase, which is considered to be beneficial to the enhancement of the catalytic properties in terms of activity and stability of the electrocatalysts. Experimentally, the investigation into the electron interaction between metal catalyst and support materials could be realized by various physical, spectroscopic, and electrochemical approaches. The electron donation behavior of Pt to carbon support materials has been demonstrated by the electron spin resonance (ESR) X-ray photoelectron spectroscopy (XPS) studies, with the conclusion that the electron interaction between Pt and carbon support depends on their Fermi level of electrons. It is considered that the electronic structure change of Pt on carbon support induced by the electron interaction has positive effect toward the enhancement of the catalytic properties and the improvement of the stability of the electrocatalyst system. However, the exact quantitative relationship between electronic interaction of carbon-supported catalyst and its electrocatalytic performance is still not yet fully established [4]. 

By tradition, electrochemistry has been considered a branch of physical chemistry devoted to macroscopic models and theories. We measure macroscopic currents, electrodic potentials, consumed charges, conductivities, admittance, etc. All of these take place on a macroscopic scale and are the result of multiple molecular, atomic, or ionic events taking place at the electrode/electrolyte interface. Great efforts are being made by electrochemists to show that in a century where the most brilliant star of physical chemistry has been quantum chemistry, electrodes can be studied at an atomic level and elemental electron transfers measured.1 The problem is that elemental electrochemical steps and their kinetics and structural consequences cannot be extrapolated to macroscopic and industrial events without including the structure of the surface electrode. 

The activation overpotential Tiac,w is due to slow charge transfer reactions at the electrode-electrolyte interface and is related to current via the Butler-Volmer equation (4.7). A slow chemical reaction (e.g. adsorption, desorption, spillover) preceding or following the charge-transfer step can also contribute to the development of activation overpotential. 

For the investigation of charge tranfer processes, one has the whole arsenal of techniques commonly used at one s disposal. As long as transport limitations do not play a role, cyclic voltammetry or potentiodynamic sweeps can be used. Otherwise, impedance techniques or pulse measurements can be employed. For a mass transport limitation of the reacting species from the electrolyte, the diffusion is usually not uniform and does not follow the common assumptions made in the analysis of current or potential transients. Experimental results referring to charge distribution and charge transfer reactions at the electrode-electrolyte interface will be discussed later. 

Activation polarization arises from kinetics hindrances of the charge-transfer reaction taking place at the electrode/electrolyte interface. This type of kinetics is best understood using the absolute reaction rate theory or the transition state theory. In these treatments, the path followed by the reaction proceeds by a route involving an activated complex, where the rate-limiting step is the dissociation of the activated complex. The rate, current flow, i (/ = HA and lo = lolA, where A is the electrode surface area), of a charge-transfer-controlled battery reaction can be given by the Butler—Volmer equation as... 

Charge transport is modeled by Ohm s law (Equation (3.10)) and the charge conservation equation (Equation (3.68)), while the current density distribution at the electrode/electrolyte interface is modeled through the Butler-Volmer equation (Equation (3.102)). It should be noted that, contrarily to Section 3.7, Equation (3.102) is here derived from Equation (3.37) rather than Equation (3.39), because the former allows for a better agreement between experimental and simulated results. Equations (3.40)-(3.42) are used to model, the exchange current density, the activation overpotential, and the ideal potential drop at the electrode/electrolyte interface, respectively. Heat transfer is modeled through Equation (3.6), and the appropriate heat terms for each domain. 

Figure 9.2 shows the short-term transient behavior of a fuel cell as obtained from a dynamic model derived from experimental electrochemical impedance studies (Qi et al., 2005). Figure 9.2a shows the cell voltage versus time due to two different resistive load changes (a resistance increase and decrease). The inset shows the existence of three distinct process timescales. The first, A VRn. is an immediate response in the cell voltage which results from pure resistive elements within the cell. The second, A VRrl. is also relatively fast (circa sub-millisecond), that results from the time it takes a charge transfer process at the electrode-electrolyte interface to... 

Activation polarization effect, which is associated with the kinetics of the electrochemical oxidation-reduction or charge-transfer reactions occurring at the electrode/electrolyte interfaces of the anode and the cathode. 

The activation polarization takes place from kinetics impediments of the charge-transfer reaction occurring at the electrode/electrolyte interface this form of kinetics is better understood applying the transition state theory. 

The two blue arrows, marked as NO3- (nitrate ions) and as c (electrons), point to the continuous flow of negative electric charge across the entire electric circuit, consisting both of the cell and the external load. Ions are the charge carriers in the electrolyte, while electrons transport the charge in the metal and the external load. The transition from electronic to ionic charge transport occurs at the electrode/ electrolyte interface upon electron transfer between the electrode and an electron acceptor or donor in the electrolyte. 

Electrochemical reactions in fuel cells occurring on an electrode surface involve several steps. The electroactive species need to reach the electrode surface and adsorb on it, and then the electron transfer occurs at the electrode/electrolyte interface. The first step is mass transfer, and the second and third steps are electrode kinetics. If the mass transfer is fast, and the absorption and charge transfer are slow, the total reaction rate is determined by the electrochemical reaction kinetics. However, in the case of slow mass transfer and fast electrochemical kinetics, the mass transfer limits the whole reaction speed. In other words, the reactant that can reach the electrode surface will be consumed immediately, and the problem will be insufficient reactant on the electrode surface. 

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