Electrode kinetics, double-layer factors

Equation (6) is valid only if it is justly assumed that the equilibrium values of qM and E are established infinitely quickly. This is not the case at low electrolyte concentrations since then the diffusion of the ions composing the double-layer becomes a rate-determining factor. In other words, mass transport complicates the charging process. For practical reasons, studies of electrode kinetics are usually made in well-conducting solutions, so that this effect can be ignored. 

When one considers a distance scale much smaller than 1 pm, surface roughness also is an issue to observed electrode behavior. The ratio of the microscopic surface area to the projected electrode area is usually designated the roughness factor, and can vary from 1.0 to 5 or so for typical solid electrodes, or much higher for porous electrodes. Capacitance, surface faradaic reactions, adsorption, and electrode kinetics all depend on microscopic area. For example, double-layer capacitance increases with roughness such that the apparent capacitance (C°bs) is larger than the value for a perfectly flat electrode (Cflat) as shown in Equation 10.1 ... 

Kinetic factors may induce a variation of electrode potential with current the difference between this potential and the thermodynamic equilibrium potential is known as the overvoltage and the electrode is said to be polarized. In a plating bath this change of potential can be attributed to the reduced concentration of depositing ions in the double layer which reduces the rate of transfer to the electrode, but the dissolution rate from the metal increases. Since the balance of these rates determines the electrode potential, a negative shift in the value occurs the concentration polarization Olconc)- Anodic effects are similar but in the opposite direction. 

Most treatments of such double-layer effects assume that the microscopic solvation environment of the reacting species within the interfacial region is unaltered from that in the bulk solution. This seems oversimplified even for reaction sites in the vicinity of the o.H.p., especially since there is evidence that the perturbation of the local solvent structure by the metal surface [18] extends well beyond the inner layer of solvent molecules adjacent to the electrode [19]. Such solvent-structural changes can yield considerable influences upon the reactant solvation and hence in the observed kinetics via the work terms wp and wR in eqn. (7a) (Sect. 2.2). While the position of the reaction site for inner-sphere processes will be determined primarily by the stereochemistry of the reactant-electrode bond, such solvation factors can influence greatly the spatial location of the transition state for other processes. 

The distance decay constant / (see below) in Miller et al. s original study was 0.9 per CH2, using ferricyanide and iron(IH) hexahydrate [44]. In a later study which accounted more thoroughly for double layer effects, 2 was determined to be 1 eV for kinetically facile redox probes such as ferricyanide, 1.3 eV for Ru-hexamine and 2.1 eV for iron(III) hexahydrate. With a better understanding of the redox probe behavior, f was found to be 1.08 + 0.20 per CH2 and independent of the redox couple and electrode potential [96]. Pre-exponential factors were also extracted from the Tafel plots. The edge-to-edge rate constants (extrapolated) are approximately 10 -10 s for all redox probes, which is reasonable for outer-sphere electron transfer. The pre-exponential factors are 5 x lO s [96]. 

An important factor to analyze the performance of a battery is to characterize the electrode kinetics reaction rate, because the chemical energy is transformed into electrical energy through the electrode kinetics. The rates of the electrode reactions depend on the nature of the electrode surface, the composition of the electrolyte solution adjacent to the electrode (outside the double layer), and the electrode potential [15]. Before we analyze the typical expressions for electrode reaction rates, we need to discuss some important concepts such as double layer, and surface overpotential. 

The measured adsorption effect at the electrode is influenced by all dissolved and/or dispersed surface-active substances according to their concentration in the solution, adsorbability at the electrode, kinetics of adsorption, structure of the adsorbed layer, and some other factors. Adsorption of organic molecules on electrodes causes a change of the electrode double-layer capacitance. It is the result of an exchange between the counterions and water molecules from solution, followed by changes in the dielectric properties and the thickness of the double layer on the electrode surface, that is, parameters that determine the electrode capacitance (Bockris et al., 1963 Damaskin and Petrii, 1971). 

Most SECM measurements involve steady-state current measurements. This can be a significant advantage in the measurement of kinetics, even for rapid processes, because factors like double-layer charging and adsorption do not contribute to the observed currents. However, one can also carry out transient measurements, recording iT as a function of time. This can be of use in measurements of homogeneous kinetics (Chapter 7) and for systems that are changing with time. It can also be used to determine the diffusion coefficient, D, of a species without knowledge of the solution concentration or number of electrons transferred in the electrode reaction (23). 

In general, the impedance of solid electrodes exhibits a more complicated behavior than predicted by the Randles model. Several factors are responsible for this. Firstly, the simple Randles model does not take into account the time constants of adsorption phenomena and the individual reaction steps of the overall charge transfer reaction (Section 5.1). In fact the kinetic impedance may include several time constants, and sometimes one even observes inductive behavior. Secondly, surface roughness or non-uniformly distributed reaction sites lead to a dispersion of the capacitive time constants. As a consequence, in a Nyquist plot the semicircle corresponding to a charge-transfer resistance in parallel to the double-layer capacitance becomes flattened. To account for this effect it has become current practice in corrosion science and engineering to replace the double layer capacitance in the equivalent circuit by a... 

When ionic liquid systems are intended to be applied for electrodepwsition their behaviour has to be assessed as comp>ared with the case of aqueous electrolytes. The main factors which affect the overall electrochemical process include viscosity, conductivity, the potential window, the ionic medium chemistry as well as the structure of the electrical double layer and redox potentials. All these prarameters will influence the diffusion rate of metallic ions at the electrode surface as well as the thermodynamics and kinetics of the reduction process. Consequently, the nudeation/growth mechanisms and the deposit morphology will be affected, too. More detailed discussions on this topic may be formd in ( Abbott et al., 2004 Abbott et al., 2004 Abbott McKenzie, 2006 Abbott et al., 2007 Endres et al., 2008 and included references). 

Electrode kinetics, to be considered in the next chapter, are profoundly influenced by the structure of the double layer at an electrode-solution interface and it is with such systems that we shall be primarily concerned. However, double layer theory, as developed for electrode-electrolyte solution interfaces, leads on to the proper interpretation of electrokinetic phenomena, an understanding of the factors affecting colloid stability, and to the elucidation of cell membrane and ion-exchange processes. 

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