Charge-transfer control

Both the galvanostatic and potentiostatic method have their own particular spheres of application, and it is not always advantageous to reject the former in favour of the latter, although there is an increasing tendency to do so. Nevertheless, the potentiostatic method does have a distinct advantage in studies of passivity, since it is capable of defining more precisely the potential and current density at which the transition from the active (charge transfer controlled M to the passive state takes place this is fax... 

Stern and Geary on the basis of a detailed analysis of the polarisation curves of the anodic and cathodic reactions involved in the corrosion of a metal, and on the assumption that both reactions were charge-transfer controlled (transport overpotential negligible) and that the /R drop involved in determining the potential was negligible, derived the expression... 

The RHSE has the same limitation as the rotating disk that it cannot be used to study very fast electrochemical reactions. Since the evaluation of kinetic data with a RHSE requires a potential sweep to gradually change the reaction rate from the state of charge-transfer control to the state of mass transport control, the reaction rate constant thus determined can never exceed the rate of mass transfer to the electrode surface. An upper limit can be estimated by using Eq. (44). If one uses a typical Schmidt number of Sc 1000, a diffusivity D 10 5 cm/s, a nominal hemisphere radius a 0.3 cm, and a practically achievable rotational speed of 10000 rpm (Re 104), the mass transfer coefficient in laminar flow may be estimated to be ... 

In studying interfacial electrochemical behavior, especially in aqueous electrolytes, a variation of the temperature is not a common means of experimentation. When a temperature dependence is investigated, the temperature range is usually limited to 0-80°C. This corresponds to a temperature variation on the absolute temperature scale of less than 30%, a value that compares poorly with other areas of interfacial studies such as surface science where the temperature can easily be changed by several hundred K. This "deficiency" in electrochemical studies is commonly believed to be compensated by the unique ability of electrochemistry to vary the electrode potential and thus, in case of a charge transfer controlled reaction, to vary the energy barrier at the interface. There exist, however, a number of examples where this situation is obviously not so. 

Can we interpret the data in figures such as those in Figure 7.13, where neither the flux nor the rate of electron transfer have reached their maximum values, i.e. is the magnitude of the current mass-transport or charge-transfer controlled ... 

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... 

Instruction Calculate the current density values as a function of overpotential (in a range of -0.200 to 0.200 V) assuming that the reaction is under mass transport control and under mixed mass transport and charge-transfer control determine the error of the approximation and plot i-T) dependencies. (Gokjovic)... 

A thoroughgoing restudy of Tafel s law, involving the use of fast-flow techniques to avoid the introduction of diffusion control at high rates (Iwasita, Schmickler, and Schultze, 1985) shows excellent verification.19 Tafel s law is one of the most tested and verified laws in nature. It Ls also one with the broadest applicability (e.g., in interfacial charge-transfer control, e.g., corrosion metabolism and photosynthesis). In... 

If the electrocrystallization is controlled by formation of two- or three-dimensional isolated nuclei, the current—overpotential relationship has a stronger dependence on 17 than predicted by the Butler—Volmer equation for charge transfer control [151]... 

Electrode Reactions under Kinetics (Charge Transfer) Control... 

FIGURE 1.20 Complex-plane impedance plot (Nyquist plane) for an electrochemical system, with the mass transfer and kinetics (charge transfer) control regions, for an infinite diffusion layer thickness. 

FIGURE 1.21 An example of a complex-plane impedance plot (Nyquist plane) for an electrochemical system under mixed kinetic/diffusion control, with the mass transfer and kinetics (charge transfer) control regions, for a finite thickness 8N of the diffusion layer. Assumption was made that Kf Kh at the bias potential of the measurement, and D0I = Dmd = D, leading to RB = RCT (krb8N/ >). 

Equation (10.27) indicates that the charge transfer becomes the rate-limiting step under the condition when kcr (kS[ + ) The term in large brackets is a function of transport control of the photocurrent. If the electrode potential is sufficiently negative in a cathodic reaction at a p -type semiconductor, CT (kSI + kbr) and interfacial charge transfer control is lost. Eventually, control passes to transport within the semiconductor (although it is affected by recombination). 

Generally the Tafel equation is obeyed for charge-transfer-controlled processes and, under certain conditions, for reaction control and diffusion control [202],... 

The following relationship is experimentally observed between applied electrochemical current density and potential for a corroding electrode in the absence of competing reduction-oxidation reactions (1,2). The applicability of this relationship relies on the presence of a single charge transfer controlled cathodic reaction and a single charge transfer controlled anodic reaction. 

Many investigators have experimentally observed that im was approximately linearly related to applied potential within a few millivolts of polarization from Econ (3). Stern and Geary simplified the kinetic expression to provide an approximation to the charge transfer controlled reaction kinetics given by Eq. (1) for the case of small overpotentials with respect to corr (4-6). Equation (1) can be mathematically linearized by taking its series expansion (e.g., ex = 1 + x + x2/2 + jc3/ 3 + x4/4 ...) and by neglecting higher terms when AE/p <0.1. This simplified relationship has the form... 

Figure 3 Electrical equivalent circuit model commonly used to represent an electrochemical interface undergoing corrosion. Rp is the polarization resistance, Cd] is the double layer capacitance, Rct is the charge transfer resistance in the absence of mass transport and reaction intermediates, RD is the diffusional resistance, and Rs is the solution resistance, (a) Rp = Rct when there are no mass transport limitations and electrochemical reactions involve no absorbed intermediates and nearly instantaneous charge transfer control prevails, (b) Rp = Rd + Rct in the case of mass transport limitations.

The information required to predict electrochemical reaction rates (i.e., experimentally determined by Evans diagrams, electrochemical impedance, etc.) depends upon whether the reaction is controlled by the rate of charge transfer or by mass transport. Charge transfer controlled processes are usually not affected by solution velocity or agitation. On the other hand, mass transport controlled processes are strongly influenced by the solution velocity and agitation. The influence of fluid velocity on corrosion rates and/or the rates of electrochemical reactions is complex. To understand these effects requires an understanding of mixed potential theory in combination with hydrodynamic concepts. 

It is useful now to describe the origins of the shape of the anodic and cathodic E-log i behaviors shown in Fig. 2. Note that the anodic reaction is linear on the E-log i plot because it is charge transfer controlled and follows Tafel behavior discussed in Chapter 2. The cathodic reaction is under mixed mass transport control (charge transfer control at low overpotential and mass transport control at high overpotential) and can be described by Eq. (1), which... 

Figure 2 Evans diagram illustrating the influence of solution velocity on corrosion rate for a cathodic reaction under mixed charge transfer-mass transport control. The anodic reaction shown is charge transfer controlled.

The secondary current distribution Both ohmic factors and charge transfer controlled overpotential kinetic effects are considered. The potential across the electrochemical interface can vary with position on the electrode. 

Therefore let us instead consider the more practical case of the tertiary current distribution. Based on the dependency of the Wagner number on polarization slope, we would predict that a pipe cathodically protected to a current density near its mass transport limited cathodic current density would have a more uniform current distribution than a pipe operating under charge transfer control. Of course the cathodic current density cannot exceed the mass transport limited value at any location on the pipe, as said in Chapter 4. Consider a tube that is cathodically protected at its entrance with a zinc anode in neutral seawater (4). Since the oxygen reduction reaction is mass transport limited, the Wagner number is large for the cathodically protected pipe (Fig. 12a), and a relatively uniform current distribution is predicted. However, if the solution conductivity is lowered, the current distribution will become less uniform. Finite element calculations and experimental confirmations (Fig. 12b) confirm the qualitative results of the Wagner number (4). 

This equation simplifies the kinetic of a charge-transfer-controlled process to two parameters the exchange current density jo and the Tafel slope b. Both values do not depend not only on the electrochemical reaction but also on the electrode material and on the electrolyte composition. 

This equation can be used when the step is made to any potential in the rising portion of the - voltammo-gram, where either - charge transfer control or mixed kinetic-diffusional control prevails. Figure 2 shows the I vs. t responses when the potential is stepped from Ei to E22 < 21 < E2, respectively. 

Corrosion current density — Anodic metal dissolution is compensated electronically by a cathodic process, like cathodic hydrogen evolution or oxygen reduction. These processes follow the exponential current density-potential relationship of the - Butler-Volmer equation in case of their charge transfer control or they may be transport controlled (- diffusion or - migration). At the -> rest potential Er both - current densities have the same value with opposite sign and compensate each other with a zero current density in the outer electronic circuit. In this case the rest potential is a -> mixed potential. This metal dissolution is related to the corro-... 

In case of a purely charge-transfer controlled current at the electrode one electrode process will dominate whereas the respective back-reaction contributes only a negligible fraction to the total current. Assuming this contribution to be <1% the back-reaction can be neglected at rj > 118/n mV with slopes B depending on n and a. At smaller values of rj deviations will appear ... 

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