Ideally polarized electrodes

In the potential region where nonequilibrium fluctuations are kept stable, subsequent pitting dissolution of the metal is kept to a minimum. In this case, the passive metal apparently can be treated as an ideally polarized electrode. Then, the passive film is thought to repeat more or less stochastically, rupturing and repairing all over the surface. So it can be assumed that the passive film itself (at least at the initial stage of dissolution) behaves just like an adsorption film dynamically formed by adsorbants. This assumption allows us to employ the usual double-layer theory including a diffuse layer and a Helmholtz layer. 

An ideally polarized electrode is rigorously defined as the electrode at which no charge transfer across the metal/solution interface can occur, regardless of the potential externally imposed on the electrode. At any fixed potential, such an electrode system attains a true state of equilibrium. 

Generally, for ideally polarized electrodes, the plots of the electrode potential against either the chemical potential of the component in question or its activity are referred to as the Esin and Markov plots the slope of the plot is called the Esin and Markov coefficient.82 Aogaki etal.19 first established the expression of the critical pitting potential with respect to the composition of the solution (i.e., the Esin and Markov relations corresponding to the critical condition of the instability obtained in the preceding sections) and also verified them experimentally in the case of Ni dissolution in NaCl solution. 

The term electrode potential is often used in a broader sense, e.g. for the potential of an ideally polarized electrode (Chapter 4) or for potentials in non-equilibrium systems (Chapter 5). 

Another definition of an ideal polarized electrode is based on the practical form of this electrode. At an ideal polarized electrode either no exchange of charged particles takes place between the electrode and the solution or—if thermodynamically feasible—exchange occurs very slowly as a result of the large activation energy. 

The interfacial tension always depends on the potential of the ideal polarized electrode. In order to derive this dependence, consider a cell consisting of an ideal polarized electrode of metal M and a reference non-polarizable electrode of the second kind of the same metal covered with a sparingly soluble salt MA. Anion A is a component of the electrolyte in the cell. The quantities related to the first electrode will be denoted as m, the quantities related to the reference electrode as m and to the solution as 1. For equilibrium between the electrons and ions M+ in the metal phase, Eq. (4.2.17) can be written in the form (s = n — 2)... 

Fig. 4.10 Capillary electrometer. The basic component is the cell consisting of an ideally polarized electrode (formed by the mercury meniscus M in a conical capillary) and the reference electrode R. This system is connected to a voltage source S. The change of interfacial tension is compensated by shifting the mercury reservoir H so that the meniscus always has a constant position. The distance between the upper level in the tube and the meniscus h is measured by means of a cathetometer C. (By courtesy of L. Novotny)...

At low overpotentials, the silver electrode prepared according to Budev-ski et al. behaves as an ideal polarized electrode. However, at an overpotential higher than —6 mV the already mentioned current pulses are observed (Fig. 5.48A). Their distribution in the time interval r follows the Poisson relation for the probability that N nuclei are formed during the time interval x... 

So far we have considered electrodes whose potentials are determined through the cell reaction of the ions with which they are in contact. Such a potential cannot be formed on an ideally polarized electrode, for example a mercury electrode in a KCl solution within a certain potential region. In this case the electrode potential is determined by the electrode charge. 

Platinum electrodes are widely used as an inert electrode in redox reactions because the metal is most stable in aqueous and nonaqueous solutions in the absence of complexing agents, as well as because of its electrocatalytic activity. The inertness of the metal does not mean that no surface layers are formed. The true doublelayer (ideal polarized electrode) behavior is limited to ca. 200-300 mV potential interval depending on the crystal structure and the actual state of the metal surface, while at low and high potentials, hydrogen and oxygen adsorption (oxide formation) respectively, occur. 

Ideal polarized electrode — Working electrode in the situation when a large change of potential is accompanied by an infinitesimal increase of the current. The ideal polarizability is characterized by a horizontal region of a potentiostatic I-E curve (so-called potential window where the electrode can be used for measurements). See also -> electrode. 

An -> ideal nonpolarizable electrode is one whose potential does not change as current flows in the cell. Much more useful in electrochemistry are the electrodes that change their potential in a wide potential window (in the absence of a - depolarizer) without the passage of significant current. They are called -> ideally polarized electrodes. Current-potential curves, particularly those obtained under steady-state conditions (see -> Tafel plot) are often called polarization curves. In the -> corrosion measurements the ratio of AE/AI in the polarization curve is called the polarization resistance. If during the -> electrode processes the overpotential is related to the -> diffusional transport of the depolarizer we talk about the concentration polarization. If the electrode process requires an -> activation energy, the appropriate overpotential and activation polarization appear. 

Figure 5.11 Potential distribution for a cell at open circuit consisting of ideally polarized electrodes.

The local Ohmic impedance Zg accounts for the difference between the loccil interfacial and the local impedances. The calculated local Ohmic impedance for Tafel kinetics with 7 = 1.0 is presented in Figure 13.9 in Nyquist format with normalized radial position as a pcirameter. The results obtained here for the local Ohmic impedance are very similar to those reported for the ideally polarized electrode and for the blocking electrode with local CPE behavior. ° ° At the periphery of the electrode, two time constants (inductive and capacitive loops) are seen, whereais at the electrode center only an inductive loop is evident. These loops are distributed around the asymptotic real value of 1/4. 

For an ideal-polarized electrode, the capacity values should be, in a large range, independent of the frequency of this alternating signal. 

Current-potential curves, particularly those obtained under steady-state conditions, are sometimes called polarization curves. We have seen that an ideal polarized electrode (Section 1.2.1) shows a very large change in potential upon the passage of an infinitesimal current thus ideal polarizability is characterized by a horizontal region of an i-E curve (Figure 1.3.5a). A substance that tends to cause the potential of an electrode to be nearer to its equilibrium value by virtue of being oxidized or reduced is called a depolarizer An... 

The ideal polarized electrode is one in which current remains constant and independent of potential over a wide range, Figure 22-6a is a current-voltage curve for an electrode that is ideally polarized in the region between A and B. Figure 22-6b shows the current-volutgc relationship for a nonpolarized electrode that behaves ideally in the region between A and H. For this electrode, the potential is independent of the current. 

Under this condilion, concentration polarization is said to be complete, and the electrode operates as an ideal polarized electrode. 

An electrode at which no charge-transfer occurs across the electrode-solution interface, regardless of the potential imposed from an outside source of voltage, is called an ideally polarized electrode. No real electrode, of course, can behave in this... 

Only nonfaradaic processes occur at an ideally polarized electrode. 

C( aeitaiice of an Electrode. Since charge cannot cross the interface at an ideally polarized electrode when the potential is changed, the behavior of this interface is similar to that of a capacitor (Fig. 1.1). When a potential is applied across a capacitor, it will charge until it satisfies the relation... 

Faradme Processes. Consider an ideally polarized electrode only nonfaradaic processes occur, no charges cross the interface, and no continuous current can flow. Upon addition of a substance that can be oxidized or reduced at the particular potential difference, current now flows—the electrode is depolarizedy and the substance responsible is called a depolarizer. 

An overpotential contribution is required for both the anodic and the cathodic reaction and, in this case, it is mainly to oxidize water at the Pt anode. As copper is deposited and the concentration of Cu ions falls, both the ohmic potential drop IR across the electrolyte and the overpotential decrease. If we assume that the solution resistance R remains fairly constant, the ohmic potential drop is directly proportional to the net cell current. The overpotential increases exponentially with the rate of the electrode reaction. Once the Cu ions cannot reach the electrode fast enough, we say that concentration polarization has set in. An ideally polarized electrode is one at which no faradaic reactions ensue that is, there is no flow of electrons in either direction across the electrode-solution interface. When the potential of the cathode falls sufficiently to reduce the next available species in the solution (H" ions, or nitrate depolarizer), the copper deposition reaction is no longer 100% efficient. 

A subsequent description by Bockris and associates drew attention to further complexities as shown in Figure 15. The metal surface now is covered by combinations of oriented structured water dipoles, specifically adsorbed anions, followed by secondary water dipoles along with the hydrated cation structures. This model serves to bring attention to the dynamic situation in which changes in potential involve sequential as well as simultaneous responses of molecular and atomic systems at and near an electrode surface. Changes in potential distribution involve interactions extending from atom polarizability, through dipole orientation, to ion movements. The electrical field effects are complex in this ideal polarized electrode model. 

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