Polarization at an electrode

Rather than describe the electrolysis of any solution with any two electrodes, we begin by considering a single reversible electrode at equilibrium and then ask what happens if we pass a current into the electrode. 

Consider a hydrogen electrode in equilibrium with H ion at a concentration c and hydrogen gas at a pressure p. The equilibrium potential of this electrode is denoted by 00 The equilibrium is Hj 2H + 2e . If the potential of the electrode is increased (made more positive), this equilibrium will be disturbed. The reaction from left to right will predominate, H2 will be oxidized, and a positive current will flow into the solution. If the potential of the electrode is lowered (made more negative), the equilibrium will be disturbed. The reaction from right to left will predominate, H2 will be liberated, and a positive current will fiow into the electrode or a negative current will flow into the solution. The current that fiows to the electrode, therefore, depends on the departure of the potential from the equilibrium value, 0 — 0o This difference between the applied potential 0 and the equilibrium potential 0 is the overpotential, or overvoltage, 

Since the current varies continuously with the potential, and therefore with the overpotential, we can expand the current in a Taylor series. Since i = 0 when t] = 0, the series 

We can write this in a slightly different way, using only the first term, 

For small values of rj, i is proportional to rj. Note also that the sign of i depends on the sign of tp The exchange current density for the reaction, o defined by Eq. (34.27), is the equilibrium value of either the anodic or cathodic current density. The value of depends on the concentrations of the electroactive materials, H and H2 in this case, and on the composition of the electrode surface. 

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A useful molecular model treatment of solvent orientation polarization at an electrode interface was given by Watts-Tobln and Mott (1961). Two orientation states of the solvent dipoles, up t and down 4, aligned with the electrode field E arising from net surface charge density q, were envisaged. The polarization in the interphase at the electrode surface was calculated in terms of the relative population Nt/(Nt + N4.) and N4/(Nt + Nl) of the two states of orientation. Nt and N4. are determined (a) by the field, (b) by temperature, and (c) by any lateral interaction forces between the oriented and unoriented dipoles. Interaction effects were not, however, taken into account in the original treatment. 

Electrical Double Layer In addition to an analytical expression for the activation polarization at an electrode which we will develop in this chapter, an understanding of the microscopic process occurring at the electrode during charge transfer is also important A very natural question often arises when discussion of the activation overvoltage is first introduced What is the physical nature of the activation polarization and how exactly does the charge transfer reaction proceed ... 

The concentration polarization is a result of decreasing surface concentration of reactant. The restriction can be a result of gas-phase transport limits, impurity absorption at the catalyst surface, liquid blockage in low-temperature fuel cells, or other reasons. The thermodynamic (Nernst) and kinetic concentration polarization at an electrode can be written as... 

Current flow at electrode surfaces often involves several simultaneous electrochemical reactions, which differ in character. For instance, upon cathodic polarization of an electrode in a mixed solution of lead and tin salt, lead and tin ions are discharged simultaneously, and from an acidic solution of zinc salt, zinc is deposited, and at the same time hydrogen is evolved. Upon anodic polarization of a nonconsumable electrode in chloride solution, oxygen and chlorine are evolved in parallel reactions. 

In fact, the occurrence of iresiduai represents an electrochemical polarization and that of iUmiting a concentration polarization the term depolarization should be used only if a polarizing agent occurring at an electrode is eliminated, e.g., Cl2 (and/or 02) at an anode is reduced by a reductant, or Zn (and/or H2) at a cathode oxidized by an oxidant. 

We consider a transfer of redox electrons at semiconductor electrodes polarized at an overvoltage t relative to the equilibrium redox potential (the Fermi level cfcredox)). The transfer current of redox electrons is given in Eqn. 8-54 by the arithmetic sum of the electron current via the conduction band, in(ti) - (0(11) > and the hole current via the valence band, ij(ii) - i (Ti) ... 

Fig. 8-42. Anodic and cathodic polarization curves observed for electron transfer of hydrated redox particles at an electrode of metallic niobium covered with a thick niobium oxide NbsOs film (12 nm thick) in acidic solution reaction is an electron transfer of hydrated redox particles, 0.25MFe(CN)6 /0.25M Fe(CN)g, in 0.1 M acetic add buffer solution of pH 4.6 at 25 C. =...

Activation Polarization Activation polarization is present when the rate of an electrochemical reaction at an electrode surface is controlled by sluggish electrode kinetics. In other words, activation polarization is directly related to the rates of electrochemical reactions. There is a close similarity between electrochemical and chemical reactions in that both involve an activation barrier that must be overcome by the reacting species. In the case of an electrochemical reaction with riact> 50-100 mV, rjact is described by the general form of the Tafel equation (see Section 2.2.4) ... 

B. Chronopotentiometry (Formerly called Voltammetry at Constant Current). These terms were applied by Delahay et al (Refs 4 5) to measurements in which the course of polarization of an electrode (immersed in an unstirred soln) under forced constant current was followed potentiometrically as a function of time. The potential-time curve recorded in the presence of a depolarizer is characterized by a transition time, during which the rate of change of potential is relatively small. This... 

When polarization occurs at an electrode with nonideal geometry (e.g., when the current is limited by rate of electron transfer or by mass transport), there is a gradient in potential in the solution adjacement to the electrode, and associated with this is a tangential as well as normal component of the current at the electrode surface.13 This causes the equipotential lines to intersect the electrode and the current lines to enter the electrode at angles other than 90°. (In the absence of polarization, or in a polarized electrode with ideal geometiy, the equipotential lines would be parallel to the electrode surface, and the current lines would intersect the electrode at an angle of 90°.)... 

Wagner number (Wa) — is the dimensionless parameter describing the so-called secondary -> current distribution at an electrode electrolyte interface (-> electrode, -> electrolyte, -> interface) under the conditions when -> overpotential cannot be neglected, but the -> concentration polarization is negligible [i]. This number is defined as... 

Recently we have published integral equation predictions for a flexible model of water next to a planar interface. Experimental motivation for this work includes electrochemical experiments on ultra-pure (Oj-free) water, surface EXAFS studies of the oxygen-metal distance for water at an electrode, and the tunnel junction device measurements of Porter and Zinn." Vossen and Forstmann have published a related calculation using a different model of water and a different approximation for the bulk water bridge functions. Below we compare the input to the two calculations. First we review some results in bulk water and solutions of non-polar solutes. 

The buildup of reaction products at an electrode is called polarization of the electrode. 

Polarization of an electrode Buildup of a product of oxidation or reduction at an electrode, preventing further reaction. 

Ac arcs have an alternating polarity at the electrodes. To reignite the arc an hf discharge is often used, which is superimposed onto the ac discharge gap. Because thermal effects are lower and the burning spot changes more frequently in the ac arc, the reproducibility is better than in the case of dc arcs. Here RSDs of the order of 5-10% may be obtained. 

Figure 16. Illustrating relative polarization performance of two processes at an electrode having two possible In Iq and corresponding b values, I and II. Process I gives better polarization performance at high c.d. despite its lower Iq value.

The description of corrosion kinetics in electrochemical terms is based on the use of potential-current diagrams and a consideration of polarization effects. The equilibrium or reversible potentials Involved in the construction of equilibrium diagrams assume that there is no net transfer of charge (the anodic and cathodic currents are approximately zero). When the current flow is not zero, the anodic and cathodic potentials of the corrosion cell differ from their equilibrium values the anodic potential becomes, more positive, and the cathodic potential becomes more negative. The voltage difference, or polarization, can be due to cell resistance (resistance polarization) to the depletion of a reactant or the build-up of a product at an electrode surface (concentration polarization) or to a slow step in an electrode reaction (activation polarization). 

Adherents to this theory have different opinions on the potential at which the film forms. Its thickness, the mechanism of formation, and, most Important, the "cause of passivity. In the earlier theories It was postulated that the passivation follows the formation of a "primary layer" of small conductivity, x lth porous character, which Is sometimes due to precipitation of metal salt on and near the electrode.(32) In the pores the current Increases, and by polarization at an "Umschlagspotentlal" (Vj, = V, Figure 1) an actual passive layer is formed. Thus the essential concept of the passivation process Is connected with the change of the properties (chemical or physical) of the primary film at a certain potential. The passive film Is free from pores and presents a barrier between the metal and the environment. It is electronically conductive and slowly corrodes In solution.(6,8,24,37)... 

When no current is flowing, the electrochemical changes occurring at an electrode are in steady state, i.e., atoms leave the electrode and become ions and the ions move to the electrode and becomes atoms. The process continuous till equilibrium is reached. A potential difference exists between electrode-electrolyte interfaces, which is known as electrode potential. The electrode potential between the electrode and electrolyte acts as a barrier to a faster rate of reaction, which is the electromotive force (emf) of the cell. External energy must be supplied so that ions are discharged at the required rate to promote current flow. Thus, when the current flows between the electrodes, several phenomena occur at the electrode surface that produce emf, which opposes the current flow. The deparmre of electrode potential from the equilibrium value upon passage of current is termed as polarization. ... 

Moreover, as soon as a current flows through the system, one of the electrodes becomes the anode and the other the cathode . However there is no automatic link between the polarity of an electrode and its role as an anode or a cathode . Unlike the notions of anode and cathode, the polarity of an electrode remains defined when the system is at open circuit. Finally, depending on the operating conditions of the electrochemical system in question, an electrode can be either the anode or cathode and also change its polarity... 

Should the copper electrode be polarized anodically, concentration of copper ion at the surface is larger than that in the body of solution. The ratio (Cu )/ (Cu )j then becomes less than unity and ( 2 - ( )i of (5.3) changes sign. In other words, concentration polarization at an anode polarizes the electrode in the cathodic or noble direction, opposite to the direction of potential change when the electrode is polarized as cathode. For a copper anode, the limiting upper value for concentration polarization corresponds to formation of saturated copper salts at the electrode surface. This limiting value is not as large as for cathodic polarization where the Cu activity approaches zero. 

Figure 3 (A) Diagram depicting the change from linearly to elliptically polarized iight upon reflection at an electrode surface. (B) Schematic diagram of an eiiipsometer setup.

Figure 4.12 (A) ORR polarization curves obtained at an electrode rotation of 400 rpm in 0.5 M H2SO4 for a pyrolyzed CoTPTZ/C catalyst and (B) pyrolysis temperature effect on the ORR potential obtained at a current density of 0.5 mA cm (For color version of this figure, the reader is referred to the online version of this book.) Reprinted from Ref. 57, with permission from Eisevier.

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