Electrode potentials rates

The modeling of ECR systems involves, as that of any other reaction system, the development of a suitable reaction model for subsequent use in reactor modeling. The reaction model for an ECR is an expression for the dependence of current density on reaction parameters such as reactant concentration, electrode potential, rate constants, pH, temperature, etc. The reactor model relates the reactor parameters to performance criteria. The objective is to evolve suitable expressions for the computation of the electrode area required for a desired conversion, batch time, etc. We devote the next section to developing reaction models for simple electrochemical systems and proceed to reactor modeling in the following section. 

At low currents, the rate of change of die electrode potential with current is associated with the limiting rate of electron transfer across the phase boundary between the electronically conducting electrode and the ionically conducting solution, and is temied the electron transfer overpotential. The electron transfer rate at a given overpotential has been found to depend on the nature of the species participating in the reaction, and the properties of the electrolyte and the electrode itself (such as, for example, the chemical nature of the metal). 

Corrosion protection of metals can take many fonns, one of which is passivation. As mentioned above, passivation is the fonnation of a thin protective film (most commonly oxide or hydrated oxide) on a metallic surface. Certain metals that are prone to passivation will fonn a thin oxide film that displaces the electrode potential of the metal by +0.5-2.0 V. The film severely hinders the difflision rate of metal ions from the electrode to tire solid-gas or solid-liquid interface, thus providing corrosion resistance. This decreased corrosion rate is best illustrated by anodic polarization curves, which are constructed by measuring the net current from an electrode into solution (the corrosion current) under an applied voltage. For passivable metals, the current will increase steadily with increasing voltage in the so-called active region until the passivating film fonns, at which point the current will rapidly decrease. This behaviour is characteristic of metals that are susceptible to passivation. 

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

The great advantage of the RDE over other teclmiques, such as cyclic voltannnetry or potential-step, is the possibility of varying the rate of mass transport to the electrode surface over a large range and in a controlled way, without the need for rapid changes in electrode potential, which lead to double-layer charging current contributions. 

The electrode current depends on the rates of the coupled reactions, but by suitable adjustment of the electrode potential (into the diffusion current region for the electrode reaction) the rate of the reduction reaction can be made so fast that the current depends only on the rate of the prior chemical reaction. The dependence of the observed current on the presence of the chemical reaction is a measure of the rate. 

Figure 4-420. Corrosion rate of a metal as a function of soiution oxidizing power (electrode potential). (From Ref [183].)...

As the corrosion rate, inclusive of local-cell corrosion, of a metal is related to electrode potential, usually by means of the Tafel equation and, of course, Faraday s second law of electrolysis, a necessary precursor to corrosion rate calculation is the assessment of electrode potential distribution on each metal in a system. In the absence of significant concentration variations in the electrolyte, a condition certainly satisfied in most practical sea-water systems, the exact prediction of electrode potential distribution at a given time involves the solution of the Laplace equation for the electrostatic potential (P) in the electrolyte at the position given by the three spatial coordinates (x, y, z). 

The most important outcome of this theory is that the rate of dissolution should be potentially greater as the pH increases, which is in conflict with simple concepts of corrosion kinetics. However, the theory has been proved to be applicable to many systems, and BonhoeflFer and Heusler found that iron in sulphuric acid corroded at a greater rate with increase in pH, whilst Kabanov etal. found that it corroded faster in alkaline solution than in acid solution for the same electrode potential. 

Under certain conditions, it will be impossible for the metal and the melt to come to equilibrium and continuous corrosion will occur (case 2) this is often the case when metals are in contact with molten salts in practice. There are two main possibilities first, the redox potential of the melt may be prevented from falling, either because it is in contact with an external oxidising environment (such as an air atmosphere) or because the conditions cause the products of its reduction to be continually removed (e.g. distillation of metallic sodium and condensation on to a colder part of the system) second, the electrode potential of the metal may be prevented from rising (for instance, if the corrosion product of the metal is volatile). In addition, equilibrium may not be possible when there is a temperature gradient in the system or when alloys are involved, but these cases will be considered in detail later. Rates of corrosion under conditions where equilibrium cannot be reached are controlled by diffusion and interphase mass transfer of oxidising species and/or corrosion products geometry of the system will be a determining factor. 

The corrosion reaction may also be represented on a polarisation diagram (Fig. 10.4). The diagram shows how the rates of the anodic and cathodic reactions (both expressed in terms of current flow, I) vary with electrode potential, E. Thus at , the net rate of the anodic reaction is zero and it increases as the potential becomes more positive. At the net rate of the cathodic reaction is zero and it increases as the potential becomes more negative. (To be able to represent the anodic and cathodic reaction rates on the same axis, the modulus of the current has been drawn.) The two reaction rates are electrically equivalent at E , the corrosion potential, and the... 

When corrosion occurs, if the cathodic reactant is in plentiful supply, it can be shown both theoretically and practically that the cathodic kinetics are semi-logarithmic, as shown in Fig. 10.4. The rate of the cathodic reaction is governed by the rate at which electrical charge can be transferred at the metal surface. Such a process responds to changes in electrode potential giving rise to the semi-logarithmic behaviour. 

The thermodynamic and electrode-kinetic principles of cathodic protection have been discussed at some length in Section 10.1. It has been shown that, if electrons are supplied to the metal/electrolyte solution interface, the rate of the cathodic reaction is increased whilst the rate of the anodic reaction is decreased. Thus, corrosion is reduced. Concomitantly, the electrode potential of the metal becomes more negative. Corrosion may be prevented entirely if the rate of electron supply is such that the potential of the metal is lowered to the value where it is found that anodic dissolution does not occur. This may not necessarily be the potential at which dissolution is thermodynamically impossible. 

When two different metals are immersed in the same electrolyte solution they will usually exhibit different electrode potentials. If they are then connected by an electronic conductor there will be a tendency for the potentials of the two metals to move towards one another they are said to mutually polarise. The polarisation will be accompanied by a flow of ionic current through the solution from the more negative metal (the anode) to the more positive metal (the cathode), and electrons will be transferred through the conductor from the anode to the cathode. Thus the cathode will benefit from the supply of electrons, in that it will dissolve at a reduced rate. It is said to be cathodically protected . Conversely, in supplying electrons to the cathode the anode will be consumed more rapidly, and thus will act as a sacrificial anode. 

The relationship of anode current density with electrode potential for mild steel in dilute aqueous soil electrolytes has been studied by Hoar and Farrer. The study shows that in conditions simulating the corrosion of mild steel buried in soil the logarithm of the anode current density is related approximately rectilinearly to anode potential, and the increase of potential for a ten-fold increase of current density in the range 10 to 10 A/cm is between 40 and 65 mV in most conditions. Thus a positive potential change of 20 mV produces a two- to three-fold increase in corrosion rate in the various electrolyte and soil solutions used for the experiments. 

Fig. 19.16 Schematic E — I diagrams of local cell action on stainless steel in CUSO4 + H2SO4 solution showing the effect of metallic copper on corrosion rate. C and A are the open-circuit potentials of the local cathodic and anodic areas and / is the corrosion current. The electrode potentials of a platinised-platinum electrode and metallic copper immersed in the same solution as the stainless steel are indicated by arrows, (a) represents the corrosion of stainless steel in CUSO4 -I- H2 SO4, (b) the rate when copper is introduced into the acid, but is not in contact with the steel, and (c) the rate when copper is in contact with the stainless steel...

Equilibrium Potential ( o) the electrode potential of an unpolarised electrode at equilibrium. At the equilibrium potential there is no net reaction. The potential is controlled by the same electrode reaction occurring anodically and cathodically at an equal rate, called the exchange current density. 

Hydrogen Overpotential (Overvoltage) the displacement of the equilibrium (or steady-state) electrode potential of a cathode required for the discharge of hydrogen ions at a given rate per unit area of electrode. 

In view of the problems referred to above in connection with direct potentiometry, much attention has been directed to the procedure of potentio-metric titration as an analytical method. As the name implies, it is a titrimetric procedure in which potentiometric measurements are carried out in order to fix the end point. In this procedure we are concerned with changes in electrode potential rather than in an accurate value for the electrode potential with a given solution, and under these circumstances the effect of the liquid junction potential may be ignored. In such a titration, the change in cell e.m.f. occurs most rapidly in the neighbourhood of the end point, and as will be explained later (Section 15.18), various methods can be used to ascertain the point at which the rate of potential change is at a maximum this is at the end point of the titration. 

Corrosion of the positive grid [Eq. (28)1 occurs equivalent to about 1 mA/lOOAh at open-circuit voltage and intact passivation layer. It depends on electrode potential, and is at minimum about 40-80mV above the PbS04/Pb02 equilibrium potential. The corrosion rate depends furthermore to some extent on alloy composition and is increased with high anti-monial alloys,... 

In general, the baser the metal, the lower (more negative) the electrical potential at the anode and the higher the potential rate of corrosion. Carbon steel and low-alloy steels (which are widely used in boiler plants) have a relatively low potential with respect to the standard hydrogen electrode and can therefore be expected to corrode readily unless active prevention measures are taken. Copper and brasses have a relatively higher potential. 

Let us mention some examples, that is, the passivation potential at which a metal surface suddenly changes from an active to a passive state, and the activation potential at which a metal surface that is passivated resumes active dissolution. In these cases, a drastic change in the corrosion rate is observed before and after the characteristic value of electrode potential. We can see such phenomena in thermodynamic phase transitions, e.g., from solid to liquid, from ferromagnetism to paramagnetism, and vice versa.3 All these phenomena are characterized by certain values... 

Figure 18 shows the dependence of the activation barrier for film nucleation on the electrode potential. The activation barrier, which at the equilibrium film-formation potential E, depends only on the surface tension and electric field, is seen to decrease with increasing anodic potential, and an overpotential of a few tenths of a volt is required for the activation energy to decrease to the order of kBT. However, for some metals such as iron,30,31 in the passivation process metal dissolution takes place simultaneously with film formation, and kinetic factors such as the rate of metal dissolution and the accumulation of ions in the diffusion layer of the electrolyte on the metal surface have to be taken into account, requiring a more refined treatment. 

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