Electrochemical Equilibrium State

The electric equilibrium state of an electrode (Me) coated with a fixed-charge polymer film is shown in Fig. The electrolyte is 

FIGURE 3.8. The electropotential ( 4 ) profile across a polymer-coated electrode in equilibrium with an electrolyte. Negative fixed charges correspond to a negative Donnan potential (A q) across the polymer/electrolyte interface. 

Now suppose the film is electroactive, such as the polymers in Figs. 3.1 and 3.2 and the electrode is polarized by applying electrode potential E. We assume that any current flow is so small that IR drops are negligible and the potential drop - f ) remains practically con- 

The electrochemical charge transfer reaction between the metallic substrate (Me, the electrode) and the polymer redox sites and 

It is important for the system analysis that redox sites are confined to the polymer matrix, i.e., electrochemical potentials of ox and red in the electrolyte, fired and filx are not defined/ Therefore the equilibrium potential across the polymer/electrolyte interface is defined by the ion-(in particular X ) partitioning equilibria, Eqn. 5. The electrode potential ( measured with the reference electrode in the electrolyte) of the electrode coated with the electroactive polymer film can thus be formulated as 

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Note that there are virtually an infinite number of combinations of cell voltage and cell composition (the activity term) that satisfy this equation. Thus, there are an infinite number of electrochemical equilibrium states, each corresponding to a different cell voltage [i]. 

In the equilibrium state, the electrochemical potentials of each ft,- ion, present simultaneously in both phases are identical ... 

In the equilibrium state the electrochemical potentials of each ion are the same in both phases, and the equations (1) to (7) are fulfilled. It is apparent from the mass conservation law that ... 

Redox potential (thermodynamic derivation). Suppose we take an electrochemical cell represented by Fig. 2.7. We shall now address the question of both the potential values and the equilibrium state that can be finally attained... 

A very important electrochemical phenomenon, which is not well understood, is the so-called memory effect. This means that the charging/discharging response of a conducting polymer film depends on the history of previous electrochemical events. Thus, the first voltammetric cycle obtained after the electroactive film has been held in its neutral state differs markedly in shape and peak position from subsequent ones [126]. Obviously, the waiting time in the neutral state of the system is the main factor determining the extent of a relaxation process. During this waiting time, which extends over several decades of time (1-10 s), the polymer slowly relaxes into an equilibrium state. (Fig. 13) After relaxation, the first oxidation wave of the polymer appears at more... 

Study of the charge-transfer processes (step 3 above), free of the effects of mass transport, is possible by the use of transient techniques. In the transient techniques the interface at equilibrium is changed from an equilibrium state to a steady state characterized by a new potential difference A(/>. Analysis of the time dependence of this transition is the basis of transient electrochemical techniques. We will discuss galvanostatic and potentiostatic transient techniques for other techniques [e.g., alternating current (ac)], the reader is referred to Refs. 50 to 55. 

The reaction produces hydroxyl ions which react directly with the Fe ions to produce an oxide precipitate. The combined anodic and cathodic reactions form the corrosion cell, the electrochemical potential of which lies between the single potential of the two half reactions. This mixed potential is termed the corrosion potential, corr> and for corrosion to proceed beyond the equilibrium state, the corrosion potential must be more positive than the equilibrium single potential of iron. For iron in water at pH 7 and with [Fe j = 10" M, for example, the potential of the anodic reaction is. 

K+ ions in the presence of valinomycin do not distribute passively at electrochemical equilibrium rather, this represents a nonequilibrium state in which creates a diffusion potential following which protons move. 

A and B, both with patchy surfaces and at the same temperature, connected electrically. Then, if the distance of separation is large compared with the size of the patches, so that the patch fields between the two conductors are negligibly small, the equilibrium state corresponds to that in which the electrochemical potentials in the two conductors are equal. Thus,... 

A further standard method for electrochemical analysis is cyclic voltammetry. A voltage ramp is increased and decreased between two potential limits and the curent is monitored. In the resulting curve, electrochemical reactions in the equilibrium state can be detected. At platinum electrodes, the formation of Pt-H complexes and the oxidation and reduction at the metal surface can clearly be observed (Fig. 23). 

Obviously, plasmas can be used very efficiently within the synthetic approach (i), and all examples given in this paper are assigned to the synthetic approach. It is much less obvious whether plasmas can be used also in the counter-direction. In order to measure a stable and reproducible electromotive force (EMF) the corresponding electrochemical (galvanic) cell must be in (local) thermodynamic equilibrium. Low-temperature plasmas represent non-equilibrium states and are highly inhomogeneous systems from a thermodynamic point of view, often not... 

There are some important general relations for a substance adsorbed from solution on an electrode. These pertain to the equilibrium state and the kinetics of the process leading to equilibrium. Adsorption kinetics receives rather intermittent attention in the electrochemical literature. One of the clearest discussions is by Mohilner [403] see also Delahay [200], Bard and Faulkner [74]. 

In order to characterize the equilibrium state of the electrochemical cells, the electronic conductor connecting the electrodes of Figure 3.1.5 is removed. Now, both electrodes may establish their individual charge-transfer equilibrium state. A stable equilibrium potential difference, E, is established between the two electrodes. 

If both electrode processes operate under standard conditions, this voltage is E°, the equilibrium standard electrode potential difference. Values of E and E° may be conveniently measured with electrometers of so large an internal resistance that the current flow is nearly zero. Figure 3.1.6 illustrates the measurement and the equilibrium state. The value of E° is a most significant quantity characterizing the thermodynamics of an electrochemical cell. Various important features of E and E° will be addressed in the following chapters. 

When an electrochemical reaction is perturbed from its equilibrium state, the relative stabilities of the species in the reaction are changed. The change due to the perturbation is reflected in the measured electrode potential, which differs from the equilibrium... 

Reversibility — This concept is used in several ways. We may speak of chemical reversibility when the same reaction (e.g., -> cell reaction) can take place in both directions. Thermodynamic reversibility means that an infinitesimal reversal of a driving force causes the process to reverse its direction. The reaction proceeds through a series of equilibrium states, however, such a path would require an infinite length of time. The electrochemical reversibility is a practical concept. In short, it means that the -> Nernst equation can be applied also when the actual electrode potential (E) is higher (anodic reaction) or lower (cathodic reaction) than the - equilibrium potential (Ee), E > Ee. Therefore, such a process is called a reversible or nernstian reaction (reversible or nerns-tian system, behavior). It is the case when the - activation energy is small, consequently the -> standard rate constants (ks) and the -> exchange current density (jo) are high. 

The Nemst equation is a thermodynamic expression of the equilibrium state of an electrochemical reaction. It can give the value of the thermodynamic electrode potential for electrochemical reactions as well as point out the reaction direction. However, it cannot show the reaction rate. To connect the reaction rate and the electrode potential, one needs to use the Butler-Volmer equation. 

Note, however, that an equilibrium state is truly met only when electrochemical potentials of products and reactants are equal. Therefore,... 

A metal CMP process involves an electrochemical alteration of the metal surface and a mechanical removal of the modified film. More specifically, an oxidizer reacts with the metal surface to raise the oxidation state of the material, which may result in either the dissolution of the metal or the formation of a surface film that is more porous and can be removed more easily by the mechanical component of the process. The oxidizer, therefore, is one of the most important components of the CMP slurry. Electrochemical properties of the oxidizer and the metal involved can offer insights in terms of reaction tendency and products. For example, relative redox potentials and chemical composition of the modified surface film under thermodynamically equilibrium condition can be illustrated by a relevant Pourbaix diagram [1]. Because a CMP process rarely reaches a thermodynamically equilibrium state, many kinetic factors control the relative rates of the surface film formation and its removal. It is important to find the right balance between the formation of a modified film with the right property and the removal of such a film at the appropriate rate. 

The corresponding equilibrium state of distributions of various metal ions usually differs from those of the soil substrate, hence entails some fractionation during transport as described before. So, fractionation can be compared to that effected by some single ligand, and Eq. 2.4 and its inversion are then used to define some effective electrochemical ligand parameter which describes the capability of some plant organ to fractionate among metals. 

We first take up the case where we have arrested the reaction at a particular stage for which the participating species involve a concomitant set of mole numbers n, such that the Gibbs free energy in the arrested stage at a specified T and P is given by G = Yli One method of achieving this state is to carry out the reaction in a reversible electrochemical cell, in the manner described in Chapter 4. A special case of particular interest, which requires no outside intervention, is the equilibrium state, with G — where the mole numbers n, and... 

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