Equality of electrochemical potentials

Equality of electrochemical potential, jl (= p + zFY) of every ion, regardless of position... 

A Criterion of Thermodynamic Equilibrium between Two Phases Equality of Electrochemical Potentials. It has been stated that ihe total driving force responsible for Ihe flow or transport of a species j is the gradient d lj/dx of its electrochemical potential. However, when there is net flow or flux of any species, this means that the system is not at equilibrium. Conversely, for the system to be at equilibrium, it is essential that there be no drift of any species—hence, that there should be zero gradients for the electrochemical potentials of all the species. It follows, therefore, that, for an interface to be at equilibrium, the gradients of electrochemical potential of the various species must be zero across the phase boundary, i.e.,... 

Hence, the equality of electrochemical potentials on either side of the phase boundary implies that the change in free energy of the system resulting from the transfer of particles from one phase to the other should be the same as that due to the transfer in the other direction. This is only another way of stating that when a thermodynamic system is at equilibrium, its free energy is a minimum, Le.,... 

Although the equilibrium principle was available (equality of electrochemical potential of each ion that reversibly equilibrates across an immiscible liquid/liquid interface), the elementary theory and consequences were not explored until recently (6). To develop an interfacial potential difference (pd) at a liquid interface, two ions M, X that partition are required. However,... 

The interfacial potential difference (pd) for the partition equilibrium interface is given by the equality of electrochemical potential in terms of all ions in equilibrium, equation (4). 

The relationship between the amount of substance on the electrode per unit area, 0t ri the concentration of bulk solution, ct, and the electrical state of the system, potential ( ) or charge (q) at a given temperature, is given by the adsorption isotherm. This is obtained from the condition of equality of electrochemical potentials for bulk and adsorbed species i at equilibrium (Bard and Faulkner, 1981). 

The thermodynamic treatment of the ITIES starts with the equality of electrochemical potential for ion i in the aqueous (w) and organic (org) phases. This equality leads directly to a version of the Nernst equation for the ITIES ... 

The electrochemical equilibrium requires the equality of electrochemical potentials for all components in the contacting phases. From this condition of electrochemical equilibrium, the dependence of Galvani potential on the activities of potential-determining ions can be derived, which represents the Nernst equation [27] for a separate Galvani potential. That is, for an interface formed by a metal (M) and solution (S) containing the ions of this metal... 

The dissolved metal atoms can be considered as an electrolyte, which dissociates producing M " cations and the simplest anions, eg. Actually, the condition = 0 cannot be achieved, because a finite value for the solubility product of metal exists, and, simultaneously, the condition of electroneutrality is valid. By using the condition of the equality of electrochemical potentials of electrons in the solution and in the metal phases, we obtain... 

Moreover, with the Volta and Galvani potential differences being taken as equal, the equality of electrochemical potentials yields the following ... 

Potentiometric methods of electroanalysis (see Chapter 7 of this handbook) depend on the ability of a membrane material to transport either cations or anions selectively. This selective behaviour results in an imbalance of concentrations on either side of the membrane which, in turn, leads to the estabhshment of a measurable potential difference across the membrane. In the simplest possible analysis, if we consider our membrane to be infinitely thin, or alternatively to have some kind of electrolyte boundary that is infinitely thin, then the equality of electrochemical potential, /I, in either of the solution phases, a and P, implies that... 

The further work on this subject connected with the names of Beutner [3], Bon-hoefifer, Kahlweit and Strehlow [4] and Karpfen and Randles [5], was mainly devoted to equilibrium potentials at ITIES, which can be described by the Nemst equation, derived in the following way. At the water/organic solvent (immiscible with water) phase boundary (w/o), an equihbrium exists between a particular univalent cationic species I in both the phases, described by equality of electrochemical potentials. 

Use of equation (8) requires knowledge of the concentration of mobile ions inside the polymer network which originated in the solution (c s)- This may be found from Donnan ion exclusion theory, which calculates the distribution of ions which develops to maintain the equality of electrochemical potentials of all ions In the system, both inside and outside the gel. Detailed derivation of this may be found elsewhere [23, 24]. The key result is that the distribution of the ions between the gel and the solution is governed by the following equation, where the primes indicate concentrations in the gel phase ... 

The school of Goldstein and of Professor Ephraim Katchalski et al. [79-80] used the expression of the equality of electrochemical potentials evaluated through the Maxwell-Boltzmann distribution function from which... 

For ion adsoiption in equilibrium on the electrode interface, the electrochemical potential Pi.., of hydrated adsorbate ions in aqueous solution equals the electrochemical potential Pi..d of adsorbed ions as shown in Eqn. 5-20 ... 

Activity effects. The exchange of trace ions in solution with others in the polymer film might, simplistically, be expected to lead to a linear uptake/solution concentration relationship. Unfortunately, this is seldom the case. The thermodynamic restraint is that of electrochemical potential. Thus electroneutrality is not the sole constraint on the ion exchange process. A second thermodynamic requirement is that the activity of mobile species in the polymer and solution phases be equal. (Temporal satisfaction of these two constraints is discussed below, with reference to Figure 4.) The rather unusual, high concentration environment in the polymer film can lead to significant - and unanticipated - activity effects (8). 

The experimentally measured reversible electrode potential, E q, includes not only the above emf but also the potential difference at the metal-platinum contact. The electrons are the electromotively active particles at this junction, and it may be assumed that at equilibrium an electrical potential difference exists between the two metals which equalizes the electrochemical potential of the electrons in the two phases. As is well known, it is equivalent to the Volta potential difference and is given by the following ... 

Figure 5-2 Distribution of + and - ions around the surface of an electrophoretic support. Fixed on the surface of the solid is a layer of - ions, (These may be + ions under suitable conditions.) A second layer of + ions is attracted to the surface. These two layers compose the Stern potentiai.The large, diffuse layer containing mostly + ions is the electro kinetic or zeta (Q potential. Extending farther from the surface of the solid is homogeneous solution.The Stern potential plus the zeta potential equals the electrochemical potential, or epsilon (e) potential.

The (Gibbs) free energy level of a solvated electron in a solution in equilibrium with the electrode is equal to the level of electrochemical potential of electron in metal p. We shall call this equilibrium electrode the electron electrode. Suppose that we are concerned with a standard solution (1 mol/1) and hence the standard potential E°. In this case, w determined at E° and corrected for the entropy of delocalized electrons (at n conforming to 1 mol/1) is the difference between standard chemical potentials of localized and delocalized electrons. 

In electrochemistry the semiconductor (phase I) is connected to an electrolyte (phase II). In equilibrium the electrochemical potential for the electrons in both phases must be equal. The electrochemical potential of the electrons in the semiconductor is equal to the Fermi energy. 

In general, the electrochemical potential of the electrons of two different materials is not the same. When a junction is made between n- and p-type semiconductors, or between a semiconductor and a metal, the system will reach thermodynamic equilibrium by equalizing the electrochemical potentials (the Fermi-energy levels) of the two materials. 

Suppose that a silver electrode is in equilibrium with a solution of silver nitrate (AgNOy), as shown in Figure 22.3. Silver is called the common ion in this case because it is the exchangeable component that is common to both the liquid and the solid. Silver ions (Ag+) can plate onto the solid metal or dissolve to increase the AgNO concentration in the liquid. Use the concentration c of Ag in solution as the degree of freedom. The condition for equilibrium is that the electrochemical potential of the silver ions in the solid must equal the electrochemical potential of the silver ions in the liquid ... 

If two metals with different work functions are placed m contact there will be a flow of electrons from the metal with the lower work function to that with the higher work fimction. This will continue until the electrochemical potentials of the electrons in the two phases are equal. This change gives rise to a measurable potential difference between the two metals, temied the contact potential or Volta potential difference. Clearly... 

The two dashed lines in the upper left hand corner of the Evans diagram represent the electrochemical potential vs electrochemical reaction rate (expressed as current density) for the oxidation and the reduction form of the hydrogen reaction. At point A the two are equal, ie, at equiUbrium, and the potential is therefore the equiUbrium potential, for the specific conditions involved. Note that the reaction kinetics are linear on these axes. The change in potential for each decade of log current density is referred to as the Tafel slope (12). Electrochemical reactions often exhibit this behavior and a common Tafel slope for the analysis of corrosion problems is 100 millivolts per decade of log current (1). A more detailed treatment of Tafel slopes can be found elsewhere (4,13,14). 

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