The Potentials of Phases

The surface potential of the phase, due to the presence of surface dipoles. At the metal-vacuum... 

The Volta potential, A very often called the contact potential, is the difference between the outer potentials of the phases, which are in electrochemical equilibrium in regard to the charged species, i.e., ions or electrons. Each two-phase electrochemical system, including a w/s system, may be characterized by the commonly known relation ... 

The energy of an ion in a given medium depends not only on chemical forces but also on the electrostatic held hence the chemical potential of an ion j customarily is called its electrochemical potential and labeled fi. The electrostatic potential energy of an ion j when reckoned per mole is given by ZjF, where / is the electrostatic (inner) potential of the phase containing the ion a plus sign for cations and a minus sign for anions. Hence, the electrochemical potential can be written as the sum of two terms ... 

Besides the Galvani potential, another important interfacial potential is the Volta potential, Aj I, sometimes ealled the eontaet potential. Aj I is the differenee of the outer potentials of the phases, whieh are in eleetroehemieal equilibrium with regard to the eharged speeies, i.e., ions or eleetrons. As for any two-phase eleetroehemieal system, ineluding the w/s system, it may be eharaeterized by the eommonly known relation ... 

Similar to galvanic cells, the membrane potential is determined by subtracting the electric potential of the phase on the left from that of the phase on the right, i.e. 

Table 1.1 Conjugate pairs of variables in work terms for the fundamental equation for the internal energy U. Here/is force of elongation, Z is length in the direction of the force, <7 is surface tension, As is surface area, , is the electric potential of the phase containing species i, qi is the contribution of species i to the electric charge of a phase, E is electric field strength, p is the electric dipole moment of the system, B is magnetic field strength (magnetic flux density), and m is the magnetic moment of the system. The dots indicate scalar products of vectors.

Then, adopting the condition of the pzc (Section 6j6j6), i.c., q = 0, it follows that the outer potential of the phase concerned, J/, is zero. Hence,... 

The basic parameters which determine the kinetics of internal oxidation processes are 1) alloy composition (in terms of the mole fraction = (1 NA)), 2) the number and type of compounds or solid solutions (structure, phase field width) which exist in the ternary A-B-0 system, 3) the Gibbs energies of formation and the component chemical potentials of the phases involved, and last but not least, 4) the individual mobilities of the components in both the metal alloy and the product determine the (quasi-steady state) reaction path and thus the kinetics. A complete set of the parameters necessary for the quantitative treatment of internal oxidation kinetics is normally not at hand. Nevertheless, a predictive phenomenological theory will be outlined. 

Whenever the total pressure is increased on a condensed phase, the chemical potential of the phase is increased. As a consequence, the pressure of the vapor in equilibrium with the condensed phase must also increase. The discussion here is limited to the liquid phase, but the basic equations that are developed are applicable also to a solid phase. 

Thus the molar enthalpy of an ion is affected by the electric potential of the phase in the same way as the chemical potential. 

Because liquid and gas are at equilibrium in the two-phase region, the chemical potentials of the phases with Vml and Vm3 must be equal. Points 1 and 3 lie on the same isotherm therefore, we can write... 

Phase transfer (a —> (5) can be treated exactly as for chemical reactions, with the affinity of phase transfer equal to the difference in chemical potentials of the phases ... 

The procedure to locate the phase transition boundaries from a dilute disordered (fluid) phase to a concentrated ordered (solid) phase involves the determination of the chemical potential of the particles in both phases. The condition of the equality of the pressures and of the chemical potentials of the phases locates the phase transition boundaries. The chemical potential of the particles in each phase is obtained using the following expression, separately for each phase ... 

Prove that the common tangent construction is equivalent to the equality of chemical potentials of the phases whose compositions are given by the points of tangency. 

Consideration of the quantity - )r requires some conceptual subtlety. This is intended to be the electrostatic potential of the solution induced by reference interactions between the solute and the solution. Any contribution to the electrostatic potential that exists in the absence of those reference interactions we will call the electrostatic potential of the phase, but of course only electrostatic potential differences, e.g. between uniform conducting materials, are expected to be physically interesting. 

The latter point suggests several further observations. Eirst, we are free to adopt an arbitrarily chosen value for the potential of the phase for convenience. The value zero (0) is such a choice, and a natural choice for detailed calculations. Second, if we take a linear combination of corresponding to neutral collections... 

With two conducting fluids in coexistence, the values of the electrostatic potentials of the phases can be regarded as a mechanical property obtainable by solution... 

These subtleties sometimes lead to a casual view of detailed molecular calculations such as are suggested by Eq. (4.22). If the potential of the phase is always irrelevant to neutral linear combinations of which are thermodynamically measurable, then perhaps it is unimportant to be precise about an assumed value. Our suggestion is that results obtained by molecularly detailed calculations of solvation free energies of single ions are compared and tabulated. Thus, precision and clarity in the assumptions underlying a calculated or tabulated result are important. Indeed, if calculated or tabulated values based upon different assumptions for the potential of the phase were to be combined, it would be essential that the assumptions be precisely known. Nevertheless, an ultimate thermodynamic test of a calculation should be made on thermodynamically measurable combinations of single ion free energies. 

Since periodic boundary conditions preserve translational homogeneity, a physical perspective on this requirement is that the potential of the phase -see p. 69 - is zero. Show that the potential... 

Figure 8.23 Comparison of experimental absolute hydration free energies for some monovalent ions with values calculated on the basis of the primitive quasi-chemical approximation, at ideal 1M standard state conditions (Asthagiri et al, 2003a), (a) with single-ion values shows an offset of positive and negative ions identifying at this level of approximation a potential of the phase contribution as discussed in Section 4.2, following p. 67. This offset vanishes with neutral combinations shown in (b).

Equation (17.6) is the relation between the escaping tendency of the electrons, fie-, in a phase and the electrical potential of the phase, 0. The escaping tendency is a linear function of 0. Note that Eq. (17.6) shows that if 0 is negative, Pe - is larger than when 0 is positive. 

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