Phase boundary potentials, definition

The electrical potential at an oil -j- water interface has been the subject of many investigations aimed at discovering the part it plays in bio-electric phenomena. These investigations tried to relate the changes of this potential to the nature of the ions in the aqueous solution. The observed results have been attributed to adsorption potentials, diffusion potentials 2 and thermodynamic phase-boundary potentials.3 It has been shown that the first of these suggestions is definitely false 4 and it seems likely that diffusion potentials and phase-boundary potentials have both made a contribution in the systems investigated hitherto. The attempts at quantitative correlation 2 can hardly be considered successful. 

The case of the prescribed material flux at the phase boundary, described in Section 2.5.1, corresponds to the constant current density at the electrode. The concentration of the oxidized form is given directly by Eq. (2.5.11), where K = —j/nF. The concentration of the reduced form at the electrode surface can be calculated from Eq. (5.4.6). The expressions for the concentration are then substituted into Eq. (5.2.24) or (5.4.5), yielding the equation for the dependence of the electrode potential on time (a chronopotentiometric curve). For a reversible electrode process, it follows from the definition of the transition time r (Eq. 2.5.13) for identical diffusion coefficients of the oxidized and reduced forms that... 

Table I presents six basic equations in a general way. Those on the left apply to transfer within a phase A, and those on the right to transfer across a phase boundary AB. The top row expresses the mutual definition of force F, proportionality constant K, and potential . The second row expresses the phenomenological proportionality between flux J and force F. The bottom row states the conservation constraints. The left equation says merely that in a given volume the difference between the accumulation rate and the emanation rate must be attributed to a source S. As stated, these equations apply to any conserved quantity which is diffusing, either within a phase under the influence of a potential gradient or across a phase under the influence of a potential difference.

The process is essentially similar to that of the establishment of the contact potential between two metals in a vacuum the equalization in the two phases of the energy levels (or electrochemical potentials), of the ion passing the phase boundary, establishes a definite difference in the electrostatic potentials of the metal and the electrolyte. The main difference from the case of simple contact potentials is that the energy level of the ion in solution is very largely determined by the energy of hydration. 

A single electrode potential, if defined as the difference in electrostatic potential between the spaces just outside the metal and the solution, is definite, but it cannot be measured by merely connecting up the phases with wires, and adjusting a potentiometer, until no current flows for this connexion introduces more than one phase boundary. Practically all electrolytic cells consist of at least three phase boundaries and the terminals at which the electromotive force of the cell is measured are, finally, of the same metal. There may, of course, be any. greater number of phase boundaries. A simple type of cell consists of two metals, M and M, dipping into a solution 8 containing the ions of each metal. 

Let the test ion in the solution be at the point jc, where the potential is y/ (Fig. 4.43). This potential is by definition the work done to bring a unit of positive charge from infinity up to the particular point. [In the course of this journey of the test charge from infinity to the particular point, it may have to cross phase boundaries, for example, the electrolyte-air boundary, and thereby do extra work (see Chapter 6). Such surface work terms cancel out, however, in discussions of the differences in potential between two points in the same medium.] If another point. 2 chosen on the normal from jr to... 

Note, that if stress is reduced to pressure P,T = —PI, (usual in fluids) this definition gives the classical result (3.203) F = gl, see (3.199). The Eshelby tensor, e.g. gives the condition of phase equilibria (Maxwell relation—equality of chemical potentials (2.116) in fluid phases), namely equality of f[n on both sides of equilibrated solid phases (n is the normal to phase boundary) and may be also used to describe surface phenomena, dislocations, etc. [1, 4, 87]. Eshelby tensors may also be defined in mixtures [2, 3]. 

Although there is no external current, anodic and cathodic processes can still occur at sites on the interface between solid and aqueous solution because of the electrolytic conductance of the corrosive medium. At electrochemical equilibrium, this leads to a definite jump in the electrical potential at the phase boundary. Kinetic barriers to certain partial reaction steps of the electrochemical process can cause the potential to be displaced from its equilibrium value. Thus, for example, instead of a dissolution of metal ... 

What we mean in this report by equilibrium and disequilibrium requires a brief discussion of definitions. Natural physicochemical systems contain gases, liquids and solids with interfaces forming the boundary between phases and with some solubility of the components from one phase in another depending on the chemical potential of each component. When equilibrium is reached by a heterogeneous system, the rate of transfer of any component between phases is equal in both directions across every interface. This definition demands that all solution reactions in the liquid phase be simultaneously in equilibrium with both gas and solid phases which make contact with that liquid. Homogeneous solution phase reactions, however, are commonly much faster than gas phase or solid phase reactions and faster than gas-liquid, gas-solid and... 

The above equations need some comment. In the first place the surface phase may presumably not be regarded as a homogeneous phase and consequently the chemical potential /i is not strictly defined. n is also not sharply defined because the boundaries of the smdace phase cannot be prescribed. However, as will be shown subsequently, more precise definitions of these quantities can be given. 

While high-resolution transmission electron miCToscopy (TEM) is a powerful technique, it samples only a tiny fraction of the grain boundary area, potentially allowing some grain boundary defects to be missed. A definitive statement as to the absence of grain boundary phases cannot be made—the phases could be too thin or too sparse to detect. For electrically conducting materials, IS averages over the entire sample and thus provides a valuable complement to TEM. 

The International Standard Organization (ISO 14040) [26] breaks the LCA framework into four main stages (1) Goal and scope definition of the study. This stage clarifies the purposes of carrying the study while the assumptions and system boundaries are described clearly. (2) Life Cycle Inventory (LCI) analysis. LCI involves data collection and calculation procedures to quantify relevant inputs and outputs of the entire system defined within the system boundaries. (3) Life cycle impact assessment involves qualifying the potential environmental impacts of the inventory analysis results. (4) The interpretation of the results from the previous phases of the study in relation to the objective of the study. This interpretation can be in form of conclusions and recommendations to decision-makers for process changes to deliver improvement in the environmentel performance. 

Many examples of such investigations undertaken at various phases of development could be cited, showing that induction is connected as a rule with contact between tissues and that it implies the activation of systems restricting the morphogenetic potential of a particular area to within the boundaries of a definite system of specialization. 

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