Electrical term, chemical potential

We call M/.chem the chemical part of the chemical potential. It is assumed to be independent of the electric potential and depends only on temperature, pressure, and the composition of the system. The chemical potential including the electric potential term is the true chemical potential that obeys the fundamental fact of phase equilibrium. Some electrochemists use the term electrochemical potential for the chemical potential in Eq. (8.1-7) and refer to the chemical part of the chemical potential as the chemical potential. We will use the term chemical potential for the tme chemical potential and the term chemical part of the chemical potential for /r,diein-... 

The electrochemical potentials pi, may now be expressed in terms of the chemical potentials pt, and the electrical potentials (see Section V-9) ... 

The percutaneous absorption picture can be qualitatively clarified by considering Fig. 3, where the schematic skin cross section is placed side by side with a simple model for percutaneous absorption patterned after an electrical circuit. In the case of absorption across a membrane, the current or flux is in terms of matter or molecules rather than electrons, and the driving force is a concentration gradient (technically, a chemical potential gradient) rather than a voltage drop [38]. Each layer of a membrane acts as a diffusional resistor. The resistance of a layer is proportional to its thickness (h), inversely proportional to the diffusive mobility of a substance within it as reflected in a... 

The analysis of oxidation processes to which diffusion control and interfacial equilibrium applied has been analysed by Wagner (1933) who used the Einstein mobility equation as a starting point. To describe the oxidation for example of nickel to the monoxide NiO, consideration must be given to the respective fluxes of cations, anions and positive holes. These fluxes must be balanced to preserve local electroneutrality throughout the growing oxide. The flux equation for each species includes a term due to a chemical potential gradient plus a term due to the electric potential gradient... 

We commence with the adsorption of nonionic surfactants, which does not require the consideration of the effect of the electrical double layer on adsorption. The equilibrium distribution of the surfactant molecules and the solvent between the bulk solution (b) and at the surface (s) is determined by the respective chemical potentials. The chemical potential /zf of each component i in the surface layer can be expressed in terms of partial molar fraction, xf, partial molar area a>i, and surface tension y by the Butler equation as [14]... 

The effective polarizability of surface atoms can be determined with different methods. In Section 2.2.4(a) a method was described on a measurement of the field evaporation rate as a function of field of kink site atoms and adsorbed atoms. The polarizability is derived from the coefficient of F2 term in the rate vs. field curve. From the rate measurements, polarizabilities of kink site W atoms and W adatoms on the W (110) surface are determined to be 4.6 0.6 and 6.8 1.0 A3, respectively. The dipole moment and polarizability of an adatom can also be measured from a field dependence of random walk diffusion under the influence of a chemical potential gradient, usually referred as a directional walk, produced by the applied electric field gradient, as reported by Tsong et a/.150,198,203 This study is a good example of random walk under the influence of a chemical potential gradient and will therefore be discussed in some detail. 

Separation into chemical and electrical terms is possible with gradients but not with quantities, i.e., p and < >, themselves. The reason is simple. The electrochemical potential p was only conceptually separated into a chemical term p and an electrical term z F< >. The conceptual separation was based on thought experiments in practice, no experimental arrangement can be devised to correspond to the thought experiment described in Section 6.3.13.1, Thus, e.g., one cannot switch off the charges and dipole layer at the surface of a solution as one can switch off the externally applied field in a transport experiment Only the combined effect of lj and ZjFij) can be determined. 

Uniform chemical potential at equilibrium assumes that the component conveys no other work terms, such as charge in an electric field. If other other energy-storage mechanisms are associated with a component, a generalized potential (the diffusion potential, developed in Section 2.2.3) will be uniform at equilibrium. 

The Nernst-Planck equation constitutes the starting point for the electrotransport models [55-57], The overall flux of the ionic species i (/,) comprises the diffusion term driven by the chemical potential gradient (dc,/dx) and the electric transference term due to the electrical potential gradient (d /dx) ... 

We recognize that we cannot determine experimentally the thermodynamic properties of a single type of ion in solution, because both positive and negative ions must be present to satisfy the condition of electrical neutrality. However, we can use equations based on those previously derived, and express the chemical potential of a single type of ion in terms of the concentration variables at a given temperature and pressure. We follow convention here and use molalities and activity coefficients. Then we have... 

The difference between the electrical potentials in the two copper wires is determined by the difference [/l"(Cu) — e(Cu)] under equilibrium conditions with certain restrictions. (The single prime refers here to all parts of the cell to the left of the boundary between the two solutions, and the double prime to all parts to the right of the boundary.) The restrictions are that the boundaries between the various parts of the cell are permeable only to certain species. Without such restrictions the electrical potential difference of the electrons in the copper wires would be zero at equilibrium. The boundary between the copper and platinum or between the copper and silver is permeable only to electrons that between the platinum with adsorbed hydrogen and the first solution is permeable to hydrogen ions but not electrons that between the second solution and the silver chloride is permeable to chloride ions but not electrons and that between the silver chloride and silver is permeable only to silver ions. We ignore the presence of the boundary between the two solutions, for the present. The conditions of equilibrium in terms of the chemical potentials are then ... 

We observe that no term on the right-hand side is dependent upon an electrical potential. In actual practice only one solution is used. There are concentration gradients of hydrogen and silver chloride within the solution, but the effect of the hydrogen and silver chloride on the chemical potentials of the hydrogen and chloride ions is small and negligible. 

As a consequence of electroneutrality in the two fluid phases, the mass content of chloride anions is no longer an independent variable and it can be eliminated in favor of the mass content of the cations sodium. A direct consequence is that the electrical field does not enter the elastic constitutive equations, that can be phrased in terms of chemical, rather than electro-chemical, potentials. 

This materials-specific term is proportional to the inverse of the thermodynamic factor and measures the increase of particle number density with chemical potential (while the electrical capacitance measures the increase of charge with electrical potential). For short times at which the profile near one electrode does not yet perceive the influence of the second one, the result is a 4t -law, and obviously differs from the heuristic approach. Thus more correctly one has to replace Cs by a Warburg-type capacitance as already discussed above (for a more exact description cf. Part I2, Section VI.7). Figure 45 shows a kinetic analysis for YBa2Cu306+r for the short- and the long-time behavior in the time domain yielding identical D5 values. (Note that in these figures different symbols have been used for Lf)... 

Secondly, selectivity is not always achievable. For example, permselectivity of ion-exchanging polymer films fails at high electrolyte concentration. We have shown that even if permselectivity is not thermodynamically found, measurements on appropriate time scales in transient experiments can lead to kinetic permselectivity. To rationalise this behaviour we recall that the thermodynamic restraint, electrochemical potential, can be split into two components the electrical and chemical terms. These conditions may be satisfied on different time scales. Dependent on the relative transfer rates of ions and net neutral species, transient responses may be under electroneutrality or activity control. 

It is evident from the last equation that the effects of the gradient and the electric field can be either additive or subtractive, because each term on the right-hand side can be of either sign. In fact, a flow of charged particles produced by a chemical potential difference across a diffusion medium can lead to charge flow and the creation of an electric potential which effectively cancels the effects of the chemical potential difference... 

Dividing the electrochemical potentials formally into their chemical and electrical terms according to (4), and separating the rf into those present in the metallic and the aqueous phases, (14) becomes... 

Equation (6.119) indicates that the chemical work in electrolytes contains a chemical term fidNj and an electrical term ZjFipdNj and the sum is called the electrochemical potential jlI of the ionic species i... 

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