Electronic chemical potential terms

Here, when a rigorous demonstration is required, one can see quite how important it is to write the complete chain with the terminal electronic junctions. Indeed, since the electrons chemical potential terms concern connexions that are made of the same metal, these terms, which cannot be obtained via experiment, end up cancelling each other out (- /c°e ) Consequently, all that remains in the voltage expression is the... 

The real potential, a , of electrons in metals, as shown in Eqn. 2-4, comprises the electrostatic surface term, - ex, due to the surface dipole and the chemical potential term, M., determined by the bulk property of metal crystals. In general, the electrostatic surface term is greater the greater the valence electron density in metals whereas, the chemical potential term becomes greater the lower the valence electron density in metals. 

Figure 2-11 compares the observed work function, 4>, with that calculated based on the jeUium model as a function of the electron density, n.,in metals here, n, is represented in terms of the Wigner-Seitz radius which is inversely proportional to the cube root of n.. The chemical potential term (p. = —1.5 to-2.5 eV) predominates in the work function of metals of low valence electron density, while on the contrary the surface term (- e x = -0-1 -5.0 eV) predominates for... 

Of course this equation then implies zero electron affinity A and the correlation between successive ionization potentials follows. Evidently there is some further information to be gained by comparing the Taylor expansion form (75) with the Taylor expansion of equation (48) around the point NfZ= 1. From the property of the chemical potential, terms in (Z—N)2 arise from flt /2, and /s, whereas terms proportional to (Z—N) arise from higher terms in the series (48). Equation (75) shows that approximate relations must obtain between the coefficients of (Z—N) and Z—N)2 and that further work is required. 

The site term H- consists of the chemical-potential term He the electron-electron interaction term, the phononic term and the electron-phonon... 

From the theoretical point of view, the electrophilicity concept has been recently discussed in terms of global reactivity indexes defined for the ground states of atoms and molecules by Roy et al.18 19. In the context of the conceptual density functional theory (DFT), a global electrophilicity index defined in terms of the electronic chemical potential and the global hardness was proposed by Maynard et al.20 in their study of reactivity of the HIV-1 nucleocapsid protein p7 zinc finger domains. Recently, Parr, Szentp ly and Liu proposed a formal derivation of the electrophilicity, co, from a second-order energy expression developed in terms of the variation in the number of electrons.21... 

Unfortunately the fact that the same label, electronegativity, is used for both scales creates ample opportunity for confusion and misunderstanding. Since the Pauling scale has the advantage of seniority and long-established usage, a solution may be to find another term for the absolute scale. One alternative is to use the name electronic chemical potential , //. 

Theoretical studies have offered additional perspectives on electronegativity. Parr and co-workers ° defined a quantity, fi, as the electronic chemical potential, which measures the escaping tendency of the electrons in the system. The value of is approximately the same as (I + A)/2, the Mulliken electronegativity, so the value Xm has been termed absolute electro-... 

In Equation 7.1, / and A are the vertical ionization potential and electron affinity, respectively. A closa look at the second equality reveals that the finite difference expression of fi is exactly the negative of MnUiken electronegativity [27, 49, 50]. This result is relevant, for it describes the electronic chanical potential as a fugacity term, that is, the propensity of electrons to abandon the atom or molecule. In this sense, the direction of the electronic charge flux is detamined by the difference in electronic chemical potential electrons will flow from the region of high electronic... 

The relationship between the electronic chemical potential p, expressed in terms of the total energy , and the number of electrons, N ... 

In short, the charge transfer problem in the case of a local perturbation on a polymer can be treated either in terms of transfer from and to a subunit of the polymer which behaves as an isolated molecule or as charge transfer from the system A to a system P having a fixed electron chemical potential. We illustrate briefly the latter case, taking as a polymer the well-known polyacetylene system, where charge transfer does seem to play an important role. 

Figure 7.9. Schematic representation of the density of states N(E) in the conduction band of two transition metal electrodes (W and R) and of the definitions of work function O, chemical potential of electrons p, electrochemical potential of electrons or Fermi level p, surface potential x, Galvani (or inner) potential (p and Volta (or outer) potential for the catalyst (W) and for the reference electrode (R). The measured potential difference UWr is by definition the difference in p q>, p and p are spatially uniform O and can vary locally on the metal surfaces 21 the T terms are equal, see Fig. 5.18, for the case of fast spillover, in which case they also vanish for an overall neutral cell Reprinted with permission from The Electrochemical Society.

The chemical interaction between carriers j (here electrons) and the surrounding medium can also be described in terms of a chemical potential J,, which is the... 

It is typical that in Eq. (3.23) for the EMF, all terms containing the chemical potential of electrons in the electrodes cancel in pairs, since they are contained in the expressions for the Galvani potentials, both at the interface with the electrolyte and at the interface with the other electrode. This is due to the fact that the overall current-producing reaction comprises the transfer of electrons across the interface between two metals in addition to the electrode reactions. 

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... 

Baird and Rehfeld express A ° in terms of the trap concentration and the chemical potentials of the empty trap and of the electron in the quasi-free and trapped states. Further, they indicate a statistical-mechanical procedure to calculate these chemical potentials. Although straightforward in principle, their actual evaluation is hampered by the paucity of experimental data. Nevertheless, Eq. (10.13) is of great importance in determining the relative stability of the quasi-free versus the trapped states of the electron if data on time-of-flight and Hall mobilities are available. 

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