Effective state density

We now consider the relationship which connects the electrochemical potential of electrons in the hopping model with that in the band model. The total concentration, N, of electron sites for the hopping model may be replaced by the effective state density, JVc, for the band model. For the two models thereby we obtain from Eqn. 2-27 the following equation ... 

We again consider a transfer of redox electrons via the conduction band medi-anism as shown in Fig. 8-23. The anodic and cathodic transfer currents of redox electrons have been given in Eqns. 8-56 and 8-57, respectively. In these equations, the state density occupied by electrons in the conduction band is approximated by the concentration of conduction band electrons at the electrode interface, n, = j Dsc(E)A(E-eF(8C))dE and the state density vacant for electrons in the conduction band is approximated by the effective state density of the conduction band, Nc Nc n, j Dsd ) 1-f(e-ef ac ) de. Further, the state density of... 

The concentration of surface holes, p is given as a function of the Fermi level ej at the stuface, the valence band edge ty at the surface, and the effective state density of the valence band Ny ( Nc)in Eqn. 9-28 ... 

The form of Eqs (2.30) and (2.31) suggests that Nc and Nv are effective state densities for electrons in the conduction band and holes in the valence band respectively. It turns out that Nc Nv 1025m-3. If we put tii=... 

The effective crosslink density is used to predict state of cure in thermoset coatings. Side reactions have been found to play an important role in cure of typical coating mixtures. 

In order to estimate the phonon scattering strength and thus the heat conductivity, we need to know the effective scattering density of states, the transition amplitudes, and the coupling of these transitions to the phonons. 

In order to distinguish these orbitals from their Hartree-Fock counterparts, they are usually termed Kohn-Sham orbitals, or briefly KS orbitals. The connection of this artificial system to the one we are really interested in is now established by choosing the effective potential Vs such that the density resulting from the summation of the moduli of the squared orbitals tpj exactly equals the ground state density of our real target system of interacting electrons,... 

To further illustrate the application of Equation 14.35 (the limiting behavior of the low pressure IE), consider the case when only the external rotations are adiabatic (translations do not contribute to the isotope effect). In this case the ratio of Q s reduces to a ratio of ratios of moments of inertia, which, provided the structure does not change on passing from active molecules to activated complex, is unity. In this simplified example, the isotope effect reduces to a simple ratio of the number of states and state densities in the activated complex and energized (active) molecules for the light (1) and heavy (h) molecules. 

An important aspect of the Gao-Marcus model is that it provides a theoretical structure for the understanding of quantum state density isotope effects in general, and is not specifically confined to the formation of ozone itself. This feature is important because as discussed above we are now aware that MIF s occur widely in nature. The theory aids in prediction of where MIF s will be likely found, and once found, in rationalizing how they were chemically produced. 

Fig. 2-17. Electron energy and state density in n-type semiconductors tn = donor level Nn = donor concentration Nc = effective conduction band state density.

Fig. 2-18. Electron energy and state density in p-type semiconductors ca = acceptor level Nf, = acceptor concentrati

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