Band concept

The Band Concept. The eigenfunctions for the delocalization of Si a electrons along the skeleton are described by Bloch functions (22-23). A good quantum number is not a space coordinate but a wave vector K. An example of a band structure is shown in Figure 7. The band gap energy (Eg) is the difference between the edges of the conduction and valence bands. 

The effective masses of electrons and holes are estimated by parabolic approximation a large curvature corresponds to a small effective mass and a small curvature corresponds to a large mass. With this band concept, light absorption and luminescence are interpreted as follows Light is absorbed by the transition from valence band to conduction band. Therefore, the broadening of the absorption spectrum originates basically from the one dimensionality of the joint density of states, which is described by (E - g) . Excited electrons and holes relax to the bottom of the bands and then recombine radiatively. Therefore, the photoluminescence of the spectrum is very sharp. The energy difference between two peaks is called the Stokes shift. 

Because CPs conduct current without having a partially empty or partially filled band, concepts from solid state physics are used to explain the electronic phenomenon in these polymers. Thus, chemists refer to solitons, polarons, and bipolarons when they discuss the fundamentals of CPs. And, Fig. 1 shows the energy level diagram for an undoped, slightly doped, and heavily doped polymer to further illustrate the concept of doping. 

RRS has also introduced the concept of a Raman excitation profile (REPy for thefth mode) [46, 4lZ, 48, 49, 50 and M]. An REP. is obtained by measuring the resonance Raman scattering strength of thefth mode as a fiinction of the excitation frequency [, 53]. Flow does the scattering intensity for a given (thefth) Raman active vibration vary with excitation frequency within an electronic absorption band In turn, this has led to transfomi theories that try to predict... 

The basic concepts of shock and particle velocities are well illustrated by an example first introduced by Duvall and Band (1968). Here we assume that a string of beads of diameter d, mass m, and spaced a fixed distance / apart on a smooth (frictionless) wire is impacted by a rigid, massive piston at velocity v. Each bead is assumed to undergo perfectly elastic, rigid-body motion upon impact with its neighbor. 

Many other measures of solvent polarity have been developed. One of the most useful is based on shifts in the absorption spectrum of a reference dye. The positions of absorption bands are, in general, sensitive to solvent polarity because the electronic distribution, and therefore the polarity, of the excited state is different from that of the ground state. The shift in the absorption maximum reflects the effect of solvent on the energy gap between the ground-state and excited-state molecules. An empirical solvent polarity measure called y(30) is based on this concept. Some values of this measure for common solvents are given in Table 4.12 along with the dielectric constants for the solvents. It can be seen that there is a rather different order of polarity given by these two quantities. 

The charge-tranter concept of Mulliken was introduced to account for a type of molecular complex formation in which a new electronic absorption band, attributable to neither of the isolated interactants, is observed. The iodine (solute)— benzene (solvent) system studied by Benesi and Hildebrand shows such behavior. Let D represent an interactant capable of functioning as an electron donor and A an interactant that can serve as an electron acceptor. The ground state of the 1 1 complex of D and A is described by the wave function i [Pg.394]

In a general concept of a symmetry-restricted anharmonic theory Krumhansl relates the phonon anomalies to the electron band topology. The latter is directly determined by the competition of nearest neighbour interactions which in turn can be a function of stress, composition and temperature Nagasawa, Yoshida Makita simulated the <110> ... 

M. C. Desjonqueres and D. Spanjaard, Concepts in Surface Physics, Second Edition, Springer Verlag, Berlin (1996) and references therein R. Haydock, V. Heine and M. J. Kelly, Electronic Structure Based on the Local Atomic Environment for Tight-Binding Bands,. Phys. C 5 2845 (1972)... 

Some typical reactions in the pseudoexcitation band are reviewed in this section. The importance of pseudoexcitation [1] in chemical reactions was supported by the detailed numerical analysis of the electronic structures of the transion states [66]. The concept of pseudoexcitation appeared in physics [67-69]. 

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