Dispersive Linear Chain model

Figure 34. Surface phonon dispersion for 2H-TaSe2. The HAS data are shown as solid circles except for weak points which appear in the TOP spectra as hybridized longitudinal modes that are shown as crosses. All the data were obtained at 60 K, well into the low-temperature phase. The calculated striped and shaded regions, corresponding to transverse and longitudinal polarizations respectively, are the slab-adapted bulk phonon bands, while the solid line is a calculation for the Rayleigh wave based on the Dispersive Linear Chain Model (shown schematically in Fig. 35). The open circles at g = 0 are from Raman scattering experiments. (This figure has been corrected from Fig. 23 in Ref. 54.)...

Figure 35. Schematic drawing of the Dispersive Linear Chain Model applied to 2H-TaSe . The force constants /, and A describe the Ta-Se and Se-Se forces within a TaSej subunit, and / gives the Se-Se force between layers, rf, and are the spring constants between Se atoms and between Ta atoms, respectively, for neighboring subunits in the same layer.

Fig.3,9. Phonon dispersion and density of state for a crystal with two atoms in the primitive unit cell, a) Qualitative general behaviour, b) Einstein approximation, c) Debye approximation, and d) Hybride Einstein-Debye model. The corresponding situation for the diatomic linear chain is shown in Fig. 2.11...

Dispersive transport in PVC was investigated. The results of Pfister and Griffits obtained by the transit method are shown in Fig. 6. The hole current forms at temperatures > 400 K clearly show a bend corresponding to the transit time of the holes. At lower temperature the bend is not seen and transit time definition needs special methods. The pulse form shows the broad expansion during transition to the opposite electrodes. This expansion corresponds to the dispersive transport [15]. The super-linear dependence of the transit time versus sample thickness did not hold for pure PVC. This is in disagreement with the Scher-Montroll model. There are a lot of reasons for the discrepancy. One reason may be the influence of the system dimensions. It is quite possible that polymer chains define dimension limits on charge carrier transfer. 

The chemistry of these polysaccharides is dominated by partial esterification of the total number of carboxyl groups. The sequence of uronic acids in the primary structure is occasionally interrupted by rhamnose, and there is usually a trace of acetyl and phenolic substituents. Models developed from experimental data considered neutral side chains with DP = 2-10 (De Vries et al., 1982). These 1,4-a-linked linear uronans are susceptible to alkali—more so if the C-6 hydroxyl is esterified, but exceptionally acid-stable when this site is unsubstituted. Dispersion stability is less at higher DP. Uronans are endowed with strong dye-fixing and mineral-sequestering properties because of their charged surface. 

SF theory is a statistical thermodynamic model in which chain conformations are formulated as step-weighted random walks in an interfacial lattice (Figure 2). A simple case involves the adsorption of a flexible, linear, homo-disperse, uncharged molecule at a uniform planar surface. Interactions among... 

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