Band transport model

Several models can explain the carrier transport in organic semiconductors. However, none of them can be independently employed to explain the carrier transport phenomena and the mechanism at the same time. Among the theoretical models, the most often used models are the band transport model (Warta and Karl, 1985 Pemstich et al., 2008 Karl et al., 1991), polaron transport model (Holstein, 1959 Emin and Holstein, 1969 Marcus, 1960), hopping transport model (Vissenberg and Matters, 1998), and multiple trapping and release model (Horowitz et al., 1995 Le Comber and Spear, 1970). 

In the frontal analysis experiment described in Section 5.3.2, the transport model of chromatography was used to fit the experimental data [40]. Neglecting axial and eddy diffusion, band broadening was accounted for by one single mass transfer rate coefficient. The mass transfer rate coefficients estimated were small and strongly dependent on the temperature and solute concentration, particularly the rate coefficients corresponding to the imprinted L-enantiomer (Fig. 5.12). Above a concentration of ca. 0.1 g/L the mass transfer rate coefficients of the two enantiomers are similar. 

In Figure 14.15a, we compare two series of band profiles. The first series was calculated as numerical solutions of the transport model (no axial dispersion, solid film linear driving force kinetics), with a number of transfer units, Nm —... 

The parameters used to calculate the band profiles of the transport-dispersive and the transport models and the parameters of the Thomas model giving the best fit to these calculated profiles are compared in Table 14.2. As for the data in Table 14.1, there are negligible differences between the values of the retention factor and... 

The spin splitting of the energy bands of semiconductors without inversion symmetry has other interesting and presumably also technological consequences. Photoemitted electrons from GaAs are spin polarized when the light used for the irradiation is circularly polarized.[49,50] (such effects may also be observed for metals, see for example [51]). The so-called three step model for photomission considers the three processes, optical excition from a valence-band state to a state in the conduction band, transport of the excited electron to the surface, and — finally — emission through the... 

This model was first used by Thomas (1944) to simulate ion exchange processes. It postulates a rate-limiting adsorption kinetic as the only effect causing band broadening. Originally, homogeneous particles without pores ( p = 0) were assumed, but this can be modified to fit in the framework presented here. It need only be stated that the concentration in the bulk phase is the same as in the particle pores. Thus, the mobile phase balance is still the same as used for the derivation of the ideal model (Equation 6.39). Compared with the transport model, the right-hand side of the stationary phase balance equation (Equation 6.67) is replaced by an equation to quantify finite adsorption kinetics (expressed, for example, by Equation 6.31) and rewritten for constant concentrations inside the particles ... 

In order to understand the electronic transport of a solid, it is necessary to know its charge carrier densities and mobilities. For most solids, the Hall coefficient (Rh) is used to determine the concentration and sign of the majority charge carriers. Once known, the mobility is determined from the conductivity values, a. The MAX phases, however, are unlike most other metallic conductors in that their Hall and Seebeck coefficients are quite small - in some cases vanishingly small - and a weak function of temperature [52, 84—87]. Furthermore, the magnetoresistance (MR) (Aq/q = q(B) — q(B = 0)/q(B = 0)]), where B, the applied magnetic field intensity, is positive, parabolic, and nonsaturating. Said otherwise, the MAX phases are compensated conductors, and a two-band conduction model is needed to understand their electronic transport. In the low-field, B, limit of the two-band model, the... 

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