Hopping mobility

Gartstein YN, Conwell EM (1994) High-field hopping mobility of polarons in disordered molecular-solids - a Monte-Carlo study. Chem Phys Lett 217 41... 

Coehoom R, Pasveer WF, Bobbert PA, Michels MAJ (2005) Charge-carrier concentration dependence of the hopping mobility in organic materials with Gaussian disorder. Phys Rev B 72 155206... 

Coehoom R (2007) Hopping mobility of charge carriers in disordered organic host-guest systems dependence on the charge-carrier concentration. Phys Rev B 75 155203... 

Eishchuk II, Arkhipov VI, Kadashchuk A, Heremans P, Bassler H (2007) Analytic model of hopping mobility at large charge carrier concentrations in disordered organic semiconductors polarons versus bare charge carriers. Phys Rev B 76 045210... 

Here, the potentiometric selectivity coefficient is given with respect to the hydroxyl ion. Single-crystal lanthanum fluoride is a wide bandgap semiconductor in which the electrical conductivity is due only to the hopping mobility of fluoride ions through the defects in the crystal. It does not respond to the La3+ ion because of the slow ion exchange of that ion. Hydroxyl ion is the only other ion that has appreciable mobility, and is the only known interference. For this reason, the measurements with a fluoride electrode are always done below pH 7, which circumvents this interference. As shown later, the consideration of ionic and/or electronic conductivity of the membrane plays a critical role also in the design of the internal contact in nonsymmetric potentiometric sensors. 

Because the room temperature hopping mobility is low (< 10-5 m2 V-1 s-1) in contrast to that typical for band conduction ( 10-1 m2 V-1 s 1), hopping conductors are sometimes referred to as low-mobility semiconductors . Another important distinction between band and hopping conductors is the very different doping levels encountered. Whereas doping levels for silicon are usually in the parts per million range, in the case of hopping conductors they are more typically parts per hundred. 

Figure 28 The polaron hopping mobility versus reduced field for different degrees of off-diagonal disorder, assuming the absence of diagonal disorder.

Small-Polaron Hopping. The microscopic hopping mobility even among identical sites in the absence of disorder acquires an extra activation associated with the relaxation of the carrier and its polarized surroundings. 

Let us apply expression (317) for the calculation of the proton current density associated with the hopping mobility of protons. Neglecting the dispersion in expression (317) and assuming that the applied electric field is small, we can write the hopping current density as follows ... 

Dubowsky S, Kesner S, Plante IS, Boston P (2008) Hopping mobility concept Sot search and rescue robots. Ind Robot Int J 35 238... 

Y.N. Gartstein and E.M. ConweU, High-field hopping mobility in molecular-systems with spatially correlated energetic disorder. Chem. Phys. Lett., 245, 351 (1995). 

The hopping mobility (m) in the high-temperature regime can be approximated from the electron transfer rates by considering the Einstein relation for diffusive motion [20, 23],... 

In this section we shall discuss simple models of electron transport. Some more detailed considerations will be presented in Chapter 7. Basically, three cases will be described here (1) electrons moving in delocalized states (motion in the conduction band) (2) trap-modulated motion in delocalized states and (3) hopping mobility. The three modes of transport are depicted schematically in Figure 35. 

The hopping mobilities are 10 -10 cm V s , nearly two orders of magnitude smaller than in the band case. 

When a polymer of (Xe > o-jon, such as polypyrrole in the oxidized state, is subjected to changes of the applied electrode potential, during the transient state electric fields develop in the polymer matrix and then disappear as electronic and ionic charge carriers migrate to new equilibrium positions [19,27,31,184]. The analyses may be based on the concepts derived for redox polymers under the condition that the hopping mobility of the electrons exceeds the counterion mobility. It has been shown [31] that in this case the system behavior is again diffusiona in character. The coated electrode behaves like a porous metal electrode with pores of limited depth. Numerous experimental reports on this behavior of conducting polymers have appeared in the literature the first was probably that of Bull et al. in 1982 [214]. 

Figure 24 Real (a) and imaginary (b) parts of the dielectric function of VB32 in the far-IR spectral range (75,110). For a satisfactory description of the experimental spectra hopping mobility and band-type mobility both must be taken into account.

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