Thermally assisted hopping

Solid mixed ionic-electronic conductors (MIECs) exhibit both ionic and electronic (electron-hole) conductivity. Naturally, in any material there are in principle nonzero electronic and ionic conductivities (a i, a,). It is customary to limit the use of the term MIEC to those materials in which a, and 0, 1 do not differ by more than two orders of magnitude. It is also customary to use the term MIEC if a, and Ogi are not too low (o, a i 10 S/cm). Obviously, there are no strict rules. There are processes where the minority carriers play an important role despite the fact that 0,70 1 exceeds those limits and a, aj,i< 10 S/cm. In MIECs, ion transport normally occurs via interstitial sites or by hopping into a vacant site or a more complex combination based on interstitial and vacant sites, and electronic (electron/hole) conductivity occurs via delocalized states in the conduction/valence band or via localized states by a thermally assisted hopping mechanism. With respect to their properties, MIECs have found wide applications in solid oxide fuel cells, batteries, smart windows, selective membranes, sensors, catalysis, and so on. 

The mobility increases with temperature this behavior is the opposite of what is observed in crystals, and provides a clear proof that conduction occurs through thermally assisted hops. Whereas a simple Arrhenius law for the zero-field mobility In (ji0) oc 1 /T can be used to fit the data in many systems [57], ithas been shown that a dependence of the type In (fi0) oc 1 /T2 is more adequate [60], although its physical interpretation can hide both disorder or polaron-related effects [55],... 

Fig. 5.4. Density of states g(E) suggested by Davis and Mott (1970). E - E is the mobility gap. The ranges E - E and Eg - E contain localized states originating from lack of long-range order. Thermally assisted hopping may take place in these ranges. A band of compensated levels is proposed to lie near the gap center. Recently, Mott (1971) suggested that the center band of localized levels may be split into a donor band and an acceptor band.

Dias FB, Kamtekar KT, Cazati T et al (2009) Exciton diffusion in polyfluorene copolymer thin films kinetics, energy disorder and thermally assisted hopping. Chem Phys Chem 10 2096-2104... 

At energies near the electrons are confined to channels and are thus not typical three dimensional free electrons. But, we have ignored quantum mechanics and in reality the electrons can tunnel from one channel to another and between various allowed regions. Furthermore as already indicated if we allow the electrons to hop there will be an additional component due to thermally assisted processes (or phonon... 

II. Commodity Materials with Routine Properties Disordered conductors in which the electronic wavefunctions are localized (by the disorder) and in which the transport is via (thermally assisted hopping. To achieve such materials (either with pure polymers or in the form of blends) all that is required is a... 

It has been established from conductivity measurements that thermally activated and field-assisted hole hopping is responsible for the charge transport in solid polysilanes [48,49]. The mobility of the hole is as high as 10 m /V sec, while the mobility of the electron is a few orders of magnitude lower. In this section, we will show the reason why only the hole is mobile in polysilanes and how we can construct electron-conductive polysilanes. 

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