Hopping, thermally activated

Hardness 115 Heat treatment 47-48 Hopping, thermally activated 40 Hydrodynamic amplification 76 Hysteresis 70 -, filler-induced 59, 76, 78... 

In oxide ion conductors, current flow occurs by the movement of oxide ions through the crystal lattice. This movement is a result of thermally activated hopping of the... 

Evidence on this question may be taken by the behavior of the electrical conductivity CT as a function of temperature. A thermally activated process T dependence on log(CT), Arrhenius plot) is expected if doping takes place, whereas j -i/4 dependence, characteristic of a variable range hopping at the Fermi level is expected for a nondoping situation. 

The conductance of the perylenebisimide (PBI) 15 was measured by the STM-BJ technique as 1 nS [73]. Note that the thiophenol handles are not conjugated to the central core, contributing to the small value. Electron transport was temperature-independent, indicating a tunneling mechanism. However, when a gate electrode reduced the core to its radical anion, the conductance became thermally activated, indicating that electron transport then follows a hopping mechanism into and out of the core. 

This notion of occasional ion hops, apparently at random, forms the basis of random walk theory which is widely used to provide a semi-quantitative analysis or description of ionic conductivity (Goodenough, 1983 see Chapter 3 for a more detailed treatment of conduction). There is very little evidence in most solid electrolytes that the ions are instead able to move around without thermal activation in a true liquid-like motion. Nor is there much evidence of a free-ion state in which a particular ion can be activated to a state in which it is completely free to move, i.e. there appears to be no ionic equivalent of free or nearly free electron motion. 

If fluctuations in the intermolecular distances and orientations give rise to a large variation in the site energy and transition probability amplitude compared to the other terms, the static disorder dominates the charge transport. A charge carrier moves by uncorrelated hops in a broad density of states. Thermal activation is required to overcome the energy differences between different sites. 

A textbook example for the successful application of the model of Arkhipov et al. is the work of van Woudenbergh et al. [173]. More recently, Agrawal et al. [106] compared injection limited currents and space-charge-limited currents in a copper-phthalocyanine sandwich cell with TTO and Al electrodes. An analysis of experimental data yields consistent values for the width of the DOS distribution as well as for inter-site separation [174]. These studies support the model of thermally activated injection into a Gaussian DOS distribution of hopping sites and confirm the notion that disorder facilitates injection because it lowers the injection barrier, although the transport velocity decreases with increasing disorder. 

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