Hopping conduction diffusion

Attaching the catalyst molecules to the electrode surface presents an obvious advantage for synthetic and sensor applications. Catalysis can then be viewed as a supported molecular catalysis. It is the object of the next section. A distinction is made between monolayer and multilayer coatings. In the former, only chemical catalysis may take place, whereas both types of catalysis are possible with multilayer coatings, thanks to their three-dimensional structure. Besides substrate transport in the bathing solution, the catalytic responses are then under the control of three main phenomena electron hopping conduction, substrate diffusion, and catalytic reaction. While several systems have been described in which electron transport and catalysis are carried out by the same redox centers, particularly interesting systems are those in which these two functions are completed by two different molecular systems. 

Such a mechanism is not incompatible with a Haven ratio between 0.3 and 0.6 which is usually found for mineral glasses (Haven and Verkerk, 1965 Terai and Hayami, 1975 Lim and Day, 1978). The Haven ratio, that is the ratio of the tracer diffusion coefficient D determined by radioactive tracer methods to D, the diffusion coefficient obtained from conductivity via the Nernst-Einstein relationship (defined in Chapter 3) can be measured with great accuracy. The simultaneous measurement of D and D by analysis of the diffusion profile obtained under an electrical field (Kant, Kaps and Offermann, 1988) allows the Haven ratio to be determined with an accuracy better than 5%. From random walk theory of ion hopping the conductivity diffusion coefficient D = (e /isotropic medium. Hence for an indirect interstitial mechanism, the corresponding mobility is expressed by... 

As is to be expected, inherent disorder has an effect on electronic and optical properties of amorphous semiconductors providing for distinct differences between them and the crystalline semiconductors. The inherent disorder provides for localized as well as nonlocalized states within the same band such that a critical energy, can be defined by distinguishing the two types of states (4). At E = E, the mean free path of the electron is on the order of the interatomic distance and the wave function fluctuates randomly such that the quantum number, k, is no longer vaHd. For E < E the wave functions are localized and for E > E they are nonlocalized. For E > E the motion of the electron is diffusive and the extended state mobiHty is approximately 10 cm /sV. For U <, conduction takes place by hopping from one localized site to the next. Hence, at U =, )J. goes through a... 

If the film is nonconductive, the ion must diffuse to the electrode surface before it can be oxidized or reduced, or electrons must diffuse (hop) through the film by self-exchange, as in regular ionomer-modified electrodes.9 Cyclic voltammograms have the characteristic shape for diffusion control, and peak currents are proportional to the square root of the scan speed, as seen for species in solution. This is illustrated in Fig. 21 (A) for [Fe(CN)6]3 /4 in polypyrrole with a pyridinium substituent at the 1-position.243 This N-substituted polypyrrole does not become conductive until potentials significantly above the formal potential of the [Fe(CN)6]3"/4 couple. In contrast, a similar polymer with a pyridinium substituent at the 3-position is conductive at this potential. The polymer can therefore mediate electron transport to and from the immobilized ions, and their voltammetry becomes characteristic of thin-layer electrochemistry [Fig. 21(B)], with sharp symmetrical peaks that increase linearly with increasing scan speed. 

An example of a layer structure mixed conductor is provided by the cathode material L CoC used in lithium batteries. In this solid the ionic conductivity component is due to the migration of Li+ ions between sheets of electronically conducting C0O2. The production of a successful mixed conductor by doping can be illustrated by the oxide Cei-jPxx02- Reduction of this solid produces oxygen vacancies and Pr3+ ions. The electronic conductivity mechanism in these oxides is believed to be by way of electron hopping between Pr4+ and Pr3+, and the ionic conductivity is essentially vacancy diffusion of O2- ions. 

The second factor, electronic conduction through an assembly of redox centers, involves electron hopping between adjacent sites. It is analyzed so as to highlight the characteristics of this transport in terms of equivalent diffusion. Field effects will also be addressed. Although bearing some... 

The interpretation of these unconventional conduction properties is still a challenge for condensed matter physicists. Several models have been proposed including thermally activated hopping [10] band structure effects due to small density of states and narrow pseudo-gap [11,12] or anomalous quantum diffusion [13,14]. Yet all these models are difficult to compare in a quantitative way with experiments. 

The second necessary condition for crystalline or vitreous solid to have high ionic conductivity is that the mobile ions have a high diffusion coefficient, i.e. it is indeed a fast ion conductor . Much attention has been given to developing models of ionic motion. The simple hopping models applied successfully in the case of defect transport are not appropriate because of the high density of mobile ions in solid electrolytes, and... 

We describe here that the redox oligomer wires fabricated with the stepwise coordination method show characteristic electron transport behavior distinct from conventional redox polymers. Redox polymers are representative electron-conducting substances in which redox species are connected to form a polymer wire.21-25 The electron transport was treated according to the concept of redox conduction, based on the dilfusional motion of collective electron transfer pathways, composed of electron hopping terms and/or physical diffusion.17,18,26-30 In the characterization of redox conduction, the Cottrell equation can be applied to the initial current—time curve after the potential step in potential step chronoamperometry (PSCA), which causes the redox reaction of the redox polymer film ... 

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