Conductivity random-walk mechanism

If both ionic conductivity and ionic diffusion occur by the same random-walk mechanism, a relationship between the self-diffusion coefficient, D, and the ionic... 

This equation shows that it is possible to determine the diffusion coefficient from the easier measurement of ionic conductivity. However, Da is derived by assuming that the conductivity mechanism utilizes a random-walk mechanism, which may not true. 

If both ionic conductivity and ionic diffusion occur by the same random-walk mechanism, a relationship between the self-diffusion coefficient, D, and the ionic conductivity, cr, can be derived. In the simplest case, assume that processes involve the same energy barrier, E, and jump distance, a (Figures 7.12 and 7.15). Further, if the diffusion is restricted to only one direction, the +x direction, and each jump is allowed, the diffusion coefficient is... 

MECHANISMS OF IONIC CONDUCTIVITY 6.2.1 Random-Walk Model... 

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... 

The situation inside an electrolyte—the ionic aspect of electrochemistry—has been considered in the first volume of this text. The basic phenomena involve— ion—solvent interactions (Chapter 2), ion—ion interactions (Chapter 3), and the random walk of ions, which becomes a drift in a preferred direction under the influence of a concentration or a potential gradient (Chapter 4). In what way is the situation at the electrode/electrolyte interface any different from that in the bulk of the electrolyte To answer this question, one must treat quiescent (equilibrium) and active (nonequilibrium) interfaces, the structural and electrical characteristics of the interface, the rates and mechanism of changeover from ionic to electronic conduction, etc. In short, one is led into electrodics, the newest and most exciting part of electrochemistry. 

In the frequency domain, Jonscher s power-law wings, when evaluated by ac-conductivity measurements, sometimes reveal a dual transport mechanism with different characteristic times. In particular, they treat anomalous diffusion as a random walk in fractal geometry [31] or as a thermally activated hopping transport mechanism [37]. 

Slack [25] and Cahill et al. [26] explored the theoretical limits on k for solids within a phonon model of heat transport. Their work utilized the concept of the minimum thermal conductivity, Kj n- At this minimum value the mean free path for all heat carrying phonons in a material approaches the phonon wavelengths [25]. In this limit, the material behaves as an Einstein solid in which energy transport occurs via a random walk of energy transfer between localized vibrations in the solid. Experimentally, K an is often comparable to the value in the amorphous state of the same composition. In principle jc in can be achieved by the introduction of one or more phonon scattering mechanisms that reduce the phonon mean free path to its minimum value over a broad range of frequencies, and therefore reduces Kl over a broad range of temperatures. In practice, there are relatively few crystalline compounds for which this limit is approached. 

---