Conductivity clusters

Of course, this equation and its theoretical underpinnings does not constitute a model as such and certainly does not address the structural specifics of Nafion, so that it is of no predictive value, as experimental data must be collected beforehand. On the other hand, the results of this study clearly elucidate the percolative nature of the ensemble of contiguous ion-conductive clusters. Since the time of this study, the notion of extended water structures or aggregated clusters has been reinforced to a degree by the morphological studies mentioned above. 

Asymmetry of the response curve to the point of the exposition end reflects the different nature of the exposition and relaxation output signals. A transition from an exposition into relaxation phase corresponds to a return of gas-sensitive matter contact with the initial atmosphere. A variety of processes take place simultaneously in that phase. They may include oxidation of adsorbed molecules by the air oxygen, desorption of the previously adsorbed molecules, competitive adsorption of the ambient atmosphere components. These circumstances cause a complicated shape of the relaxation curve. In general, its course reflects the dynamics of the surface concentration of conductivity clusters. Almost all relaxation curves are characterized by presence of a maximum. It is often more prominent that the corresponding exposition maximum. The origin of this phenomenon is determined by higher conductivity of clusters formed by the oxidized molecules of compounds adsorbed during the exposition phase. 

Exposition maximum reflects the amount of adsorbed ingredients which form conductivity clusters. The ratio between the height of exposition maximum above the final level of the exposition signal and its absolute value, characterize behavior of ingredients forming clusters with higher conductivity during adsorption. 

Finally, the dynamics of the back front of the relaxation maximum formation is also informative. This part of the curve characterizes the gross process of the conductivity clusters decomposition. The decomposition process comprises (1) desorption of the exhaled air components from the gas sensitive matter and (2) oxidation of these components by the atmospheric oxygen at the begitming of relaxation. 

Fig. 1.1. A random conducting network with the conducting blocks (denoted by black squares) with concentration above the percolation threshold. If one assumes the conducting clusters to be formed when the blocks are connected by the nearest-neighbour sites (not by the marginally touching corners), the percolation problem is a random site problem. The current I through the network decreases to zero if the conducting block concentration p falls below the percolation threshold Pc, as shown in the figure on the right side.

In this limit, we consider clusters of conducting defects and their mean size is the percolation correlation length The voltage Vi between two such neighbouring clusters is given by Vi = V /L. The field between two clusters is increased as the field is zero inside a conducting cluster. The maximum value will be between the clusters with minimal distance between them i.e. one unit cell of the lattice. When the field between two such clusters... 

Bowman and Stroud (1989) solved numerically the Laplace equation at all the sites of the lattice made of insulators (with probability I — p) and conductors (probability p) and got the values of the potential across each bond. This is solved by taking into account the condition that no potential difference can be maintained within a conducting cluster. They found that Eh (defined as the field giving the breakdown of the first bond) decreases towards 0 as p approaches pc, with an exponent equal to 1.1 0.2 in d = 2 and equal to 0.7 di 0.2 in d = 3 for both site and bond percolation. These values are consistent with the above predictions, namely that the exponent of Eh must be equal to the correlation length exponent z/. We recall that... 

The electric properties of soft ferromagnetic nanoparticles in an insulating matrix strongly depend on the concentration of a metallic filler x and are varied between properties of the matrix and those of the filler. In binary nanocomposites a critical concentration (percolation threshold Xq) is reached when a continuous current-conducting cluster of the filler particles is formed through out the sample. 

Figure 7.12. Percolation in a random mixture of equisized conducting and insulating particles. At a threshold concentration of conducting particles the mixture starts to conduct current. One of the coherent clusters of those particles then spans the vessel. The fraction of particles that are part of those conducting clusters is the percolation probability.

If the carrier concentration is very low, most of the carriers are trapped, and consequently no electric current exists. With increasing carrier concentration, however, several conduction clusters emerge (Fig. 1). Ambegaokar and coworkers argued that an accurate estimate of G is the critical percolation conductance Gc [10], which is the largest value of the conductance such that the subnet of the network with Gij > Gc still contains a conducting sample-spanning cluster. At the onset of percolation, the critical number Be can be written as... 

Proton conductivity Clustering increases the proton conductivity... 

According to the percolation theory, the percolation threshold, (j), is the critical volume fraction, where an infinite continuous conducting cluster spanning across the sample is formed. Due to the presence of a conducting or percolation path across the entire sample, a change from an insulator to a semiconductor occurs. Above the percolation threshold, the electrical conductivity is related to the content of conducting filler by a simple power law ... 

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