Percolation activation energy

When a film is very thin, it may not be continuous, and conduction is subject to the percolation effect, whereby charge migrates by hopping or tunneling between island sites [50,51]. Such a process is activation controlled, and such thin films do not obey Ohm s law. The activation energy can be decreased by the presence of an applied electric field, making development of a rigorous theory difficult. The resistivity can be expressed by the relationship [5]... 

Ray, S., Paul, S., and Moulik, S. P. (1996), Physicochemical studies on microemulsions V. Additive effects on the performance of scaling equations and activation energy for percolation of conductance of water/AOT/heptane microemulsion, /. Colloid Interface Sci, 183(1), 6-12. 

In summary, the difiusion of K into C o films produces a minimum resistivity phase that is barely metallic with p = 2.2 milliohm-cm at composition K3.oo o.o5C6o, and a high resistivity (max) phase at composition Ks.ooio.osCjo. Intermediate compositions yield activated conduction with x-dependent activation energy, which can be explained by a simple model with immiscible phases where the metallic phase maximally avoids percolation. The recognition that the normal state has a granular microstructure will also be important in understanding superconductivity in thin films. 

As discussed in the physical model, the conductivity is caused by both the vehicle and Grotthuss mechanisms. The main difference between the conductivity of the vapor and liquid-equilibrated membranes stems from their respective water contents. A percolation-type equation is used for the conductivity although, at higher water contents, the conductivity should level out and ideally approach that of liquid water at infinite dilution (i.e., the polymer is dissolved in an infinite amount of water). The temperature dependence of the conductivity is due to the change in the equilibrium constant for the dissociation of the sulfonic acid sites and the activation energies for the Grotthuss mechanism and vehicle mechanisms [39]. Finally, the expressions given in Table 5.2 are valid for pure water and the... 

The activation energy of dc relaxation (due to through current appearing when the percolation channels appear) E (caused by mobile protons and other small ions) corresponds to a linear... 

Zhang et al. have shown that the conductivity curves can be transposed to each other by means of time temperature superposition (TTS) [62]. Furthermore, an Arrhenius plot of the corresponding shift factors exhibits that the dynamic percolation is a thermally activated process. With regard to the considered polycarbonate-MWCNT example, the Arrhenius plot of the fit parameter 2/cFy leads to the same result (Figure 5.26(b)). Since Vy f xo 1 constant, this means the reaction rate depends only on the activation energy, which is approximately 115 kJ/mol for this system. 

Percolation Parameters and Activation Energy for Different W/O Microemulsion Systems in Presence of Additives at W = 25... 

Percolation Threshold, Scaling Law Parameters, and Activation Energies at the Percolation Threshold for Water-Induced Percolation of the Water/SDS + Myrj 45 (1 1)/Cyclohexane Microemulsion Systems in Different Conditions... 

Both in the pre- and postpercolation stages, the temperature dependence of conductance can furnish with the information on the activation energies required for the conductance process to occur with some specific and involved fast and slow physicochemical courses. With the help of Arrhenius type equation, in a suitable form, the processing of data can evaluate the required activation energy of percolation, p. Thus... 

H. Mays and J. Ilgenfrintz 1996 Intercluster exchange rates in AOT water-in-oil microemulsions Percolation, material transport mechanism and activation energy, J. Chem. Soc. Faraday Trans. 92, 3145-3150. 

---