Dynamic bond percolation theory

More detailed theoretical approaches which have merit are the configurational entropy model of Gibbs et al. [65, 66] and dynamic bond percolation (DBP) theory [67], a microscopic model specifically adapted by Ratner and co-workers to describe long-range ion transport in polymer electrolytes. 

The brief discussion above shows that the structure of a polymer electrolyte and the ion conduction mechanism are complex. Furthermore, the polymer is a weak electrolyte, whose ions form ion pairs, triple ions, and multidentate ions after its ionic dissociation. Currently, there are several important models that attempt to describe the ion conduction mechanisms in polymer electrolytes Arrhenius theory, the Vogel-Tammann-Fulcher (VTF) equation, the Williams-Landel-Ferry (WLF) equation, free volume model, dynamic bond percolation model (DBPM), the Meyer-Neldel (MN) law, effective medium theory (EMT), and the Nernst-Einstein equation [1]. 

Water is well known for its unusual properties, which are the so-called "anomalies" of the pure liquid, as well as for its special behavior as solvent, such as the hydrophobic hydration effects. During the past few years, a wealth of new insights into the origin of these features has been obtained by various experimental approaches and from computer simulation studies. In this review, we discuss points of special interest in the current water research. These points comprise the unusual properties of supercooled water, including the occurrence of liquid-liquid phase transitions, the related structural changes, and the onset of the unusual temperature dependence of the dynamics of the water molecules. The problem of the hydrogen-bond network in the pure liquid, in aqueous mixtures and in solutions, can be approached by percolation theory. The properties of ionic and hydrophobic solvation are discussed in detail. 

Figure 8.8. (a) Formation of a sample-spanning bond-percolation cluster on a square lathee at the percolation threshold (p = 0.6). (b) Cluster of conductive zones in a conductor-insulator mixture formed above the percolation threshold [46, 155]. (Image (a) reprinted with permission from Stauffer D, Aharony A. Introduction to percolation theory, London Taylor Francis, 1994 (b) reproduced from Chem Phys Lett, 375(5-6), Malek K. Dynamic Monte-Carlo simulation of electrochemical switching of a conducting polymer film, 235-44, 2002, with permission from Elsevier.)... 

Very valuable information could be obtained from the measurement of diffusion of impurities,not able to form H-bonds with water molecules, along the water coexistence curve in a quite wide temperature range. In fact the percolation theory by Stanley and Texeira, predicts for a behaviour similar to D while the H-bonds fluctuation approach in the Cohen-Turnbulf sbheme would inply for a behaviour similar to D since the local dynamics is a result of a larg region cooperative behaviour. Unfortunately such experimental data are not available in the literature. 

---