Hydrogen bond network being percolating

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. 

Over the last decade, there has been considerable interest in the development of off-lattice models and theories describing percolation phenomena. Interest in percolation concepts has been spurred by the rather wide variety of applications for which such ideas are thought to be useful. These applications include the electrical conductivity and dielectric properties or permeability of composite materials, gelation, analysis of hydrogen bond networks, and reactions in porous catalysts. Recent progress in the development of off-lattice or, as they are most often called, continuum models of percolation began with the work of Coniglio et and Haan... 

By changing the site site Mayer function, this formalism can be applied to a number of different physical situations. For example, if the site-site Mayer functions are chosen as those of an interaction site model of water, then the formalism could be used to study hydrogen bonding as a percolation problem, as has been done in the lattice context by Stanley and Texeira. Another possibility is to choose the Mayer functions to model polyfunctional chemical bonding. The formalism could then form the basis of treatment of gelation in polymer networks. 

In order to form an extended (that is, percolating) network that connects a large fraction of molecules of the entire system, there should be three or more hydrogen bonds per water molecule (unless molecules form large disconnected linear chains, which are unlikely and not seen in liquid water). Since each water molecule can easily form four hydrogen bonds, it can support such a network. Indeed this very ability to form a hydrogen-bond network has always been hypothesized to be the main reason for many anomalies exhibited by water (as shall be discussed later) [1-6]. 

In experiments, the percolation transition of hydration water can be detected by conductivity and dielectric measurements. Formation of a condensed hydrogen-bonded network of water should provide a media for the charge transport (proton or ions) and should change qualitatively the dielectric properties of the system. Sharp stepwise increase of the conductivity of the system with increasing water content at some threshold hydration level may directly indicate the appearance of an infinite hydrogen-bonded water network via a percolation transition. The dielectric response is also expected to increase drastically at the percolation threshold. Note, however, that the strongly attractive sites on the surface, which immobilize water molecules, may complicate interpretation of the results. As these effects occur on the surfaces, their experimental observation is possible first in the system with high surface/volume ratio (in various porous media). 

O2 diffusion through the membrane seems to be limited by the percolation network of the diffusion path, which is not only defined by the amount of water in the membrane, but also by the different chemical structure of the membranes. It is difficult to make comparisons of gaseous diffusion behavior among polymers with different structures because polymer morphology can change drastically without appreciable changes in density, and the presence of water and the hydrogen bonds formed between polymer-water moieties also has major effects on system properties. However, some points can be made from these particular studies. 

The reinforcement by cellulose nanofibres instead of micro-sized fibres is recognized as being more effective due to interactions between the nano-sized elements that make up a percolated network connected by hydrogen bonds or entanglements. 

Formation of the hydrogen-bonded water networks may affect conductivity of a system in a drastic way, as these networks provide the paths for the conduction of protons, ions, or other charges in the system. So, the qualitative changes in the conductivity may be expected at hydrations, close to the percolation transition of water. Surface conductivity of quartz increases relatively slowly with increasing hydration level until the completion of the adsorbed water monolayer, but much faster at higher hydrations [582]. The hydration dependence of the dielectric losses of hydrated collagen... 

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