Percolation gelation

P-E loop observation methods ballistic galvanometer, 441 Sawya-Tower bridge, 439 percolation gelation analogy, 292 permeation gas, 204... 

Percolation theory describes [32] the random growth of molecular clusters on a d-dimensional lattice. It was suggested to possibly give a better description of gelation than the classical statistical methods (which in fact are equivalent to percolation on a Bethe lattice or Caley tree, Fig. 7a) since the mean-field assumptions (unlimited mobility and accessibility of all groups) are avoided [16,33]. In contrast, immobility of all clusters is implied, which is unrealistic because of the translational diffusion of small clusters. An important fundamental feature of percolation is the existence of a critical value pc of p (bond formation probability in random bond percolation) beyond which the probability of finding a percolating cluster, i.e. a cluster which spans the whole sample, is non-zero. 

In random bond percolation, which is most widely used to describe gelation, monomers, occupy sites of a periodic lattice. The network formation is simulated by the formation of bonds (with a certain probability, p) between nearest neighbors of lattice sites, Fig. 7b. Since these bonds are randomly placed between the lattice nodes, intramolecular reactions are allowed. Other types of percolation are, for example, random site percolation (sites on a regular lattice are randomly occupied with a probability p) or random random percolation (also known as continuum percolation the sites do not form a periodic lattice but are distributed randomly throughout the percolation space). While the... 

The percolation processes were first developed by Flory [235] and Stockmayer [236] to describe polymerization process, which result in gelation, that is, the formation of very large networks of molecules connected by chemical bonds. But, their theory was developed only for a special kind of network, namely, the Bethe lattice, an infinite branching structure without any closed loops. Broadbent and Hammersley have developed a more general theory and have introduced it into the... 

In a related experimental study, Cirkel and Okada compared mechanical and electrical percolation that developed during the gelation of 3 1 (v/v) 2-propanol/ water solutions of Nafion 117 in the acid and Na+ forms.Attention should be paid to the particular manner in which these samples were prepared, as different conditions may yield different results. Also, caution should be applied in comparing these results with those of percolation studies using preformed films, such as that of Hsu et al. ... 

Physical gels, as exemplified by gelatin gels, exhibit many common features with chemical gels. Among them, we found the topological disorder of the network formed by the polymer chains, and the formal similarity of the process of gelation with a percolation problem. 

Both the Flory-Stockmayer mean-field theory and the percolation model provide scaling relations for the divergence of static properties of the polymer species at the gelation threshold. 

This model leads to A = 0.67 at the gel point, using the zero-frequency values for s and u. Use of the values for s and u calculated by treating the gelation phenomena as a three-dimensional percolation model of a supra-conductor/resistor network (electrical analogy), gives A = 0.72 0.02. 

Experimental e"(t) curves exhibit an inflection point that corresponds to the maximum rate of change of conductivity, associated to the maximum decrease of mobility. For this reason this inflection point has been attributed to gelation (Wasylyshyn and Johari, 1997). In some cases good agreement between the inflection time and the gel time obtained by rheological methods was observed. A very complex explanation taking into account inter-molecular H bonds, protonic conduction, and a bond percolation law has been proposed to explain this mobility change (Johari and Wasylyshyn, 2000). 

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