Computer simulation percolation theory

Alternatively, Leung and Eichinger [51] proposed a computer simulation approach which does not assume any lattice as the classical and percolation theory. Their simulations are more realistic than lattice percolation, since spatially closer groups form bonds first and more distant groups at later stages of network formation. However, the implicitly introduced diffusion control is somewhat obscure. The effects of intramolecular reactions were more realistically quantified, and the results agree quite well with experimental observations [52,53],... 

The authors of the cluster theory draw the conclusion that the theory affords a sufficiently rigorous theoretical derivation of Doolittle s equation (72). Verification of the free volume theory advanced by Cohen and Grest was carried out by Hiwatari using computer simulation [97], showed that glass transition in liquids can really be described in terms of the percolation theory, the value of Pcr in this case being close to 0.2. Unlike Cohen and Grest s assumptions, however, this transition is not accompanied by a drastic change in the fluidity of the liquid near Per-... 

It is evident that the description of many real porous materials is complicated by a wide distribution of pore size and shape and the complexity of the pore network. To facilitate the application of certain theoretical principles the shape is often assumed to be cylindrical, but this is rarely an accurate portrayal of the real system. With some materials, it is more realistic to picture the pores as slits or interstices between spheroidal particles. Computer simulation and the application of percolation theory have made it possible to study the effects of connectivity and tortuosity. 

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. 

More recently, percolation theory and computer simulation of the dissolution process was applied. This latter approach resulted in 2D and 3D percolation thresholds (that is, composition thresholds at which infinite connected paths of the fast dissolving component were formed) as well as in images of the atomic scale disorder induced by dealloying. 3D site percolation thresholds 20 at.% in a fee lattice), leading to an infinite connected cluster of nearest neighbors of less noble atoms, were considered to correlate with the absolute parting limits of alloys with high such as... 

ASTM biometer test method D 5210 and soil burial test methods results are in good accord, some results being computer simulated by percolation theory [113]. 

Actually, even the sophisticated studies combining electrochemistry and surface analysis seem unable to yield any further decisive information on the detailed mechanism of selective dissolution. Atomic arrangements in which dissolution of atoms A can proceed throughout a rough electrode structure enriched in B t) e have been recognized as amenable to percolation theory [193]. The same theory was also applied to the passivation of binary Fe-Cr alloys in which, as suggested in Ref 105, 106, passivation of the more soluble element, Fe, is enhanced by a coimected surface lattice of passive Cr atoms. The main power of percolation theory is to provide diagnostic criteria for computer simulations in terms of concentration thresholds. 

Percolation theory offers a description of gelation that does not exclude the formation of closed loops and so does not predict a divergent density for large clusters. The disadvantage of the theory is that it generally does not lead to analytical solutions for such properties as the percolation threshold or the size distribution of polymers. However, these features can be determined with great accuracy from computer simulations, and the results are often quite different from the predictions of the classical theory. Excellent reviews of percolation theory and its relation to gelation have been written by Zallen [19] and Stauffer et al. [24]. 

The exponents x and y which define the mass distribution and the growth process of weight-average molecular mass are found experimentally to be in good agreement with the percolation theory. The experimental determinations (see Eqs. 23 and 15) x= 2.20 + 0.04 and y = 1.71 + 0.06 have to be compared with x = 2.2 and y = 1.74 deduced from computer simulation following the percolation model. 

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