Percolation-type phenomenon

For small molecules, the decrease in D occurs at I slightly larger than the mesh size. The small molecule is gradually decelerated passing through several numbers of mesh units. This mechanism is frequently referred to as the Ant in the Labyrinth mechanism in percolation theory [33, 34]. Application of percolation to anomalous diffusion in the mesh space suggests the possible appearance of low-dimensional (tube-like) transportation inside the space. This phenomenon will be detected by another type of anomalous behavior in DDDC or TDDC. 

Some types of carbon black (Ketjenblack EC-2000 and Gulf ab 550-P) in certain cured epoxy resin systems showed to have a percolation threshold of less than 0.5 %wt., see Figure 5.23. The commercial relevance of this knowledge was recognised [33] and additional experiments were performed to obtain more insight in this phenomenon. Some experimental results of this investigation are collected in Table 5.6. 

Heterogeneous reaction kinetics in areas such as chemistry, biology, geology, solid-state physics, astrophysics and atmospheric science can be understood in terms of fractal kinetics. Recently, Rastogi et al. [42] performed an experiment to visualize the phenomenon in a solid-gas reaction. Mercurous chloride thin film was prepared on micro-slide and put in the iodine chamber. A white continuous interface was covered with yellow HgClI after 15 min (Fig. 13.17). The interface becomes percolation cluster type after 2 h. At the end of the reaction (after 72 h) red crystals are found embedded on the reaction interface. For the reaction to obey fractal-like kinetics, the reaction between thickness of the boundary layer at time t is complex. These authors have further observed an identical relation for the above reaction, where k° is some... 

The ion conductance in a microemulsion depends on its type. In an o/w (Winsor I) microemulsion, the conductance is almost like that of an aqueous medium in a w/o (Winsor II) microemulsion, it is very low, whereas in the bicontinuous (Winsor III) condition, the conductance can be conspicuously large. Depending on the composition and temperature, a dramatic increase in conductance may occur this phenomenon is called percolation. 

Composites can be divided into two subgroups statistical mixtures and matrix-inclusion type composites. The effective dielectric function of the first subgroup can be calculated by equations, which are symmetrical with respect to phase indices. Statistical mixtures exhibit the so called percolation Phenomenon which is extremely important in conductor-insulator composites. Percolation threshold is a critical... 

In these equations, represents the volume fraction of the conductor constituent and the critical volume fraction corresponding to the percolation threshold, a is the binary composite conductivity and the conductor constituent conductivity, O2 being equal to zero since the other constituent is assumed to be of the insulator type. Equation (2a) states that the percolation phenomenon is a rigorous one, the conductivity being null as long as... 

The experimental results presented here, below and beyond the gel point, show clearly that the formation of polyurethane gel by polycondensation is a critical phenomenon which cannot be described by the mean-field theory. The good agreement of exponent values found experimentally and calculated by Monte Carlo simulations shows that this type of polycondensation process can be described by the percolation model. Recent experimental results " performed on different kinds of gelation process seem to indicate that, more generally, percolation and gelation, with permanent crosslinks, belong to the same class of universality. 

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