Subject percolation threshold

As it was mentioned above, even if at least one of the metal particle sizes is of nanometer range, the electron energy quantization could affect the physical properties of the nanogranular metal. The influence of the quantum-size effects (QSE) on the electronic transport in granular metals is especially pronounced in the vicinity of the percolation threshold [85] and it is the main subject of the present section. 

Beyne and Froment [1993] applied percolation theory to a US-Y zeolite catalyzing a process subject to diffusion limitations and to consecutive coking leading to site coverage and to pore blockage. After a certain process time, the percolation threshold was reached at some radial position of the particle and blockage of the volume behind it occurred. 

It is known that carbon-black filled polymers conduct electric current only with the concentration of carbon black exceeding the threshold of percolation ((p ). In heterogeneous polymer blends carbon black is distributed nonuniformly between polymer phases. If the concentrations of carbon black in both phases of a blend are lower than (p, the blend can conduct electric current only subject to the condition that the part of carbon black is localized at the interface and its concentration here reaches the percolation threshold [12]. So if the concentration of carbon black in both phases of a blend is only slightly lower than (p, even a minor accumulation of carbon black at the interface confers conductivity on the polymer blend. This enables the extent of carbon black aggregation at the interface to be judged by the conductivity value. 

For completeness, note that several researchers have exploited the well-developed analytical theories of the stmcture of fluids to model percolation in mixtures of interacting particles. By proposing various extensions of the multicomponent Omstein-Zernike equation, coupled with connectivity definitions from continuum percolation theories, simplified analytical expressions are derived for the percolation threshold of a composite system subjected to interparticle and medium-induced interactions. However, to date, simulations dominate the study of dynamic percolation. 

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