Percolation processes

A. E. Rodrigues and D. Tondeur, eds.. Percolation Processes, NATO ASI No. 33, Sijthoff Noordhoff, Alpen aan den Rijn, 1980. 

Rodrigues A. E., Tondeur D. (1981) Percolation Processes Theory and Applications, NATO ASI Series, Vol. 33, Sijthoff Noordhoff, The Netherlands. 

The electron transport properties described earlier markedly differ when the particles are organized on the substrate. When particles are isolated on the substrate, the well-known Coulomb blockade behavior is observed. When particles are arranged in a close-packed hexagonal network, the electron tunneling transport between two adjacent particles competes with that of particle-substrate. This is enhanced when the number of layers made of particles increases and they form a FCC structure. Then ohmic behavior dominates, with the number of neighbor particles increasing. In the FCC structure, a direct electron tunneling process from the tip to the substrate occurs via an electrical percolation process. Hence a micro-crystal made of nanoparticles acts as a metal. 

Broadbent, SR Hammersley, JM, Percolation Processes I. Crystals and Mazes, Proceedings of the Cambridge Philosophical Society 53, 629, 1957. 

In outline, a percolation process is used to produce an aqueous coffee extract, which in turn is dehydrated to yield water-soluble solids. Instant and soluble coffees are synonymous for these water-soluble coffee extract solids. Usually some of the volatile aroma and flavor compounds, which are lost during the processing, are added back immediately before packaging. 

Perchlorotoluene, 6 327 Perchlorylation, 12 183 Perchloryl fluoride, 18 279 Percolation leaching, 16 153 Percolation processes of filled polymers, 11 303 for wood, 26 358-359 Percolation theory, 20 345 23 63 Percolation transition, 10 16 Percutaneous transluminal coronary angioplasty (PTCA), 3 712 -per- designation, 7 609t PE resins, applications of, 20 206t. See also Polyethylene (PE)... 

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... 

Thus, the whole area of fillings for the large lattices considered is concentrated into a narrow range of threshold values of ZB, and ZBsmall effect on diffusion mass transfer that extends from the external surface of a lattice to its bulk. 

The mass balance aspects of distillation and percolation processes are often confused with their kinetics. Transfer of successive mass increments usually takes place over successive time increments but how the progress variable varies with time is often unknown in natural processes. Fortunately, knowledge of time-dependence is by no mean compulsory to achieve the description of the process in terms of mass balance. 

In the case of redox sites covalently bound to a polymer backbone, when only Dg contributes to charge transport. Equation 2.12 has systematically failed to explain the dependence of D pp with the concentration of redox sites. Blauch and Saveant have shown that for completely immobile centers, charge transport is basically a percolation process random distribution of isolated clusters of electrochemically coimected sites [33,40]. Only by dynamic rearrangements can these clusters become in contact and charge transport occur, giving rise to the concept of bound diffusion where each... 

Spices (rosemary, sage, thyme) contain considerable amounts of flavonols and flavones, mainly in the glycoside form (154). Thus, phenolic analyses in spices were often considered in order to determine the optimum time for plant collection to give maximum flavonoid contents and for health benefits (154,155). Flavonoids (naringin, luteolin, apigenin, and chrysoeriol) were extracted from spices using a percolation process at room temperature with solvents (MeOH and EtOAc), and HPLC analysis was carried out (155). 

Huruguen, J. P, M. Authier, J. L. Greffe, and M. P. Pileni. 1991. Percolation process induced by solubilizing cytochrome c in reverse micelldsgngmuir7 243-249. 

Clay regeneration a process in which spent coarse-grained adsorbent clays from percolation processes are cleaned for reuse by de-oiling them with naphtha, steaming out the excess naphtha, and then roasting in a stream of air to remove carbonaceous matter. 

In the temperature interval of —70 to 0°C and in the low-frequency range, an unexpected dielectric relaxation process for polymers is detected. This process is observed clearly in the sample PPX with metal Cu nanoparticles. In sample PPX + Zn only traces of this process can be observed, and in the PPX + PbS as well as in pure PPX matrix the process completely vanishes. The amplitude of this process essentially decreases, when the frequency increases, and the maximum of dielectric losses have almost no temperature dependence [104]. This is a typical dielectric response for percolation behavior [105]. This process may relate to electron transfer between the metal nanoparticles through the polymer matrix. Data on electrical conductivity of metal containing PPX films (see above) show that at metal concentrations higher than 5 vol.% there is an essential probability for electron transfer from one particle to another and thus such particles become involved in the percolation process. The minor appearance of this peak in PPX + Zn can be explained by oxidation of Zn nanoparticles. 

Network structures are still determined by nodes and strands when long chains are crosslinked at random, but the segmental spacing between two consecutive crosslinks, along one chain, is not uniform in these systems which are currently described within the framework of bond percolation, considered within the mean field approximation. The percolation process is supposed to be developed on a Cayley tree [15, 16]. Polymer chains are considered as percolation units that will be linked to one another to form a gel. Chains bear chemical functions that can react with functions located on crosslinkers. The functionality of percolation units is determined by the mean number f of chemical functions per chain and the gelation (percolation) threshold is given by pc = (f-1)"1. The... 

Percolation Process for Hydrogen Bonded Networks in Water. 

The flow process analyzed above may be described quantitatively using the percolation theory. The main concepts of this theory have been presented by Broadbent et al. (11), Frisch et al. (12) and Kirkpatrick (13). For an exhaustive analysis of the theoretical developments concerning percolation, the reader is referred to these reviews. Actually, most of the studies have been devoted to a static description of the structures generated by the percolation process. 

In this paper, we will consider only the dynamic aspects of this percolation problem, i.e., the stochastic distribution of velocities between the flow structures. To analyze a percolation process, it is useful to represent the scattering medium (i.e. the packed bed) by a lattice as depicted in Figure 2. The sites of the lattice correspond to the contact points between the particles whereas the bonds correspond to the pores connecting two neighbour contact points. The walls of these pores are delimited by the external surface of the particles. The percolation process is... 

The bed scale corresponds to the whole bed or to a volume containing a large number of particles. That is the level at which we want to derive models for the investigated transport processes. However these processes are generally ruled by gas-liquid-solid interactions occurring at the particle scale. That is the reason why it is necessary to model these processes at the particle scale. The change of scale or volume averaging between both levels is ruled by the percolation process, i.e., by the velocity distribu-... 

To describe the transport processes at the particle scale, we have to adopt a representation of the transport cell which is associated to each bond in the lattice defined by the percolation process (see Figure 3). This cell is assumed to be exactly the same at any position within the bed. The randomness of the process is indeed accounted for by the percolation process, i.e. by the connections between the pores. 

In this study, we have shown how gas-liquid flow through a random packing may be represented by a percolation process. The main concepts of percolation theory allow us to account for the random nature of the packing and to derive a theoretical expression of the liquid flow distribution at the bed scale. This flow distribution allows us to establish an averaging formula between the particle and bed scales. Using this formula, we propose the bed scale modelling of some transport processes previously modelled at the particle scale. 

Percolation Processes in A2MF4 Series. Random two-dimensional antiferromagnets have recently been studied besides magnetic measurements, EPR has proved to be a powerful tool in the elucidation of percolation processes. 

As mentioned earlier, typical three-dimensional plots of s and s" versus frequency and temperature (see Fig. 14) suggest superimposing two processes (percolation and saddle-like) in the vicinity of the percolation. Therefore, in order to separate the long-time percolation process, the DCF was fitted as a sum of two functions. The KWW function (64) was used for fitting the percolation process and the product (25) of the power law and the stretched exponential function (as a more common representation of relaxation in time domain) was applied for the fitting of the additional short-time process. The values obtained for Dp of different porous glasses are presented in the Table I. The glasses studied differed in their preparation method, which affects the size of the pores, porosity and availability of second silica and ultra-porosity [153-156]. 

Thus, the non-Debye dielectric behavior in silica glasses and PS is similar. These systems exhibit an intermediate temperature percolation process associated with the transfer of the electric excitations through the random structures of fractal paths. It was shown that at the mesoscale range the fractal dimension of the complex material morphology (Dr for porous glasses and porous silicon) coincides with the fractal dimension Dp of the path structure. This value can be obtained by fitting the experimental DCF to the stretched-exponential relaxation law (64). 

---