Percolation theory application

Caraballo, I., Fernandez-Arevalo, M., Holgado, M. A., and Rabasco, A. M. (1993), Percolation theory Application to the study of the release behaviour from inert matrix system, Int. I. Pharm., 96,175-181. 

Lagues et al. [17] found that the percolation theory for hard spheres could be used to describe dramatic increases in electrical conductivity in reverse microemulsions as the volume fraction of water was increased. They also showed how certain scaling theoretical tools were applicable to the analysis of such percolation phenomena. Cazabat et al. [18] also examined percolation in reverse microemulsions with increasing disperse phase volume fraction. They reasoned the percolation came about as a result of formation of clusters of reverse microemulsion droplets. They envisioned increased transport as arising from a transformation of linear droplet clusters to tubular microstructures, to form wormlike reverse microemulsion tubules. 

M. Sahimi 1993, Application of Percolation Theory, Taylor Francis, London. 

The common disadvantage of both the free volume and configuration entropy models is their quasi-thermodynamic approach. The ion transport is better described on a microscopic level in terms of ion size, charge, and interactions with other ions and the host matrix. This makes a basis of the percolation theory, which describes formally the ion conductor as a random mixture of conductive islands (concentration c) interconnected by an essentially non-conductive matrix. (The mentioned formalism is applicable not only for ion conductors, but also for any insulator/conductor mixtures.)... 

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)... 

A quite serious problem, however, still obscures most applications of the percolation theory to the transport of magmas. Most major elements, such as Si, Mg, Ca,... can be considered as compatible since their concentration in the peridotite source and the basaltic melt are similar within a factor of 3. Equation (9.4.37) indicates, as would equations (8.3.17) and (8.3.19) in the most general case, that major elements are slower than the liquid, especially for small porosities. But, what is the liquid made of, then The velocity of a medium is the weighted average velocity of its constituents [see equation (8.1.4)]. The basalt velocity is that of Si, Mg, Ca,... weighted by their... 

Leuenberger H. The application of percolation theory in powder technology. Invited rev Adv Powder Technol, 1999 10 323-352. 

G. C. Wall and R. J. C. Brown,/. Colloid Interface Sci., 82,141 (1981). The Determination of Pore-Size Distributions from Sorption Isotherms and Mercury Penetration in Interconnected Pores The Application of Percolation Theory. 

Percolation is widely observed in chemical systems. It is a process that can describe how small, branched molecules react to form polymers, ultimately leading to an extensive network connected by chemical bonds. Other applications of percolation theory include conductivity, diffusivity, and the critical behavior of sols and gels. In biological systems, the role of the connectivity of different elements is of great importance. Examples include self-assembly of tobacco mosaic virus, actin filaments, and flagella, lymphocyte patch and cap formation, precipitation and agglutination phenomena, and immune system function. 

Application of percolation theory concepts to the study of suspensions has attracted much interest. Major aspects of the general theory are briefly recounted in the following subsection, after which, an analogy between percolation and suspension flows is detailed together with its main predictions. We conclude with a discussion of supporting experimental results obtained for two-dimensional suspensions. 

Crine and co-workers (32—33) have developed a trickle-bed reactor model based upon percolation theory which more closely approximates the physiochemical processes on a particle and reactor-scale than previous models. Details which explain the model development have not been given by these authors so it has not gained wide applicability. 

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. 

It is too early to assess the full potential of this promising method of isotherm analysis. So far it has been applied to only a limited number of experimental isotherms and some of the findings have been puzzling. For example, a few unrealistically high values of Z have been derived (Seaton, 1991). Furthermore, the physical significance of L is difficult to understand. It seems likely that this method of isotherm analysis (and possibly other procedures based on percolation theory) will become especially useful when the range of applicability can be clearly specified in terms of isotherm type and the range of pore size, shape and disposition. 

Matrix Systems with Different Particle Sizes Another disadvantage in the application of percolation theory to the rationalization of the pharmaceutical design was the prerequisite of an underlying regular lattice. Usually, drug delivery systems contain substances with different particle sizes. Therefore, the particles cannot be considered as each occupying one lattice site. 

Application of the percolation theory allows explanation of the changes in the release and hydration kinetics of swellable matrix-type controlled delivery systems. According to this theory, the critical points observed in dissolution and water uptake studies can be attributed to the excipient percolation threshold. Knowledge of these thresholds is important in order to optimize the design of swellable matrix tablets. Above the excipient percolation threshold an infinite cluster of this component is formed which is able to control the hydration and release rate. Below this threshold the excipient does not percolate the system and drug release is not controlled. 

Imbert, C.,Tchoreloff, P., Leclerc, B., and Couarraze, G. (1997), Indices of tableting performance and application of percolation theory to powder compaction, Eur. J. Pharm. Biopharm., 44, 273-282. 

We are not going to deal with all these examples of application of percolation theory to catalysis in this paper. Although the physics of these problems are different the basic numerical and mathematical techniques are very similar. For the deactivation problem discussed here, for example, one starts with a three-dimensional network representation of the catalyst porous structure. Systematic procedures of how to map any disordered porous medium onto an equivalent random network of pore bodies and throats have been developed and detailed accounts can be found in a number of publications ( 8). For the purposes of this discussion it suffices to say that the success of the mapping techniques strongly depends on the availability of quality structural data, such as mercury porosimetry, BET and direct microscopic observations. Of equal importance, however, is the correct interpretation of this data. It serves no purpose to perform careful mercury porosimetry and BET experiments and then use the wrong model (like the bundle of pores) for data analysis and interpretation. 

The exponent p in Eq. (7.91) depends on the physical situation and is typically calculated to be in the range 1-2. At elevated temperatures the carriers are thermally excited over the potential fluctuations and the application of percolation theory is less clear. 

Armand (1994) has briefly summarised the history of polymer electrolytes. A more extensive account can be found in Gray (1991). Wakihara and Yamamoto (1998) describe the development of lithium ion batteries. Sahimi (1994) discusses applications of percolation theory. Early work on conductive composites has been covered by Norman (1970). Subsequent edited volumes by Sichel (1982) and Bhattacharya (1986) deal with carbon- and metal-filled materials respectively. Donnet et al. (1993) cover the science and technology of carbon blacks including their use in composites. GuF (1996) presents a detailed account of conductive polymer composites up to the mid-1990s. Borsenberger and Weiss (1998) discuss semiconductive polymers with non-conjugated backbones in the context of xerography. Bassler (1983) reviews transport in these materials. 

Sahimi, M. (1994) Applications of Percolation Theory, London, Taylor Francis. 

Percolation theory provides a well-defined model applicable to a wide variety of spatially random phenomena, both macroscopic and microscopic (Table X). The characteristic length scales for these phenomena... 

Application of Percolation Theory to Describing Kinetic Processes in Porous Solids... 

Most of the pore structures (e.g., spongy structures) consist of extensive three-dimensional networks in which there is a profusion of interconnections between voids within the structure. The latter interconnections affect considerably the kinetics of various processes in porous solids. This effect can adequately be described by employing the ideas developed in percolation theory 7-13). In the framework of this theory, the medium is defined as an infinite set of sites interconnected by bonds. Percolation theory can be applied to porous solids via identification of network sites with voids, and bonds with necks. Thus, the theory is applicable primarily to spongy porous structures but in some cases also to corpuscular structures. 

---