Percolation structures

Galgali and his colleagues [46] have also shown that the typical rheological response in nanocomposites arises from frictional interactions between the silicate layers and not from the immobilization of confined polymer chains between the silicate layers. They have also shown a dramatic decrease in the creep compliance for the PP-based nanocomposite with 9 wt% MMT. They showed a dramatic three orders of magnitude drop in the zero shear viscosity beyond the apparent yield stress, suggesting that the solid-like behavior in the quiescent state is a result of the percolated structure of the layered silicate. 

The earliest fully atomistic molecular dynamic (MD) studies of a simplified Nation model using polyelectrolyte analogs showed the formation of a percolating structure of water-filled channels, which is consistent with the basic ideas of the cluster-network model of Hsu and Gierke. The first MD... 

Agrawal, D.L., Cook, N.G.W. and Myer, L.R. (1991) The effect of percolating structures on the petrophysical properties of Berea sandstone. In Rock Mechanics as a Multidisciplinary Science, Balkema, pp. 345-354... 

This leads us to the conclusion that a percolation structure appears inappropriate for the modeling of filler networks in elastomers. Consequently, we will consider an alternative network structure in the next section that refers to a space-filling configuration of kinetically aggregated filler clusters. In particular, this model will be shown to be in agreement with experimental results concerning the effect of filler concentration on the storage modulus. 

Deutscher, G., Zallen, R., and Adler, J., eds. (1983). Annals of the Israel Physical Society, Vol. 5 Percolation Structures and Processes. Hilger, Bristol, England. 

Domb C (1983) Ann Israel Phys Soc, Percolation Structures and Processes,5 17 G.Deut-scher,Zallen R, Adler J (ed)... 

Universal interfacial energy constant (this model assumes that all systems percolate at a universally valid threshold value of the interfacial energy Ag [28]), The merit of this work is that they have drawn attention to the role of the interfaces, even if they have failed to develop any ideas about the nature of the interaction at the interfaces, or the percolation structures, or the mechanisms of formation. For this reason it is not immediately obvious that two cornerstones of this theory, namely Ag and the influence of polymer viscosity, are not sufficiently well founded experimentally and cannot explain the percolation phenomenon. 

B. Wessling, unpublished results of investigations about the 3-dimensionaI form of percolation structures. 

Support for the idea of a percolated structure connected by solid bridges may be found in the Frisk and Laurent [ 1996] patent on the reduction of permeability through a polyester wall container reduction by a factor of 100 was reported after addition of w = 5 wt% clay (aspect ratio p = 1000 to 1500). This large effect cannot be explained by the standard mechanism of tortuosity [see Utracki, 2004, vol. 2], but it is logical if combined with the intrinsie reduction of matrix permeability caused by solidification of polymer on clay platelets that form a continuous barrier to CO2 fiux. 

Figure 2 Oil-in-water microemulsions with dispersed structure (center) and percolated structure (right).

Figure 8 Schematic representation of the processes leading to birefringence (and turbidity) in a W/O microemulsion, in relation to an applied electric square pulse E. Below a (second) threshold value of the field strength and far from critical conditions, or under any conditions if the pulse is terminated at a time indicated by the dashed line, only birefringence is observed due to the formation of AJ, and Above the threshold of the field strength, close to critical conditions, and with a sufficiently long square pulse, turbidity contributes to the signal due to phase separation or/and percolation. The double wall of the particles symbolizes the water/oil interface. Symbols A, surfactant monomer An, microemulsion droplet (An), cluster LCmp, liquid-crystalline microphase or/and percolation structure. Primed symbols stand for polarized structures oriented parallel to E (- ) reversible step with respect to turning the field on or off (->) irreversible step. (Reprinted with permission from Refs. 6 and 41. Copyright 1989 and 1994 American Chemical Society.)...

Upon further addition of acrylamide, the interaction potential becomes so attractive that transient clusters form. Above a threshold volume fraction, a large increase in the electrical conductivity is observed, which is an indication of a percolation phenomenon [25] (Fig. 2). The percolation threshold decreases with increasing AM/H2O ratio, i.e., with increasing attractive interactions, in good agreement with theoretical analyses [26] and data obtained for other microemulsions containing alcohols as cosurfactants [27-29]. As shown in Sec. III.C, this percolating structure has an effect on the formation of polymer latex particles and the polymerization mechanism. 

Favier, V., Dendievel, R., Canova, G., Cavaille, J.Y., Gilormini, P., 1997. Simulation and modeUng of three-dimensional percolating structures case of a latex matrix reinforced by a network of cellulose fibers. Acta Mater. 45, 1557—1565. 

Fig. 8. Time evolution of the unmixing structure showing the dynamical percolation-to-cluster transition. In regime I the percolating structure grows with dynamical self-similarity. The transition takes place in regime II and clusters of spheres arc found in regime III. From H. Hasegawa, T. Shiwaku, A. Nakai, and T. Hashimoto (1988).

Overview of the critical exponent for SAWs on various percolation structures as substrate (j/feg = 3/4 is the value for regular lattices in d = 2). 

A faster mechanism of domain growth was proposed for the coarsening of interconnected domain structures [10], for d=3, when the volume fraction of the minority phase is sufficiently large to maintain such a percolating structure. The key mechanism then is the deformaricni and breakup of tubelike regions in the domain structure. The characteristic velocity field Vf around domains having linear dimensions i is... 

R. Blanc and E. Guyon, in Percolation, Structures and Processes—Annals of the Israel Physical Society (G. Deutcher, R. Zallen, and J. Alder, eds.), Israel Physical Society, Jerusalem. Vol. 5. 1983, p. 229. 

Schematic description of the polymer/needle-like clay percolating structure. (Reproduced from Krishnamoorti, R. and Giarmehs, E.P., Macromolecules, 30,409 1997. With permission from American Chemical Society.)...

---