Percolation phenomenon

Electrochemical redox studies of electroactive species solubilized in the water core of reverse microemulsions of water, toluene, cosurfactant, and AOT [28,29] have illustrated a percolation phenomenon in faradaic electron transfer. This phenomenon was observed when the cosurfactant used was acrylamide or other primary amide [28,30]. The oxidation or reduction chemistry appeared to switch on when cosurfactant chemical potential was raised above a certain threshold value. This switching phenomenon was later confirmed to coincide with percolation in electrical conductivity [31], as suggested by earlier work from the group of Francoise Candau [32]. The explanations for this amide-cosurfactant-induced percolation center around increases in interfacial flexibility [32] and increased disorder in surfactant chain packing [33]. These increases in flexibility and disorder appear to lead to increased interdroplet attraction, coalescence, and cluster formation. 

Cardoso et al. [115] have shown that AOT concentration is related to percolation. The percolation phenomenon was followed by a steep increase in the micellar conductivity [115]. Huang and Lee [49] observed a drastic reduction in the recovery (around 40%) of the horse radish peroxidase when AOT concentration was at 5 mmol 1 and further increase in AOT concentration to 10 mmol 1- produced no recovery at all. 

Sequences folding into the same structure form neutral networks in sequence space. A mathematical model based on random graph theory was designed [16] in order to allow for the derivation of analytical expressions. Neutral networks are represented by graphs in sequence space that show an interesting percolation phenomenon depending on the... 

A mean-field theory (Kirkpatrick176) manages to account for this percolation phenomenon. In the framework of the CPA, a real resistance is considered immersed in a perfect effective medium, with the requisite that this substitution will not induce, on average, an additional potential difference. The effective conductivity obtained in this way is very satisfactory It shows a percolation... 

A description of the percolation phenomenon in ionic microemulsions in terms of the macroscopic DCF will be carried out based on the static lattice site percolation (SLSP) model [152]. In this model the statistical ensemble of various... 

Kaler et al. [50] reported on the viscosity changes in association with a percolative phenomenon for systems containing the commercial surfactant TRS 10-80, octane, tertiary amyl alcohol, and various brines. Their viscosity results were interpreted as evidence for a smooth transition from an oil-continuous to a bicontinuous one in which both oil and water span the sample. A second transition was observed and was attributed to a transition from a bicontinuous to a water-continuous system. 

Basically, the process of tablet compression starts with the rearrangement of particles within the die cavity and initial elimination of voids. As tablet formulation is a multicomponent system, its ability to form a good compact is dictated by the compressibility and compactibility characteristics of each component. Compressibility of a powder is defined as its ability to decrease in volume under pressure, and compactibility is the ability of the powdered material to be compressed into a tablet of specific tensile strength [1,2], One emerging approach to understand the mechanism of powder consolidation and compression is known as percolation theory. In a simple way, the process of compaction can be considered a combination of site and bond percolation phenomena [5]. Percolation theory is based on the formation of clusters and the existence of a site or bond percolation phenomenon. It is possible to apply percolation theory if a system can be sufficiently well described by a lattice in which the spaces are occupied at random or all sites are already occupied and bonds between neighboring sites are formed at random. 

The percolation phenomenon is visible only in systems with sufficiently attractive interactions, and shows that there are pore openings in the overlapping region of the interfacial layers. A collective phenomenon must be supposed to explain such a strong anomaly of a transport coefficient. 

The formation of a tablet has been described as a site and bond percolation phenomenon (19), and percolation theory may undoubtedly provide valuable insights into the compaction process. The application is however less straightforward than for drug release since the particles in a powder are in contact also before a coherent tablet has formed, and in this sense, the system thus percolates from the outset. In compaction applications, particles are therefore instead considered to belong to the same cluster if they are connected by a bond of nonzero strength (20). Nevertheless, the relative density (or solid... 

However, if exact results are very difficult to obtain, it is possible to use numerical simulations. The main difficulty is that every simulation is feasible only for finite lattice sizes. The percolation phenomenon is a statistical phenomenon and only mean values are relevant. Thus the simulations should ideally be done over all possible lattice configurations. This is not possible for large lattices. Monte Carlo simulation techniques are generally used to overcome this difficulty. Some sample algorithms can be found in the textbook by Stauffer and Aharony [101]. 

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. 

Another approach to determining the viscoelastic properties of dense microemulsions at high frequencies is to conduct ultrasonic absorption experiments. In such experiments it has been found that the percolation process is correlated to a shift of the ultrasonic dynamics from a single relaxation time to a distribution of relaxation times [121]. Other experiments showed an increase in the hypersonic velocity for samples at and beyond the percolation threshold. The complex longitudinal modulus deduced from such experiments is also correlated with the occurrence of the percolation phenomenon, which suggests that the velocity dispersion is clearly correlated with structural transformations [122]. 

In order to understand why the nanoparticles are monodisperse, the microemulsion systems have to be well characterized. Important parameters are the radius of the inner water cores, which depends on R the possible change in the microemulsion due to the presence of reactants in the inner water cores a possible percolation phenomenon within the microemulsion the localization and site of solvation of the precursor ion the distribution of reactants in the inner water cores and the rate of exchange of the content of the aqueous droplets. 

A similar observation of increasing A gx when the temperature is increased toward the haze point was made in a comprehensive study by Lang et al. [29]. The results were later correlated with the percolation phenomenon of microemulsions as revealed by conductivity measurements [33]. Surprisingly high values of the second-order exchange rate constant... 

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. 

A percolation phenomenon was found in ionie miero-emul-sion droplets when the water fraction, tiie temperature, the pressure, the strength of the electric field, or the ratio of water to the surfactant was varied (95-98, 101). Basieally, the pereolation behavior is manifested by the rapid inerease in eleetrical conductivity a and static dielectric permittivity e as the system approaehes flie percolation threshold (Fig. 17). 

Figure 40 shows the static permittivity of an asphal-tene-stabilized model W/O emulsion versus the applied external electric field (170). The static permittivity increases with the applied electric field. This is an indication of a low degree of attraction between the aqueous droplets and, initially, a low level of flocculation. The applied electric field will induce a flocculation that consequently leads to an increase in Sg First to a small extent only, later more pronounced as the critical voltage is approached. However, when the critical electric field is exeeeded, a steep decline in the static permittivity to a value of 5-7, is observed. This can be viewed as a percolation phenomenon according to a static model (171, 172). 

Nagy [242] has discussed in detail the parameters to be optimized and the conditions to be established in W/O microemulsions for synthesis of metals and metal borides. Parameters that demand attention for standardization of a microemulsion system are the (a) water pool size (dependent on the w value), (b) changes brought about by dissolved reactants, (c) a possible percolation phenomenon in the system, (d) site of solvation of the precursor ions, (e) distribution of the reactants in the droplets and (f) exchange rate among the reactants. 

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... 

This outstanding reinforcing effect was ascribed to a mechanical percolation phenomenon (Favier et al. 1995a, b). 

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... 

Conductive polymer composites (CPC) exhibit a series of unique features, such as comparatively low room temperature resistivity, percolation phenomenon, resistivity sensitivity to temperature, pressure and gas, and nonlinear voltage-current relationship [1-5]. They found wide industrial applications in the fields of antistatic materials, self-regulating heaters, over-temperature protection devices, and electromagnetic interference shielding. Therefore, fundamental and applied studies of CPC are currently of great interest. 

In the case of PHA/cellulose whisker materials, studies were conducted using a latex of poly(3-hydroxyoctanoate) (PHO) as a matrix and a colloidal suspension of hydrolyzed cellulose whiskers as natural and biodegradable fillers. Due to the geometiy and aspect ratio of the cellulose whiskers, the formation of a rigid filler network, called the percolation phenomenon, was observed, leading to higher mechanical PHO properties. ... 

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