Percolation microemulsions

Percolated microemulsions composed of biocompatible substances, such as some lecithin-based organogels, have been considered interesting vehicles for the delivery of drugs [288],... 

For percolating microemulsions, the second and the third types of relaxation processes characterize the collective dynamics in the system and are of a cooperative nature. The dynamics of the second type may be associated with the transfer of an excitation caused by the transport of electrical charges within the clusters in the percolation region. The relaxation processes of the third type are caused by rearrangements of the clusters and are associated with various types of droplet and cluster motions, such as translations, rotations, collisions, fusion, and fission [113,143]. 

In type I phase behavior, an Si type of aqueous micellar sj tem (and its extension to an O/W microemulsion when swollen micelles occur or to a percolated microemulsion if a large amount of oil is solubilized in the micellar core) is in equilibrium with almost pure oil. This is the phase behavior exhibited in the polyphasic region of the so-called Winsor I ternary diagram. This phase behavior has also been labeled 2, since it appears as two phases with the surfactant-rich phase being the water or lower phase. 

Among the reactions that are carried out in microemulsions, polymerization is probably the most studied, as can be found in recent reviews [155-157]. It takes place in a O/W or W/O microemulsion structure, in percolated microemulsion [158-160], and in bicontinuous systems [161,162]. 

Figure 23 Schematic picture of the excitation transfer via parallel relaxation channels in the fractal cluster of droplets in the percolating microemulsions.

In the first case (when using butanol), the curve can be analysed using the percolation theory of conductivity [18]. In this model, the effective conductivity is practically zero as long as the volume fraction of the conductor (water) is below a critical value (the percolation threshold). Beyond this value, k suddenly takes a non-zero value and increases rapidly with further increase in In the above case (percolating microemulsions), the following equations were derived theoretically. 

In the equations a is a constant and the other terms have their usual significance. The Ep values can be conveniently evaluated from the use of the linear equation which has been done by different workers for their systems of percolating microemulsions both without and with additives. The values obtained are quite large, and are system and condition dependent. A generalization of the Ep values is yet to be found, the trends are system specific. For instance, it may not follow a trend with respect to additives either there can be a maximum, a minimum, or a different mode of variation with changing concentration of an additive [48,49,95,96]. It has been observed that the percolation-resisting additives may... 

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

On the other hand, dodecylmethylbutylammonium bromide- and benzyldymethyl-headecylammonium chloride-based w/o microemulsions, which consist of reversed micelles below the percolation threshold, form a bicontinuous stracture above the percolation threshold [279]. 

It has been reported that the percolation of conductance of water/AOT/n-heptane microemulsions is assisted by sodium cholate and retarded by sodium salicylate [282]. 

The addition of linear chained alkyl alcohols shifts the percolation of AOT microemulsions to higher temperature, whereas the opposite effect is obtained by adding polyoxyethylene alkyl ethers [261]. 

The possibility of realizing via percolated w/o microemulsion conductor/insulating composite materials with very large dielectric constant and exotic optical properties has been pointed out [284],... 

Percolation in microemulsions and concomitant microstructural changes are the focal points of this review. A complete understanding of percolation phenomena in reverse microemulsions will require an understanding of droplet interactions and the associated thermodynamics of droplet fusion, fission, aggregation to form clusters of varying fractal... 

Electrical conductivity is an easily measured transport property, and percolation in electrical conductivity appears a sensitive probe for characterizing microstructural transformations. A variety of field (intensive) variables have been found to drive percolation in reverse microemulsions. Disperse phase volume fraction has been often reported as a driver of percolation in electrical conductivity in such microemulsions [17-20]. 

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. 

The last, and less extensively studied field variable driving percolation effects is chemical potential. Salinity was examined in the seminal NMR self-diffusion paper of Clarkson et al. [12] as a component in brine, toluene, and SDS (sodium dodecylsulfate) microemulsions. Decreasing levels of salinity were found to be sufficient to drive the microemulsion microstructure from water-in-oil to irregular bicontinuous to oil-in-water. This paper was... 

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. 

Another example of chemical-potential-driven percolation is in the recent report on the use of simple poly(oxyethylene)alkyl ethers, C, ), as cosurfactants in reverse water, alkane, and AOT microemulsions [27]. While studying temperature-driven percolation, Nazario et al. also examined the effects of added C, ) as cosurfactants, and found that these cosurfactants decreased the temperature threshold for percolation. Based on these collective observations one can conclude that linear alcohols as cosurfactants tend to stiffen the surfactant interface, and that amides and poly(oxyethylene) alkyl ethers as cosurfactants tend to make this interface more flexible and enhance clustering, leading to more facile percolation. 

FIG. 2 Low-frequency conductivity at 45°C as a function of composition, a (weight fraction decane relative to decane and brine) for brine, decane, and AOT microemulsions exhibiting the phase behavior illustrated in Fig. 1. The breakpoint at a = 0.85 corresponds to the onset of percolation. This conductivity increases by two orders as a decreases from 0.85 to 0.7. (Reproduced by permission of the American Institute of Physics from Ref. 37.)... 

FIG. 5 Order parameter for disperse pseudophase water (percolating clusters versus isolated swollen micelles and nonpercolating clusters) derived from self-diffusion data for brine, decane, and AOT microemulsion system of single-phase region illustrated in Fig. 1. The a and arrow denote the onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. The other arrow (b) indicates where AOT self-diffusion begins to increase. 

A somewhat different water, decane, and AOT microemulsion system has been studied by Feldman and coworkers [25] where temperature was used as the field variable in driving microstructural transitions. This system had a composition (volume percent) of 21.30% water, 61.15% decane, and 17.55% AOT. Counterions (sodium ions) were assigned as the dominant charge transport carriers below and above the percolation threshold in electrical... 

As described in the introduction, certain cosurfactants appear able to drive percolation transitions. Variations in the cosurfactant chemical potential, RT n (where is cosurfactant concentration or activity), holding other compositional features constant, provide the driving force for these percolation transitions. A water, toluene, and AOT microemulsion system using acrylamide as cosurfactant exhibited percolation type behavior for a variety of redox electron-transfer processes. The corresponding low-frequency electrical conductivity data for such a system is illustrated in Fig. 8, where the water, toluene, and AOT mole ratio (11.2 19.2 1.00) is held approximately constant, and the acrylamide concentration, is varied from 0 to 6% (w/w). At about = 1.2%, the arrow labeled in Fig. 8 indicates the onset of percolation in electrical conductivity. 

FIG. 8 Low-frequency conductivity (a) of water, toluene, and AOT reverse microemulsions at 25°C as a function of acrylamide (cosurfactant) concentration, (wt%). The Op and arrow at f = 1.2% shows the approximate onset of percolation in low-frequency conductivity. 

FIG. 9 Measured self-diffusion coefficients at 25°C for toluene (A), water ( ), acrylamide ( , and AOT ( ) in water, toluene, and AOT reverse microemulsions as a function of cosurfactant (acrylamide) concentration, f (wt%). The breakpoint at about 1.2% acrylamide approximately denotes, the onset of percolation in electrical conductivity. 

While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains. 

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