Percolation temperature

The dielectric relaxation properties in a sodium bis(2-ethylhexyl) sulfosuc-cinate (AOT)-water-decane microemulsion near the percolation temperature threshold have been investigated in a broad temperature region [47,143,147]. The dielectric measurements of ionic microemulsions were carried out using the TDS in a time window with a total time interval of 1 ps. It was found that the system exhibits a complex nonexponential relaxation behavior that is strongly temperature-dependent (Figure 8). 

The dielectric relaxation at percolation was analyzed in the time domain since the theoretical relaxation model described above is formulated for the dipole correlation function T(f). For this purpose the complex dielectric permittivity data were expressed in terms of the DCF using (14) and (25). Figure 28 shows typical examples of the DCF, obtained from the frequency dependence of the complex permittivity at the percolation temperature, corresponding to several porous glasses studied recently [153-156]. 

Figure 34 shows the temperature dependencies of the static fractal dimensions of the maximal cluster. Note that at percolation temperature the value of the static fractal dimension Ds is extremely close to the classical value 2.53 for a three-dimensional lattice in the static site percolation model [152]. Moreover, the temperature dependence of the stretch parameter v (see Fig. 34) confirms the validity of our previous result [see (62)] Ds = 3v obtained for the regular fractal model of the percolation cluster [47]. 

Yu. Feldman, N. Kozlovich, I. Nir, N. Garti, V. Archipov, Z. Idiyatullin, Yu. Zuev, V. Fedotov, Mechanism of transport of charge carriers in the sodium bis(2-ethylhexyl) sulfosuccinate-water-decane microemulsion near the percolation temperature threshold, J. Phys. Chem., 1996, 100, 3745-3748. 

The dependence of the percolation temperature of a w/o microemuision (H2O/ AOT/isooctane) on the concentration of triblock copolymers ( j-POE-/ -PI-Z -POE) and water droplets was straightforwardly suggested by Eicke et al. [1211 on the basis of a thermodynamic model. Two distinct ranges of the [copolymer]/[nano-droplet] ratio were observed to correlate the percolation temperature. 

FIG. 8 Typical thermal cycle for the study of W/O microemulsions exhibiting percola-tive behavior. The cycle starts with an isothermal period of 20 min at a temperature equal to the percolative temperature evaluated by dielectric and conductivity measurements. After the DSC-EXO measurement, a second isotherm of 40 min follows on the frozen sample. The heating measurement, DSC-ENDO, ends with a third isotherm at a temperature Tl < Tf at which the sample is again in the hquid state. The last measurement (Cp Run) completes the thermal analysis. The thermal rate dTIdt of the latter run is higher than the 2 K/min rate used in both the exothermic and endothermic stages. Thermal rates var5dng from 4 to 10 K/min are apphed depending on the surfactant used to formulate the system. (From Ref. 14.)... 

In the literature, there are numerous studies about the influence of different additives upon the electrical percolation of microemulsions [45-51]. Recently, the influence of crown ethers and aza crown ethers on the percolation temperature... 

Traditionally, the percolation temperature (Tp) was obtained in terms of the sigmoidal Boltzmann equation (SBE) proposed by Moulik and coworkers [50]. Percolation temperatures obtained by both methods are compatible. In the following discussion we will use values obtained from the SBE. 

We determined the percolation temperature of AOT/isooctane/water microemulsions ([AOT] = 0.5 M and W = 22.2) in the presence of different polyethylene glycols and polyethylene glycol dimethyl ethers concentrations. The obtained results are shown in Figures 4.1 and 4.2, respectively. In all cases, we have observed a decrease in the percolation temperature of the system as the polyethylene glycols and polyethylene glycol dimethyl ethers concentration increases. This behavior is significantly different from that observed with crown ethers, where we had observed [48,49] an increase in the percolation temperature of the system as the crown ether concentration increased, until a maximum value was... 

In addition, as Moulik et al. [45] had proposed for the influence of hydrotropes on percolation phenomena, the bridging of water droplets by the polyethylene glycols and polyethylene glycol dimethyl ethers may be also responsible for the decrease in the percolation temperature. The incorporation of polyethylene glycols... 

Tp difference between the percolation temperature in presence and absence of polyethylene glycol dimethyl ethers... 

Feldman, Y, Kozlovich, N., Nir, I., and Garti, N. 1995 Dielectric relaxation in sodium bis(2-ethylhexyl) sulfosuccinate-water-decane microemulsions near the percolation temperature threshold, Phys. Rev. E 51 478—491 and references therein. 

The percolation threshold of an ME system can also be recorded along a temperature gradient by keeping the composition of the ingredients constant. The percolation threshold then becomes the percolation temperature or phase-inversion temperature. Examples can be found in the following references [56,57]. 

When the temperature was further increased above Tp, nanogels caused the phase separation at T = Tp. We investigated the dynamics of the phase separation as a function of c, 4>, and w. Here, the composition of the sample was always different from the critical composition. The phase separation was initiated by a thermal jump from a temperature Ti of 0.5 °C below Tp to a temperature Tf of 0.5 °C above T. Here Ti was always higher than the percolation temperature Tp. The scattered intensity exhibited a peak at a finite wave vector q. The peak height increased with time, and its position q shifted to smaller and smaller values. These behaviors are reminiscent of those of spinodal decomposition (SD). However, it should be noted that the time scale greatly differs from that of SD. We tried to scale the intensity distribution I q,t) with the scaling law of ordinary SD [7],... 

---