Theory and experiment of electrical conductivity and percolation locus in water-in-oil microemulsions

Abstract

An extensive set of measurements of low-frequency conductivity cr of a three-component microemulsion system, AOT-water-decane, as a function of temperature and volume fraction of the dispersed phase has been made, a can be calculated at low 0 by means of a charge-fluctuation model, while it can be interpreted for higher values of (p in terms of power-law behavior. The percolation locus in the (p-T plane has been determined starting from the vicinity of the lower consolute point up to 0 -0.65. This line can be successfully interpreted in terms of a modified version of the analytical theory of percolation given by Xu and Stell.PACS numbers: 82.70.KjThe AOT(surfactant)-water-decane(oil) three-component microemulsion (AOT denotes sodium di-2-ethylhexylsulfosuccinate) is an ideal system for studying electrical-conductivity percolation phenomena since throughout the isotropic one-phase region it forms a water-in-oil microemulsion. A water-in-oil microemulsion can be effectively considered as a heterogeneous two-component system made up of conducting spherical droplets of water, coated by a monolayer of surfactant molecules, immersed in a continuous nonconducting oil medium. From a liquid-state-physics point of view a water-in-oil microemulsion, can be considered as a collection of conducting hard spheres interacting among themselves via an attractive potential. There has been a number of experimental'"^ and theoretical^''^ studies of electrical-permittivity and -conductivity percolation phenomena in the literature in this AOT-based model microemulsion system over the last few years. In particular, we have recently experimentally established the validity of dynamic scaling for the dielectric relaxation phenomena.^ As far as the static conductivity percolation is concerned, the picture that emerges from the experiments is as follows: The low-frequency conductivity a (below 100 kHz) has a power-law behavior with exponents which are different below and above the percolation threshold. At a given volume fraction of the microemulsion droplets 0, a temperature threshold Tp exists above which there is a dramatic increase in the conductivity. On the other hand, at a given temperature, there exists a volume-fraction threshold 0^ above which the system has high conductivity. Kim and Huang^ showed that 0p and Tp are uniquely related to each other. The locus of percolation points in the r-0 plane, which we shall simply call the percolation line, seems to originate from the vicinity of the cloud-point curve (the critical temperature is about 40 °C and the critical volume fraction about 0.

Percolating Microemulsions of Nonionic Surfactants Probed by Dielectric Spectroscopy

“…According to Cametti et al, [8] the width parameter a CC of the dielectric relaxation process should relate to the universal exponent u of dynamical scaling as a CC % 1Àu for temperatures close to T P . For both samples peak values of a CC % 0.45 are observed, see Figure 3 b.…”

“…to obtain the dispersion amplitude, De, the principal relaxation time, t, the (symmetrical) relaxation-time distribution parameter, a CC , and the infinite-frequency permittivity, e 1 , describing ê(n) and the conductivity, s. Typical complex permittivity spectra (with removed conductivity contribution) and their fits with Equation (8) are shown in Figure 2. The obtained parameters, with the exception of e 1 % 3.2, are summarized in Figure 3.…”

Small-angle light scattering in dense microemulsions, transition from droplet to bicontinuous phase

“…3 we report the intensity of the scattered light for all the smallest measured exchange wave vector as a function of the temperature for the sample with r = 0.5. The arrow indicates the conductivity percolation threshold [7]. As can be observed, in the temperature range 37-60~ the intensity shows three different peaks.…”

“…When the system crosses the corresponding threshold, conductivity increases by six orders of magnitude. Extensive measurements of conductivity and dielectric constant have shown that a static percolation picture holds above the percolation threshold, a dynamic one holding below it [7]. The percolation line and the coexistence curve in the (T, r has been well accounted in terms of the Baxter theory for adhesive hard spheres [10].…”

“…Within the temperature range of the one-phase region there is a percolation line. This line, defined as the locus of the electrical percolation threshold [7], is located for low concentrations near the critical point and increasing volume fraction evolves towards low temperatures. Below this percolation line, where droplets maintain their size constant, it is possible to change continuously their packing fraction.…”