Mechanism of the cooperative relaxation in microemulsions near the percolation threshold

Abstract

Cooperative dynamics of three-component water-oil-surfactant microemulsions based on sodium bis͑2-ethylhexyl͒ sulfosuccinate surfactant were investigated near the percolation threshold. The measurements were made by means of the time domain dielectric spectroscopy method in the temperature interval 12°C-40°C, including the percolation range. The data treatment was carried out in time domain in terms of the macroscopic dipole correlation functions ͑DCFs͒ related to the structural and kinetic properties of the system. It is shown that the DCF can be described by the Kohlrausch-Williams-Watts ͑KWW͒ expression exp͓Ϫ͑t/͒ ͔ ͑where is the relaxation time and is the stretched parameter͒, reflecting the peculiarities of the dipole interactions in a self-similar medium. For a physical interpretation of the phenomenological parameters and , a generalization of the known model of the cooperative relaxation was made. The model developed was adjusted for a description of the relaxation in microemulsions that have a fractal nature in the percolation region. The results obtained testify that parameters and in the KWW function are related to the structure of the system and reflect the cooperative behavior of microemulsion droplets near the percolation threshold. It was shown also that the macroscopic law of the relaxation of the KWW type is insensitive to the microscopic details of charge transport in the system and that there is a limited temporal range for the applicability of the stretched law of relaxation in time domain. In order to extend the initial temporal interval of the applicability of the relaxation function the correlation to the KWW term was found. ͓S1063-651X͑96͒09511-6͔

Percolating Microemulsions of Nonionic Surfactants Probed by Dielectric Spectroscopy

“…These features are typical for percolation phenomena. [5,7,9,10,13] For "doted" nonionic microemulsions, where the ions essentially reside within the water droplets, the percolation-induced rise of conductivity was already reported previously. [11,22] Far below the percolation threshold isolated reverse micelles dominate in these systems.…”

“…[11,12] Investigations of the conductivity, s, and the dielectric relaxation (via probing the total complex permittivity, ĥ (n) = e'(n)Ài[e''(n) + s/(2pne 0 )] of the sample as a function of frequency n; e 0 is the electric field constant) of ionic W/O microemulsions not only revealed a marked rise of s, when the percolation limit of the reverse micelles is approached, but also related maxima in the principle relaxation time t [associated with the peak frequency of the dielectric loss, e''(n)] and of the static permittivity, e = lim n!0 -e'(n). [5,7,9,10,13] These effects are generally assigned to the exchange of charges between the reverse micelles, which is strongly facilitated when the droplets start to aggregate to loose clusters that continue to grow until the percolation limit is reached. Charge carriers in these systems are the surfactant ion, such as AOT À , and the usually much smaller and more mobile counterion, for example, Na + .…”

“…Therefore, we report herein measurements of the total complex permittivity, ĥ (n), as a function of temperature, T, for two different compositions of a water (KCl,10 À3 mol L À1 )/n-octane/penta(ethylene glycol) dodecyl ether (W/O/C 12 E 5 ) microemulsion, a system which was extensively studied with other techniques.…”

“…[a] Dr. S. Schrçdle For W/O/C 12 E 5 it is known that the reverse micelles in the homogeneous phase are spherical [21] and start to aggregate when the temperature is decreased, [18] opposite to AOT systems which percolate with rising T. [10] Measurements were therefore started close to the upper limit of phase separation, 310.27 K for a = 0.8 and 314.65 K for a = 0.9, and the temperature was subsequently lowered in 0.1 K steps (see Experimental Section). Figure 2 shows some ê(n) spectra of the sample with a = 0.8 close to the percolation temperature that are typical for the obtained data.…”

“…[1,2] On the oil-rich side of the phase diagram reverse micelles are formed which, in a first approximation, can be described as spherical water droplets with typical diameters in the range of % 10-60 nm, separated from the continuous oil phase by a surfactant monolayer. [3] In recent years such water-in-oil (W/O) microemulsions with ionic surfactants [generally bis(2-ethylhexyl)-sulfosuccinate, AOT] aroused considerable interest as model systems for the investigation of percolation transitions [4][5][6][7][8][9][10] and associated charge transport. [11,12] Investigations of the conductivity, s, and the dielectric relaxation (via probing the total complex permittivity, ĥ (n) = e'(n)Ài[e''(n) + s/(2pne 0 )] of the sample as a function of frequency n; e 0 is the electric field constant) of ionic W/O microemulsions not only revealed a marked rise of s, when the percolation limit of the reverse micelles is approached, but also related maxima in the principle relaxation time t [associated with the peak frequency of the dielectric loss, e''(n)] and of the static permittivity, e = lim n!0 -e'(n).…”