Viscosity, conductivity, and dielectric relaxation of waterless glycerol-sodium bis(2-ethylhexyl) sulfosuccinate-isooctane microemulsions: The percolation effect.

Abstract

The waterless microemulsion glycerol-AOT-isooctane [AOT, sodium bis(2-ethylhexyl) sulfosuccinate] was systematically studied as a function of temperature T, volume fraction (glycerol plus AOT) \ensuremath{\varphi}, molar ratio n=[glycerol]/[AOT], and the salt content ${\mathit{p}}_{\mathit{s}}$ in the glycerol. The properties studied are dynamic viscosity \ensuremath{\eta}, electric conductivity \ensuremath{\sigma}, and dielectric relaxation ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{R}}^{\mathrm{*}}$. At fixed T, n, and ${\mathit{p}}_{\mathit{s}}$ an increase in the conductivity and dynamic viscosity is observed when the volume fraction increases. Dielectric relaxation may be represented as a generalized Davidson-Cole distribution of the relaxation time. The quantities (1/\ensuremath{\sigma})(d\ensuremath{\sigma}/d\ensuremath{\varphi}) and (1/\ensuremath{\eta})(d\ensuremath{\eta}/d\ensuremath{\varphi}) pass through a maximum, as does the static permittivity ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{s}}$ (in the latter case the maximum is often followed by a minimum). At the same time the inverse of the characteristic frequency of dielectric relaxation 1/${\ensuremath{\nu}}_{\mathit{R}}$ passes through a maximum. The results are discussed in the framework of percolation theory. The application of the asymptotic laws of percolation is discussed. For viscosity, the analysis of the results provides a good comparison between theoretical and experimental values taking as critical percolation exponents \ensuremath{\mu}'\ensuremath{\simeq}2 (for \ensuremath{\varphi}g${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$), where ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$ is the percolation threshold and s'\ensuremath{\simeq}1.2 (\ensuremath{\varphi}${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$), which are the values predicted by the dynamic theory of percolation. By determining the \ensuremath{\eta}(\ensuremath{\varphi}) curves for various conditions, we were able to establish the variations of ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$(T), ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$(n), and ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$(${\mathit{p}}_{\mathit{s}}$). It was observed that ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$ decreases when T and n increase or when ${\mathit{p}}_{\mathit{s}}$ decreases. This corresponds to an increase in the interactions between droplets within the system. Finally, according to the value of \ensuremath{\varphi}, the viscosity may increase or decrease with increasing temperature. This curious effect can be explained by appropriate application of percolation theory.