CLUSTER FORMATION IN WATER-IN-OIL MICROEMULSIONS AT PERCOLATION - EVALUATION OF THE ELECTRICAL-PROPERTIES

We study water-in-oil microemulsion systems in the droplet phase and i n the vicinity of a percolation transition in the non-percolating regi on. We focus on the electrical conductivity and permittivity, quantiti es that show large variations when approaching the percolation thresho ld. The accepted model for the interpretation of the increasing conduc tivity-very large compared to that of the bathing oil phase-is related to clustering of the microemulsion droplets and migration of charges within the aggregates. Power laws have been used to interpret the beha viour of the static dielectric properties and scaling functions propos ed for the frequency-dependent conductivity and permittivity. We revie w some relevant experiments in this field and the proposed interpretat ions, and formulate a phenomenological model of conduction. It is base d on the physical picture of cluster formation due to attractive inter actions among the constituent water droplets, anomalous diffusion in t he bulk of fractal aggregates and polydispersity of the clusters. The model gives quantitative expressions for both conductivity and permitt ivity over the entire frequency range of the percolative relaxation ph enomena, including the static behaviour. A closed expression is derive d for the scaling function of a scaling variable which involves freque ncy, the cut-off cluster size and the parameters of the bulk component s. The results are also expressed in the time domain in terms of the p olarization time correlation function. The latter exhibits a rather in teresting behaviour, since it gradually evolves from an exponential de cay to a power-law decay and to a stretched exponential as time increa ses. The time-scales of the different stages are obtained from the typ ical decay times of the single droplet and the largest cluster. We hav e analysed many different sets of data obtained for different microemu lsion systems as functions of the composition of the dispersed phase, the temperature and the frequency of the applied field, with a very go od agreement with the model in all cases.