Citation:
Abstract:
We use ultrasonic techniques and Brillouin scattering to study the elastic response of AOT surfactant solutions. This micellar solution features a short-range attractive interaction between the droplets. We find behavior consistent with a dynamic rigidity percolation wherein clusters that span the system can form in the solution at surfactant volume fractions above Φ ≈ 0.16. The percolation clusters contribute a real shear modulus causing an increase in the sound velocity if the frequency is higher than the characteristic relaxation rate of the cluster (∼108 Hz). By contrast, at low frequencies the solution behaves as an effective medium with isolated micelle aggregates imbedded in the oil continuum, and the anomalous contribution of the shear modulus disappears. This experiment provides a unique measurement of the scaling of the elastic properties for a percolating system. In particular, the rigidity exponent is found to be τ′ ⋍ 2.5, consistent with the theoretical predictions.