Sound propagation in sodium di-2-ethyl-hexylsulfosuccinate micelles and microemulsions

We present the results of a systematic study of the propagation of sound in sodium di-2-ethyl-hexylsulfosuccinate (AOT) micelles and microemulsions. The dispersion in the sound velocity v is determined over three and a half decades in frequency by using both ultrasonic and Brillouin-scattering techniques. The dispersion in the sound velocity is also measured as a function of the volume fraction of micelles or microemulsions. In addition, we measure the dependence of the sound velocity dispersion on the linear hydrocarbon chain length of the solvent molecules, and on the size of the microemulsion droplets. A consistent physical picture emerges that accounts for all of the results. The sound velocity in the micelle or microemulsion phases is greater than that in the solvent, leading to the observed increase of v with. In addition, due to the overlapping of the surfactant tails, there is a weak, short-range attractive interaction between the droplets, causing them to form short-lived, extended networks. These networks can support shear, leading to a further increase in v at higher, provided the frequency of the sound is sufficiently high that the instantaneous networks remain intact over the period of the sound wave. This results in the additional frequency dispersion in v at high. The strength of the attractive interaction, and hence the dispersion in the sound velocity, depends on the chain length of the solvent molecule and the diameter of the microemulsion droplet. The use of an effective-medium model is critical in confirming the validity of the physical picture. The effective-medium model includes the contribution of a shear modulus of one of the phases and can account for the dependence of v for all the systems. The shape of the full Rayleigh-Brillouin spectra is shown to be describable by a formalism that includes the relaxation of the extended networks. Finally, since the micelle or microemulsion networks cannot support shear unless they extend across the whole system, we show that the additional shear modulus contributed by the droplet phase exhibits scaling behavior when the volume fraction exceeds a critical value defined by the rigidity percolation threshold. This allows us to measure both the critical volume fraction and the exponent for rigidity percolation. However, since this additional shear modulus only occurs at high frequency, this effect is an example of dynamic rigidity percolation.