The consequences of internal reflection of multiply scattered light at the boundaries of disordered media are studied. We show that the effect of internal reflection due to index mismatch can be quantitatively accounted for with a single parameter by incorporating a reflection coefficient into the boundary condition for the diffusive light. We measure the angular correlation functions in transmission and reflection at different thicknesses for both high- and low-index mismatch. By including the effect of internal reflection, we are able to obtain consistent quantitative agreement between experiment and theory. Extensions to other experiments including diffusing-wave spectroscopy, coherent backscattering, frequency correlations, and pulse propagation are discussed.
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 upsilon 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 phi 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 upsilon with phi. 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 upsilon at higher phi, 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 upsilon at high phi. 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 phi dependence of upsilon 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.
We show that the process of irreversible, kinetic colloid aggregation exhibits universal behavior, independent of the detailed chemical nature of the colloidal particles. Modern methods of statistical physics, applied to a kinetic growth process, provide a good basis to model the observed behavior. Two limiting regimes of colloid aggregation are identified: rapid aggregation, limited solely by the diffusion of the growing clusters; and slow aggregation, limited by the reaction rate that leads to the formation of bonds between the clusters. In each regime the cluster structure is fractal, with fractal dimension d(f) approximately 1.8 for diffusion-limited clusters and d(f) approximately 2.1 for reaction-limited clusters. A scaling method is used to compare dynamic light scattering data obtained from completely different colloids aggregated under the two limiting conditions. These data provide a critical comparison of the behavior of the different colloids, and confirm the universality of each limiting regime of colloid aggregation.
The coarsening of a three-dimensional foam is studied with multiple light-scattering techniques. Scaling behavior is observed with the average bubble diameter growing in time as t(z) where z = 0.45 /- 0.05. Changes in the packing conditions during coarsening give rise to a dynamical process that also exhibits temporal scaling. Neighboring bubbles undergo sudden structural rearrangement events at a rate per unit volume that decays as t(-y) where y = 2.0 /- 0.2.
The structure and dynamics of three-dimensional foams are probed quantitatively by exploiting the strong multiple scattering of light that gives foams their familiar white color. Approximating the propagation of light as a diffusion process, transmission measurements provide a direct probe of the average bubble size. A model for dynamic light scattering is developed that can be used to interpret temporal fluctuations in the intensity of multiply scattered light. The results identify previously unrecognized internal dynamics of the foam bubbles. These light-scattering techniques are direct, noninvasive probes of bulk foams and therefore should find wide use in the study of their properties.