Publications by Year: 1989

1989
Pine, D. J. ; Weitz, D. A. ; Maret, G. ; Wolf, P. E. ; Herbolzheimer, E. ; Chaikin, P. M. Dynamical Correlations of Multiply Scattered Light. In Scattering and Localization of Classical Waves in Random Media; 1989; pp. 312-372. Publisher's VersionAbstract

Motion of particles in optically dense media gives rise to temporal fluctuations in the intensity of multiply scattered light. We show that useful information about the dynamics of the scatterers can be obtained from measurements of the temporal autocorrelation functions of these fluctuations in the multiply scattered light. We develop a phenomenological theory, which models the transport of light as a random walk between scatterers, and obtain explicit expressions for the autocorrelation functions for several experimental geometries. These expressions are compared with experiments probing the dynamics of colloidal suspensions and are shown to be in excellent agreement with the data. The dependence of the autocorrelation functions on the experimental geometry provides a powerful means of exploring the particle dynamics over vastly different length and time scales. Thus, this technique extends the conventional single scattering technique of Dynamic Light Scattering to the multiple scattering regime. We call this new technique Diffusing Wave Spectroscopy (DWS). We illustrate the power of DWS by applying it to measure the particle size in concentrated suspensions and to study the diffusion of particles in porous media and the flow of particles under shear. In addition, we show that DWS can be extended to study the dynamics of interacting colloids by including the consequences of the correlations between the particle positions and velocities. DWS can also be used to study the nature of the transport of light in disordered systems and, in particular, the limitations of using a continuum diffusion approximation. To exploit this, we show that other quantities, such as the angular dependence of the coherent backscattering cone and the absorption dependence of the incoherent backscattering intensity, depend on the distribution of light paths through the sample in the same way as the temporal autocorrelation functions obtained in backscattering.

Ye, L. ; Weitz, D. A. ; Sheng, P. ; Bhattacharya, S. ; Huang, J. S. ; Higgins, M. J. Dynamic rigidity percolation in inverted micelles. Physical Review Letters 1989, 63, 263-266. Publisher's VersionAbstract

Inverted micelles are found to exhibit marked viscoelasticity with a pronounced dependence on volume fraction. The frequency dependence, measured using both ultrasonic and Brillouin techniques, reflects the dynamics of the interactions between the micelles. At low frequencies they behave as isolated spheres, while at high frequencies they behave as an instantaneous connected network. The rigidity of this network exhibits power-law scaling with volume fraction, consistent with rigidity percolation.

ye1989.pdf
Weitz, D. A. ; Pine, D. J. ; Pusey, P. N. ; Tough, R. J. A. Nondiffusive brownian-motion studied by diffusing-wave spectroscopy. Physical Review Letters 1989, 63, 1747-1750. Publisher's VersionAbstract

On a short time scale, Brownian particles undergo a transtion from the initial ballistic trajectories to diffusive motion. Hydrodynamic interactions with the surrounding fluid lead to a complex time dependence of this transition. We directly probe this transition for colloidal particles by measuring the autocorrelation function of multiply scattered, transmitted light. We show that a quantitative interpretation is possible because the transport of the light is diffusive, resolving a conflict in previous measurements.

weitz1989.pdf
MacKintosh, F. C. ; Zhu, J. X. ; Pine, D. J. ; Weitz, D. A. Polarization memory of multiply scattered-light. Physical Review B 1989, 40, 9342-9345. Publisher's VersionAbstract

Light backscattered from an optically dense random medium is shown to exhibit a pronounced polarization dependence. An unexpected memory of the incident circular polarization of multiply scattering light arises because the wave’s helicity is randomized less rapidly than is its direction. A simple model is developed to account for the observed polarization dependence of the intensity and temporal correlations of the intensity fluctuations of backscattered light.

mackintosh1989.pdf
Lindsay, H. M. ; Klein, R. ; Weitz, D. A. ; Lin, M. Y. ; Meakin, P. Structure and anisotropy of colloid aggregates. Physical Review A 1989, 39, 3112-3119. Publisher's VersionAbstract

We study the complex, disordered structure of clusters formed by several kinetic aggregation processes. By expanding the structure factor into spherical harmonics, detailed information about both the structure and anisotropy of the clusters at all length scales is obtained. The scaling of the expansion terms with cluster mass and order of the expansion is investigated. For cluster-cluster aggregates, we find that the fractal dimension, which reflects the scaling of the orientationally averaged structure, also describes the scaling of the spherical harmonics, which reflect the anisotropies of the structure. By contrast, clusters formed by single-particle diffusion-limited aggregation do not appear to exhibit the same degree of scale invariance. Cluster-cluster aggregates are found to exhibit considerably more anisotropy than those formed by single-particle diffusion. The consequences of the anisotropies for quasielastic light scattering experiments are discussed.

lindsay1989.pdf
Lin, M. Y. ; Lindsay, H. M. ; Weitz, D. A. ; Ball, R. C. ; Klein, R. ; Meakin, P. Universality in colloid aggregation. Nature 1989, 339, 360-362. Publisher's VersionAbstract

THE aggregation of colloidal particles is of fundamental importance in colloid science and its applications. The recent application of scaling concepts1,2 has resulted in a much deeper understanding of the structure of colloidal aggregates and the kinetics of their formation. Two distinct, limiting regimes of irreversible colloid aggregation have been identified3. Diffusion-limited colloid aggregation occurs when there is negligible repulsive force between the colloidal particles, so that the aggregation rate is limited solely by the time taken for clusters to encounter each other by diffusion. Reaction-limited colloid aggregation occurs when there is still a substantial, but not insurmountable, repulsive force beween the particles, so that the aggregation rate is limited by the time taken for two clusters to overcome this repulsive barrier by thermal activation. These regimes correspond to the limiting cases of rapid and slow colloid aggregation that have long been recognized in colloid science4. An intriguing possibility suggested by recent work is that each of these limiting regimes of colloid aggregation is universal, independent of the chemical details of the particular colloid system. Here we investigate the aggregation of three chemically different colloidal systems under both diffusion-limited and reaction-limited aggregation conditions. A scaling analysis of light-scattering data is used to compare the behaviour and provides convincing experimental evidence that the two regimes of aggregation are indeed universal.

lin1989.pdf
Lin, M. Y. ; Lindsay, H. M. ; Weitz, D. A. ; Ball, R. C. ; Klein, R. ; Meakin, P. Universality of fractal aggregates as probed by light scattering. Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences 1989, 423, 71-87. Publisher's VersionAbstract

Fractal colloid aggregates are studied with both static and dynamic light scattering. The dynamic light scattering data are scaled onto a single master curve, whose shape is sensitive to the structure of the aggregates and their mass distribution. By using the structure factor determined from computer-simulated aggregates, and including the effects of rotational diffusion, we predict the shape of the master curve for different cluster distributions. Excellent agreement is found between our predictions and the data for the two limiting regimes, diffusion-limited and reaction-limited colloid aggregation. Furthermore, using data from several completely different colloids, we find that the shapes of the master curves are identical for each regime. In addition, the cluster fractal dimensions and the aggregation kinetics are identical in each regime. This provides convincing experimental evidence of the universality of these two regimes of colloid aggregation.

lin1989.pdf