Publications by Year: 1990

1990
Huang, J. S. ; Ye, L. ; Weitz, D. A. ; Sheng, P. ; Bhattacharya, S. ; Higgins, M. J. Dynamic Rigidity Percolation in Inverted AOT Micellar Solutions. In Progress in Colloid & Polymer Science; 1990; Vol. 81, pp. 70-75. Publisher's VersionAbstract

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.

Klein, R. ; Weitz, D. A. ; Lin, M. Y. ; Lindsay, H. M. ; Ball, R. C. ; Meakin, P. Theory of Scattering from Colloidal Aggregates. In Progress in Colloid and Polymer Science; 1990; Vol. 81, pp. 161-168. Publisher's VersionAbstract

Static and dynamic light scattering are major experimental tools to study colloidal aggregates. The theoretical methods for a proper analysis of such experiments are reviewed. It is shown how several interrelated features of the aggregation process determine the experimentally accessible quantities. These features are the structure of the clusters as characterized by their fractal dimension and their anisotropies and the shape of the cluster mass distribution. Using computer-generated clusters, obtained under the conditions of diffusion-limited and of reaction-limited cluster aggregation, and using results for the cluster mass distribution obtained from the Smoluchowski equation for irreversible growth, the static scattering intensity and the correlation function of quasi-elastic light scattering are calculated. The latter is shown to depend sensitively on rotational diffusion processes and on the cluster mass distribution. Finally, it is shown how the growth kinetics can be extracted from the angle dependence of the first cumulant.

Wu, X. L. ; Pine, D. J. ; Chaikin, P. M. ; Huang, J. S. ; Weitz, D. A. Diffusing-wave spectroscopy in a shear-flow. J. Opt. Soc. Am. B 7 1990, 7 15-20. Publisher's VersionAbstract
We present a new technique for measuring velocity gradients for laminar shear flow, using dynamic light scattering in the strongly multiple-scattering regime. We derive temporal autocorrelation functions for multiply scattered light, taking into account particle displacements arising from deterministic shear flow and random Brownian motion. The laminar shear flow and Brownian motion are characterized by the relaxation rates [see link for figures], respectively, where [see link for figures] is the mean shear rate of the scatterers, k0 = 2πn/λ is the wave number in the scattering medium, l* is the transport mean free path of the photons, and D is the diffusion coefficient of the scatterers. We obtain excellent agreement between theory and experiment over a wide range of shear rates, [see link for range]. In addition, the autocorrelation function for forward scattering is independent of the scattering properties of the medium and depends only on the mean shear rate and sample thickness when τS is much less than τB. Thus the mean shear rate can be simply determined by a single measurement.
wu1990.pdf
Qiu, X. ; Wu, X. L. ; Xue, J. Z. ; Pine, D. J. ; Weitz, D. A. ; Chaikin, P. M. Hydrodynamic interactions in concentrated suspensions. Physical Review Letters 1990, 65, 516-519. Publisher's VersionAbstract
We study the effects of hydrodynamic interactions on the diffusion of hard spheres in concentrated suspensions. Using a multiple-light-scattering technique that measures the early-time behavior, we find Deff/D0=1-(1.86±0.07)φ, where φ is the volume fraction of spheres, Deff is the effective diffusion coefficient, and D0 is the free-particle diffusion coefficient. This agrees with the linear φ term calculated theoretically for short-time self-diffusion. The short-time diffusion coefficient is also found to be continuous across the freezing transition.
qiu1990.pdf
Pine, D. J. ; Weitz, D. A. ; Zhu, J. X. ; Herbolzheimer, E. Diffusing-wave spectroscopy: Dynamic light scattering in the multiple scattering limit. Journal De Physique 1990, 51, 2101-2127. Publisher's VersionAbstract

Dynamic light scattering is extended to optically thick (opaque) media which exhibit a very high degree of multiple scattering. This new technique, called diffusing-wave spectroscopy (DWS), exploits the diffusive nature of the transport of light in strongly scattering media to relate the temporal fluctuations of the multiply scattered light to the motion of the scatterers. A simple theory of DWS, based on the diffusion approximation for the transport of light, is developed to calculate the temporal electric field autocorrelation functions of the multiply scattered light. Two important scattering geometries are treated : transmission and backscattering. The theory is compared to experimental measurements of Brownian motion of submicron-diameter polystyrene spheres in aqueous suspension. The agreement between theory and experiment is excellent. The limitations of the photon diffusion approximation and the polarization dependence of the autocorrelation functions are discussed for the backscattering measurements. The effects of absorption of light and particle polydispersity are also incorporated into the theory and verified experimentally. It is also shown how DWS can be used to obtain information about the mean size of the particles which scatter light.

pine1990.pdf
Liu, J. ; Ye, L. ; Weitz, D. A. ; Ping, S. Novel acoustic excitations in suspensions of hard-sphere colloids. Physical Review Letters 1990, 65, 2602-2605. Publisher's VersionAbstract

We use Brillouin scattering to measure the longitudinal-phonon dispersion curves for a suspension of hard-sphere colloids. Two distinct propagating acoustic excitations are observed when the wavelength of the sound is comparable to, or smaller than, the size of the spheres. One excitation has a velocity intermediate between that of the fluid and the solid phases and is interpreted as an acoustic wave propagating through the composite medium of fluid and solid spheres. The second has a velocity slower than both that of the solid and that of the fluid phase and is interpreted as a coupled interfacial, or Stoneley, wave.

liu1990.pdf
Lin, M. Y. ; Klein, R. ; Lindsay, H. M. ; Weitz, D. A. ; Ball, R. C. ; Meakin, P. The structure of fractal colloidal aggregates of finite extent. Journal of Colloid and Interface Science 1990, 137, 263-280. Publisher's VersionAbstract

The structure of fractal colloid aggregates formed in both the diffusion- and the reaction-limited regimes is studied by static light scattering experiments. The crossover region of the structure factor of the clusters is measured, and the effects of the finite extent of the fractal structure on the scattering are investigated. The polydispersity of the cluster mass distribution markedly changes the shape of the measured scattering intensity. A form for the structure factor obtained from computer-generated clusters is found to describe the colloidal aggregates very well, for both regimes. Other available models for the crossover region are also discussed. In addition, the effects of the optical plasma resonance in the case of metallic colloids and the effects of cluster restructuring on the static scattering are discussed.​​​​​​

lin1990.pdf
Lin, M. Y. ; Lindsay, H. M. ; Weitz, D. A. ; Klein, R. ; Ball, R. C. ; Meakin, P. Universal diffusion-limited colloid aggregation. J. Phys.: Condensed Matter 1990, 2 3093-3113. Publisher's VersionAbstract

The authors study the process of diffusion-limited colloid aggregation (DLCA) using both static and dynamic light scattering. Static light scattering is used to measure the fractal dimension of the clusters as well as their structure factor, which is found to be in good agreement with that obtained from calculation using computer-generated clusters. Dynamic light scattering is used to probe both translational and rotational diffusion motion of the clusters. A method to separate their respective contributions is developed, allowing a quantitative determination of the average hydrodynamic radius. In addition, they determine the ratio of the hydrodynamic radius to the radius of gyration for individual aggregates, and find beta =0.93. A method is developed to scale all the dynamic light scattering data onto a single master curve, whose shape is sensitive to key features of the DLCA process. Good agreement is found between the prediction of the shape of the master curve and that obtained from experiments. Using several completely different colloids, they find that the shape of their master curves are identical, their fractal dimensions are identical and their aggregation kinetics are identical. This provides strong evidence of the universality of the DLCA regime of colloid aggregation.

lin1990.pdf
Lin, M. Y. ; Lindsay, H. M. ; Weitz, D. A. ; Ball, R. C. ; Klein, R. ; Meakin, P. Universal reaction-limited colloid aggregation. Physical Review A 1990, 41, 2005-2020. Publisher's VersionAbstract
We study slow, or reaction-limited, colloid aggregation (RLCA) with both static and dynamic light scattering and develop a self-consistent interpretation of the results. Static light scattering is used to determine the fractal dimension of the clusters and the cutoff mass of the power-law cluster-mass distribution. Using this same cutoff cluster mass, we can predict the shape of the temporal autocorrelation function measured by dynamic light scattering. Good agreement with experiments is obtained provided the effects of rotational diffusion are included. In addition, we determine the ratio of the hydrodynamic radius to the radius of gyration of individual RLCA clusters and find β=1.0. A scaling method is used for the q-dependent first cumulants of the temporal autocorrelation functions to obtain a single master curve for data obtained at different times in the aggregation process. The shape of this master curve is very sensitive to several key features of the process of reaction-limited colloid aggregation. It allows us to unambiguously determine the exponent for the power-law cluster-mass distribution, τ=1.5±0.05. Furthermore, we show that the master curves for three completely different colloids, gold, silica, and polystyrene, are indistinguishable. In addition, the fractal dimensions of their RLCA clusters, as measured by static light scattering, are all df=2.1±0.05, while the aggregation kinetics for each colloid are exponential. This demonstrates that reaction-limited colloid aggregation is universal, independent of the detailed chemical nature of the colloid system.
lin1990.pdf
Durian, D. J. ; Weitz, D. A. ; Pine, D. J. Dynamics and coarsening in 3-dimensional foams. Journal of Physics-Condensed Matter 1990, 2 SA433-SA436. Publisher's VersionAbstract

We show that diffusing-wave spectroscopy can be used as a non-invasive probe of the bulk properties of three-dimensional foams. A new picture accounting for the origin of the temporal fluctuations of multiply scattered light is developed and corroborated with direct observations through a microscope. Our interpretation and measurements yield the growth law for the coarsening of foam bubbles and new insight into their dynamics.

durian1990.pdf