We obtain useful information from the intensity autocorrelations of light scattered from systems which exhibit strong multiple scattering. A phenomenological model, which exploits the diffusive nature of the transport of light, is shown to be in excellent agreement with experimental data for several different scattering geometries. The dependence on geometry provides an important experimental control over the time scale probed. We call this technique diffusing wave spectroscopy, and illustrate its utility by studying diffusion in a strongly interacting colloidal glass.

We examine the contribution of rotational diffusion to quasielastic light scattering (QELS) from fractal colloid aggregates, both theoretically and experimentally. Rotational diffusion makes a substantial contribution to QELS when the size of the clusters is large compared with the inverse of the scattering wave vector, due to the anisotropy of the clusters at all length scales smaller than the cluster size. We evaluate the rotational contributions to QELS by performing a multipole expansion of the light scattered from computer-simulated clusters. Experimentally, rotational contributions are observed through measurement of the wave-vector dependence of the first cumulant. We find excellent agreement between cumulants calculated through our multipole-expansion technique and those obtained in our experimental measurements.

We examine the optical properties of aggregate clusters and consider the effects of multiple scattering. The long-range fractal correlations can modify the mean index of refraction of the clusters, but multiple scattering has no effect on the wave-vector dependence of the scattering. By contrast, the short-range correlations inherent in a connected cluster lead to high-order multipole interactions which cannot be treated with a mean-field approach. These are shown to determine the wavelength dependence of the absorption and depolarized scattering from metallic clusters in good accord with experiment.

We study patterns formed by the viscous fingering instability in a porous media. When the displacing fluid preferentially wets the medium, the finger width is much larger than the pore size and, when normalized by the square root of the permeability, is found to scale with capillary number as Ca^−1/2. While traditional theories based on Hele-Shaw geometry give this dependence for the most unstable wavelength, they are unable to explain the magnitude of the finger. We consider here the effect of a velocity dependent capillary pressure in addition to the more conventional static term, and suggest that it may control the scaling of the finger width on Ca. We demonstrate the existence of this dynamic capillary pressure, which offers new insight into the basic physics of the motion of a fluid interface in porous media.

The aggregation of colloids is of substantial interest both fundamentally and practically. The level of interest has risen in recent years with the observation that colloidal aggregates are often well characterized as scale-invariant, or fractal, objects, providing a quantitative description of the structure of these random, irregular clusters.^1–4 The consequences of the scale invariance on light scattering from the clusters has been widely exploited. In static light scattering, the dependence of the scattering intensity on the scattering wave vector q allows a convenient way of determining the fractal dimension of the clusters, while Quasi-Elastic Light Scattering (QELS) has proved useful in monitoring the kinetics of the aggregation process. The combination of the scale-invariant structures of the aggregates and the power-law distributions which often occur leads to elegant scaling behavior of the dynamic light scattering.^5,6 For the large clusters (qR_g ≳1) often found in aggregation, rotational diffusion can play an important role in determining the decay of the autocorrelation of the scattered light measured in QELS. While scaling arguments have been used to account for the contribution of rotational diffusion, it is nonetheless important to determine this effect more quantitatively.

We measure the velocity dependence of the capillary pressure, ΔPc(v), between two fluids in a porous medium. At zero velocity, the interface is pinned, and a critical ΔPc must be achieved before the interface moves. For nonzero velocities, there is an additional dynamic component to ΔPc, which scales as v12 when a wetting fluid displaces a nonwetting fluid. We suggest that this dynamic component of ΔPc can stabilize viscous fingers, and obtain excellent agreement with experiment.

A Comment on the Letter by P. Wiltzius, Phys. Rev. Lett. 58, 710 (1987).

We study the influence of the fractal structure on the physical properties of colloidal gold aggregates. The optical properties are strongly influenced by both the long- and the short-range correlations of the aggregate structure, as well as the electronic plasma resonance of the gold particles. The absorption of the aggregates is dominated by the electromagnetic interaction between nearest-neighbour particles. The angular dependence of the polarized scattering reflects the long-range fractal correlations of the particles in the clusters, while that of the depolarized scattering reflects the short-range correlations of the local field corrections. The fractal structure also affects dynamic light scattering, so that rotational diffusion effects play an important role in the decay of the autocorrelation function. Finally, we show that the very tenuous nature of the fractal structure makes the aggregates quite susceptible to deformation under shear stress.

 

We study the onset of the Taylor instability for colloidal crystals in a narrow-gap Couette Cell. There is a natural competition between the radial flow required for Taylor rolls and the resistance to such motion caused by the anisotropy of the flowing solid. A new, combined Taylor–shear-melting instability is found at rotation rates above those expected for the formation of rolls, but below the shear rate required for shear melting in the absence of the Taylor instability. The control parameter for the shear melting transition appears to be a critical shear stress rather than the shear rate.

Reaction-limited cluster aggregation is modeled with the kinetic rate (Smoluchowski) equations, using a kernel determined intrinsically by the clusters fractal geometry. The kernel scales with cluster mass as M1Mλ−12 (M1≫M2), and Mλ1 (M1≊M2), with λ=1 in three dimensions, resulting in exponential kinetics and a cluster mass distribution CM∼M−τ, with τ=(3/2), in excellent accord with experiments. The singular nature of this solution forces the adjustment of the cluster fractal dimension, df, thereby determining its value.

The cluster-mass distributions produced in the kinetic aggregation of aqueous gold colloids are measured over an extended range of masses for two limiting kinetic regimes, diffusion-limited (DLA) and reaction-limited (RLA) aggregation. Markedly different distributions are found, with DLA having a peaked distribution, while RLA has a power-law distribution. In both cases the distributions are shown to exhibit dynamic scaling, as has recently been predicted. The data are interpreted with the Smoluchowski equations, and are used to determine the form of the appropriate kernel for each regime.

We study patterns formed by the viscous fingering instability in a porous medium. The wetting properties of the medium have a profound influence on the width of the individual fingers and consequently on the shape of the overall pattern. If the displaced fluid preferentially wets the medium, the finger width is comparable to the pore size, independent of other parameters. In contrast, if the displacing fluid preferentially wets the medium, the finger width is much larger than the pore size, and, when normalized by the square root of the permeability, is found to scale with the capillary number approximately as N−12Ca.

We report a high-resolution, small-angle x-ray study of aggregated gold colloids over the range 0.0003 to 0.08 Å−1. We are able to fit our data with a simple model that correctly accounts for nonfractal short-range order with a crossover to long-range fractal correlations. This provides new information on the structure of real aggregates, and new insight into the aggregation processes which lead to their formation.

We have examined both the structure and surface chemistry of gold clusters formed by the kinetic aggregation of colloidal gold particles. The highly disordered, ramified aggregates can be very accurately described as self-similar or fractal objects with a fractal dimension equal to 1.75. Spectroscopic studies performed with surface-enhanced Raman scattering (SERS), clearly indicate that colloidal gold surfaces are highly heterogeneous, consisting both of donor and acceptor sites which can be identified as Au(0) and Au(I). respectively. Aggregation occurs when negatively charged species are displaced from the gold surface by more strongly bound molecular adsorhates, with the rate determined by the nature and concentration of the displacing species. The new insights afforded by the fractal description of the structure of the aggregates and the SERS probe of the chemical nature of the colloid surface should lead to a more complete understanding of the basic mechanisms of colloid aggregation. This potential is illustrated with a quantitative description of the dynamics of aggregate growth measured by dynamic light scattering.​​​​​​

We show that there are two regimes of irreversible, kinetic aggregation of aqueous colloids, determined by the short-range interparticle potential, through its control of the sticking probability upon approach of two particles. Each regime has different rate-limiting physics, aggregation dynamics, and cluster-mass distributions, and results in clusters with different fractal dimensions. These results set limits on the fractal dimension, df, for gold aggregates of 1.75<~df<~2.05(±0.05).

The large lattice spacings in colloidal crystals produce elastic constants ~ 10¹⁰ less than conventional solids. It is therefore easy to study flow properties at stress/elastic constant ratios higher than previously available. The highly nonlinear plastic flow regime studied in oscillating and steady state flow yields periodic patterns. These patterns correspond to alternating regions of ordered crystallites which are mirror image structures. The pattern observed in oscillatory flow in a tube is also unusual in that the core is liquid while at larger radius one finds a solid on the tube wall. This traditionally unstable configuration may be the result of an anomalous stress-rate relation at the fluid-solid boundary. Experiments in couette geometry produce vertical stripes which correspond to coherent motion of dislocations at the boundaries separating two mirror image structures. The stripes move in the direction opposite from the rotation of the inner cylinder, at velocities close to the transverse sound velocity.

Four-probe resistivity measurements on organic conductors have been extended to 6 GPa. The organic metal HMTSF-TCNO appears to undergo a phase transition to a three-dimen-sionaliy ordered conducting state near 4 GPa. X-ray and Raman scattering confirm the transition. Unexpectedly, the degree of charge transfer in HMTSF-TCNO is relatively insensitive to pressure.

We show that the clusters formed by the irreversible aggregation of uniform aqueous gold colloids exhibit dilation symmetry and are well described as fractals with a Hausdorff or fractal dimension of ~1.75. The detailed structure of the clusters is studied with transmission electron microscopy, and is confirmed with small angle neutron scattering. The value of the fractal dimension obtained is in excellent agreement with that predicted by theory and computer simulation for cluster-cluster aggregation. We also discuss preliminary measurements of the kinetics of aggregation, which indicate that there are two limiting regimes with substantially different behavior. One is dominated by the particle-particle sticking time leading to relatively slow growth initially, but an increasing rate of growth as the aggregation proceeds. In contrast, the other is dominated by the diffusion time for clusters to collide leading to much faster aggregation, but with a decreasing rate of growth as the aggregation proceeds.

We study the dynamics of diffusion-limited cluster-cluster aggregation of aqueous colloids using quasielastic light scattering. Scaling behavior is found for the dependence of the mean cluster size on both time and initial concentration, and limits are placed on the scaling exponents of the cluster mass distribution. The fractal nature of the resultant clusters directly affects the exponents, illustrating the inherent relationship between the dynamic and static properties of kinetic aggregation processes.