A Reply to the Comment by E. G. D. Cohen and I. M. de Schepper.

We study the adsorption and desorption of hexane in porous Vycor, as the ambient vapor pressure is varied, through sorption isotherm, ultrasonic velocity and attenuation, and light scattering measurements. On adsorption, we show that the fluid fills the pore space uniformly until capillary condensation occurs; however, small, randomly distributed, vapor bubbles remain, as detected by a large increase in the attenuation of the ultrasound. On desorption, the mismatch in the index of refraction between the empty pores and the surrounding filled pores leads to intense scattering of light that reveals the presence of long-range correlations in the pore space. These correlations have a fractal dimension of 2.6, which is very near the value predicted for invasion percolation. Finally, we also investigate the time dependence of the changes in the adsorbed fluid mass and use these measurements to identify three distinct regimes with vastly differing mechanisms for mass transport. The results presented here provide information on the differences in pore-space correlations on filling and drainage, and highlight the critical role of the connectivity of the pores to the surface in determining the desorption behavior.

We have critically tested the application of the diffusion approximation to describe the propagation of ultrasonic waves through a random, strongly scattering medium. The transmission of short ultrasonic pulses has been measured through a concentrated suspension of glass beads immersed in water. The transmitted sound field is found to exhibit temporal fluctuations with a period determined by the width of the incident pulse. Provided that appropriate boundary conditions are used to account for the reflectivity of the interfaces, the time dependence of the ensemble-averaged transmitted intensity is shown to be well described by the diffusion equation. This enables us to determine both the diffusion coefficient for the sound waves as well as the inelastic absorption rate. The consistency of these results is established by varying the experimental geometry; while the transmitted pulse shape changes markedly, the values for the diffusion coefficient and absorption rate obtained through a description using the diffusion approximation remain unchanged. We have also measured the absolute transmitted intensity of the sound as the sample thickness is varied; this provides an accurate measure of the transport mean free path and thus also the energy transport velocity. These results convincingly demonstrate the validity of using the diffusion approximation to describe the propagation of sound waves through strongly scattering media.

The frequency-dependent viscoelastic shear modulus of concentrated suspensions of colloidal hard spheres is shown to be strongly modified as the volume fraction approaches the glass transition. The elastic or storage component, G', becomes larger than the viscous or loss component, G''. The frequency dependence of G' develops a plateau while that of G'' develops a minimum. We propose a physical model to account for these data, using a description of the glasslike behavior based on mode-coupling theory, and a description of the high-frequency behavior based on hydrodynamic flow calculations.

We present a novel experimental method to measure linear viscoelastic moduli of complex fluids using dynamic light scattering. A generalized Langevin equation is used to relate the mean square displacement of a probe particle to the storage and loss moduli of the bulk complex fluid. We confirm the experimental validity of this technique by comparing the light scattering results with mechanical measurements for several complex fluids. This method probes the moduli over a greatly extended frequency range and provides significant new insight into the elastic susceptibility of complex fluids.

The elastic shear modulus of monodisperse emulsions is shown to exhibit a universal dependence on droplet volume fraction phi when scaled by the Laplace pressure of the droplets, increasing as phi(phi - phi(c)). where phi(c) approximate to 0.635, the value of random close packing of solid spheres. Surprisingly the osmotic pressure required to compress the emulsions to increase phi is nearly the same as the shear modulus over a large range of volume fraction, while the bulk osmotic modulus differs significantly. Models based on the structural disorder of the emulsions are discussed to account for these data.

We report experimental evidence for the divergence of the collective diffusion coefficient in a quasi-two-dimensional fluid. The system studied is a monolayer of nearly monodisperse self-assembled disks of the diblock copolymer polystyrene-b-polymethylmethacrylate, supported in the air/water interface, and the method used to measure the collective diffusion coefficient is dynamic evanescent wave light scattering. In all cases studied, in a system of interacting particles the collective diffusion coefficient, which depends on the sum of the time integrals of the velocity autocorrelation and crosscorrelation functions for all pairs of particles, is proportional to the self-diffusion coefficient. It has been predicted that the self-diffusion coefficient of a two-dimensional fluid does not exist, i.e., that the apparent self-diffusion coefficient defined by the time integral of the velocity autocorrelation function diverges as t→∞, implying that so, also, will the collective diffusion coefficient of a two-dimensional fluid. Our experimental data are consistent with this qualitative expectation and they also agree with the asymptotic dependence on time (t→∞), wave vector (Q→0), and surface density of the self-diffusion coefficient of a two-dimensional fluid predicted by Yuan and Oppenheim [H.H.-H. Yuan and I. Oppenheim, Physica 90A, 1 (1978); 90A, 21 (1978); 90A, 561 (1978)].

Time-dependent hydrodynamic interactions in a colloidal suspension of hard spheres are studied, both experimentally and through computer simulation. The focus is on the behavior at small wave vectors, which directly probes the temporal evolution of hydrodynamic interactions between nearby particles. The computer simulations show that the time-dependent diffusion coefficient has the same functional form for all wave vectors, with a single characteristic scaling time for each length scale and for each volume fraction. Wave-vector-averaged effective diffusion coefficients, measured experimentally using diffusing wave spectroscopy, also scale to the same functional form. In this case, the scaling time is dependent on both volume fraction and particle size; it decreases sharply with decreasing particle radius, reflecting the greater contribution from smaller wave vectors that is contained in the scattering from the smaller particles. For a direct comparison of simulation and experiment, we simulate the experimentally observed correlation functions, by averaging the wavevector-dependent computer-simulation data with the weighting appropriate to the experimental technique. Although the overall scaling is similar, there are quantitative differences in the simulated and measured relaxation times. We suggest these differences are due to the compressibility of the suspension, and that the resultant pressure waves make an unexpectedly significant contribution to the hydrodynamic interactions.

We use a combination of numerical simulations and laboratory experiments to study the time-dependent collective diffusion coefficient D(q, t) in concentrated colloidal suspensions. At short times, the particle configuration is frozen, and D(q, t) probes the temporal and spatial evolution of hydrodynamic interactions, via their effects on the particle velocities. We find that D(q, t) exhibits a surprising scaling behavior, with a single, q-dependent relaxation time, suggesting that the suspension behaves as an effective medium for hydrodynamic interactions over a wide range of length scales and time scales.

We show that density measurements can provide an alternative method for determining the number and species of ions adsorbed onto colloidal particles. We cause charge-stabilized colloidal dispersions of polystyrene spheres to aggregate by adding various salts. The solvents are mixtures of H2O and D2O in which the colloids are neutrally buoyant after aggregation, which we verify by centrifugation of the samples, By this method we are able to determine the density of the aggregated colloids. We find that the density depends on the species of salt added to initiate the aggregation and can be calculated on the assumption that a cation of the added salt binds with each ionizable group on the surface of the colloidal particles. (C) 1995 Academic Press, Inc.

We generalize the theory of diffusing-wave spectroscopy (DWS) to include the effects of fluctuations of the amplitudes of the scattered fields. Thus DWS can be used to probe the internal dynamics of flexible particles. We study the thermally induced shape fluctuations of monodisperse emulsion droplets as a function of the droplet volume fraction phi. We find that a droplet's mean-squared deviation from spherical shape increases with phi, while the characteristic rate of relaxation of the shape deformations decreases with phi. Our generalization of the theory of DWS allows us to measure the autocorrelation function of the fluctuating amplitude of the field scattered from a droplet. We use fluid dynamics and scattering theory to calculate this autocorrelation function theoretically for an isolated droplet. The significant contribution of many independent modes of deformation results in a distinctly nonexponential relaxation. The measured behavior agrees with the theory as phi approaches zero. At higher values of phi throughout the range of colloidal liquids we find a surprising scaling behavior, which implies that particle interactions bring about the enhancement and slowing down of shape fluctuations without altering the spectrum of excited deformation modes. We relate the form of the scaling function to the particle radial distribution function. In ''compressed'' emulsions with phi as high as 0.8, shape fluctuations may be the only dynamical behavior that can occur. We suggest that in these systems the amplitude of the shape fluctuations is related to the emulsion's elastic modulus.