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 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.
Diffusing-wave spectroscopy and interferometry, the extensions of dynamic light scattering to materials which exhibit a very high degree of multiple scattering, have been used to measure the early-time, short length scale motion of Brownian particles. The transition from ''ballistic'' to ''diffusive'' motion is observed. In very dilute samples, this transition is described very well by theories which explicitly account for the time-dependent hydrodynamic interaction between a Brownian particle and the surrounding fluid. For particle volume fractions exceeding a few per cent, the data deviate from the theory for dilute suspensions, but exhibit a remarkable scaling with the suspension viscosity.
Times Cited: 0 33rd Microsymposium on Macromolecules: Optics and Dynamics of Polymers/6th Meeting of European-Macromolecular-Club Jul 15-16, 1993 Prague, czech republic Int union pure & appl chem, macromolec div; acad sci czech republic; inst macromolec chem, prague; czech chem soc
We measure the dispersion of the longitudinal sound waves in a suspension of solid spheres using Brillouin scattering. We fmd two distinct propagating longitudinal modes when the wavelength of the sound becomes comparable to the sphere diameter. The higher-frequency mode has a velocity intermediate between those of the pure solid and pure liquid phases, and its velocity increases with increasing solid volume fraction. The dispersion curve of this mode has distinct gaps, and the group velocity goes to zero near these gaps. We interpret this mode as a compressional ''citation which propagates through both the liquid and the solid, as expected for a composite medium. The gaps in the dispersion curve result from the very large scattering of the excitation by the spheres, and occur at frequencies where the scattering from a single, isolated sphere is predicted to be a maximim due to a resonance in the sphere. By contrast, the lower-frequency mode has a velocity that is less than those in either the pure solid or the pure fluid. We interpret this mode as a surface acoustic excitation, which propagates between adjacent spheres by means of the exponentially decaying portion of the excitation in the fluid at the surface of the spheres. A summary of a theoretical treatment is also presented.
We study the propagation of sound in complex colloidal systems. By combining Brillouin scattering with ultrasonic techniques, we measure the dispersion in the acoustic propagation over three decades in frequency. Acoustic propagation is sensitive to the bulk compressibility of the medium, and probes new structural and dynamic properties of the colloidal system. We study two colloidal systems. The first is a system of inverted micelles or microemulsions, where the droplet size is significantly smaller than the wavelength of the sound. By measuring the dispersion of the sound velocity as a function of droplet volume fraction, we identify an increased rigidity of the system at high frequencies. The increase in the modulus scales as (phi - phi(c))tau, where phi is the volume fraction of droplets and phi(c) is a critical volume fraction. This is consistent with rigidity percolation. The second system we study consists of a suspension of hard sphere colloids whose diameter is comparable to the wavelength of sound. We measure the dispersion curve for the phonons in this system at different volume fractions of spheres. A new acoustic excitation is found when the wavelength of the sound is comparable to the sphere diameter. This acoustic excitation possesses unusual properties and is attributed to a surface excitation that can propagate coherently between adjacent spheres.
Times Cited: 9 Symp on complex liquid systems Jul 05-10, 1992 Polistena, italy Banca populare polistena; reg calabria; prov reggio calabria; univ messina; hamamatsu photon italia; microcontrole; laserpoint; lasersource; cnr, grp natl struct mat; ciso calabria
We discuss the entension of dynamic light scattering to very strongly scattering media, where the propagation of light is described by the diffusion approximation, allowing the distribution of the light paths to be determined. The temporal evolution of the length of each of these paths, due to the dynamics of the scattering medium, is calculated, and an expression for the temporal autocorrelation function of the intensity fluctuations of the scattered light is obtained. This relates the measured decay of the autocorrelation function to the dynamics of the medium. This technique is called diffusing wave spectroscopy (DWS). To extend its utility, we consider the consequences of interactions between the scattering particles on the light scattering. To illustrate its applications, we consider several examples of new physics that can be investigated using DWS. We study the transient nature of hydrodynamic interactions between a particle and the surrounding fluid. We are able to probe the decay of the velocity correlation function of the particles, and we demonstrate its algebraic decay, with a t(-3/2) rime dependence. We also show that the time-dependent self diffusion coefficient exhibits an unexpected scaling behavior, whereby all the data, from samples of different volume fractions, can be scaled onto a single curve. Finally, we discuss the applications of DWS to the study of the dynamics of foams, and show how it can be used to probe the rearrangement of the bubbles within the foam as they coarsen.
We use ultrasonic attenuation and light scattering to study spatial correlations in the pores of Vycor on filling and draining with hexane. On filling, the hexane initially adsorbs uniformly, but when capillary condensation occurs, vapor microbubbles are formed and persist until the sample is completely full. However, no long-range correlations of the bubbles are observed. By contrast, on drainage, the empty pores exhibit long-range correlations with a fractal dimension of 2.6. This results from the pore connectivity, suggesting that this behavior can be modeled by invasion percolation.
The structure of colloidal crystals formed from suspensions of hard-sphere colloids is studied. The samples are contained in a thin cell. By rocking the samples, we are able to form shear-aligned colloidal crystals with extended, long-range order. The aligned crystals persist after the shear ceases, enabling us to use laser-light crystallography to determine their structure. We observe an unusual ordering, wherein the structure is a nearly perfect single twin of a face-centered cubic crystal, with crystals of different twins formed on each side of the cell. We exploit the coherence of the laser source to observe a speckle-like fluctuation of the intensity in the Bragg peaks. However, this fluctuation occurs only in one scattering direction, and therefore reflects a remnant disorder in the stacking of the hcp planes. We introduce a simple model which accounts for both the nature of the disorder in the stacking as well as the specklelike fluctuations. Our observation of this speckle also confirms recent predictions.
We report the results of static and dynamic evanescent wave light scattering studies of a monolayer of a diblock copolymer, polystyrene-b-polymethylmethacrylate (PS-b-PMMA) with weight averaged molecular weights (M(w)) of 880 000:290 000 supported at the air/water interface. Our studies probe the interfacial structural and dynamic proper-ties of the monolayer on a length scale which is a fraction of the wavelength of light. The static light scattering studies were carried out as a function of polymer surface coverage and temperature; we also report some preliminary data for the dependence of the static structure function on the relative molecular weights of the PS and PMMA blocks. The complementary dynamic light scattering studies were carried out only as a function of surface coverage. Our data suggest that, upon spreading in the air/water interface, PS-b-PMMA (880:290 K) copolymers form thin disklike aggregates containing about 240 molecules. These data are consistent with a model in which each such aggregate is a ''furry disk'' with a dense core consisting of a layer of collapsed PS blocks atop a thin layer of extended PMMA blocks on the water surface and a brushlike boundary of extended PMMA blocks. The data show that the furry disks diffuse freely when the surface coverage is small, but when the surface coverage is large, they are immobile. Our data also suggest that the furry disks can aggregate to form even larger ''islands'' of disks with an extension greater than 20 mum. The static structure function of the assembly of furry disks is well described, over a wide range of surface coverage, by the structure factor of a two-dimensional hard disk fluid modulated by a two-dimensional hard disk form factor.
We study oil in water emulsions when the interaction between the droplets becomes strongly adhesive, causing them to stick together. However, the droplets still retain their integrity and do not coalesce. By using emulsions with droplets that are monodisperse in size, we are able to clearly observe their structure when the emulsions become adhesive. We show that the structure of strongly adhesive emulsions reflects a complex interplay among the strength of the adhesion, the droplet volume fraction, phi, and the time evolution of the adhesion. Initially, strong adhesion of the droplets leads to the formation of an emulsion gel. Moreover, the gel possesses a well-defined characteristic length scale, d(c), as evidenced by an intense ring of small angle light scattering. The characteristic length scale decreases as the droplet volume fraction increases. At low phi, the structure of the emulsion gel is fractal on length scales shorter than d(c), and the measured fractal dimension suggests that the gelation mechanism is controlled by diffusion-limited cluster aggregation. However, at higher phi, the short range structure is more compact, rather than fractal, and a different mechanism must be responsible for the gelation. If the strength of the adhesion is increased still further, the droplets become more deformed, resulting in massive restructuring of the emulsion gel. The structure fractures into independent, more compact flocs, eliminating the overall rigidity of the emulsion gel. These results help rationalize some of the diverse structures that are observed upon flocculation of the more usually studied polydisperse emulsions.
The mean-square displacement [DELTA-r2(tau)] of particles in concentrated suspensions is measured at times sufficiently short to observe the transient nature of hydrodynamic interactions. For all volume fractions-phi, the velocity autocorrelation function decays as a power law R(tau) is similar to tau–3/2. A remarkable scaling with phi is observed for the time-dependent self-diffusion coefficient D(s)(tau) = [DELTA-r2(tau)]/6-tau: If D(s)(tau) is scaled by its asymptotic value and if time is scaled by a viscous time inversely proportional to the shear viscosity of the suspension, all the data fall onto a single master curve.
The breakdown of the diffusion approximation in describing temporal autocorrelation functions of multiply scattered light can be probed by collecting light from different polarization channels. Contrary to the claim of Freund and Kaveh, the diffusion approximation cannot be used to predict the value of gamma, nor can it be used to make any statement about the universality of the value of gamma.
The coalescence of monodisperse silicone oil-in-water emulsions stabilized with sodium dodecyl sulfate has been studied. We report the existence of a sharp destabilization threshold, controlled by surfactant chemical potential, osmotic pressure, and droplet diameter, at which the rate of coalescence increases dramatically. We present evidence that the stability of the emulsions can be characterized by two microscopic parameters: a minimum stable value of the surfactant chemical potential and a maximum value of the pressure exerted upon a droplet-droplet interface.
We report the formation of a solid gel network from purely liquid emulsion droplets. The gel remains rigid at droplet volume fractions as low as 10(-3). The gelation process is identified as diffusion-limited cluster aggregation. We find a surprising order in the gel structure. This ordering is induced by the aggregation kinetics, which result in an unexpected spatial correlation between the growing clusters, ensuring that the network is formed from clusters of nearly equal size and spacing.
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.