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.
The coarsening of a three-dimensional foam is studied with multiple light-scattering techniques. Scaling behavior is observed with the average bubble diameter growing in time as t(z) where z = 0.45 /- 0.05. Changes in the packing conditions during coarsening give rise to a dynamical process that also exhibits temporal scaling. Neighboring bubbles undergo sudden structural rearrangement events at a rate per unit volume that decays as t(-y) where y = 2.0 /- 0.2.
The structure and dynamics of three-dimensional foams are probed quantitatively by exploiting the strong multiple scattering of light that gives foams their familiar white color. Approximating the propagation of light as a diffusion process, transmission measurements provide a direct probe of the average bubble size. A model for dynamic light scattering is developed that can be used to interpret temporal fluctuations in the intensity of multiply scattered light. The results identify previously unrecognized internal dynamics of the foam bubbles. These light-scattering techniques are direct, noninvasive probes of bulk foams and therefore should find wide use in the study of their properties.
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.