Diffusion and structure in dense binary suspensions

Anisotropic remixing of a phase separated binary colloidal system with particles of different sizes in an external modulation

We explore the phase behavior of a binary colloidal system under external spatially periodic modulation. We perform Monte Carlo simulations on a binary mixture of big and small repulsive Lennard-Jones particles with a diameter ratio of 2:1. We characterize structure by isotropic and anisotropic pair correlation functions, cluster size distribution, bond angle distribution, order parameter, and specific heat. We observe the demixing of the species in the absence of external modulation. However, the mixing of the species gets enhanced with increasing potential strength along with the alignment of the particles transverse to the modulation. The de-mixing order parameter shows discontinuity with increasing modulation strength, characterizing a first order phase transition. The peak in specific heat increases linearly with the size of the system. We also look into the dynamical behavior of the system via computing Mean Square Displacement (MSD) along both parallel and perpendicular directions to the modulation. We observe a decrease in the diffusion coefficient for both types of particles as we increase the strength of the modulation.

Diffusing Wave Spectroscopy Measurements of Colloidal Suspension Dynamics

Diffusing wave spectroscopy (DWS) is used to measure the dynamics of charged silica particles between the volume fractions 0.065 ≤ ϕ ≤ 0.352 (weight percentages from 12.7 to 55.8 wt %). The short-time diffusivity averaged over the scattering vectors sampled by DWS D ¯ (ϕ) decreases with an increasing concentration. An effective hard-sphere model that accounts for hydrodynamic interactions and a double-layer repulsion fits the values up to an effective volume fraction ϕ e f f = ϕ b ^ 3 ≈ 0.6 , where b ^ is the excluded shell radius normalized by the particle radius b ^ = b/a = 1.3. While DWS measurements of diffusivity are sensitive to repulsive interactions, we show that they are relatively insensitive to attraction, such as those due to secondary minima in the interaction potential or weak depletion interaction.

Self-diffusion in two-dimensional binary colloidal hard-sphere fluids

We present a systematic experimental study of the dynamic behavior of monodisperse and bidisperse two-dimensional colloidal hard-sphere fluids. We consider the diffusive behavior of the two types of particles for systems with a variety of compositions and total area fractions. In particular, we measure the short- and long-time diffusion coefficients for both species independently. We find that the short-time self-diffusion coefficients show an approximately linear dependence on the area fraction and that the long-time self-diffusion coefficients are well described by an expression dependent upon only the area fraction and contact value of the radial distribution function. Finally, we consider the effect of composition change and find some variation in the long-time self-diffusion coefficients, which we ascribe to the complex packing effects exhibited by binary systems.

Analysis of light scattered by turbid media in cylindrical geometry

The angle dependence of the transmitted light through a cylindrical turbid sample (latex suspension, developing milk gel, draining/coarsening milk, and protein foams) in a standard light scattering setup was analyzed in terms of the transport mean free path length or scattering length l* (a measure for the turbidity) and the absorption length labs. By variation of the concentration of an absorbing dye, the independence of l* and labs was demonstrated. The resulting value of the specific extinction coefficient of the dye was found to be in fair agreement with direct spectroscopic determination and practically identical in milk and latex suspensions. The validity of this technique for obtaining l* was demonstrated by monitoring the acid-induced gelation of milk. The possibility to simultaneously determine l* and labs was used to follow the time development of a draining and coarsening protein foam which contained an absorbing dye. It was shown that labs can be used as a measure for the volume fraction of air in the foam. This method of monitoring the transmission of multiple light scattering provides an easy way to determine l* and, specifically for foams, quantitative data dominated by the bulk of the foam.

Short-time diffusivity of dicolloids

The short-time diffusivity of dicolloid particles as a function of particle volume fraction ϕ from 0.01 ≤ ϕ ≤ 0.6 is measured using diffusing wave spectroscopy. The diffusivities of symmetric and asymmetric dicolloids are compared with similarly sized spheres. The short-time diffusivity is independent of salt concentration and decreases with increasing volume fraction for both spheres and asymmetric dicolloids. Symmetric dicolloids have a higher diffusivity than spheres at similar volume fractions. This difference is accounted for by rescaling the dicolloid volume fraction based on the ratio of the random close-packing volume fractions of spheres and dicolloids. Finally, a useful method is provided for calculating the diffusivity of symmetric dicolloid particles of arbitrary aspect ratio based on the calculated hydrodynamic resistance of Zabarankin [Proc. R. Soc. A 463, 2329 (2007)].

Temperature-sensitive poly(N-isopropyl-acrylamide) microgel particles: a light scattering study

We present a light scattering study of aqueous suspensions of microgel particles consisting of poly(N-Isopropyl-Acrylamide) cross-linked gels. The solvent quality for the particles depends on temperature and thus allows tuning of the particle size. The particle synthesis parameters are chosen such that the resulting high surface charge of the particles prevents aggregation even in the maximally collapsed state. We present results on static and dynamic light scattering (SLS/DLS) for a highly diluted sample and for diffuse optical transmission on a more concentrated system. In the maximally collapsed state the scattering properties are well described by Mie theory for homogenous hard spheres. Upon swelling we find that a radially inhomogeneous density profile develops.

Transport equation for the time correlation function of scattered field in dynamic turbid media

I derive a transport equation for the time correlation function in transmission and reflexion and inside a turbid medium. This equation goes beyond the diffusion approximation that is at the root of the well-established diffusing-wave spectroscopy technique. It takes into account all the transport regimes from ballistic to diffusive and the relaxation in direction at each scattering event. The derivation is based on a generalized form of the Bethe-Salpeter equation coupled to a generalized form of the scattering operator. The method presented can be easily adapted to compute the correlation function in systems with several time scales encountered, for example, in biology and polymer physics. The obtained equation is easily solvable numerically using a Monte Carlo scheme.

A new model system for diffusion NMR studies of concentrated monodisperse and bidisperse colloids

A method to prepare monodisperse and simultaneously NMR-visible and fluorescent colloidal particles is described, and a systematic approach to obtain spectrally resolved diffusion coefficient for every component in a monodisperse colloidal suspension is presented. We also prepared bidisperse colloidal suspensions, where each colloid component has a distinct NMR spectral signature, and obtained the diffusion coefficients of both colloid species simultaneously in concentrated colloidal suspensions, with volume fractions between 20 and 50%. The colloidal model system developed in this work enables the study of colloidal phase behavior in binary mixtures for different number and size ratios.

Light propagation in strongly scattering, random colloidal films: the role of the packing geometry

We study the propagation of light through randomly packed films of micron-sized spheres. Dried films consist of strongly scattering core-shell particles mixed with polymer spheres, which are then dissolved to tune the number of contacts, Z, among the remaining scatterers. The transport mean free path l* is measured from the width of the coherent backscattering cone; l*=2.1 microm when Z ~ 4-5, but increases twofold (scattering weakens) in a film with Z ~ 9-10. The results contradict the standard diffusive transport model, but are explained by accounting for optical coupling of contacting spheres.

Tunable colloids: control of colloidal phase transitions with tunable interactions

Systems of spherical colloidal particles mimic the thermodynamics of atomic crystals. Control of interparticle interactions in colloids, which has recently begun to be extensively exploited, gives rise to rich phase behaviours as well as crystal structures with nanoscale and micron-scale lattice spacings. This provides model systems in which to study fundamental problems in condensed matter physics, such as the dynamics of crystal nucleation and melting, and the nature of the glass transition, at experimentally accessible lengthscales and timescales. Tunable control of these interactions provides reversible control. This will enable quantitative studies of phase transition kinetics as well as the creation of advanced materials with switchability of function and properties.

Photonic properties of strongly correlated colloidal liquids

The optical and structural properties of dense colloidal suspensions in the presence of long-range electrostatic repulsion are determined from both light and small-angle neutron scattering experiments. Short-range structural order induces an enhancement of the scattering strength while at the same time the total transmission shows strong wavelength dependence, reminiscent of a photonic crystal. Interestingly, the interplay between diffusive scattering and local order leads to negative values of the scattering anisotropy parameter. The tunable optical properties of these liquids furthermore suggest potential applications such as transparency switches or filters.

Beyond the diffusing-wave spectroscopy model for the temporal fluctuations of scattered light

We extend the theory of diffusing-wave spectroscopy using a random-walk approach and a numerical solution of the radiative transfer equation. The theory is not restricted to the diffusive regime and allows one to describe the crossover between the single-scattering and the diffusive regimes, which has been observed experimentally. It also predicts a lower bound of the scattered-field correlation time at long paths. This extended theory should have broad experimental applications in the field of imaging through biological tissues.

Self-diffusion in dilute colloidal suspensions with attractive potential interactions

The colloidal short-time self-diffusivity D(s)(s)(phi) is significantly retarded relative to hard sphere suspensions for the case of interparticle potential interactions induced by a nonadsorbing polymer. A comparison of diffusing wave spectroscopy measurements with direct calculations of D(s)(s)(phi) demonstrates that depletion effects on structure explain the observed retardation. We show that coexistence boundaries place unexpectedly severe constraints on the amount of D(s)(s)(phi) retardation possible for stable suspensions. The measured retardation is demonstrated to be an indicator of suspension metastability.

Structure, Dynamics, and Optical Properties of Concentrated Milk Suspensions: An Analogy to Hard-Sphere Liquids

A systematic study of the effects of volume fraction increment on the optical properties, the structure, and the dynamics of the casein micelles and fat droplets in milk was performed using diffusing wave spectroscopy. Four types of milk were investigated, NIDO full fat milk, fat-free milk, whey and fat-free milk, and finally lactose and fat-free milk. Independent measurements to calculate the dependence of the viscosity and the index of refraction of the milk serum and casein micelles as a function of the volume fraction were also performed. We compare the experimentally determined quantities photon transport mean free path (l*) and self-diffusion coefficient D(s) with the predictions from theoretical calculations using classical colloidal models such as a hard-sphere fluid. We demonstrate that all types of milk with and without fat content behave, structurally, like colloidal hard-sphere systems up to volume fractions well over 45%. In the case of dynamic measurements, both lactose- and fat-free and whey- and fat-free milk behave also like hard-sphere systems whereas fat-free milk and fat-containing NIDO milk deviate slightly at volume fractions over 35%. Finally, a comparative measurement and theoretical calculation of the casein micelle's size was performed.

Viscosity of bimodal and polydisperse colloidal suspensions

We present a theoretical framework for the viscosity of bimodal and polydisperse colloidal suspensions. For colloidal dispersions both interparticle forces between pairs of particles and many-particle effects such as depletion forces can have a significant effect on rheology. As hydrodynamic interactions are also important for colloidal systems, a theoretical description that includes hydrodynamic and thermodynamic interactions is required. An integral equation theory for multicomponent systems accounts for the contribution of thermodynamic interactions to the viscosity of dispersions. Introduction of small particles into a system of larger particles causes depletion forces between the large particles that increase the viscosity, while replacing large particles with an equal volume fraction of small particles increases the free volume in the system and decreases the viscosity. The integral equations model both of these effects in concentrated suspensions and provide a microscopic interpretation of free volume changes as changes in radial distribution functions. For a bimodal mixture they predict a dependence of the viscosity on size ratio, composition, and total volume fraction. Polydispersity is modeled by a small number of components whose sizes and weights are chosen to match the moments of the size distribution. This theory predicts a reduction in viscosity due to polydispersity and explains conflicting experimental measurement of the viscosity of hard-sphere colloids. Existing theoretical approaches that neglect the multiparticle correlations, included through the integral equations, yield qualitatively incorrect results for the change in the viscosity relative to monodisperse systems.

Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions

We have studied the properties of dense colloidal suspensions with a combination of small-angle neutron scattering (SANS) and diffusing wave spectroscopy (DWS). Contrary to single light scattering, DWS provides dynamic information on length scales, from 1 to 100 nm, comparable to SANS. This offers a unique range of accessible length and time scales perfectly suited for the (noninvasive) investigation of highly concentrated systems. By this we obtain valuable information about the structural properties and the short-time diffusion of electrostatically stabilized, but strongly screened, hard-sphere-like colloidal suspensions with volume fractions up to 30%. We furthermore discuss the consequences of local structural ordering on the optical properties, such as optical density and polarization. Quantitative agreement is found when comparing transmission measurements (optical density) with parameter-free numerical calculations based on the structural characterization from SANS.

Probing Static Structure of Colloid-Polymer Suspensions with Multiply Scattered Light

Time-dependent measurements of light propagation were conducted in aqueous dispersions of 523 nm diameter polystyrene at concentrations between 0.1 and 0.4 solids volume fraction in order to assess how particle correlation is influenced by depletion interactions arising from the addition of soluble polyethyleneoxide (PEO). In the absence of polymer, the transport scattering length can be predicted from Mie scattering theory and the Percus-Yevick (P-Y) model for static structure of a dense hard-sphere colloidal solution. Depletion forces arising from the addition of PEO of varying molecular weights influenced the spatial ordering of the dispersion and caused a further increase in the transport scattering length beyond that predicted by hard-sphere static structure factor but similar to that predicted by the mean sphere approximation (MSA) to the P-Y model described by Ye et al. (1996). Onset of flocculation occurred with increased PEO addition and correlated with PEO molecular weight. Phase separation was noted by no further change in the transport scattering length, except when flocculation was induced by the highest molecular weight PEO. The use of time-dependent measurements of light propagation in dense systems provides an alternative to small-angle light, neutron, and X-ray scattering characterization of interaction potentials in dense, multiply scattering samples and promises further fruitful investigation of colloidal particle interactions in suspensions. Copyright 1999 Academic Press.

Investigation of static structure factor in dense suspensions by use of multiply scattered light

Near-infrared, frequency-domain photon migration measurements of phase shift are used to derive accurate values of isotropic scattering coefficients in concentrated, interacting suspensions of aqueous polystyrene microspheres with volume concentrations ranging from 1% to 45% by solids and mean diameters ranging from 135 to 500 nm. Under conditions of high ionic strength, the isotropic scattering coefficient can be quantitatively predicted by the Percus-Yevick model for hard-sphere interactions and Mie theory. In addition, the attractive interactions between scatterers arising from the addition of soluble poly(ethylene glycol) with molecular weights of 100 and 600 K cause hindered scattering. The increases in static structure and decreases in isotropic scattering coefficient agree with that predicted by Mie theory and the depletion interaction model developed by Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)]. These results demonstrate the success of monitoring interaction between particles by use of multiple-scattered light and the necessity of incorporating models for these interactions when predicting scattering of dense, concentrated suspensions.

Penetration depth for diffusing-wave spectroscopy

The depth at which diffusing photons are assumed to be deposited in a random scattering medium has traditionally been treated as a phenomenological parameter comparable to the photon transport mean free path. We show how to average properly over an exponential distribution of depositions weighted additionally by the transmission probability, and compare our prediction for the autocorrelation of intensity fluctuations in the transmitted light with experimental data on an ideal system. The improved correlation function, where distinguishable from the prior form, provides slightly better agreement with data as long as the sample is thicker than approximately 10 transport mean free paths. However, in contrast with static transmission, proper averaging over a range of penetration depths does not extend the validity of diffusing-wave spectroscopy to significantly smaller slab thicknesses. The most significant errors in the theory must therefore arise from approximations other than the treatment of the source of diffusing photons.