Determination of hydrodynamic properties in highly charged colloidal systems using static and dynamic light scattering

Scattering of light by colloidal aluminosilicate particles produces the unusual sky-blue color of Río Celeste (Tenorio volcano complex, Costa Rica)

Río Celeste (Sky-Blue River) in Tenorio National Park (Costa Rica), a river that derives from the confluence and mixing of two colorless streams--Río Buenavista (Buenavista River) and Quebrada Agria (Sour Creek)--is renowned in Costa Rica because it presents an atypical intense sky-blue color. Although various explanations have been proposed for this unusual hue of Río Celeste, no exhaustive tests have been undertaken; the reasons hence remain unclear. To understand this color phenomenon, we examined the physico-chemical properties of Río Celeste and of the two streams from which it is derived. Chemical analysis of those streams with ion-exchange chromatography (IC) and inductively coupled plasma atomic emission spectroscopy (ICP-OES) made us discard the hypothesis that the origin of the hue is due to colored chemical species. Our tests revealed that the origin of this coloration phenomenon is physical, due to suspended aluminosilicate particles (with diameters distributed around 566 nm according to a lognormal distribution) that produce Mie scattering. The color originates after mixing of two colorless streams because of the enlargement (by aggregation) of suspended aluminosilicate particles in the Río Buenavista stream due to a decrease of pH on mixing with the acidic Quebrada Agria. We postulate a chemical mechanism for this process, supported by experimental evidence of dynamic light scattering (DLS), zeta potential measurements, X-ray diffraction and scanning electron microscopy (SEM) with energy-dispersive spectra (EDS). Theoretical modeling of the Mie scattering yielded a strong coincidence between the observed color and the simulated one.

Short-time diffusion of charge-stabilized colloidal particles: generic features

Analytical theory and Stokesian dynamics simulations are used in conjunction with dynamic light scattering to investigate the role of hydrodynamic interactions in short-time diffusion in suspensions of charge-stabilized colloidal particles. The particles are modeled as solvent-impermeable charged spheres, repelling each otherviaa screened Coulomb potential. Numerical results for self-diffusion and sedimentation coefficients, as well as hydrodynamic and short-time diffusion functions, are compared with experimental data for a wide range of volume fractions. The theoretical predictions for the generic behavior of short-time properties obtained from this model are shown to be in full accord with experimental data. In addition, the effects of microion kinetics, nonzero particle porosity and residual attractive forces on the form of the hydrodynamic function are estimated. This serves to rule out possible causes for the strikingly small hydrodynamic function values determined in certain synchrotron radiation experiments.

Generic behavior of the hydrodynamic function of charged colloidal suspensions

We discuss the generic behavior of the hydrodynamic function H(q) and diffusion function D(q) characterizing the short-time diffusion in suspensions of charge-stabilized colloidal spheres, by covering the whole fluid regime. Special focus is given to the behavior of these functions at the freezing transition specified by the Hansen-Verlet freezing rule. Results are presented in dependence on scattering wavenumber q, effective particle charge, volume fraction, salt concentration, and particle size, by considering both the low-charge and high-charge branch solutions of static structure factors. The existence of two charge branches leads to the prediction of a re-entrant melting-freezing-melting transition for increasing particle concentration at very low salinity. A universal limiting contour line is derived for the principal peak height value of H(q), independent of particle charge and diameter, and concentration and salinity, which separates the fluid from the fluid-solid coexistence region. This line is only weakly dependent on the value of the structure factor peak height entering the Hansen-Verlet rule. A dynamic freezing criterion is derived in terms of the short-time cage diffusion coefficient, a quantity easily measurable in a scattering experiment. The higher-dimensional parameter scans underlying this study make use of the fast and highly efficient deltagamma-scheme in conjunction with the analytic rescaled mean spherical approximation input for the static structure factor. Our results constitute a comprehensive database useful to researchers performing dynamic scattering experiments on charge-stabilized dispersions.

Dynamics in dense suspensions of charge-stabilized colloidal particles

The dynamic behavior of charge-stabilized colloidal particles in suspension was studied by photon correlation spectroscopy with coherent X-rays (XPCS). The short-time diffusion coefficient, D(Q) , was measured for volume concentrations phi < or = 0.18 and compared to the free particle diffusion constant D(0) and the static structure factor S(Q) . The data show that indirect, hydrodynamic interactions are relevant for the system and hydrodynamic functions were derived. The results are in striking contrast to the predictions of the PA (pairwise-additive approximation) model, but show features typical for a hard-sphere system. The observed mobility is however considerably smaller than the one of a respective hard-sphere system. The hydrodynamic functions can be modelled quantitatively if one allows for an increased effective viscosity relative to the hard-sphere case.

Collective diffusion in charge-stabilized suspensions: Concentration and salt effects

The authors present a joint experimental-theoretical study of collective diffusion properties in aqueous suspensions of charge-stabilized fluorinated latex spheres. Small-angle x-ray scattering and x-ray photon correlation spectroscopy have been used to explore the concentration and ionic-strength dependence of the static and short-time dynamic properties including the hydrodynamic function H(q), the wave-number-dependent collective diffusion coefficient D(q), and the intermediate scattering function over the entire accessible range. They show that all experimental data can be quantitatively described and explained by means of a recently developed accelerated Stokesian dynamics simulation method, in combination with a modified hydrodynamic many-body theory. In particular, the behavior of H(q) for de-ionized and dense suspensions can be attributed to the influence of many-body hydrodynamics, without any need for postulating hydrodynamic screening to be present, as it was done in earlier work. Upper and lower boundaries are provided for the peak height of the hydrodynamic function and for the short-time self-diffusion coefficient over the entire range of added salt concentrations.

Many-body hydrodynamic interactions in charge-stabilized suspensions

In this joint experimental-theoretical work we study hydrodynamic interaction effects in dense suspensions of charged colloidal spheres. Using x-ray photon correlation spectroscopy we have determined the hydrodynamic function H(q), for a varying range of electrosteric repulsion. We show that H(q) can be quantitatively described by means of a novel Stokesian dynamics simulation method for charged Brownian spheres, and by a modification of a many-body theory developed originally by Beenakker and Mazur. Very importantly, we can explain the behavior of H(q) for strongly correlated particles without resorting to the controversial concept of hydrodynamic screening, as was attempted in earlier work by Riese [Phys. Rev. Lett. 85, 5460 (2000)].

Colloid interaction and pair correlation function of one-dimensional colloid-polymer systems

The interaction and pair correlation function of weakly charged colloidal particles in quasi-one-dimensional colloid-polymer systems are determined by enhanced video microscopy and digital image analysis. The pair correlation function is found to depend not only on the polymer concentration, but also on the degree of confinement; in particular, it depends on whether the channel width is such that mutual passage of the colloid particles is possible or not. These findings are compared with exact results on short-range order in linear continuous systems.

Diffusion and microstructural properties of solutions of charged nanosized proteins: Experiment versus theory

We have reanalyzed our former static small-angle x-ray scattering and photon correlation spectroscopy results on dense solutions of charged spherical apoferritin proteins using theories recently developed for studies of colloids. The static structure factors S(q), and the small-wave-number collective diffusion coefficient D(c) determined from those experiments are interpreted now in terms of a theoretical scheme based on a Derjaguin-Landau-Verwey-Overbeek-type continuum model of charged colloidal spheres. This scheme accounts, in an approximate way, for many-body hydrodynamic interactions. Stokesian dynamics computer simulations of the hydrodynamic function have been performed for the first time for dense charge-stabilized dispersions to assess the accuracy of the theoretical scheme. We show that the continuum model allows for a consistent description of all experimental results, and that the effective particle charge is dependent upon the protein concentration relative to the added salt concentration. In addition, we discuss the consequences of small ions dynamics for the collective protein diffusion within the framework of the coupled-mode theory.

The liquidlike ordering of lipid A-diphosphate colloidal crystals: The influence of Ca2+, Mg2+, Na+, and K+ on the ordering of colloidal suspensions of lipid A-diphosphate in aqueous solutions

A comprehensive study was performed on electrostatically stabilized aqueous dispersion of lipid A-diphosphate in the presence of bound Ca2+, Mg2+, K+, and Na+ ions at low ionic strength (0.10-10.0-mM NaCl, 25 degrees C) over a range of volume fraction of 1.0 x 10(-4)< or =phi< or =4.95 x 10(-4). These suspensions were characterized by light scattering (LS), quasielastic light scattering, small-angle x-ray scattering, transmission electron microscopy, scanning electron microscopy, conductivity measurements, and acid-base titrations. LS and electron microscopy yielded similar values for particle sizes, particle size distributions, and polydispersity. The measured static structure factor, S(Q), of lipid A-diphosphate was seen to be heavily dependent on the nature and concentration of the counterions, e.g., Ca2+ at 5.0 nM, Mg2+ at 15.0 microM, and K+ at 100.0 microM (25 degrees C). The magnitude and position of the S(Q) peaks depend not only on the divalent ion concentration (Ca2+ and Mg2+) but also on the order of addition of the counterions to the lipid A-diphosphate suspension in the presence of 0.1-microM NaCl. Significant changes in the rms radii of gyration (R2G) 1/2 of the lipid A-diphosphate particles were observed in the presence of Ca2+ (24.8+/-0.8 nm), Mg2+ (28.5+/-0.7 nm), and K+ (25.2+/-0.6 nm), whereas the Na+ salt (29.1+/-0.8 nm) has a value similar to the one found for the de-ionized lipid A-diphosphate suspensions (29.2+/-0.8 nm). Effective particle charges were determined by fits of the integral equation calculations of the polydisperse static structure factor, S(Q), to the light-scattering data and they were found to be in the range of Z*=700-750 for the lipid A-diphosphate salts under investigation. The light-scattering data indicated that only a small fraction of the ionizable surface sites (phosphate) of the lipid A-diphosphate was partly dissociated (approximately 30%). It was also discovered that a given amount of Ca2+ (1.0-5.0 nM) or K+ (100 microM) influenced the structure much more than Na+ (0.1-10.0-mM NaCl) or Mg2+ (50 microM). By comparing the heights and positions of the structure factor peaks S(Q) for lipid A-diphosphate-Na+ and lipid A-diphosphate-Ca2+, it was concluded that the structure factor does not depend simply on ionic strength but more importantly on the internal structural arrangements of the lipid A-diphosphate assembly in the presence of the bound cations. The liquidlike interactions revealed a considerable degree of ordering in solution accounting for the primary S(Q) peak and also the secondary minimum at large particle separation. The ordering of lipid A-diphosphate-Ca2+ colloidal crystals in suspension showed six to seven discrete diffraction peaks and revealed a face-centered-cubic (fcc) lattice type (a=56.3 nm) at a volume fraction of 3.2 x 10(-4)< or =phi< or =3.9 x 10(-4). The K+ salt also exhibited a fcc lattice (a=55.92 nm) at the same volume fractions, but reveals a different peak intensity distribution, as seen for the lipid A-diphosphate-Ca2+ salt. However, the Mg2+ and the Na+ salts of lipid A-diphosphate showed body-centered-cubic (bcc) lattices with a=45.50 nm and a=41.50 nm, respectively (3.2 x 10(-4)< or =phi< or =3.9 x 10(-4)), displaying the same intensity distribution with the exception of the (220) diffraction peaks, which differ in intensity for both salts of lipid A-diphosphate.

Structure and dynamics of electrostatically interacting magnetic nanoparticles in suspension

We investigate the structure and dynamics of charge-stabilized CoFe(2)O(4)-SiO(2) core-shell magnetic nanoparticles in suspensions. Small angle x-ray scattering and x-ray photon correlation spectroscopy allow us to analyze the intraparticle (core-shell) and interparticle structure of the suspension, as well as their dynamic and hydrodynamic behavior. Due to the weak magnetic interactions, the liquidlike structure is governed by screened Coulomb interactions. The hydrodynamic interactions of the measured systems are significantly stronger than predicted by current theories.

Structure of peptide solutions: a light scattering and numerical study

We investigated the interactions between protein molecules in solution, in particular for low salt concentrations and thus strong electrostatic interactions where a treatment based on the second virial coefficient is not sufficient. Static and dynamic light scattering experiments on solutions containing the peptide human calcitonin (hCT) were combined with calculations based on the Ornstein-Zernike equation with the hypernetted chain (HNC) closure and computer simulations within the primitive electrolyte model. The simulation illustrates the distribution of proteins in solution and the formation of (transient) protein aggregates. It furthermore allows us to predict the physical stability of hCT solutions in dependence of ionic strength, pH and hCT concentration.

Hydrodynamic interactions in quasi-two-dimensional colloidal suspensions

The effects of the hydrodynamic interactions on the short-time dynamics of colloidal, hard-sphere-like particles confined between two parallel walls are measured by digital videomicroscopy. We find that such effects can be described in terms of an effective two-dimensional hydrodynamic function H(k), defined as a straightforward adaptation to two dimensions of the corresponding object describing collective dynamics for the three-dimensional (3D) suspensions. Interestingly, the behavior of H(k) is qualitatively similar to the hydrodynamic function of 3D suspensions of hard spheres. We also found that for values of k where the static structure factor is 1, the dynamics is determined only by self-diffusion.

Effective screening of hydrodynamic interactions in charged colloidal suspensions

We investigate the hydrodynamic interaction in suspensions of charged colloidal silica spheres. The volume fraction as well as the range of the electrostatic repulsion between the spheres is varied. Using a combination of dynamic x-ray scattering, cross-correlated dynamic light scattering, and small angle x-ray scattering, the hydrodynamic function H(q) is determined experimentally. The effective hydrodynamic interactions are found to be screened, if the range of the direct interaction is relatively long and the static density correlations are strong. This observation of effective hydrodynamic screening is in marked contrast to hard-sphere-like systems.

Structure and dynamics of concentrated dispersions of polystyrene latex spheres in glycerol: static and dynamic x-ray scattering

X-ray photon correlation spectroscopy and small-angle x-ray scattering measurements are applied to characterize the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions between 2.7% and 52%. The static structures of the suspensions show essentially hard-sphere behavior. The short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient, which are based on a hard-sphere model [C. W. J. Beenakker and P. Mazur, Physica A 126, 349 (1984)]. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension [P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996)]. Our measurements are parametrized in terms of a viscoelastic model for the intermediate scattering function [W. Hess and R. Klein, Adv. Phys. 32, 173 (1983)]. Within this framework, two relaxation modes are predicted to contribute to the decay of the dynamic structure factor, with mode amplitudes depending on both wave vector and volume fraction. Our measurements indicate that, for particle volume fractions smaller than about 0.30, the intermediate scattering function is well described in terms of single-exponential decays, whereas a double-mode structure becomes apparent for more concentrated systems.

Stokesian dynamics study of quasi-two-dimensional suspensions confined between two parallel walls

We present a Stokesian dynamics (SD) computer simulation study of the static and dynamical properties of a monolayer of spherical colloidal particles restricted to diffuse in the midplane between two parallel walls. SD simulations account for hydrodynamic interactions (HI's) among the particles, and between particles and walls. Three different types of systems are studied: first, a monolayer of neutral spheres and neutral hard walls; second, particles interacting by a repulsive Yukawa-type potential of range depending on the wall separation. As a third system, the interesting case of charged particles between charged parallel walls with a longer-range attractive part in the pair potential is investigated, using the experimentally determined effective pair potential of Acuna-Campa et al. [Phys. Rev. Lett. 80, 5802 (1998)]. Various measurable quantities are calculated in dependence of the particle concentration and the wall distance: short- and long-time self-diffusion coefficients, radial distribution functions and static structure factors, hydrodynamic functions, mean squared displacements, and van Hove real-space correlation functions. We assess the importance of HI's by comparing our results with simulation results where HI's are fully or partially disregarded. Some of our results are also compared with experimental data, and good agreement is found. Remarkable effects are investigated, like the hydrodynamic enhancement of self-diffusion for the case of strongly charged particles, and the strong increase of the hydrodynamic function at small wave numbers.

Photon correlation spectroscopy: X rays versus visible light

We have performed combined dynamic light scattering (DLS) and dynamic x-ray scattering (DXS) experiments on dense colloidal suspensions. The intermediate scattering functions obtained with these two techniques are compared directly. In the case of optically index matched samples, the comparison demonstrates that DXS yields accurate and reliable results. It is shown that the hydrodynamic interaction H(q) can be determined experimentally, without taking recourse to any theoretical model, by combining DXS and DLS. The combination of the two methods probes the dynamics over more than one decade in scattering vector. Experiments on optically opaque samples, where DLS fails, demonstrate the necessity to use x rays in these systems.