Probing Electrostatic Forces in Colloidal Suspensions through Turbidity Data

Osmotic Bulk Modulus of Charged Colloids Measured by Ensemble Optical Trapping

The optical-bottle technique is used to measure osmotic bulk moduli of colloid suspensions. The bulk modulus is determined by optically trapping an ensemble of nanoparticles and invoking a steady-state force balance between confining optical-gradient forces and repulsive osmotic-pressure forces. Osmotic bulk moduli are reported for aqueous suspensions of charged polystyrene particles in NaCl solutions as a function of particle concentration and ionic strength, and are compared to those determined by turbidity measurements under the same conditions. Effective particle charges are calculated from the bulk moduli and are found to increase as a function of ionic strength, consistent with previously reported results.

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.

Assessment of Small-Angle and Angle-Averaged Structure Factor for Monitoring Electrostatic Colloidal Interactions Using Multiply Scattered Light

The isotropic scattering coefficients of 143-nm diameter polystyrene latex suspensions were measured using frequency-domain photon migration (FDPM) at 687 and 828 nm as a function of volume fraction (0.05-0.3) and ionic strength (1.0 to 120 mM NaCl equivalents) in order to derive the angle-integrated structure factor, S(q), and structure factor at zero wave vector, S(0). The effective surface charges of the dispersions were estimated by fitting the measured isotropic scattering coefficients at each wavelength as a function of volume fraction to the solution of the Orstein-Zernike integral equation using the hard sphere Yukawa potential model and mean spherical approximation as a closure relation. The estimates of surface charges were comparable at both wavelengths, but decreased with ionic strength. At 120 mM NaCl equivalents, the values of S(0) obtained from FDPM matched those predicted by the Percus-Yevick model, and decreased with volume fraction, consistent with prediction by the Carnahan-Starling equation.

Interaction potentials, structural ordering and effective charges in dispersions of charged colloidal particles

As colloidal dispersions of charged particles exhibit a wide variety of commercial, technological and scientific applications, a considerable theoretical effort has been devoted to finding an effective interaction potential from primitive models. The forces derived from this potential should justify the spatial ordering experimentally observed under certain conditions. This paper reviews the advances in these theoretical studies as well as some experiments (based on the mentioned order) that try to corroborate them. Special attention has been paid to the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Nowadays, many of these theoretical investigations suggest that it could be applied if some of its parameters are renormalized. Nevertheless, to achieve a renormalization procedure in a strict way (from a primitive model) is a difficult task as a result of the size and charge asymmetries between small ions and macroions. Thus, several procedures for computing renormalized charges in a simple way have been developed. However, the notion of effective charge has also been widely used (as a adjustable parameter) in order to justify results found for several kinds of colloids (like solid particle dispersions or micellar systems) by means of quite different experimental techniques. Renormalization (as well as ion condensation) approaches, experiments and the controversial relationship between theoretical and phenomenological effective charges are also reviewed in this work.

Investigation of Particle Interactions in Concentrated Colloidal Suspensions Using Frequency Domain Photon Migration: Monodisperse Systems

Frequency domain photon migration (FDPM) measurements were conducted to assess particle interactions of concentrated, monodisperse, polystyrene samples obtained directly from industry by using multiple scattering light. The angle-integrated static structure factor, S(q), and static structure factor at small wave vector q, S(0), were obtained from FDPM measurements at high volume fractions ranging from 0.05 to 0.3, and were compared with those obtained from the monodisperse hard sphere Percus-Yevick (HSPY) model. Effects of different colloid sizes on structure factor evaluated at two different wavelengths were also investigated. Results show that the monodisperse HSPY model is suitable for accounting for particle interactions and local microstructures in these colloidal suspensions. Upon using the HSPY model, particle sizes of polystyrene suspensions were recovered from FDPM measurements at high volume fractions (up to 0.3), which agree well with the DLS measurement of diluted sample ( approximately 0.001). The study of polydispersity effect shows that the FDPM method can be successfully used for recovering the mean particle size of polydisperse colloidal suspension with low polydispersity (<16%) under the assumption of monodisperse hard sphere systems.

Ionic condensation theories and the liquidlike structures observed in colloidal dispersions

Though the notion of effective charge has been widely used to fit experimental data, the possibility of predicting this adjustable parameter through a model remains unclear. A likely reason for this is the complexity involved in the theoretical approaches in the case of fluids with large asymmetries between their components. This paper deals with several condensation theories for spherical colloids, developed to provide effective charge values from simple models. Liquidlike structures are formed in colloidal dispersions for a set of latexes with different properties (charge, size, and polymeric composition). Effective charges are determined from experimental structure factors using a Derjaguin-Landau-Verwey-Overbeek potential and an Ornstein-Zernike scheme. The numerical coincidence between effective and post-condensation charges is fairly acceptable only for latexes with small size and charge. A simple approach based on the Manning condensation theory for linear polyelectrolytes is also discussed.