Structure and short-time dynamics in concentrated suspensions of charged colloids

Abstract

We report a comprehensive joint experimental-theoretical study of the equilibrium pair-structure and short-time diffusion in aqueous suspensions of highly charged poly-acrylate (PA) spheres in the colloidal fluid phase. Low-polydispersity PA sphere systems with two different hard-core radii, R(0) = 542 and 1117 Å, are explored over a wide range of concentrations and salinities using static and dynamic light scattering (DLS), small angle x-ray scattering, and x-ray photon correlation spectroscopy (XPCS). The measured static and dynamic scattering functions are analyzed using state-of-the-art theoretical methods. For all samples, the measured static structure factor, S(Q), is in good agreement with results by an analytical integral equation method for particles interacting by a repulsive screened Coulomb plus hard-core pair potential. In our DLS and XPCS measurements, we have determined the short-time diffusion function D(Q) = D(0) H(Q)∕S(Q), comprising the free diffusion coefficient D(0) and the hydrodynamic function H(Q). The latter is calculated analytically using a self-part corrected version of the δγ-scheme by Beenakker and Mazur which accounts approximately for many-body hydrodynamic interactions (HIs). Except for low-salinity systems at the highest investigated volume fraction φ ≈ 0.32, the theoretical predictions for H(Q) are in excellent agreement with the experimental data. In particular, the increase in the collective diffusion coefficient D(c) = D(Q → 0), and the decrease of the self-diffusion coefficient, D(s) = D(Q → ∞), with increasing φ is well described. In accord with the theoretical prediction, the peak value, H(Q(m)), of H(Q) relates to the nearest neighbor cage size ∼2π∕Q(m), for which concentration scaling relations are discussed. The peak values H(Q(m)) are globally bound from below by the corresponding neutral hard-spheres peak values, and from above by the limiting peak values for low-salinity charge-stabilized systems. HIs usually slow short-time diffusion on colloidal length scales, except for the cage diffusion coefficient, D(cge) = D(Q(m)), in dilute low-salinity systems where a speed up of the system dynamics and corresponding peak values of H(Q(m)) > 1 are observed experimentally and theoretically.

Ultrafiltration of charge-stabilized dispersions at low salinity

“…(10) for u eff (r) are used. For a charge-stabilized suspension whose colloidal interactions are described by an OCM-type potential, the BM-PA method predicts H(q) in good overall agreement with simulation and experimental result [27,30,31,65]. Fig.…”

“…The good accuracy of the BM-PA and simplified MCT methods of calculating D c and η for charge-stabilized dispersions was assessed already in earlier works by the comparison with Stokesian dynamics simulation and experimental results for colloidal particle suspensions [30,31].…”

“…This assumption is justified for charged colloids if the salt concentration is small enough that near-contact configurations are unlikely, or if the solvent dielectric constant nearly matches that of the particles, or if the charged particles are additionally sterically stabilized by surface-grafted short polymers [43]. Systems describable by the OCM model range from charge-stabilized suspensions of rigid colloidal spheres [31] to ionic microgels [44] and globular protein solutions [32,33]. We use here the OCM for calculating the colloid radial distribution function (RDF), g(r), and associated colloid static structure factor, S(q), that in turn are needed for the calculation of η, K and D c .…”

“…(29), and the shear-relaxation part is obtained using Eq. (31). We employ here the BM-PA input for H(y), and the HNC S(y) based on the OCM potential with PB cell model values for Z eff and κ eff .…”

“…The cell model is combined with the hypernetted chain (HNC) integral equation method of calculating the particle radial distribution function and static structure factor that in turn are used in our calculation of D c and the high-frequency, η ∞ , and the shear relaxation, ∆η, contributions to the low-shear viscosity η. The semi-analytical methods used here in calculating these transport coefficients have been well assessed in their good accuracy by the comparison with dynamic simulation results where HIs are fully included [27,30], and with experimental data for charge-stabilized colloidal particles [31] and protein solutions [32,33]. The osmotic pressure and transport coefficient results constitute the input to the here employed cross-flow UF boundary layer model previously applied by Roa et al [34] to solvent-permeable hardsphere suspensions.…”