Dynamic dielectric response of concentrated colloidal dispersions: comparison between theory and experiment

Effects of ionic valence on aggregation kinetics of colloidal particles with and without a mixing flow

HYPOTHESIS

The classical Schulze-Hardy rule states that the critical coagulation concentration (CCC) of colloidal particles is inversely proportional to the counter-ionic valence at powers ranging from 2 to 6. However, the inverse Schulze-Hardy rule has recently been proposed, suggesting that the CCC can also be inversely proportional to the co-ionic valence. Previous studies on these rules did not consider the effect of flow on aggregation kinetics and the CCC. This study aims to investigate the effect of multivalent counter-ions and co-ions on aggregation kinetics and the CCCs in systems with and without a mixing flow.

EXPERIMENTS

We measured the aggregation rate coefficients of polystyrene sulfate latex particles as a function of the salt concentration with different ionic species. Furthermore, we analyzed these measurements using theoretical models based on hydrodynamic pair-diffusion in a random flow and trajectory analysis in two steady flows. The analysis was conducted using zeta potentials determined through electrophoretic measurements.

FINDINGS

Although the trajectory analysis underestimates the CCCs, the hydrodynamic pair-diffusion model can capture the shift of critical coagulation concentrations in the mixing flow to higher values than those in Brownian aggregation and also shows a better agreement with the experimental results. This result suggests that combining random flow and Brownian diffusion is crucial for developing a consistent framework for predicting both Brownian aggregation and aggregation in a mixing flow.

AC Conductivity Measurements of Ultradilute Colloidal Suspensions in HEPES Buffer

Impedance spectroscopy was used to probe the AC conductivity of extremely dilute colloidal suspensions (2.5 × 10^-5 ≤ Φ_w/v ≤ 4.0 × 10^-2) comprising of polystyrene microspheres (PS; κa ≫ 1 and ζ = -65 mV), gold nanoparticles (Au NPs; κa > 1 and ζ = -26 mV), and Au-coated PS metallodielectric particles (Au-PS) in HEPES buffer. When AC electric fields of strength 10 mV and 1 MHz were applied via 100 μm gap interdigitated microelectrodes across 10 μL samples, a highly resistive (θ_capacitive < 1°) and nonmonotonic response was obtained with particle concentrations at steady state. While the suspensions were less resistive (than the buffer) below a critical concentration, they became more resistive above it. More interestingly, particle-particle interactions took place in suspensions with concentrations as low as 0.005% w/v. We believe this unique behavior is linked to the ion size asymmetry in the HEPES molecule that provides an ideal microenvironment for counterionic polarization around the particles. The exact mechanism of polarization in HEPES, however, still remains elusive as the current theoretical models for simple electrolytes fail to explain our data.

Electric Permittivity and Dynamic Mobility of Dilute Suspensions of Platelike Gibbsite Particles

In this work we discuss the electrokinetic evaluation of model platelike particles. By model particles we mean homogeneous and controlled size and shape. The electrokinetic analysis in such complex geometries cannot be limited to a single data point as in usual electrophoresis in constant (dc) fields. The information can be made much richer if alternating (ac) fields with a sufficiently wide range of frequencies are used. In this case, two techniques can be applied: one is the determination of the frequency spectrum of the electric permittivity or dielectric constant (low-frequency dielectric dispersion), and the other is the electroacoustics of suspensions and the determination of the frequency dispersion of the electrophoretic mobility (dynamic or ac mobility). In this work, these techniques are used with planar gibbsite (γ-Al(OH)3) particles, modeled as oblate spheroids with a small aspect ratio. As in other laminar minerals, a particular charge distribution, differing between edges and faces, gives rise to very peculiar electrokinetic behavior. It is found that pH 7 approximately separates two distinct field responses: below that pH the dielectric dispersion and dynamic mobility data are consistent with the existence of individual, highly charged platelets, with charge mainly originating on edge surfaces. At pH 4, a low-frequency relaxation is observed, which must originated from larger particles. It is suggested that these are individual ones bridged by negatively charged fiberlike structures, coming from the partial decomposition of gibbsite particles. On the other side of the measured pH spectrum, the overall charge of the particles is low, and this probably produces aggregates with a relatively large average size, with relaxation frequencies on the low side. This is confirmed by dynamic mobility data, showing that a coherent picture of the nanostructure can be reached by combining the two techniques.

Diverging electrophoretic and dynamic mobility of model silica colloids at low ionic strength in ethanol

Electroacoustics and laser Doppler electrophoresis were employed to measure the mobility of surface-modified silica colloids in ethanol as a function of the ionic strength. Sufficiently low volume fractions were chosen to exclude effects of interparticle interactions. At high ionic strength, the electrophoretic mobility μ(e) is equal to the (electroacoustic) dynamic mobility μ(d) at 3.3 MHz. However, the ratio μ(d)/μ(e) increases significantly to ∼5 at low ionic strength. This increase may be related to the porous outer layer of the surface-modified silica spheres.

Electrodynamics of soft multilayered particles dispersions: dielectric permittivity and dynamic mobility

A theory is presented for the electrodynamics of dispersions of spherical soft multilayered (bio)particles consisting of a hard core surrounded by step-function or diffuse-like polymeric layers with distinct electrohydrodynamic and structural features.

Transition from dilute to concentrated electrokinetic behavior in the dielectric spectra of a colloidal suspension

Dielectric spectroscopy is used to measure the complex permittivity of 200 and 100 nm diameter polystyrene latex suspended in potassium chloride (KCl) solutions over the frequency range 10(4)-10(7) Hz as a function of particle volume fraction (ϕ) and ionic strength. Dilute suspension dielectric spectra are in excellent agreement with electrokinetic theory. A volume fraction dependence of the dielectric increment is observed for low electrolyte concentrations (0.01, 0.05, and 0.1 mM) above ϕ ≈ 0.02. This deviation from the dilute theory occurs at a critical frequency ω* that is a function of volume fraction, particle size, and ionic strength. The dielectric increment of suspensions at the highest salt concentration (1 mM) shows no volume fraction dependence up to ϕ = 0.09. Values of ω* are collapsed onto a master curve that accounts for the length and time scales of ion migration between neighboring particles. The measured conductivity increment is independent of volume fraction and agrees with theory after accounting for added counterions and nonspecific adsorption.

The actual dielectric response function for a colloidal suspension of spherical particles

In this paper, we present a theoretical analysis of the dielectric response of a dense suspension of spherical colloidal particles based on a self-consistent cell model. Particular attention is paid to (a) the relationship between the dielectric response and the conductivity response and (b) the connection between the real and imaginary parts of these responses based on the Kramers-Kronig relations. We have thus clarified the analysis of Carrique et al. (Carrique, F.; Criado, C.; Delgado, A. V. J. Colloid Interface Sci. 1993, 156, 117). We have shown that both the conduction and displacement current components are complex quantities with both real and imaginary parts being frequency dependent. The dielectric response exhibits characteristics of two relaxation phenomena: the Maxwell-Wagner and the alpha-relaxations, with the imaginary part being the more sensitive instrument. The inverse Fourier transform of the simulated dielectric response is compared with a phenomenological, two-exponential response function with good agreement obtained. The two fitted decay times also compare well with times extracted from the explicit simulations.

High-frequency behavior of the dynamic mobility and dielectric response of concentrated colloidal dispersions

A matched asymptotic analysis of the system of equations governing the electrokinetic cell model of ref 4 (Ahualli, S.; Delgado, A.; Miklavcic, S.; White, L. R. Langmuir 2006, 22, 7041) is performed. Asymptotic expressions are obtained for the dynamic mobility and complex conductivity response of a dense suspension of charged spherical particles to an applied electric field. The asymptotic expressions are compared with full numerical calculations of the linear response functions as a function of surface (zeta) potential, electrolyte strength, and particle density. We find that the numerical procedure used is robust and highly accurate at a very high frequency under a wide range of double-layer conditions. The asymptotic form for the dielectric response of the system is accurate to megahertz frequencies. The asymptotic formulas for the other response functions have limited viability as predictive tools within the current range of experimentally accessible frequencies but are useful as checks on numerical calculations.