An electric bottle for colloids.

Particle concentration is a dominant control parameter for colloids and other soft matter systems. We demonstrate a simple technique, "dielectrophoretic equilibrium," implemented as an "electric bottle," a planar capacitor in a larger volume. The uniform field in the capacitor traps particles in this force-free region at a higher density than in the zero field regions outside. We show how the technique measures the equation of state and we initiate and grow colloidal crystals. "Dielectrophoretic equilibria" enable the study of a complete concentration-dependent phase diagram from a single microscopic sample, obviating the previous need for preparing a large number of samples.

Comment on "A broad frequency range dielectric spectrometer for colloidal suspensions: cell design, calibration, and validation".

Recently, a simple analytical model was derived from the standard electrokinetic theory to deal with electrode polarization in low frequency dielectric measurements [Hollingsworth and Saville, J. Colloid Interface Sci. 257 (2003) 65-76]. Comparisons were made between dielectric constant-frequency relationships extracted from data on electrolyte solutions using the analytical model and the well-known RC-circuit analog. Electrolyte spectra interpreted with the analytical approach remained smooth (and constant) down to much lower frequencies than was the case with the RC model. It was also shown how the RC model arises naturally from the analytical model as an asymptotic expansion in inverse powers of the electrode spacing. Numerical calculations indicated substantial differences between the two models at low frequencies due to higher order terms omitted in the RC model. As it turns out, the comparison contained a numerical error. Here we revisit the methodology to show that although the two formulations disagree, they do so (in a numerical sense) only at much smaller electrode separations than those used in the aforementioned example. The purpose of this Letter is to correct the numerical error and show, explicitly, how the RC-circuit analog coefficients are related to the asymptotic expansion at low frequencies.

Dielectric spectroscopy and electrophoretic mobility measurements interpreted with the standard electrokinetic model.

We report results from complementary electrokinetic measurements-dielectric relaxation and electrophoretic mobility-undertaken to test the applicability of the standard electrokinetic theory with a model system. Dielectric spectra were obtained at frequencies between 1 kHz and 40 MHz with a new, two-electrode cell design [Hollingsworth and Saville, J. Colloid Interface Sci. 257 (2003) 65-76]; mobility data were acquired with an electrophoretic light scattering instrument. Data from the two-electrode cell were collected at different electrode separations and interpreted with newly developed procedures to remove the influence of electrode polarization. Methodology A employs extrapolation to infinite electrode separation to compute the dielectric constant and conductivity as functions of frequency. The contributions from suspended particles are reported in terms of dielectric constant and conductivity increments. Methodology B uses a theoretical model of electrode polarization and the standard electrokinetic model in a nonlinear regression scheme. Results are presented in several forms: frequency-dependent dielectric constant and conductivity increments, frequency-dependent dielectric constants and conductivities, and the complex dipole coefficient. It is shown that the standard model provides a consistent methodology for interpreting particle behavior; zeta-potentials inferred from mobility and dielectric relaxation agree to within experimental error. Moreover, the cell design and interpretation are straightforward and provide relatively simple ways to obtain complementary measurements over a wide frequency range. The results unambiguously show that electrokinetic character of this dispersion follows the standard model.

A broad frequency range dielectric spectrometer for colloidal suspensions: cell design, calibration, and validation.

Electrode polarization complicates low-frequency measurements of the dielectric response of electrolyte solutions and colloidal suspensions. To deal with this longstanding problem, a new dielectric cell was developed along with a model based on the standard electrokinetic theory. The parallel plate cell utilizes a thin chamber that is easily filled and emptied; different chamber thicknesses are readily accommodated. The analytical form of the theoretical impedance model makes data analysis straightforward. Using standard electrolytes, the device and the theoretical model were tested over a wide range of frequencies for several electrolyte concentrations. Excellent agreement was found between the theory and the experimental data. The methodology developed to account for polarization effects exhibits a significant improvement over the conventional approaches and points up a deficiency in often-used equivalent circuit models.