Electrolyte dependence of particle motion near an electrode during ac polarization

Abstract

The phase angle between the imposed ac electric field and the oscillations in particle height is the key parameter governing the sign of interparticle force during two-dimensional directed assembly. The phase angle depends on a number of experimental parameters, including the frequency of the electric field and dispersing electrolytes. The origin of electrolyte dependence in this phase angle has been a mystery for a decade. Electrolyte dependence arises from polarization of the particle's diffuse layer, which affects the dynamic electrophoretic mobility of the particle. A full description of the magnitude and phase angle of the dynamic electrophoretic mobility was incorporated into a nonlinear integro-differential equation of motion for a 5.7 \ensuremath{\mu}m diameter particle suspended in 0.15 mM KOH, KCl, NaHCO${}_{3}$, NH${}_{4}$OH, and NaOH at frequencies between 5 and 1000 Hz. Integration of the equation revealed that the phase angles for a particle in KOH, NH${}_{4}$OH, and NaOH were smaller than the phase angles calculated for a particle in KCl and NaHCO${}_{3}$, which is consistent with previously published experiments. Although the phase angles for each electrolyte are spread over only \ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}, the results cluster around 90\ifmmode^\circ\else\textdegree\fi{}, which is the crucial boundary between particle aggregation (>90\ifmmode^\circ\else\textdegree\fi{}) and separation (90\ifmmode^\circ\else\textdegree\fi{}). A family of curves of the oscillation in particle height collapsed to a master curve when the amplitude of motion was scaled with the product of the dynamic electrophoretic mobility and electric field strength. These results constitute the first a priori prediction of electrolyte-dependent motion of a particle near an electrode during ac polarization.