(320g) Symmetry Breaking During AC Electrophoresis Normal to An Electrode

AC electrophoresis of a single particle proximate to an electrode is important to the 2D crystallization of colloidal particles.¹ Particle assembly is a complicated function of electric field strength and frequency. Fagan et. al.² observed that a break in symmetry in a single particle’s motion along the direction of the applied electric field strongly correlated with the lateral equilibrium spacing of a 2D colloidal crystal. The break in symmetry was captured in the phase angle (θ) between the particle’s height above the electrode and the electric field driving motion. To date, no a priori model can predict this phase angle. Here, we present a model that predicts a symmetry-breaking phase angle for the first time. The full model, including colloidal and hydrodynamic forces, and including the Basset force not previously cited in this context, showed that θ can increase from 0° at low frequencies, cross 90° at ~100 Hz and then increase to 180° as frequency was increased.  The remaining unknown is the mechanism underlying the role of ion identity in particle motion. Particles repel each other in KOH during directed assembly but attract each other in NaHCO₃. We now believe that this electrolyte dependence arises in the apparent electrokinetic charge on the particle, which can be approximated by the Stokes drag coefficient multiplied by the dynamic electrophoretic mobility of the particles.  The latter quantity is known to depend on the ion mobilities. As a first inquiry, we calculated the frequency dependent electrophoretic mobility of the particle as a function of the dispersing electrolyte’s ion mobilities. Preliminary results from this updated model suggest the  particle's dynamic electrophoretic mobility is important to solving the mystery of electrolyte dependent particle motion.  

1.      Prieve, D. C.; Sides, P. J.; Wirth, C. L., 2-D assembly of colloidal particles on a planar electrode. Current Opinion in Colloid & Interface Science (2010) 15 (3).

2.      Fagan, J. A., Sides, P. J.; Prieve, P. C., Vertical oscillatory motion of a single colloidal particle adjacent to an electrode in an ac electric field. Langmuir (2002) 18 (21).