Predicting the disorder-order transition of dielectrophoretic colloidal assembly with dielectric spectroscopy.

The dielectrophoretic assembly of colloidal suspensions into crystalline arrays is described by a master scaling that collapses the disorder-order transition as a function of field strength, frequency, and particle size. This master scaling has been verified for particle diameters ranging from 2a = 200 nm to 3 μm by light scattering (Lumsdon et al., Langmuir 2004, 20, 2108-2116; McMullan and Wagner, Langmuir 2012, 28, 4123-4130), optical laser tweezer measurements (Mittal et al., J. Chem. Phys. 2008, 129, 064513), and small-angle neutron scattering (McMullan and Wagner, Soft Matter 2010, 6, 5443-5450). In this work, we reconcile the empirical phase diagram with direct measurements of the colloid polarizability using dielectric spectroscopy. Dielectric spectroscopy confirms the origin of the order-disorder transition frequency dependence, including its quadratic scaling with particle radius, a(2), and provides an alternative method to search for optimal self-assembly conditions.