Steady electrical and micro-rheological response functions for uncharged colloidal inclusions in polyelectrolyte hydrogels

The electric-field-induced response of an uncharged colloidal sphere embedded in a quenched polyelectrolyte hydrogel is calculated from a model where the polymer network is treated as an elastic, porous skeleton saturated with an aqueous electrolyte. We present exact analytical solutions for the steady response to a uniform electric field, as well as the steady susceptibility, defined as the ratio of the particle displacement to the strength of an optical or magnetic force. Even though the particle is uncharged, it attains a finite electric-field-induced displacement owing to hydrodynamic coupling with electroosmotic flow. The steady susceptibility decreases with increasing charge and decreasing electrolyte concentration; in general, charge imparts a small correction to the classical theory for an uncharged linearly elastic continuum.