Electrophoretic microrheology of a dilute lamellar phase: Relaxation mechanisms in frequency-dependent mobility of nanometer-sized particles between soft membranes

Viscoelastic properties of complex fluids in the microscopic scale can be studied by measuring the transport properties of small, embedded probe particles. We have measured the complex electrophoretic mobility [Formula presented] of nanometer-sized particles dispersed in a lyotropic lamellar phase, which shows two relaxation processes at approximately [Formula presented] (high frequency relaxation, HF) and [Formula presented] (low frequency relaxation, LF). It is shown quantitatively that these processes are caused by the trapping of particles within two local structures of characteristic size in the lamellar phase: the interbilayer distance and the persistence length. The origin of observed relaxations is further investigated and augmented in this study with data obtained by two other complementary methods, dielectric spectroscopy and the direct observation of fluorescently labelled probe particles under an optical microscope. It is shown that the local distortion field of the lamellar phase is induced by the extra steric interaction involving the collision of a colloidal particle with the membrane. The resulting distortion field hinders the Brownian motion of colloidal particles parallel to the membranes (not vertical), and causes the observed HF relaxation. On the other hand, the origin of LF relaxation is presumably a result of the defects in the lamellar structure. Since the results of this study show that the transport property is strongly influenced by microscopic environments, this method is referred to as electrophoretic microrheology.