Particle tracking microrheology of lyotropic liquid crystals.

We present comprehensive results on the microrheological study of lyotropic liquid crystalline phases of various space groups constituted by water-monoglyceride (Dimodan) mixtures. In order to explore the viscoelastic properties of these systems, we use particle tracking of probe colloidal particles suitably dispersed in the liquid crystals and monitored by diffusing wave spectroscopy. The identification of the various liquid crystalline phases was separately carried out by small-angle X-ray scattering. The restricted motion of the particles was monitored and identified by the decay time of intensity autocorrelation function and the corresponding time-dependent mean square displacement (MSD), which revealed space group-dependent behavior. The characteristic time extracted by the intersection of the slopes of the MSD at short and long time scales, provided a characteristic time which could be directly compared with the relaxation time obtained by microrheology. Further direct comparison of microrheology and bulk rheology measurements was gained via the Laplace transform of the generalized time-dependent MSD, yielding the microrheology storage and loss moduli, G'(ω) and G''(ω), in the frequency domain ω. The general picture emerging from the microrheology data is that all liquid crystals exhibit viscoelastic properties in line with results from bulk rheology and the transition regime (elastic to viscous) differs according to the specific liquid crystal considered. In the case of the lamellar phase, a plastic fluid is measured by bulk rheology, while microrheology indicates viscoelastic behavior. Although we generally find good qualitative agreement between the two techniques, all liquid crystalline systems are found to relax faster when studied with microrheology. The most plausible explanation for this difference is due to the different length scales probed by the two techniques: that is, microscopical relaxation on these structured fluids, is likely to occur at shorter time scales which are more suitably probed by microrheology, whereas bulk, macroscopic relaxations occurring at longer time scales can only be probed by bulk rheology.