We have investigated the rheological properties of lyotropic liquid crystals (LCs) formed by self-assembled neutral lipids and water, their relationship with the topology of the structure, and their dependence on temperature and water content. The phase diagram of a representative monoglyceride-water system, determined by combining cross-polarized optical microscopy and small-angle X-ray scattering (SAXS), included four structures: lamellar, hexagonal, gyroid bicontinuous cubic (Ia3d), and double diamond bicontinuous cubic (Pn3m), as well as several regions of two-phase coexistence of some of the above structures. Rheology in the linear viscoelastic regime revealed a specific signature that was characteristic of the topology of each structure considered. The order-order transitions lamellar-to-cubic and cubic-to-hexagonal, as well as the order-disorder transitions from each LC to an isotropic fluid, were easily identified by following the development of the storage and loss moduli, G' and G'', respectively. The viscoelastic properties of both bicontinuous cubic phases were shown to be strongly frequency-dependent, following a pseudo-Maxwell behavior, with multiple relaxation times. Cubic-to-cubic transitions were nicely captured by scaling the longest relaxation time, tau, with either temperature or water volume fraction. Therefore, the set of the three main parameters used to establish the rheological behavior of the structure, that is, G', G'', and relaxation time, tau, constitutes a consistent ensemble to identify the structures of the liquid crystal. Finally, relaxation spectra, extracted for all liquid crystalline phases, allowed an additional possible identification criterion of the various structures considered.
