(328c) Rheology of Lamellar Mesophases

Lamellar mesophases typically contain alternating water/surfactant, water/oil/surfactant layers or immiscible segments of a block coopolymer. The equilibrium (minimum energy) phase is one where the layers are aligned with layer normals in the same direction. Under shear, one would expect the layers to align with unit normal velocity gradient direction. In this alignment, the fluid should have viscosity only a few times that of water by the inverse sum rule for the viscosity. However,
real lamellar fluids have viscosities that are several orders of magnitudes higher than water. For this reason, lamellar mesophases are used in products which require very high viscosity, such as hair conditioners and butter substitutes. The reason for these high viscosity is a puzzle.

The rheology of lamellar mesophases is complicated due to the two-way coupling between structure and rheology. A perfectly aligned lamellar phase, for example, exhibits fluid like behaviour when the normal to the lamellae is along the shear or vorticity direction, but has a solid like resistance to flow when the normal is along the flow direction. In addition, even though a perfect defect free stack of layers is the final equilibrium state, real samples are rarely defect free due to kinetic constraints. The lamellar spacing is typically small compared to macroscopic scales (the distance between layers in lyotropic liquid crystalline phases is usually a few hundred Angstroms and a macroscopic sample contains 10⁴ − 10⁶ lamellae), and so a flowing lamellar mesophase cannot be modeled using a microscopic description. It is necessary to use different simulation techniques (molecular, mesoscale, macroscale) for accurately capturing the rheology of lamellar phases.

First, we present a multiscale modeling methodology to link molecular and mesoscale simulations. Here, the object is to transfer relevant parameters from the molecular simulations to the mesoscale model based on a concentration field (phase field) description. This mesoscale model is then used to examine the rheology of a lamellar phase under a linear shear flow. For sufficiently large system sizes, the final steady state is not a perfectly aligned state, but rather a disordered state where there is a dynamical balance between the annealing of defects under shear and the spontaneous creation of defects. Order parameters are used to quantify the extent of disorder in the system, and these are found to be linked to the rheology.

At the next higher scale, a defect description is used where the background layered structure is averaged out and only the defects are retained in the description. Here, the motion and interaction of edge dislocations, and the mechanism of defect cancellation and defect creation, and their effects on rheology are analysed. Edge dislocations acts as centers of elastic stress concentration as in the case of solids, but they also acts as flow generating centers and they generate liquid
stresses as well in lamellar mesophases. These are treated in as defect suspensions (similar to particle suspensions) with highly anisotropic interactions and creation/destruction mechanisms to model their effect on rheology.