Complex-tensor theory of simple smectics

The same properties that make smectic phases so interesting concomitantly contrive to make them challenging to model. They're interesting becacuse they are excellent systems for exploring self-assembly and topology since they accommodate both dislocation- and disclination-type defects. However, these cause the traditional complex scalar order parameter proposed by de Gennes to be multi-valued, creating ambiguity. While this is not a fatal issue for theoreticians treating isolated defects, it causes crippling issues for numerical approaches that seek to model situations involving many defects. One option is to employ microscopic models that explicitly simulate each microscopic layer but this is computationally costly and developing a macroscopic order parameter that can be used to simulate many defects on a global coordinate system is required.

We present a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation and a phenomenological Landau theory that accounts for bulk, compression and curvature free energies. This proposed field theory is analogous to the Landau-de Gennes theory for nematics. This theory has the capacity to model both parallel and perpendicular contributions, but can also reduce to previous employed models of simple smectics. Homeotropic and planar anchoring are included through equivalents to the nematic Rapini-Papoular and Fournier conditions, respectively. We implement an overdamped a time-dependent Ginzburg–Landau model to solve for the  relaxation dynamics of simple smectic systems. 

We demonstrate the theory’s capability in describing both dislocations and disclinations, as well as arrested configurations and colloid-induced local ordering. Though versatile, this theory considerably simplifies numerics, facilitating future studies of smectic phases and their topological defects under large deformations in non-trivial geometries

Event resources