This paper describes, for the first time, the construction of equilibrium configurations for smectic~A liquid crystals subjected to nonuniform physical boundary conditions, with two-dimensional dependence on the director and layer normal, and a nonlinear layer function. A novel technique, utilizing Lagrange multipliers and the Euler-Lagrange equations, is developed to derive the underlying model equations describing key properties of liquid crystals confined between two boundaries exhibiting spatial imperfections. The results of the model are shown to be consistent with previous published findings in simple domains while novel results are obtained on how the structure of the liquid crystals changes in response to boundary perturbations. Domain sizes are considered representing those currently used in applications while predictions in smaller domains at the limit of current technologies are also made. In particular, it is shown that the curvature along a boundary impacts on the liquid crystal's structure distant from the boundary feature and therefore previously developed mathematical models, that essentially reduced the problem to a single spatial dimension, cannot be used in such circumstances. Consequences for practical applications are discussed.
Original languageEnglish
Article number032703
JournalPhysical Review E
Volume101
Issue number3
Publication statusPublished - 16 Mar 2020

    Research areas

  • smectic A, non-uniform domain, smectic layers, liquid crystals, boundary value problem, partial differential equations

ID: 2690352