Static Continuum Theory
Up to now, the description of liquid crystals has been primarily in regard to its microscopic atomic and molecular structure and its interaction with light. However, when a liquid crystal is subject to a macroscopic external force, the strains exhibited in its splay, twist, and bend have dimensions of the order 10−6 m. In comparison with molecular sizes of about 10−10 m, it is clear that for many cases, specific molecular structure can be ignored when studying strain-induced changes in the director orientation of the liquid crystal, and the liquid crystal can be treated as a liquid continuum. The continuum theory of liquid crystals is derived from the well-developed classical theory of anisotropic fluids in continuum physics, and as in that theory, can treat the liquid crystal both statically and dynamically.
In the static continuum theory, the liquid crystal’s initial energy state equation is first determined, and the appropriate boundary conditions for the system under study are set; then the calculus of variations is employed to minimize the orientational energy of the liquid crystal (the Helmholtz free energy). The minimum orientational energy expressions then form a set of equilibrium equations, the solutions of which are the stable states of the system.
In applying an external force, because the liquid crystal is incompressible, its reaction will not be in a change of volume but rather an internal stress (before) and strain (after) ...