Abstract

Expanding a distortion free energy in terms of spatial gradients of density is a standard approach to construct an elastic theory of condensed matter. When applied to nematic liquid crystals, this so-called gradient expansion leads to the celebrated Frank theory that serves as the sound basis on which to analyze the response of nematic liquid crystals to electric fields and boundary constraints. The success of the theory has been thoroughly proven except the anomalous surface contribution associated with K13 (splay-bend elasticity). The K13 term involves a gradient of the nematic director normal to the boundary, and hence the straightforward minimization of free energy under a given boundary condition becomes mathematically ill-posed, running into various unphysical behaviors.

More than a decade ago, I showed (at least I think I showed) that K13 is an artifact of gradient expansion as applied to a nonlocal interaction free energy by way of the density functional theory. When consistently done, the gradient expansion always results in K13 =0 eliminating all the lingering problems that K13 has created.

The purpose of this talk is to revisit this issue. Close look at the K13 issue at the molecular level not only solves its own problem but also gives us a chance to shed new light on such fundamental structural characteristics of liquid crystals as chirality, flexoelectricity, and more.