Normal-distortion-mode approach to liquid crystal elastic energy

Abstract

It is shown that Frank’s ‘‘saddle’’ distortion contribution to the nematic liquid-crystal distortional elastic energy is required, in addition to the splay, twist, and bend energies retained in more recent treatments. ‘‘Normal distortion modes’’ for these four distortions are described. Measurement methods and their interpretations are discussed for the corresponding four elastic constants ${\mathrm{k}}_{11}$ (splay), ${\mathrm{k}}_{22}$ (twist), ${\mathrm{k}}_{33}$ (bend), and ${\mathrm{k}}_{44}$ (saddle). Previously reported values for ${\mathrm{k}}_{11}$ and ${\mathrm{k}}_{22}$ are actually for ${\mathrm{k}}_{11}$+${\mathrm{k}}_{44}$ and ${\mathrm{k}}_{22}$+${\mathrm{k}}_{44}$ respectively. The Nehring-Saupe molecular approach yields ${\mathrm{k}}_{44}$=(1/2(${\mathrm{k}}_{11}$+${\mathrm{k}}_{22}$).