Confinement and magnetic-field effect on chiral ferroelectric nematic liquid crystals in Grandjean-Cano wedge cells

Abstract

We explore the structure and magnetic-field response of edge dislocations in Grandjean-Cano wedge cells filled with chiral mixtures of the ferroelectric nematic mesogen DIO. Upon cooling, the ordering changes from paraelectric in the cholesteric phase $\phantom{\rule{4pt}{0ex}}{\mathrm{N}}^{*}$ to antiferroelectric in the smectic ${\mathrm{SmZ}}_{\mathrm{A}}^{*}$ and to ferroelectric in the cholesteric ${\mathrm{N}}_{\mathrm{F}}^{*}$. Dislocations of the Burgers vector $b$ equal to the helicoidal pitch $\mathcal{P}$ are stable in all three phases, while dislocations with $b=\mathcal{P}/2$ exist only in the $\phantom{\rule{4pt}{0ex}}{\mathrm{N}}^{*}$ and ${\mathrm{SmZ}}_{\mathrm{A}}^{*}$. The $b=\mathcal{P}/2$ dislocations split into pairs of ${\ensuremath{\tau}}^{\ensuremath{-}1/2}{\ensuremath{\lambda}}^{+1/2}$ disclinations, while the thick dislocations $b=\mathcal{P}$ are pairs of nonsingular ${\ensuremath{\lambda}}^{\ensuremath{-}1/2}{\ensuremath{\lambda}}^{+1/2}$ disclinations. The polar order makes the ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ disclinations unstable in the ${\mathrm{N}}_{\mathrm{F}}^{*}$ phase, as they should be connected to singular walls in the polarization field. We propose a model of transformation of the composite ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ line-wall defect into a nonsingular ${\ensuremath{\lambda}}^{\ensuremath{-}1/2}$ disclination, which is paired up with a ${\ensuremath{\lambda}}^{+1/2}$ line to form a $b=\mathcal{P}$ dislocation. The ${\mathrm{SmZ}}_{\mathrm{A}}^{*}$ behavior in the in-plane magnetic field is different from that of the ${\mathrm{N}}_{\mathrm{F}}^{*}$ and ${\mathrm{N}}^{*}$: the dislocations show no zigzag instability, and the pitch remains unchanged in the magnetic fields up to 1 T. The behavior is associated with the finite compressibility of smectic layers.

Topics & Concepts