Capillary and winding transitions in a confined cholesteric liquid crystal

Abstract

We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature and pore width is studied. Two phenomena are observed: (i) an isotropic-cholesteric transition which exhibits an oscillatory structure with respect to pore width, and (ii) an infinite set of winding transitions caused by commensuration effects between cholesteric pitch and pore width. The latter transitions have been predicted and analysed by other authors for cholesterics confined in a fixed pore and subject to an external field promoting the uniaxial nematic phase; here we induce winding transitions solely from geometry by changing the pore width at zero external field (a setup recently explored in Atomic-Force Microscopy experiments). In contrast with previous studies, we obtain the phase diagram in the temperature vs pore width plane, including the isotropic-cholesteric transition, the winding transitions and their complex relationship. In particular, the structure of winding transitions terminates at the capillary isotropic-cholesteric transition via triple points where the confined isotropic phase coexists with two cholesterics with different helix indices. For symmetric and asymmetric monostable plate anchorings the phase diagram are qualitatively similar.

Chiral Phases of a Confined Cholesteric Liquid Crystal: Anchoring-Dependent Helical and Smectic Self-Assembly in Nanochannels

“…The continuous change in the optical birefringence indicates a gradual formation of the confined cholesteric state. However, for larger pore diameters than those explored here, one expects a discontinuous, bulklike behavior, as, for example, found in simulation studies on cholesteric colloidal particles confined in slitlike pores …”

“…After all, at some characteristic diameter a transition toward the bulk behavior is expected. Moreover, depending on the commensurability of the pitch of the radially aligned helices with R geometrically induced winding transitions could occur as a function of R variation for this anchoring condition …”

“…However, for larger pore diameters than those explored here, one expects a discontinuous, bulklike behavior, as, for example, found in simulation studies on cholesteric colloidal particles confined in slitlike pores. 9 Confined Chiral Nematic State as a Function of Channel Diameter and Wall Anchoring. A comparison of the optical rotatory power of the cholesteric LC embedded in membranes of different channel sizes gives additional interesting insight with regard to the molecular ordering in geometrical confinement.…”

“…Moreover, depending on the commensurability of the pitch of the radially aligned helices with R geometrically induced winding transitions could occur as a function of R variation for this anchoring condition. 9 The absence of the SmA phase in the case of normal anchoring is not too surprising. The curved interface of the cylindrical channel wall results in splay deformations and corresponding deformations of the smectic layers.…”

“…The term “chirality”, introduced 1894 by Lord Kelvin, refers to the fact that an object cannot be superimposed to its mirror image. This asymmetry has turned out as decisive in a huge variety of natural phenomena and technological processes, where chiral entities interact, react, and self-assemble, in particular in interface-dominated and nanostructured systems. − …”