Chirality in liquid crystals: From microscopic origins to macroscopic structure

Abstract

Molecular chirality leads to a wonderful variety of equilibrium structures, from the simple cholesteric phase to the twist-grain-boundary phases, and it is responsible for interesting and technologically important materials like ferroelectric liquid crystals. This paper will review some recent advances in our understanding of the connection between the chiral geometry of individual molecules and the important phenomenological parameters that determine macroscopic chiral structure. It will then consider chiral structure in columnar systems and propose a new equilibrium phase consisting of a regular lattice of twisted ropes.

The Theory of Everything

“…Indeed the first experimental measurements of critical exponents were made on classical fluids near their liquid-vapor critical points (39). Good examples would be the spontaneous crystallization exhibited by ball bearings placed in a shallow bowl, the emission of vortices by an airplane wing (40), finite-temperature ferromagnetism, ordering phenomena in liquid crystals (41), or the spontaneous formation of micelle membranes (42). To this day the best experimental confirmations of the renormalization group come from measurements of finite-temperature critical points (43).…”

Magnetochiral scattering of light: Optical manifestation of chirality

“…We have shown that g vanishes when the H is achiral. Furthermore, g has the same sinusoidal behaviour g ∼ sin(2γ) as the chiral order parameter ψ defined by Harris et al [19][20][21] for the "twisted H". In Sec.…”

“…Harris et al [19][20][21] as a function of N. The comparison between the two curves in Fig. 5 clearly reveals that the two chiral measures g and ψ, are, statistically speaking, proportional.…”

“…Osipov et al [26] have developed a molecular measure of chirality based on the behaviour of the response functions that characterize molecular optical activity. Harris et al [19][20][21] have proposed a new elegant way, based on group theory, to measure the degree of chirality exhibited by a geometric object. They have constructed a variety of rotationally invariant pseudoscalars and have applied them to quantify the degree of chirality of molecules of arbitrary shape, showing how these parameters govern a particular observable, such as the pitch of a cholesteric liquid crystal [19][20][21] and the optical rotatory power [22].…”

“…We have also employed this parameter to probe the chirality of random systems, which are in general chiral. Finally, we have compared it to recently defined chiral measures in literature [19][20][21].…”