Statistical models of elasticity in main chain and smectic liquid ...

Chapter ThreePolarisation of chiral liquidcrystal elastomerThe subject ofthischapterispiezoelectricity inliquidcrystal elastomers.Whilst there are mechanisms of piezoelectricity in liquid crystal elastomersthat do not require chirality, such as the flexoelectric effect, here amechanism that relies on chirality is considered. This mechanism is basedon a polymer chain of chiral monomers being deformed so that a binormalbias develops. The resulting polarisation relaxes away even in a non-idealrubber due to the relaxation of the director, n. After looking at two nonidealcases: an elastomer composed of a random mixture of polymer chains ofdifferent lengths, and a network formed by a two stage cross-linking processusing rod cross linkers for the second stage, three ways around this problemare suggested:(i) Dynamics where the director, n, responds more slowly than the polymernetwork,(ii) Rigid anchoring of the director — e.g. in the smectic A phase,(iii) Binary mixtures of chiral and non-chiral chains.3.1 Introduction3.1.1 Piezoelectricity in CrystalsIn 1880 Pierre and Jacques Curie published their experimental discovery ofpiezoelectricity. They discovered that certain crystals when subjected to amechanical stress developed a surface charge. The name piezoelectricity isderived from the Greek word piezein meaning to squeeze or press, and has49