Switching behaviour and electro-optic response due to the soft mode ferroelectric effect in chiral smectic A liquid crystals

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Abstract
The switching characteristics and the electro-optic response due to the electroclinic effect in chiral smectic A liquid crystals are analysed theoretically. We give an exact analytic solution to the dynamic equation of the tilt angle (θ) up to the θ4 term in the Landau expansion of the free energy. The non-linear behaviour of θ and the characteristic time under an applied electric field are described near the S*A→SC* transition. They both have a finite value at the transition which depends on the field. The characteristic time (τθ) exhibits a critical slowing down at sufficiently low fields, which occurs only in the early stages of the switching. At late stages, the switching time exhibits a maximum at a particular temperature which depends on the field, and then decreases in a very narrow temperature range near the transition. The θ4 term is important in explaining certain properties even for very small θ, and it becomes essential for θ > 5°. The optical response of an electroclinic liquid crystal cell is considered in detail. We derive an expression for the output intensity of light passing through an electroclinic cell. The delay and rise times for the optical signal are shown to a first approximation to be 0·379 τθ and 2·577 τθ, respectively.