Abstract
Abstract Complete elastic free energy expressions for ferroelectric SmC* and antiferroelectric SmCa* phases are derived within a quadratic expansion in terms of the spatial derivatives of the biaxial tensor order parameter Q* as well as an orthogonal triad. It is found that there exist 25 non-chiral terms, 5 of which are found to be eventually reduced as certain surface contributions, and 5 chiral terms in bulk elastic energy. As a few simple applications of the present free energy, the SmCA*-SmC* phase transition is discussed and the helical pitch in SmCa* and SmC* phases is explicitly derived in terms of the molecular tilt angle and the microscopic order parameters.
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