J. Phys. II France
Volume 4, Numéro 1, January 1994
Page(s) 169 - 187
DOI: 10.1051/jp2:1994122
J. Phys. II France 4 (1994) 169-187

Theory of longitudinal ferroelectric smectics

J. Prost1, R. Bruinsma2 and F. Tournilhac3

1  Groupe de Physico-Chimie Théorique, ESPCI, 10 rue Vauquelin, 75231 Paris, France
2  Physics Dept., UCLA, Los Angeles, CA 90024, U.S.A.
3  Groupe de Chimie et Electrochimie des Matériaux Moléculaires, ESPCI, 10 rue Vauquelin, 75231 Paris, France

(Received 21 June 1993, accepted in final form 14 October 1993)

Recently, it was discovered that a-chiral smectic layers can undergo a phase transition into a polar smectic. The new phase is fundamentally different from that of the existing chiral Sm-C $^{\ast}$ ferroelectrics. In this paper we examine the underlying mechanism responsible for the new form of ferroelectricity. A Landau theory is presented to discuss the competition between ferroelectricity and other forms of ordering such as anti-ferroelectricity. An effective free energy is constructed to describe the coupling between layer undulations and the polarizability of the sample. We find that in the new phase the Landau-Peierls instability is absent and that second sound can propagate along the layers. Our considerations call for a number of experiments which we believe are crucial for a clarification of the true nature of the observed phases.

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