Microscopic model of the spontaneous polarization in ferroelectric liquid crystals

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Abstract
A microscopic model is introduced which describes the coupling between the tilt of molecules from the normal to smectic layers in ferroelectric liquid crystals and the rotation of a molecule around its long axis. The single particle potential consists of a dipolar and a quadrupolar term. The microscopic model is shown to be consistent with the extended thermodynamic model, which takes into account the bilinear as well as the biquadratic coupling between the tilt of molecules and the induced transverse polarization, and which describes the anomalous thermodynamic behaviour of ferroelectric liquid crystals in the smectic C* phase. It is shown that close to the transition to the smectic A phase the thermodynamic description is exact, but overestimates the spontaneous polarization at lower temperatures. The results are compared with experimental data. It is demonstrated that the quadrupolar order is larger than the dipolar order except very close to the transition.