Molecular orientational distribution function of a chiral de Vries smectic liquid crystal from birefringence measurements.

An alternative method for determining the orientational distribution function and the order parameter from the electric field-induced birefringence measurements of a chiral liquid crystal compound in its Smectic A is being introduced. A chiral mesogen based on a 5-phenyl-pyrimidine benzoate core terminated by a trisiloxane group on one side and the chiral alkyloxy chain on its opposite side is designed and synthesized to exhibit the "de Vries" smectic characteristics. The compound exhibits first order Smectic A-Smectic C phase transition, evidenced by the results of differential scanning calorimetry. The material is being investigated by electro-optical experiment in its smectic phases. We present a model that incorporates the generalised Langevin-Debye model which includes the Maier-Saupe effective mean-field potential term in order to explain the change in birefringence with the electric field. A good agreement between the experimental results and the predictions from the model leads to the determination of the molecular orientational distribution function in Smectic A phase. Furthermore, the temperature dependency of the Saupe orientational order parameter ⟨P⟩ is obtained using the parameters of the model. Based on the experimental and theoretical results, we show that de Vries Smectic A phase exhibits a broad volcano-like tilt angle distribution with the two maxima occurring at finite tilt angles closer to the Smectic A-Smectic C transition temperature, and a sugarloaf-like distribution occurs in the tilt for temperatures close to the Isotropic-Smectic A phase transition.