A modified Langevin-Debye model for investigating the electro-optic behaviour of de Vries smectic liquid crystals

An external electric field applied across a planar-aligned cell in Smectic A* phase of de Vries smectic liquid crystal induces director redistribution over a cone, resulting in a substantial increase in the birefringence and the apparent optical tilt angle. Such an electro-optic response is modelled by Shen et al. [Y. Shen et al., Phys. Rev. E 88, 062504 (2013)], who modified their previous hollow cone with a diffuse cone model by introducing the molecular distribution function limited over a range of tilt angles, that lie in between θ_min and θ_max. The limits in these two tilt angles are assumed to be temperature independent though the tilt angle in between the two values can be temperature dependent. However, the high resolution measurements of birefringence and the layer thickness indicate the presence of temperature dependent diffuse cone angle in SmA* phase.. In the proposed model, we replace θ_min by θ_T, a temperature dependent fitting parameter and the change shows that a better fit of the experimental data to the model is obtained. We determine the temperature dependence of θ_min and show that this angle increases as SmA* to SmC* phase transition temperature is approached.