Analysis of the Order Parameters (Spontaneous Polarization and the Tilt Angle) and the Critical Field Close to the Smectic A–Smectic C* Transition in HDOBAMBC

Abstract

We introduce a mean field model to describe the smectic A- smectic C* (AC*) transition in HDOBAMBC. Our mean field model considers a linear coupling between the spontaneous polarization (Ps) and the tilt angle (θ) in the presence of the electric field coupled to the spontaneous polarization. From our model, we derive the expression for Ps, θ and the critical field Ec as a function of temperature. The temperature dependences of the order parameters (spontaneous polarization Ps and the tilt angle θ) and the critical electric field Ec are analyzed using the experimental data from the literature according to power-law formulae close to the smectic A–smectic C* transition (Tc = 109.7°C) in HDOBAMBC. From our analyses, we obtain the values of β = 0.24 and φ = 0.42 for the critical exponent of the spontaneous polarization Ps and the tilt angle θ, respectively in HDOBAMBC. We also obtain from our analysis the values of δ = 0.46 and δ = 0.27 for the critical exponent of the critical electric field Ec away from the Tc (AC*) and close to the Tc (AC*), respectively in HDOBAMBC.Our results indicate that a mean-field to tricritical crossover behaviour can occur in the ferroelectric liquid crystal of HDOBAMBC.