Periodic Pattern Formation in Side-Group Polymer Nematic Solutions at the Twist Frederiks Transition

Abstract

Periodic pattern formation at the Frederiks transition in the magnetic field has been studied for dilute solutions of a polymethacrylate with mesogenic side groups in a nematic solvent, pentylcyanobiphenyl (5CB). For this purpose, a combination of dielectric measurements and direct pattern observations was used to determine the twist elastic constant K₂, the rotational viscosity γ₁, and the wavelength of the periodic distortion λ. For polymer concentrations 0 ≤ w ≤ 1 % the values of λ were found to follow a power law λ ∼ (B - B_c)^-β with β ≈ 1/2, where B_c is the critical field for formation of periodic patterns. A strong effect of the polymer molecules on B_c has been observed, due to the contribution of the macromolecules to the shear Miesowicz viscosity coefficient η_a being large compared to the effect on γ₁. In a simple phenomenological model, which is constructed analogous to the Landau theory for second order phase transitions, and uses an expansion of the growth rate of the patterns in powers of the wavenumber k = 2π / λ, we describe correctly the observed power law.