Finding the optimum curvature strains and elasticity constant K_4 for nematic liquid crystals using minimization of the Frank-Oseen free energy density functional

Abstract

Abstract

The study was conducted to obtain the six optimum curvature strains of Frank-Oseen free energy density functional shown by the minimum value of the functional. The six curvature strains determine the orientation of liquid crystals, namely splay, twist, and bend. The study also determines the elasticity constants K₄, where the combination of K₂ and K₄ are the saddle-splay constant. The influence of these constants is not too large compared to the other constants, but still needs to be taken into account. To obtain the six curvature strains and elastic constants K₄, this study used simulated annealing method, a method that uses the analogy of the temperature decreasing gradually in order to obtain the configuration of crystalline state. Based on this study, it was found that the orientation of splay and twist gives a greater contribution than the orientation of bend in the PAA and MBBA nematic materials, respectively at temperatures of 125^o C and 25^o C and by using the values of K₁, K₂, and K₃ at these temperaturesit is obtained that the magnitude of K₄is in accordance with that recommended by Ericksen.

Keywords:elasticity constant, Frank-Oseen free energy density, MBBA, nematic, PAA, simulated annealing