Influence of the saddle-splay constant on the director field distribution in strong magnetic fields

The role of anchoring effects in thin nematic films confined between two parallel plates was theoretically examined. The bulk and surface free energy densities were expanded up to $\mathcal{O}(\varepsilon^2)$ and the perturbated contributions were calculated. It is shown that the minimum of the free energy corresponds to the solution of the Euler–Lagrange equations and satisfies the Ericksen inequalities. The identified bifurcation points can estimate the influence of the saddle-splay constant $k_{24}$ towards periodic perturbations of a director in the presence of strong magnetic field.