Boundary-layer method for the analytical calculation of stable textures of bent-core liquid crystal fibers

We study the equilibrium textures of molecular orientation inside cylindrical fibers made of coaxial layers of bent-core smectics. We propose a free-energy model taking into account surface-like and bulk contributions--including layer-compression and electrostatic terms among others--with constant values of the material parameters. We follow the usual variational procedure of minimization of the free energy with respect to the tilt-angle profile θ(r) and obtain an Euler-Lagrange equation and its boundary condition. We solve the variational equations for the equilibrium configurations using a boundary-layer approximation and find multiple solutions. Since the equilibrium tilt profiles are found to be radially inhomogeneous, we select those with minimum distortions in order to find the lowest free-energy state. We minimize further the free energy of the system with respect to the fiber radius and find wider intervals of stability than those previously reported, depending on the balance of the material's spontaneous polarization, elastic and electric divergence-of-polarization constants, and surface-tension coefficients. The bulk and surface-layer structures thus found could be used to calculate the allowed modes of propagation of electromagnetic waves inside the fiber.