Adjusted Structures in Nematic Liquid Crystals

Controlling the orientational ordering of liquid crystal molecules by confined surfaces is one of the main reasons for the widespread use of liquid crystals in the industry. The anchoring condition is an essential feature of the liquid crystalline materials in vicinity of boundaries. As known, surface interaction energy in a confined liquid crystal can be studied in the framework of Rapini-Papoular model. However, for the uneven surfaces, other models, such as a model based on Fukuda theory should be used. The surface-like energy is not usually considered in energy calculations. In this work, we consider a nematic slab confined with two infinite surfaces and investigate the director field and anchoring effects in the total energy of the slab with a sinusoidal surface by taking into account this term of energy. We consider a surface with a grooved sinusoidal form and calculate the anchoring energy within the framework of Fukuda theory. We also obtain the dependence of energy on geometric parameters, such as grooves amplitude. By utilizing theoretical model proposed by Fukuda, we determine the director components and anchoring energy of the system under an external electric field. The variation of the director components and surface effects are discussed. It is shown that the anchoring energy has a maximum value in the absence of the field. Moreover, we find that the trend of anchoring energy variations is reduced due to the presence of an electric field.