Keywords: 
• 液晶 /
• 受限体系 /
• Onsager模型 /
• 自洽场

Abstract: Liquid-crystal polymers in confined system is a fundamental issue in soft matter. Theoretical method plays an-important role in studying these systems. The intention of this work is to give a thorough review of the theoretical methodologies used in tackling confined liquid crystals. At first, some basic concept of liquid crystal, such as a vital order parameter for orientation, phases of liquid crystal, the uniaxial and biaxial of liquid crystal, are presented. After that, a brief review of the development of liquid-crystal theories, which include the Onsager model, the Maier-Saupe model, the McMillan model, the Landau-de Gennes expansion, the Frank elastic model and the self-consistent field model for liquid-crystal polymers, are given. All these theories have their own advantages and disadvantages. For example, the phenomenological Frank elastic model is the most widely used model due to its simplicity. In contrast, parameters in the self-consistent field model are physically meaningful, however, it is rather complicated. During recent decades, with these theories and suitable boundary treatment, plenty confined liquid crystal systems are investigated. In this review, we focus on three kinds of confined systems: 1) the surface wetting behavior in slits; 2) the two-dimensional liquid crystals confined by a boundary line and 3) defects in the orientational field of rigid rods on spherical surface. At the end of this review, we give a list of frontier issues and an outlook for the coming ten years.