Phenomenological Description Of Nematic Elastomers

Liquid crystalline elastomers are a new type of polymers, which are composed of cross-linked liquid crystalline polymers, and possess not only the optical and electric properties of liquid crystals but also the elastic properties of rubbers. Elastic properties mean that they can maintain their shapes and have the ability to return to their original configurations when deformed. For this reason, LCEs are sometimes also called solid liquid crystals. Mesogens in LCEs exhibit the same order as they exhibit in uncrosslinked systems, and there are nematic, smectic, cholesteric, and other elastomers. In this article, we will focus on nematic elastomers(NEs). Besides these properties, nematic elastomers have many other novel properties, among which the most remarkable is soft elasticity and semi-soft elasticity. Soft elasticity exists when some deformations cost no energy. Due to the superior performance and potential application value, LCEs have been widely investigated in recent years, but there are still many problems to be solved.In this article, we will adopt a different approach to develop a new phenomenological description that can show the symmetry properties of semi-soft NEs more clearly. The article is mainly divided into five chapters: In the first chapter, we introduce LCEs briefly; In the second chapter, we introduce the basic energy model of the LCEs; In the third chapter, we construct for NEs a phenomenological theory with both the strain tensor and the nematic order tensor included; In the fourth chapter, we introduce the potential application of LECs. In the fifth chapter, we give a simple summary. In Section 1.1,we give a simple description of LCEs. In section 1.2, we introduce the definition of the order parameters and order tensor; we also introduce the conformation and the energy of the polymer. In section 2.1, we briefly introduce the rubber elastic energy; In Section 2.2, we briefly introduce neo-classical theory; In Section 2.3, we briefly introduce the soft elasticity and semi-soft elasticity; In the main body of the article in the fourth chapter, we will use a new method to construct phenomenological models of elastomers: In Section 3.2, we will firstly make a brief review of the elastic theory, and then introduce the concept of strain tensor and how the elastic energy of a normal elastic medium can be constructed from the strain tensor. In 3.3, we construct for NEs a phenomenological elastic energy based on the strain tensor only; in 3.4, we construct for NEs a phenomenological theory with both the strain tensor and the nematic order tensor included; in Section 3.5, we study the relation between the neo-classical theory and the phenomenological theory presented in this article.LCEs are made by the mixture of liquid crystal molecules with polymer network, so they have not only anisotropy quality of liquid crystalline and flexibility of the polymer network, but also have good field response and deformation recovery quality. Under external stimuli, such as electromagnetic field, temperature field, visible light and ultraviolet radiation, LCEs can produce considerable the recoverable deformation by changing the arrangement of mesogens, such as bending, shrinkage, twist and curl. We are most interested in the shape reversibility of LCEs. The changeable size of LCEs is very large, where the contraction rate can be as high as 400 to 500 percent in milliseconds scale. Based on these properties, LCEs can be made into films, fibers and the response surface, free suspension of micron particles and nano-sized particles etc., LCEs can also be made into temperature-controlled actuators, artificial muscles, tunable lasers, optical data storage, and switching reflector. In chapter 8,We introduce these applications in detail. Finally, we make a summary for LCEs.