Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation
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Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation M. de Luca1 and A. DeSimone1 1 SISSA - International School for Advanced Studies, Via Bonomea 265, 34136, Trieste, Italy ABSTRACT Liquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the ''nematic director''. This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking. INTRODUCTION Liquid crystal elastomers combine the properties and the micro-structure of elastic and nematic systems. They are made of cross-linked polymeric chains among them, with rigid nematic rods embedded. The rubber-like behavior is due to the deformation of the polymeric network and the nematic properties are due to the ability to rotate that nematic molecules exhibit when an external stimulus is applied (electric or magnetic field). The coupling between the deformation and the orientational order present in nematic elastomer gives rise to very interesting phenomena. Just as (fluid) liquid crystals, the nematic properties appear only below a certain temperature (TNI) that represents the threshold between the so called ''isotropic'' and ''nematic'' phase. When the material is in the isotropic phase, all the nematic molecules are randomly oriented and the material behaves similarly to regular rubber. Actually, during the material synthesis, in particular in the cross-linking process, a specific direction is impressed in the material, so that, even in the isotropic phase the material behaves as an anisotropic rubber-like material. Below the temperature threshold TNI, nematic molecules tend to align with the direction impressed in the material so that, without imposing any constraint and without applying any external field a nematic elastomer exhibits a macroscopic deformation that consists in an extension along th
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