Statistical models of elasticity in main chain and smectic liquid crystal elastomers

James Michael Adams

Cambridge University

Liquid crystal systems typically consist of rod like molecules that spontaneously align along a chosen direction (the director) below a certain temperature or above a certain concentration. When these molecules are connected to polymers, the alignment of the molecules can alter the conformation of the polymer backbone. This effect can be seen on a macroscopic level by cross-linking the polymer chains together to form a liquid crystal elastomer (LCE). In this thesis the elastic properties of main chain and smectic liquid crystal elastomers are modelled, and a mechanism of piezoelectricity in LCEs is explored. These three projects are summarised below. In the strongly nematic state main chain liquid crystalline polymers have hairpin defects along their length. When these chains are cross-linked together they show unusual soft elastic properties experimentally. The elastic properties of a main chain elastomer are modelled here by calculating the stiffness of chains with hairpin defects and of those without. The dramatically different spring constants motivate a non-affine model for deformation of the resulting elastomer. The chains with hairpin defects are less stiff than those without and so take up more of the macroscopic strain. As the elastomer is stretched the macroscopic strain becomes more concentrated in the elastically weaker hairpinned chains, and so the rubber shows a plateau in its stress-strain curve. A mechanism of developing a polarisation in chiral main chain LCE is analysed. In this mechanism the dipoles of the chiral monomers can be aligned by a shear deformation. It is shown that the polarisation of a pure LCE is zero in equilibrium due to rotation of the director. The response of the director must be altered in a specific way in order to realise a non-zero result. Three methods of circumventing this result are explored: oscillating shear, pinning the director with smectic layers, and using a mixture of chiral and non-chiral chains. Each of these methods is shown to produce a polarisation which is much larger per unit stress than that of quartz crystal. A fully non-linear model of elasticity in smectic A elastomers is developed from a phantom network model. The rigid constraints required by the layered smectic system are analysed from a geometric perspective. The results of this model are then compared to a wide range of experimental observations: extreme Poisson ratios, in-plane modulus, modulus before and after threshold when the elastomer is stretched along the layer normal. This model is then used to look for soft modes in biaxial smectic A elastomers and smectic C elastomers. A general procedure for the calculation of soft modes is developed and specific examples of soft modes given.

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