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Modelling Smectic Liquid Crystal Elastomers

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The Mathematics of Liquid Crystals

Liquid crystal elastomers (LCEs) are rubbery materials that composed of liquid crystalline polymers (LCPs) crosslinked into a network. The rod-like mesogens incorporated into the LCPs are have random orientations in the high temperature isotropic phase, but can adopt the canonical liquid crystalline phases as the temperature is lowered. In this talk I will describe some modelling work of the layered smectic phase of LCEs.

Smectic liquid crystal elastomers have highly anisotropic mechanical behaviour. This arises in side chain smectic-A systems because the smectic layers behave as if they are embedded in the rubber matrix [1] (the same cannot be said of main chain smectic systems). The macroscopic mechanical behaviour of these solids is sensitive to the buckling of the layers, so it is a multiscale problem. A coarse grained free energy that includes the fine-scale buckling of the layers has been developed [2], which enables continuum modelling of these systems. I will describe how this continuum model, when augmented with an additional energy term describing layer buckling and other effects such as finite chain extension, can be used to model deformation of smectic-A elastomers in different experimentally accessible geometries.

Modelling smectic-C elastomers, with their tilted director, present a bigger challenge to calculating their coarse grained energy. The constraint placed on the director by the layer normal results in some unusual properties of their soft modes such as negative Poisson ratio. I will describe the geometry of these deformation modes in smectic-C elastomers [3].

[1] C. M. Spillmann et al, Phys. Rev. E 82 , 031705, (2010). [2] J. Adams, S. Conti and A. DeSimone, Mathematical Models and methods in Applied Sciences, 18, 1 (2008). [3] A. W. Brown and J. M. Adams, Phys. Rev. E, 85, 011703 (2012) .

This talk is part of the Isaac Newton Institute Seminar Series series.

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