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ABSTRACT
In this work we will derive an anisotropic generalisation of the finitely extensible chain model, due to Kuhn and Grün, which is well known in rubber elasticity. This provides a chain energy that couples elastic behaviour to a probability distribution describing the orientations of liquid crystal monomers within a main-chain elastomer. The key point is to invoke a maximum relative entropy assumption on the distribution of bond angles in an observed chain. The chain energy’s fourth order Taylor expansion is also given, which couples to the second and fourth moments of the nematic distribution function only.
Acknowledgments
The author would like to thank John Ball for ongoing discussion that lead to the results in this work, as well as Maria-Carme Calderer and Peter Palffy-Muhoray for providing insights in our discussions, and to the organisers of the MLC program at the Isaac Newton institute. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n° 291053.