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Solids with spatially varying photonic structure offer gaps to light of a wider range of frequencies than do simple photonic systems. We solve numerically the field distribution in a solid cholesteric with a linearly varying inverse pitch (helical wavevector) using equations we derive for the general case. The simple idea that the position where the Bragg condition is locally satisfied is where reflection takes place is only true in part. Here, reflection is due to a region where the waves are forced to become evanescent, and the rate of variation of structure determines over which distance the waves decay and therefore how complete reflection is. The approximate local Bragg-de Vries schemes are shown to break down in detail at the edges of the gap, and an analytical estimate is given for the transmission coefficient., Comment: 8 pages, accepted by EPJ E, corrections for publication implemented

Biological molecules can form hydrogen bonds between nearby residues, leading to helical secondary structures. The associated reduction of configurational entropy leads to a temperature dependence of this effect: the "helix-coil transition". Since the formation of helices implies a dramatic shortening of the polymer dimensions, an externally imposed end-to-end distance R affects the equilibrium helical fraction of the polymer and the resulting force- extension curves show anomalous plateau regimes. In this article, we investigate the behaviour of a cross-linked network of such helicogenic molecules, particularly, focusing on the coupling of the (average) helical content present in a network to the externally imposed strain. We show that both an elongation and compression can lead to an increase in helical domains under appropriate conditions., Comment: Latex, 17 pages, 11 figures, final version

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of finding explicit forms for soft deformations (the approach of Olmsted)., Comment: 10 pages, 10 figures, RevTex, AmsTex

Polymer entanglements lead to complicated topological constraints and interactions between neighbouring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they effectively confine each individual chain in a tube-like geometry. In polymer networks, due to crosslinks preventing the reptation constraint release, entanglements acquire a different topological meaning and have a much stronger effect on the resulting mechanical response. We apply the classical ideas of reptation dynamics to calculate the effective rubber-elastic free energy of an entangled rubbery network. We then compare the results with other theoretical approaches and establish a particularly close mapping with the hoop-model, with equally good description of experimental data. The present consistent reptation theory allows further development of dynamic theory of stress relaxation.

Dense rubbery networks are highly entangled polymer systems, with significant topological restrictions for the mobility of neighbouring chains and crosslinks preventing the reptation constraint release. In a mean field approach, entanglements are treated within the famous reptation approach, since they effectively confine each individual chain in a tube-like geometry. We apply the classical ideas of reptation dynamics to calculate the effective rubber-elastic free energy of anisotropic networks, nematic liquid crystal elastomers, and present the first theory of entanglements for such a material., Comment: amended version (typos corrected, appendix extended)