Soft Condensed Matter

A Survey of Liquid Crystal Elastomers

Conventional elasticity goes back to Robert Hooke in the 17th Century. Its rules are clear and were long thought to provide a complete and exhaustive mechanical classification of matter: Further, for most solids: Over recent years we have predicted new classes of solids that disobey all these rules and patterns, and require a careful extension of elasticity theory. The new phenomena have all been found experimentally in liquid crystal elastomers in experimental groups here, elsewhere in the UK, in Germany, Russia and Holland, and in the USA.
LC elastomers arise from networks of liquid crystal polymers, which we first describe below before sketching the new elastic phenomena we have discovered.

Liquid Crystal Polymers

Combining liquid crystallinity and rubber elasticity requires liquid crystal polymers - rodlike molecules concatenated end-to-end to form main chain (MC), or pendant to a flexible backbone to form side chain (SC) polymers.

On cooling to the nematic (orientationally ordered) state, MC molecules adopt highly extended conformations with hair pins.
Their unusual chain statistics leads to anomalous dielectric and NLO response as well as extreme forms of the phenomena discussed below.
SC molecules can either extend or flatten - our classification of LC polymers into their 3 possible characteristic forms is generally accepted. Much earlier work of the group was to establish the statistical mechanical foundations of polymer liquid crystallinity and molecular conformations.

Liquid Crystal Elastomers

All elastomers are liquid-like and hence highly mobile at the molecular level. They almost flow, but not quite since cross-links between their polymer chains percolate to form a very weak solid. If liquid crystalline chains are crosslinked together, the network forms an elastomer usually with the same symmetry as that of the chains at the same temperature - Nematic, Cholesteric or Smectic. An overview with diagrams of the effects described below is in the first chapter of our book.
Spontaneous distortions
Since liquid crystalline polymers change shape on entering an LC phase and since these chains comprise the network, so then does the network suffer a large shape change. A movie was shown on the previous page of the mechanical response on heating and cooling. Alternating periods of light and dark will cause the same effect in elastomers where the rod-like elements can be bent on absorbing a photon. Similar spontaneous responses occur when smectic elastomers are formed, in particular large spontaneous shears when heating and cooling between the SmA and SmC phases.
Soft Elasticity
Since liquid crystalline elastomers are very mobile at the molecular level, the director (the net direction of orientational order) can be easily induced to rotate by the application of strains. A very subtle effect can then arise that we have christened "soft elasticity". Chains are elongated by the orientational order. Rotating the director causes the elongation to point in another direction and equally the solid to elongate in that direction (with a contraction in the original direction). In general shears also arise as this redirection proceeds. However the chain shape distribution (and hence entropy) is unchanged and the liquid crystal order is also unchanged. The free energy does not rise, even though there has been a non-trivial shape change. This is at odds with the simple Hookean classification of the states of matter! The experimental demonstrations of this prediction of entirely new behaviour are now conclusive. A sketch of this effect is in the first chapter of our book.

More complex phases of liquid crystal elastomers

Cholesteric elastomers
Cholesteric elastomers (where the director field is twisted) can be deformed by mechanical strains. They are coloured because they Bragg-reflect light of the same wavelength as their pitch. As they are strained, they change colour. They lase because of their large density of states at their band edges. The lasing colour is equally shifted when the rubber is stretched. We predicted these effects of strain on photonics. Many of the experimental confirmations of the theory have been carried out in the BSS group, Cavendish Lab.
Smectic elastomers
Smectic elastomers are layered, in addition to having underlying nematic (orientational) order. Smectic A elastomers respond in effect as 2-D elastomers when stretched in the plane since the energy required to change the layer spacing (ie stretch or compress along the layer normal) is much higher than rubber distortions. It at first responds as a conventional solid when stretched along the layer normal until a rotational instability to shear deformation occurs. These are highly non-linear effects, only really calculable with a fully-non-linear theory of rubber elasticity with the rigid constraints of layer spacing perservation.
SmC elastomers have the rigid layer constraints of SmA elastomers, but can deform in-plane by the rotation of their directors, which are no longer along the layer normal. We have described the spontaneous shears associated with attaining the SmC state from SmA, and predicted that there should be soft in-plane shear deformations. Chiral SmC elastomers are ferro-electric while being rubbery. They are capable of deformations and changes to the direction of permanent polarisation that are orders of magnitude greater than in ceramic ferro-electrics. We have predicted a number of strange elasto-electric effects that await experimental test.