Relation of stress and strain

Small molecular mass liquid crystals do not respond to extension and shear stress. Liquid crystalline polymers may exhibit a high elastic state at some temperature due to the entanglements. However, the liquid crystalline network itself is an elastomer, showing rubber elasticity. In the presence of external stress, liquid crystalline networks deform remarkably and then relax back after the release of stress. The elasticity of liquid crystalline networks is more complicated than the conventional network, such as the stress induced phase transition, the discontinuous stress-strain relationship and the non-linear stress optical effect, etc. 

The stress-strain relationship of nematic networks is given by 

It is shown that the elasticity of the nematic networks is catalogued into three temperature ranges  

This demonstrates that liquid crystallinity is not exhibited by many polymer networks because their liquid crystal to isotropic transitions are too low to be observed. But the residual liquid crystallinity affects the stress-strain relationship at higher temperatures. These results form a deviation from classical rubber elasticity theory. 

We have only dealt with the main chain nematic networks so far. Actually many liquid crystalline networks are formed by crosslinking the backbones of side chain liquid crystalline polymers. The side chain nematic polymers have three nematic phases and their backbones have either prolate or oblate conformations, depending on their phase. It is expected that the rubber elasticity of a side chain nematic polymer network is more complex. For instance, the stress-induced Ni-Nm phase transition is predicted as the network shape transforms from oblate to prolate. Liquid crystalline networks have a bright potential in industry. 

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