Order and Disorder in Liquid-Crystalline Elastomers - Liquid Crystal Elastomers: Materials and Applications - page 211

limit of an elastomer into account, i.e., the minimum density of crosslinks, c 0 ,
needed to form a continuous rubbery network (see also Sect. 3.1 ) . The elastic
properties of the material should depend on the excess of crosslinks over this
minimum, leading to the proportionality x ~( c c 0 ) 1/2 .
In conclusion, in analogy to the general theory for quenched disordered systems
we can expect a transition to disorder in smectic-A elastomers for high-enough
crosslink concentrations. However, this analogy might fail because in smectic
elastomers the crosslinks are not rigidly “frozen” defects, but consist of flexible
chains embedded in the slowly fluctuating elastomer gel. This could make the
situation different from, for example, smectics confined to aerogel (or aerosil)
networks, though the “softer” aerosil analogy might still be appropriate. Evidently,
predictions from general theories of quenched disorder, when applied to LC
elastomers, have to be treated with severe care. In the absence of theory for random
crosslinks embedded in a fluctuating layered system, no definite predictions for the
nature of these disordering effects in an elastomer network can be made.

5 Smectic Elastomers

5.1 “Single Crystal” Smectic Elastomers

In this section we will review high-resolution X-ray studies of well-aligned smectic
elastomer samples. Recently, siloxane samples [ 7 , 127 , 135 ] were studied, prepared
by a two-stage process similar to that described in Sect. 3.3 for nematic LSCEs [ 136 ,
137 ] . In the first step, the sample is slightly crosslinked in the isotropic phase while
solvent still abundantly present. Subsequently, the solvent is slowly removed with the
sample being kept under a uniaxial load. During this process the isotropic sample is
thought to pass through a nematic phase and subsequently becomes smectic. In the
transient nematic phase, the director is oriented in the direction of the uniaxial stress,
which determines the long direction of the sample (smectic layer normal). This
orientation is fixed by the second crosslinking step in the smectic phase.
Thermoelastic measurements on such samples reveal a spontaneous elongation
along n at the transition to the smectic phase, indicating a prolate polymer backbone
conformation in the smectic elastomer [ 137 ]. On another hand, SANS results for
end-on side-chain polymers in the smectic phase indicate an oblate chain confor-
mation, with the backbone preferentially confined in the plane of the layers
(Sect. 2.2 ). Thus, the chain distribution and macroscopic shape of the smectic
elastomer change their sign if crosslinking is made under uniaxial mechanical stress
in the isotropic and/or nematic phase. This result is remarkable and indicates that
the oblate chain conformation of a smectic end-on polymer can be easily turned into
prolate by a low uniaxial extension during solvent evaporation.
When analyzing experimental results, it is important to consider how the smectic
elastomer sample was prepared. If the smectic layers are aligned by a surface or an