Order and Disorder in Liquid-Crystalline Elastomers - Liquid Crystal Elastomers: Materials and Applications - page 201

Fig. 7 Orientational order parameter of a nematic main-chain elastomer from D-NMR around the
N-I transition for different crosslink concentrations x [ 90 ]
The origin of the observed behavior is quite clear: internal stress (independently
of its origin) shifts the first-order N-I transition towards the critical point and
further into the supercritical regime, characterized by zero latent heat and a
continuous S ( T ) profile. The necessary condition is a linear coupling of the nematic
order parameter S with a conjugate field s that adds a term ~-s S to the free-energy
expansion in the vicinity of the phase transition point [ 91 ]. The transition to a
supercritical domain occurs whenever s exceeds the critical value s c . In nematic
elastomers, s is the mechanical stress that may be associated with the monodomain
state, imprinted internally in the system through the pattern of crosslinks. It could
also come from an external field applied to the sample. Another important source
of the nonuniform stress in the sample is due to random quenched disorder.
In practice, crosslinking agents are always anisotropic and frequently made of
fragments that are mesogenic themselves. Thus, one can always identify the
direction of anisotropy, which is quenched because the crosslinks are not totally
free to rotate under thermal motion [ 92 , 93 ]. As a result, there is a local preferred
direction of orientational and spatial order that acts as a random orienting (and
pinning) field. For a more quantitative discussion of the N-I transition we refer to
Lebar et al. [ 94 ] .
From the discussion so far, the natural question arises whether it is possible to
create an ideal nematic network without internal stress, in which the orientational
order relaxes to zero at high temperatures in the isotropic phase. The actual answer
is no, because in any case the random quenched disorder, introduced by crosslinks,
is expected to affect the transition. Although the crosslinks are on average randomly
functionalized into the polymer backbone, local variations in their density and
orientation lead to quenched randomness. This will manifest itself macroscopically
as a mechanical random field that induces smearing of the phase transition. Theory
predicts different regimes of the N-I transition affected by quenched disorder [ 93 ] .
The scalar order parameter S is predicted to be homogeneous in space, whereas the
director n follows equilibrium randomly quenched texture with a characteristic size
typical for elastomer domains. Depending on the strength of the disorder, one may