Order and Disorder in Liquid-Crystalline Elastomers - Liquid Crystal Elastomers: Materials and Applications - page 221

at low temperatures is about half that for E70/30. x( T ) behaves as if we are in a
“para-smectic” regime of a first-order smectic-isotropic transition and reflects
mainly changes associated in S ( T ) and c( T ), the orientational and translational
order parameters, respectively. Note that in the purely smectic elastomer E100/0,
disordering effects of similar strength occurred only at a crosslink concentration of
about 20% (Sect. 5.2.2 ). The smaller value observed in E60/40 can be attributed to
its rather soft layer system, due to the wide nematic range and the reduced value of
the elastic modulus B . Obviously E70/30, with a larger smectogenic component,
represents an intermediate case between E60/40 and the purely smectic elastomer
E100/0.
Interpretation of the above results is not straightforward. The overall results of
Fig. 17 are reminiscent of the extended short-range layer correlations found in low-
molecular-mass smectics confined in random silica aerogels or aerosils (see
Sect 4.2 and Fig. 10 ). In the latter case, the lineshape has been fitted to a combina-
tion of a Lorentzian (describing the thermal layer fluctuations) and a squared
Lorentzian (describing the effect of random fields), the latter becoming dominant
at lower temperatures. It is clear from Fig. 16a that the present smectic elastomer
lineshapes could be represented by such a combination of terms. As discussed in
Sect. 4.3, short-range order induced by the random crosslinks can be characterized
by the correlation length x ¼ (B/2 L ) 1/2 ~ [B/2( c c 0 )] 1/2 . Using the data from

Fig. 16 and B- values derived from stretching experiments, we can make some
estimates. First, at the same crosslink density of 10%, the compression modulus
B of E60/40 is about a third of that for E70/30. If the value x 50 nm, characteris-

tic of the low temperature state of E70/30, is divided by 3 we arrive at x 29 nm,

which is close to the saturated correlation length x 27 nm of E60/40. Second, a

reasonable value of the percolation limit of the present elastomers is c 0

0.04.
Then, neglecting a possible temperature dependence of the modulus B , the ratio
x 5% /x 10% should be (6) 1/2 2.4. Considering first E70/30, taking x 5% 150 nm (at

the transition point to nematic phase) and x 10% 50 nm at low temperatures, we

arrive at a ratio x 5% /x 10% ¼ 3, close to our estimate. However, for E60/40 we find

a ratio x 5% /x 10% 6, which is too large. This discrepancy could indicate that for

E70/30 10% the distortion of the smectic layers at low temperatures is due to
random fields, whereas for the more nematogenic E60/40 10% the contribution
from thermal disorder is still appreciable.
From the discussion so far we conclude that the available theories of random
disorder can describe some important details of the disorder in fully smectic
elastomers. The results around the SmA-N transition in elastomers indicate the
complex interplay of thermal and random disorder mechanisms. Currently, there is
no consistent theory to describe disorder in the SmA-N phase transition region,
which constitutes a major theoretical challenge. Upon increasing the crosslink
density, the fully smectic compound E100/0 showed a wide lineshape variation
from Gaussian via stretched Gaussian to Lorentzian. A stretched Gaussian with
b 0.7 corresponds approximately to a square Lorentzian and thus could indicate

the onset of disorder, in agreement with theory. The further evolution might be
attributed to increasing dominance of the thermal disorder component.