The Isotropic-to-Nematic Conversion in Liquid Crystalline Elastomers - Liquid Crystal Elastomers: Materials and Applications - page 166

a b

30 30

25 25

20 20

15 15

10 10

5 5

0 0

330 340 350 360 330 340 350 360

T (K) T (K)

Fig. 14 The best simultaneous M n, 1 ( T )(a) and M n, 2 ( T )(b) fits of the theoretical model from
Sect. 4.2 ( dark gray line ) to the experimental data ( triangles ) for the LCE shown in Fig. 12 . Also
shown are the forced 0fit( light-gray solid line ) and the forced G ≲ G C fit ( black line ). For

the displayed LCE, the best fit is obtained for G / G C

s T* ¼

¼ 1.5 and s T ¼ 1.0 K. Data taken from [ 3 ]

(i.e. 0, G ≳ G C ) gives by far the best possible match between the theoretical

prediction and the experiment.
Unlike the first two scenarios , where the parameters were set by fitting only the
experimental M n, 1 ( T ) data, for the mixed scenario the fit was made simultaneously
for both the M n, 1 ( T ) and M n, 2 ( T ) datasets. In this way, the relative values of the
parameters were determined with relatively high precision (the typical maximum
error for any parameter among a,B,C, or G for the displayed fit is about 15%).
Actually, since these parameters are not independent, only the relative values
(ratios) of these parameters can be determined from the 2 H-NMR data, e.g. G / G C .
Their absolute values are accessed from an additional calorimetric measurement,
e.g. a measurement of the latent heat released at the phase transition.
Obviously, the involvement of the heterogeneity of the transition temperatures
makes a sensible description of the phase transition in LCEs. However, one finds
an even better match with the experimental data when considering only the
heterogeneity of the mechanical field G instead (

s T* 6¼

0). The
w S ( T ) profiles corresponding to the disorder in T * are different from the profiles
corresponding to the disorder of G . This is so since the changes in T * merely result
in a shift of T PN-N, while the shape of S LdG ( T ) is preserved, whereas the changes in
G also alter the temperature profile of S LdG ( T ). Exploiting this fact, it is found that
the high-temperature tails of M n, 2 ( T ) can be reproduced more accurately by
distributing the internal fields G rather than the transition temperatures T *
(Fig. 15 ) . On the basis of such a comparison one can conclude that the disorder
in S mainly arises from the disorder in the local mechanical fields G . Although a
model in which all the LdG parameters undergo some distribution is probably
closest to the real picture, due to a large number of independent free parameters

s T* ¼ 0, hGi 6¼ 0, s G 6¼