The Isotropic-to-Nematic Conversion in Liquid Crystalline Elastomers - Liquid Crystal Elastomers: Materials and Applications - page 149

Fig. 3 Evolution of the order
parameter for various fields
ranging from no field ( G ¼ 0)
to below-critical ( G < G C ),
and supercritical ( G > G C ).
The dotted lines denote the
discontinuity for the cases
G ¼ 0 and G < G C , the
dashed line stands for the
continuous evolution of the
order parameter at the critical
point ( G ¼ G C ) and T IN
denotes the transition
temperature of the case
without a field ( G ¼

0.6

G =0

0.4

G < G c

G > G c

0.2

G = G c

0)

0.0

-5 0 5 10

T - T IN (K)

;

1
2

3 cos 2

S ¼ y 1 (2)

where denotes the angle between the molecular axis and the director n. In the

isotropic phase, the molecular orientations are random and

y

cos 2

h yi¼ 1/3, which

yields S ¼ 0.

Externally applied fields that conjugate to the nematic order parameter can
induce some orientational order in the isotropic phase (which is called the parane-
matic order, in analogy with, e.g. paramagnetism) and suppress or even eliminate
the I-N discontinuity for strong field values. An additional linear term

0, while in the nematic phase S 6¼

GS must be
added to the free-energy expansion to account for the coupling between the applied
field G and the order parameter S :

1
2 aðT T ÞS 2

1
3 BS 3

1
4 CS 4

F ¼ þ þ GS: (3)

Providing the field is smaller than its critical value:

G C ¼B 3 27 C 2

= ; (4)

the discontinuity decreases but the phase transition remains first order (see Figs. 2
and 3 ). The discontinuity vanishes at G ¼ G C and the transition becomes continuous
(second order) at a single critical point. When G > G C , the transition is driven
beyond the critical point to the supercritical regime. The term “supercritical”