Liquid Crystal Elastomers and Light - Liquid Crystal Elastomers: Materials and Applications - page 99

Fig. 1 Transparent LCE sample attached to yellow tape ( left ). Sample between crossed polarizers
( right )

flexible materials, monodomain nematic LCEs therefore behave optically as
birefringent crystals, and allow light transmission when placed between crossed
polarizers, as shown in Fig. 1 .

2.1 Refractive Indices

The refractive indices of the propagating eigenmodes in nematic LCEs depend on
the principal values of the relative dielectric tensor as in ordinary nematics, that is,
the index of the ordinary mode is given by

n o ¼ e ?

(14)

and the index of the extraordinary mode is

e ? e k
e ? þðe k e ? Þð k

n e ¼

2 ;

(15)

n Þ

where k is the wave vector. Since the dielectric permittivity is linear in the order
parameter [cf. ( 3 )], as in the case of ordinary nematics, any change in orientational
order will result in a change of the refractive indices. In addition to temperature,
fields of particular interest in the case of LCEs are mechanical strain and changes in
composition. Measuring the individual refractive indices of LCEs is more challeng-
ing than for conventional liquid crystals, nonetheless this has been carried out using
both Abbe refractometers [ 6 ] and Brewster angle measurements [ 7 ].
It is straightforward to measure the birefringence as function of temperature [ 8 ]
as well as strain [ 9 ]. One experimental consideration to take into account is the
change in sample thickness due to strain. The response can be readily understood in
terms of the simple model described in the Introduction. LCEs have been swollen
with both isotropic and anisotropic solvents [ 8 , 10 , 11 ]. Isotropic solvents reduce
the number density of mesogens and, hence, the critical temperature T c ¼ rU= 5 k .

They also reduce the crosslink density and the influence of the network. Nematic
solvents, on the other hand, up to first order do not reduce the mesogen density, but