Electro-Opto-Mechanical Effects in Swollen Nematic Elastomers - Liquid Crystal Elastomers: Materials and Applications - page 131

0

γ

y

- 0.05

-0.1

γ

x

-0.15

- 0.2

0 0.2 0.4 0.6 0.8 1

sin 2 q

g x ( closed symbols ) and g y ( open symbols ) as a function of sin 2 Fig. 10 Strains y for SNE-3

( diamonds ), SNE-7 ( squares ), and SNE-14 ( triangles ), where y is the rotation angle of the director
estimated from the birefringence data. The crosses represent the data for SNE-7D obtained by
polarized FTIR measurements. From [ 19 , 33 ]

x

1

k − 1

z

1

y

1

k

1

Fig. 11 Deformation of small volume element represented by ( 8 ). The arrow indicates the
director. The rotation angle of director is 0 ,30 ,45 ,60 and 90 from left to right. k elongation,
k 1 contraction

A linear correlation is observed, and the slope ( 0.13) is almost identical with that

( 0.12) of the plot using the birefringence data for the similar specimen (SNE-7).

This good agreement indicates that the results obtained by the two different
methods are consistent. The linear relation g x ~ sin 2

y and the two-dimensional
deformation are the two key features of the deformation induced by director
rotation for unconstrained nematic elastomers.
Several researchers theoretically considered the deformation mode induced
by director rotation in nematic elastomers without external mechanical constraints
[ 1 , 38 , 39 ]. The theory is based on the soft elasticity characteristic of ideal nematic
elastomers [ 40 ] . The expected deformation is a pure shear combined with body
rotation, which is illustrated in Fig. 11 . When the director rotates by 90 , the cube
elongates by k along the realigned director ( z ) and contracts by k 1 along the initial
director ( x ) with no dimensional change along the rotation axis of the director ( y ).
The corresponding deformation gradient tensor is expressed [ 39 ] as: