Electro-Opto-Mechanical Effects in Swollen Nematic Elastomers - Liquid Crystal Elastomers: Materials and Applications - page 132

0
@

1
A

k 1 sin 2 1 ð 1 Þ y 0 ðk 1 Þ sin y cos y

l ¼ (8)

0 1 0

k 1 sin 2

ð 1 Þ sin y cos y 01 þðk 1 Þ y

where k is a measure of the anisotropy of the dimensions of the constituent polymer
chains and is equivalent to the dimensional ratio l x (0 )/ l x (90 )or l z (90 )/ l z (0 ). The
anisotropic Gaussian network model relates k to the orientational order parameter
of network backbone ( S B )[ 1 ]:

1 þ 2 S B

k 2

¼ (9)

1 S B

The dimension l i ( i ¼ x , y , z ) along the i -axis at y ¼ y is obtained as:

l z

l x ¼ l x l x l xx l xx þ

l x l xz

(10a)

l y ¼ l y 0

(10b)

l x

l z ¼ l z

l zz þ

l z l zx

(10c)

where l ij ( i , j¼x , y , z ) is the ij component of l. For sufficiently thin films with

l z 0 / l x 0 1( l z 0 / l x 0 10 2 in the present case), the contribution of the shear l xz

to

l x in ( 10a ) is negligible. The expression for g i using ( 1 ) is given by [ 19 ]:

sin 2

1
k

g x ¼ 1 y (11a)

g y ¼ 0 (11b)

sin y cos y

l x
l z

1
k

sin 2 g z ¼ k ð 1 Þ y þ 1 (11c)

Most characteristically, the theory predicts g x proportional to sin 2 y and g y ¼ 0

independent of y, which accords with the experimental observation.
The value of k estimated from the slope in Fig. 10 for the specimen with
c x ¼ 0.1. This value of S B is compara-

ble to the orientational order parameter for the dangling mesogen ( S

7 mol% is 1.15, which corresponds to S B

0.1) that
was estimated from the absorbance data without an electric field in Fig. 9a . The
modest values of S B and S originate from the swelling effect because S in the dry
state is 0.3-0.4.
In a recent paper [ 41 ], Corbett and Warner provided a more detailed theoretical
explanation for the EOM effects observed by taking into account the deviation from
ideal soft elasticity and possible misalignment of the initial director. They also