Liquid Crystal Elastomers and Light - Liquid Crystal Elastomers: Materials and Applications - page 98

1.3 Liquid Crystal Elastomers

LCEs are polymer networks incorporating mesogenic molecules as part of their
architecture, either as parts of the polymer main chains, or as pendant side chains.
As proposed by de Gennes, these materials show combined aspects of elasticity and
liquid crystallinity. The polymer chains containing mesogenic units may be
regarded as performing an anisotropic random walk between crosslinks; the anisot-
ropy is due to orientational order. The step length tensor is of the form

l ab ¼ l ? d ab þðl k l ? Þn a n b ; (12)

where n a is a component of the nematic director.
The free energy can be approximated as the sum of liquid crystalline and
elastomeric contributions, as well as a coupling term. For nematic LCEs, this
takes the form

F nlce ¼ F nem þ F el gQ ab e ba ; (13)

where the last term represents the simplest symmetry-allowed coupling between
orientational order and strain. The coupling constant

g

is proportional to the
crosslink density and the step length anisotropy l k l ? , and can be positive or
negative.
This coupling indicates that changes in the order parameter will affect the strain,
and conversely, that changes in shape will affect the orientational order. Specifi-
cally ( 13 ) and ( 11 ) show that the effect of the order parameter on strain is the same
as that of an external stress

s ab , and ( 13 ) and ( 4 ) show that the effect of strain on the
orientational order is the same as that of an applied external field E a E b . This means
that applying a uniaxial strain to a nematic LCE with 0 will tend to increase

orientational order and align the director along the strain direction, while changes in
orientational order give rise to strain deformations. Young's modulus for typical
LCEs is of the order of 10 5 Pa, which also gives a measure of the coupling constant

g >

.
Finally, conventional liquid crystals and isotropic rubbers as well as LCEs conserve
volume to a good approximation. Much of the behavior of LCEs to be discussed
below can be understood on basis of this simple description.

g

2 The Effects of LCEs on Light

We now consider how the properties of LCEs affect light. Light propagation in
typical uniaxial nematic liquid crystals is the same as in uniaxial solid crystals; two
eigenmodes are allowed, the extraordinary mode with polarization parallel, and the
ordinary mode, with polarization perpendicular to the plane defined by the wave
vector k and the optic axis - the nematic director - n. Although they are soft and