Phenomena and Problems in
Liquid Crystal Elastomers
Mark Warner, Cavendish Cambridge.
Classical Rubber
Locally a polymeric liquid – mobile
Make more complex, keep locally fluid
More complex solids
Nematic fluid
n
cool
Nematic polymers have shape
anisotropy
Crosslink:
elastomers respond to
molecular shape change
monodomain
Nematic Rubber
n
block of rubber
l
1
R0
R
Change shape with dT
crosslink
anisotropic
chains

1
Fnem  12  Tr  0      
initial shape
T

1/ λ
current shape
μ  ns RT ~ 105 J/m3
Roughly 300% strains.
Temperature changed by hot air blower.
Monodomain elastomer.
Close to real-time movement.
2
Tajbakhsh and Terentjev
Cavendish Laboratory
Strain L/L0
3.5
3
2.5
Cross-section
~2mm2
2
1.5
1
20
40
60
80
100
Temperature ( C)
120
Load=15g
Load=10g
Load=5g
No Load
6
Smectic liquids
Nematic fluid with layered positional order.
Layer modulus 107 N/m2.
n
(DJ Cleaver et al, Sheffield)
k
cool
Smectic A
Smectic C
2-D elastomer – layers so strong
Spontaneous shears of smectic sheet
(also possible with slab)
(a) 25ºC (heating)
(b) 90ºC (heating)
(c) 130ºC
qE
qE
LE
LE
(Hiraoka and Finkelmann, 2005)
n k
layers
P
Reduce order by bending some rods
- Photo alternative to thermal disruption of order.
Absorb photon into dye molecule
trans isomer
(straight)
Recovery
thermal or stimulated
cis isomer
(bent)
Azo benzene
Optical strains.
Optical
Can be very fast.
Bend.
Polydomain response.
Thermal
Non-uniform response
Birubber strip, H Finkelmann, Freiburg.
Nematic elastomer + green dye guest; laser pulse.
Dye photoisomerises
top has lower nematic order – differential photo-contraction???
Green laser pulse
Palffy-Muhoray
* Curvature of photo-beams very rich (2 neutral planes)
* Optically write structures in films
Photo-bending of sheets (Ikeda, Nature, 2003)
E
Most peculiar dynamics – why does it continue curling after eclipsing itself?!
What should the photo-stationary shape be?
Uncurling in the absence of UV.
(in light – stimulated decay)
Responsive surfaces and thin films
light beam
localised strains
photo-rubber
a
H

uz
z
uzzH
l
uzr
urz
r
Substrate
Elongation on illumination
Rotate order rather than change magnitude
Stretch transverse to director
• Body accommodates  ( )
rotating chain distribution.
• Need shear & stretch.
• Entropy, energy constant.

thereafter hard.
inscribed 
1/ 2
( )

Fnem   Tr  0    
1
2
T
1
( )

   32 
Stretch transverse to director
1/ 2
 ( )
Minimised by (Olmsted):
 soft  1(/ 2)   01/ 2
force/area
hard
  sin 1
r ( / 1 ) 2  1
r  1 ( / 1 ) 2
stretch
Response by rotation pervades
all LC elastomer mechanics
Photo-bend also for polydomains –
depends on light polarisation
E
45o
E
k
Light incident
Curl direction ↔ light polarisation
(heat a minor effect?)
Polydomain photo-elastomer (thin)
(MW & DC, PRL 06)
Incident light
Local molecular mobility
Domains suffer director
rotation away from E 
large change in natural shape
1

 1
1

E
Photo contraction l along E non-monotonic with intensity I
recovered l,
all domains
isotropic
1.0
l
back rotation complete
0.9
1+S
director
rotation
gives strain
0.8
~
I
0.7
0
2
NMR? Mechanics?
Unpolarised light?
4
6
8
10
12
back rotation starts
order parameter collapses
(“bleaching”) in back-rotated domains
SmC* ferro electric
Spontaneous shear L ~ 0.4
Actuation based on shear.
L k
qn
c
p
Ferro-electric films respond to:
• stress/strain
• electric field
• light
• heat
Slab geometry for film
Apply shear -2L
Reverse polarisation
Film bistable??
^
k0
^
n
^
qn
0
c^0
p^0
^
k0
-2L
^
-c0
^
p
^
z
x^
Cholesterics – helically twisted nematics:
Elastomers:
Separate left from right handed molecules.
Change colour on stretching.
Lase when pumped – lasing colour changes with stretch . . .
(tuneable laser from an elastic photonic band solid)
Deformations in practice (Quasi-convexification)
Replace gross deformations by microstructure of (soft) strains with
lower energy which satisfies constraints in gross sense.
Stripes
Macroscopic extension
(crossed polars)
Kundler & Finkelmann
Practical geometry – put stripes in where needed for lowest energy:
(Depends on strip aspect ratio.)
(soft)
Conti et al (1/4 of strip)
Zubarev, Finkelmann et al
Terentjev et al
Jump away from
0 ; global order S < 0
n
q ~Q0
z
  0
initially (and finally)
z
Q0
Jump back toward  0
n
z
q0
q~q0
Q~0
Detect by NMR?
Collapse of local order Q; global order less negative
Local and global order = 0
1.0
l
0.9
1+S
0.8
~
I
0.7
0
2
4
6
8
10
12
Local order Q0 rotated away from E; global S<0
Mahadevan et al (Phys. Rev. Letts., 2004)
Light intensity I(x) falls with x (absorption length d )
Contraction decreases with x
Bending (curling) of beam or sheet
thickness
w>d: thick
w<d: thin film
rad. curvature
Balance torques – get 2 neutral planes at depths xn
Curvature (1/R) non-monotonic in d/w
(absorption length/thickness)
“thick”
“thin”
Optimal d ~ w/3
(more examples)