Simulation of liquid crystal elastomers at the microscale. Azobenzene-based LCE are subject to shape-change when irradiated by light.

1. Liquid Crystal Elastomer Simulations at the
Microscale
Jean-Christophe Lavocat
Supervisors : Diederik Wiersma (LENS) - Niek Van Hulst (ICFO)
March 2012

2. What are LCE ? Macro and Micro Actuators
LCE could be used as light activated motors 1
1 Yamada, et al. Photomobile Polymer Materials: Towards
Light-Driven Plastic Motors (Angewandte Chemie - 2008)

3. What are LCE ? Macro and Micro Actuators
LCE could be used as potential micropumps 1
LCE could be used as potential arti

4. cial muscles 2
1 Van Oosten, et al. Printed arti

5. cial cilia from liquid-crystal network
actuators modularly driven by light (Nature - 2009)
2 Camacho-Lopez, et al. Fast liquid-crystal elastomer swims into the
dark (Nature - 2004)

6. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Table of Content
1 Introduction to Liquid Crystal Elastomers
Background theory on Liquid Crystal Elastomer
Actuation mechanisms
Applications
2 Modeling of light absorbing LCE - Stationnary
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
3 Modeling of light absorbing LCE - Time Dependent
Dye concentration law
Isomers concentration evolution
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 3 / 19

7. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal Elastomer
Actuation mechanisms
Applications
Table of Content
1 Introduction to Liquid Crystal Elastomers
Background theory on Liquid Crystal Elastomer
Actuation mechanisms
Applications
2 Modeling of light absorbing LCE - Stationnary
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
3 Modeling of light absorbing LCE - Time Dependent
Dye concentration law
Isomers concentration evolution
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 4 / 19

8. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal Elastomer
Actuation mechanisms
Applications
Background theory on Liquid Crystal Elastomer
Liquid Crystals Properties
Rod-like molecular structure
Rigid shape
Tuning of the alignment
Nematic alignment of LC
Elastomers Properties
High Elasticity
Low Young's modulus
High yield strain
Elastomer without and with strain
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 4 / 19

9. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal Elastomer
Actuation mechanisms
Applications
Background theory on Liquid Crystal Elastomer
LC Elastomers (LCE) are polymer
networks formed by cross linking
liquid crystalline polymers.
LCE network
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 5 / 19

10. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal Elastomer
Actuation mechanisms
Applications
Background theory on Liquid Crystal Elastomer
LC Elastomers (LCE) are polymer
networks formed by cross linking
liquid crystalline polymers.
LCE network
LCE networks can also include
active molecules such as Azo
dyes.
LCE network with Azo dyes
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 5 / 19

11. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal Elastomer
Actuation mechanisms
Applications
Light activation of LCE
It is also possible to excite the material with photons.
Dyes absorb energy. They go from trans-state to cis-state
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 6 / 19

12. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal Elastomer
Actuation mechanisms
Applications
Light activation of LCE
It is also possible to excite the material with photons.
By absorbing UV photons, the LCE changes shape
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 6 / 19

13. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal Elastomer
Actuation mechanisms
Applications
Parameters
High Frequency Photodriven Oscillator3
3 White et al. High frequency photodriven polymer oscillator (Soft
Matter - 2008)
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 7 / 19

14. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
Table of Content
1 Introduction to Liquid Crystal Elastomers
Background theory on Liquid Crystal Elastomer
Actuation mechanisms
Applications
2 Modeling of light absorbing LCE - Stationnary
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
3 Modeling of light absorbing LCE - Time Dependent
Dye concentration law
Isomers concentration evolution
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 8 / 19

15. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
Deformation due to light
In linear elasticity (small deformations), materials follow the
Hooke law.
= E
: stress tensor
E : Young modulus
: strain tensor
The strain deforms the material Light induce a strain
= 0 + light
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 8 / 19

16. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
Light activation of the dyes - Mechanism
Stationnary
' : concentration of dye in the material
P : photocompliance4
light = 'PI(x)
Time dependent
4 Van Oosten, et al. Glassy photomechanical liquid-crystal network
actuators for microscale devices (EPJ E - 2007)
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 9 / 19

17. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
First simulation : Steady state - Beer Law
Light Intensity Profile − Beer Absortpion
600
300
d = 6μm
d = 1μm
0 2.5 5
Intensity (W/m2)
x (μm)
I0=64 mW/cm2
Steady state
I = I0ex'=d
Eect enhanced (light is
applied on the surface)
Intensity gradient changes
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 10 / 19

18. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
First simulation : Steady state - Beer Law
Static bending of an LCE cantilever
I0=64 mW/cm2
d/'=6m
I0=64 mW/cm2
d/'=1m
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 11 / 19

19. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
Beer Law : Absorption length's eet
4
3
2
Uniaxial Alignment − Bending Radius
0 1 2 3
Absorption Length (μm)
Bending Radius (mm)
Analytical expression
FEM simulation
I0=10 mW/cm2
LC Uniaxial alignement
Depends on the relative
absorption length
drel=d='dye
Can maximize the
bending by adjusting the
concentration of dye
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 12 / 19

20. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
Beer Law : Absorption length's eet
6
4
2
Bending Radius : Uniaxial vs Splay
0 1 2 3
Absorption Length (μm)
Bending Radius (mm)
Uniaxial alignment
Splay alignment
I0=10 mW/cm2
LC Splayed alignement
Orientation of the
bending is constant
Bending is modi

21. ed with
light wavevector
Fabrication complicated
in the nanoscale
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 12 / 19

22. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
EM

23. eld - Eect due to absorption
Maxwell equations - I0=30 W/cm2
Steady state
Absorption due to the
material
Re
exions at the boundaries
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 13 / 19

24. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
EM

25. eld - Eect due to absorption
4
2
Bending Radius in function of absorption length
0 1 2 3
Absorption Length (μm)
Bending Radius (cm)
Theoretical
FEM Simulation − Maxwell
Maxwell equations - I0=30 W/cm2
Steady state
Absorption due to the
material
Re
exions at the boundaries
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 13 / 19

26. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
EM

27. eld - Eect due to intensity
2.5
Bending Radius in function of intensity
0 250 500 750 1000
Incoming Intensity (W/m2)
Bending Radius (cm)
Theoretical
FEM Simulation − Maxwell
Maxwell equations -d = 0.5m
Bending increases with
intensity
Asymptotic limit
Eect reduced
Re
exions at the boundaries
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 14 / 19

28. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration law
Isomers concentration evolution
Table of Content
1 Introduction to Liquid Crystal Elastomers
Background theory on Liquid Crystal Elastomer
Actuation mechanisms
Applications
2 Modeling of light absorbing LCE - Stationnary
Light induced deformation
EM Field - Beer Absorption Law
EM Field - Maxwell formalism
3 Modeling of light absorbing LCE - Time Dependent
Dye concentration law
Isomers concentration evolution
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 15 / 19

29. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration law
Isomers concentration evolution
Light activation of the dyes - Mechanism
Stationnary
' : concentration of dye in the material
P : photocompliance4
light = 'PI(x)
Time dependent
light = 'Pnc (I ; t)
P depends on the molecular alignment, cross link density and
glass-transition temperature
4 Van Oosten, et al. Glassy photomechanical liquid-crystal network
actuators for microscale devices (EPJ E - 2007)
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 15 / 19

30. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration law
Isomers concentration evolution
Time dependent : dye excitation
nt
t
= Int +
nc
nt : dye fraction of
trans-state molecules
nc : dye fraction of
cis-state molecules
I : Light intensity
Light penetrates the material and is
absorbed by the dye in trans-state.
Photon absorbed : trans ! cis
(excitation rate )
Change of absorption (k / nt )
Back relaxation : cis ! trans
(relaxation time )
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 16 / 19

31. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration law
Isomers concentration evolution
Time dependent - Beer absorption
= 0:1s ; = 0:02s = I0 = 3:55W/m2 drel = 1m
Time evolution of cis/trans isomers
concentration in the material
Light intensity within the material,
in function of x/d. Time varying.
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 17 / 19

32. Introduction to Liquid Crystal Elastomers
Modeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration law
Isomers concentration evolution
Transient case - Video
In

33. nite Waving Sheet
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 18 / 19

34. Acknowledgement
Hao Zeng
Camilla Parmeggiani
Kevin Vynck
Giacomo Cerretti
Diederik Wiersma
Thank you for your
attention