liquid crystal elastomer simulations at the microscale
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Liquid Crystal Elastomer Simulations at theMicroscale
Jean-Christophe Lavocat
Supervisors : Diederik Wiersma (LENS) - Niek Van Hulst (ICFO)
March
What are LCE ? Macro and Micro Actuators
LCE could be used as light activated motors 1
1 Yamada, et al. Photomobile Polymer Materials: TowardsLight-Driven Plastic Motors (Angewandte Chemie - 2008)
What are LCE ? Macro and Micro Actuators
LCE could be used as potential micropumps 1
LCE could be used as potential artificial muscles 2
1 Van Oosten, et al. Printed artificial cilia from liquid-crystal networkactuators modularly driven by light (Nature - 2009)
2 Camacho-Lopez, et al. Fast liquid-crystal elastomer swims into thedark (Nature - 2004)
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Table of Content
1 Introduction to Liquid Crystal ElastomersBackground theory on Liquid Crystal ElastomerActuation mechanismsApplications
2 Modeling of light absorbing LCE - StationnaryLight induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
3 Modeling of light absorbing LCE - Time DependentDye concentration lawIsomers concentration evolution
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 3 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal ElastomerActuation mechanismsApplications
Table of Content
1 Introduction to Liquid Crystal ElastomersBackground theory on Liquid Crystal ElastomerActuation mechanismsApplications
2 Modeling of light absorbing LCE - StationnaryLight induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
3 Modeling of light absorbing LCE - Time DependentDye concentration lawIsomers concentration evolution
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 4 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal ElastomerActuation mechanismsApplications
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
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal ElastomerActuation mechanismsApplications
Background theory on Liquid Crystal Elastomer
LC Elastomers (LCE) are polymernetworks formed by cross linkingliquid crystalline polymers.
LCE network
LCE networks can also includeactive molecules such as Azodyes.
LCE network with Azo dyes
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 5 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal ElastomerActuation mechanismsApplications
Background theory on Liquid Crystal Elastomer
LC Elastomers (LCE) are polymernetworks formed by cross linkingliquid crystalline polymers.
LCE network
LCE networks can also includeactive molecules such as Azodyes.
LCE network with Azo dyes
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 5 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal ElastomerActuation mechanismsApplications
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
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal ElastomerActuation mechanismsApplications
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
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Liquid Crystal ElastomerActuation mechanismsApplications
Parameters
High Frequency Photodriven Oscillator3
3 White et al. High frequency photodriven polymer oscillator (SoftMatter - 2008)
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 7 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
Table of Content
1 Introduction to Liquid Crystal ElastomersBackground theory on Liquid Crystal ElastomerActuation mechanismsApplications
2 Modeling of light absorbing LCE - StationnaryLight induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
3 Modeling of light absorbing LCE - Time DependentDye concentration lawIsomers concentration evolution
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 8 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
Deformation due to light
In linear elasticity (small deformations), materials follow theHooke law.
σ = Eε
σ : stress tensorE : Young modulus
ε : strain tensor
The strain deforms the material Light induce a strain
ε = ε0 + εlight
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 8 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
Light activation of the dyes - Mechanism
Stationnary
ϕ : concentration of dye in the materialP : photocompliance4
εlight = ϕPI(x)
Time dependent
· · ·
4 Van Oosten, et al. Glassy photomechanical liquid-crystal networkactuators for microscale devices (EPJ E - 2007)
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 9 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
First simulation : Steady state - Beer Law
0 2.5 5
300
600
Light Intensity Profile − Beer Absortpion
Inte
nsity
(W
/m2 )
x (µm)
d = 1µm
d = 6µm
I0=64 mW/cm2
Steady state
I = I0e−xϕ/d
Effect enhanced (light isapplied on the surface)
Intensity gradient changes
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 10 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
First simulation : Steady state - Beer Law
Static bending of an LCE cantilever
I0=64 mW/cm2
d/ϕ=6µmI0=64 mW/cm2
d/ϕ=1µm
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 11 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
Beer Law : Absorption length’s effet
0 1 2 3
2
3
4Uniaxial Alignment − Bending Radius
Absorption Length (µm)
Ben
ding
Rad
ius
(mm
)
Analytical expressionFEM simulation
I0=10 mW/cm2
LC Uniaxial alignement
Depends on the relativeabsorption length
drel=d/ϕdye
Can maximize thebending by adjusting theconcentration of dye
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 12 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
Beer Law : Absorption length’s effet
0 1 2 3
2
4
6Bending Radius : Uniaxial vs Splay
Absorption Length (µm)
Ben
ding
Rad
ius
(mm
)
Uniaxial alignment
Splay alignment
I0=10 mW/cm2
LC Splayed alignement
Orientation of thebending is constant
Bending is modified withlight wavevector
Fabrication complicatedin the nanoscale
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 12 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
EM field - Effect due to absorption
Maxwell equations - I0=30 W/cm2
Steady state
Absorption due to thematerial
Reflexions at the boundaries
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 13 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
EM field - Effect due to absorption
0 1 2 3
2
4Bending Radius in function of absorption length
Absorption Length (µm)
Ben
ding
Rad
ius
(cm
)
TheoreticalFEM Simulation − Maxwell
Maxwell equations - I0=30 W/cm2
Steady state
Absorption due to thematerial
Reflexions at the boundaries
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 13 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
EM field - Effect due to intensity
0 250 500 750 1000
2.5
Bending Radius in function of intensity
Incoming Intensity (W/m2)
Ben
ding
Rad
ius
(cm
)
TheoreticalFEM Simulation − Maxwell
Maxwell equations -d = 0.5µm
Bending increases withintensity
Asymptotic limit
Effect reduced
Reflexions at the boundaries
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 14 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration lawIsomers concentration evolution
Table of Content
1 Introduction to Liquid Crystal ElastomersBackground theory on Liquid Crystal ElastomerActuation mechanismsApplications
2 Modeling of light absorbing LCE - StationnaryLight induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism
3 Modeling of light absorbing LCE - Time DependentDye concentration lawIsomers concentration evolution
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 15 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration lawIsomers concentration evolution
Light activation of the dyes - Mechanism
Stationnary
ϕ : concentration of dye in the materialP : photocompliance4
εlight = ϕPI(x)
Time dependent
εlight = ϕPnc(I , t)
P depends on the molecular alignment, cross link density andglass-transition temperature
4 Van Oosten, et al. Glassy photomechanical liquid-crystal networkactuators for microscale devices (EPJ E - 2007)
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 15 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration lawIsomers concentration evolution
Time dependent : dye excitation
δntδt
= −ΓInt +ncτ
nt : dye fraction oftrans-state molecules
nc : dye fraction ofcis-state molecules
I : Light intensity
Light penetrates the material and isabsorbed by the dye in trans-state.
Photon absorbed : trans → cis(excitation rate Γ)
Change of absorption (k ∝ nt)
Back relaxation : cis → trans(relaxation time τ)
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 16 / 19
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration lawIsomers concentration evolution
Time dependent - Beer absorption
τ = 0.1s ; Γ = 0.02s α = I0Γτ = 3.55W/m2 drel = 1µm
Time evolution of cis/trans isomersconcentration 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
Introduction to Liquid Crystal ElastomersModeling of light absorbing LCE - Stationnary
Modeling of light absorbing LCE - Time Dependent
Dye concentration lawIsomers concentration evolution
Transient case - Video
Infinite Waving Sheet
Jean-Christophe Lavocat Liquid Crystal Elastomer Simulations at the Microscale 18 / 19
Acknowledgement
Hao Zeng
Camilla Parmeggiani
Kevin Vynck
Giacomo Cerretti
Diederik Wiersma
Thank you for yourattention
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