liquid crystal elastomer simulations at the microscale

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



Liquid Crystal ElastomerActuation mechanismsApplications

Table of Content








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





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





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





Light activation of LCE

It is also possible to excite the material with photons.

By absorbing UV photons, the LCE changes shape





Parameters

High Frequency Photodriven Oscillator3

3 White et al. High frequency photodriven polymer oscillator (SoftMatter - 2008)




Light induced deformationEM Field - Beer Absorption LawEM Field - Maxwell formalism

Table of Content








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





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)





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





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





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





Beer Law : Absorption length’s effet

0 1 2 3

2

4

6Bending Radius : Uniaxial vs Splay


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





EM field - Effect due to absorption

Maxwell equations - I0=30 W/cm2

Steady state

Absorption due to thematerial

Reflexions at the boundaries





EM field - Effect due to absorption

0 1 2 3

2

4Bending Radius in function of absorption length


Ben

ding

Rad

ius

(cm

)

TheoreticalFEM Simulation − Maxwell

Maxwell equations - I0=30 W/cm2

Steady state

Absorption due to thematerial






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





Dye concentration lawIsomers concentration evolution

Table of Content








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)





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)





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.





Transient case - Video

Infinite Waving Sheet


Acknowledgement

Hao Zeng

Camilla Parmeggiani

Kevin Vynck

Giacomo Cerretti

Diederik Wiersma

Thank you for yourattention

liquid crystal elastomer simulations at the microscale

Science

light nature

micro actuatorslce

potential artificial

van oosten

thedark nature

artificial cilia

potential micropumps

photomobile polymer