Ferro-electric SmC* elastomers Mark Warner Cavendish Laboratory, Cambridge. Rubber, Liquid Crystal Elastomers what is unusual about solid liquid crystals? Nematic: thermal and optical elongation (I to N) Smectic A: thermal and optical shears (A to C), mechanics, 2-D rubber, electro-mechano-clinic effect Smectic C*: soft ferro-electric solids, director rotation and mechanics Niagara, August, 2011
1 Classical Rubber Constant volume Poisson ratio = 1/2 polymer chains mean shape isotropic crosslink block of rubber deformed spans deform too: step length of random walk arc length of chain 1 distribution of chains distorted entropy lowered (heat released) free energy rises maximum entropy (disorder) (demo: stretch long rubber strip) Rubber locally liquid. Accessible entropy of chains exploring configurations.
Free energy density geometry squares of distortions: Hooke s law. # strands/vol shear modulus - energy scale ~10 5 J/m 3 1 entropy unit per strand x geometry No chemistry! Same physics as perfect gas. Modulus same magnitude but penalises shape, not volume. Entanglements, dangling ends, Mooney-Rivilin neglect Hyperelastic: ; const. volume. Distortions huge non-linear elasticity.
Nematic Polymers have natural shape anisotropy. O-C 6 H 13 Pendant mesogens (side chain nematic polymers) Silicone rubber (CH 2 ) 10 O Mesogens in back-bone (main chain nematic polymers) O Si N O O O O O O O (CH 2 ) 8 N O-C 6 H 13 Rods order nematically, induce shape change in backbones.
Nematic polymers - anisotropic random walks Gaussian distribution, mean shape: prolate spheroid Shape anisotropy Shape matrix Nematic order distorts molecular shape, molecular shape drives rubber elasticity. Crosslink nematic polymers to form nematic elastomers Monodomains 20cm x 1.5cm x (1mm 0.1µm) perfect order, transparent, birefringent Change order by heating, light or solvent. H Finkelmann
Solid liquid crystals give new phenomena: (i) order parameter change [heat, light, solvent] director rotation [light, electric fields] (ii) stress} LC strain mechanical response Applications Sensing chemical, mechanical, bio-medical Micro & nano actuation, microfluidic pumps, valves, mixers Cholesterics mechanically tuneable photonic solids; mirrorless, tuneable lasers. Chiral separation. Smectics soft ferro-electrics,.... } director & order, polarisation response (piezo and flexo-electric response) It is a truth universally acknowledged, that materials in possession of many new phenomena must be in want of applications. (Jane Austin, P&P, 1813)
Nematic Rubber (rods not shown) block of rubber 1 spans deform: crosslink anisotropic chains Deformation gradient tensor
Energy of Nematic Rubber number density of strands Example: initial shape current shape/direction energy scale 10 5 J/m 3 initially isotropic Isotropic anisotropy: Nematic - change order & molecular shape macroscopic shape
Roughly 300% strains. Temperature changed by hot air blower. Monodomain elastomer. Close to real-time movement. Tajbakhsh and Terentjev Cavendish Laboratory 2 3.5 film 3 Strain L/L 0 2.5 2 1.5 1 20 40 60 80 100 120 Temperature ( C) Cross-section ~2mm 2 Load=15g Load=10g Load=5g No Load 6
Reduce order by bending some rods - Photo alternative to thermal disruption of order. Thermal or optical change Absorb photon into dye molecule Azo benzene trans isomer (straight) Recovery thermal or stimulated cis isomer (bent)
Inhomogeneous optical strains light E Photo-bending of polydomain nematic glass sheets (Yu, Nakano & Ikeda, 03) Absorption: higher intensity at front face film
Tabirian, Bunning, White (translate beam) film Monodomain nematic cantilever bends where beam strikes it. Horizontal narrow light beam from left, polarised along cantilever (also n). Point of bend moved up and down changes frequency. Seems to be limited by inertia rather than photo-mechanics.
Rotation of director profound mechanical effect. extend perpendicular to n 0 force/area Low energy cost since rotate rather than distort distribution of nematic chains; no change in entropy, no change in LC order. (expect this when rotate director on cone in SmC) Extent of response related to spontaneous elongation. (Finkelmann)
Opto-mechanical experiment (Finkelmann et al, Terentjev et al, Zubarev et al, Urayama) rotation universal from Director rotation stretch perpendicular original director rotation and plateau to
Deformations in practice (Quasi-convexification) Stripes Replace gross deformations by microstructure of (soft) strains with lower energy which satisfies constraints in gross sense. Macroscopic extension (crossed polars) Kundler & Finkelmann Zubarev et al Terentjev et al
Length scales Elastic versus Frank: nematic penetration depth Distance over which director varies to give same elastic and Frank energy densities where Interfacial thickness in textures small and textures coarsened immediately. [q.v. Lagerwall for SmC*]
Smectic A free energy density Underlying nematic Smectic layer spacing Director tilt penalty Material vectors and plane normals deform differently x v embedded vectors Two types of smectic elastomers (a) Layers anchored in solid matrix (b) Layers ghosts in solid matrix k θ n Weilepp and Brand, 1998 W & T, 1994 (linear theories) k embedded planes Case (a) new layer spacing v
Smectic A elastomers rubbery in 2D, solid in 3 rd D Make into rubber as before. Layers can be plane of film or perpendicular. [case (a)] k n z λ zz x λ xx λ xz 10 7 J/m 3 10 5 J/m 3 rotation n = 0.5, 0.5 n = 1, 0 λ zx 2-D rubber mechanics + possibility to rotate layer planes 1-D solid mechanics (strong coupling of layers to chains)
Anisotropy of mechanical response (Smectic dominates rubber) 80 σ (kpa) 60 z 40 x Finkelmann σ 20 0 L/LO 0 0.05 0.1 0.15 0.2 0.25 σ Extension along layer normal Smectic energy scale n = 0.5, 0.5 Eventually unstable Extension in plane rubber energy scale x z n = 1, 0
Clarke-Meyer-Helfrich-Herault Instability 150 125 σ nom (kpa) 100 75 50 (theory) In-plane shear cheaper 25 n = 0.5, 0.5 0 1.00 1.05 1.10 1.15 1.20 1.25 50 λ zz d o d o /cosθ θ L z φ 40 30 20 θ from X-rays Textured lower energy strains in conflict with BCs 10 0 0 0.1 0.2 0.3 0.4 0.5 0.6 ε
Shear SmA in layer plane see weak rotation of director mechano-clinic effect Kramer and Finkelmann non-linear elasticity theory, Lubensky et al Also giant electro-mechano clinic effect in SmA* (Lehmann, Kremer,... Nature, 2001) Smectic A liquid effects found in soft solids, with additional mechanical complexion actuation, adaptive optics,...
Making Smectic C monodomain elastomers st 1 deformation Electric field nd (b) (a) 2 deformation θ (a) 2-stage crosslinking with stretches; Finkelmann & Benne (1994) (b) Photo crosslink SmC* in E field, bookshelf geometry; Zentel, Brehmer (1994) (c) Blow bubbles; Schuring, Stannarius, et al (2001) (d) Free standing liquid films with E field, then crosslink; Gebhard, Brehmer, et al (1998, 2001) (e) In-plane shears of SmA sheets, then second linking; Hiraoka & Finkelmann (2005) All unwound in SmC* case.
Smectic C elastomers Spontaneous shears of smectic sheet (also possible with slab) SmC cool SmA 25ºC 90ºC 130ºC q E q E L E L E layers n k (Hiraoka and Finkelmann, 2005) SmC* unwound since formed in SmA* phase elastic cost of winding too high.
Transition SmA to SmC elastomer Spontaneous distortion is now a shear L ~ 0.4 Actuation and soft elasticity as before based on shear. SmA cool SmC* Stannarius,et al (2005), LCE Unwound SmC* ( ferro-electric ). Highly responsive films strain from stress, electric field, light, heat, chiral solvent.
Photo-ferroelectric-electroclinic-elastic effect? (Giesselmann et al, liquid SmC*) SmC* SmA* Light remove tilt and P mechanical strain from opto-clinic response??
Slab geometry for SmC* solid Apply shear -2L. Rotate n about k by 180 degrees. Reverse polarisation Notionally no elastic cost as in nematic shape response Film bistable, textures?? How achieve?
Rotate director by f on cone about layer normal k z y x anti-clockwise, f > 0 k f = p ±2π/3 ±π/2 f = 0 ±π clockwise, f < 0 Suitable director rotations cost no elastic energy, but don t obey boundary conditions e.g. no bulk yz-shear:
Textures: impose alternate shears and φ-rotations in laminates suppress other shears λ yz λ yz y z x λ xz λ xz +λ yz +λ yz No bulk ; best can do for slab. Can do better for sheet.
Obey boundary conditions e.g. no macro-shear except imposed get laminates (not aligned with layers) ±π ±2 π /3 ±π/3 φ=0 k 0 χ s f P shear complete P reversed rotation complete z y x P _ + + + + P Laminates rotated by ξ about y. Layers cut by laminates, internal surfaces charged P Layers don t rotate
Summary Nematic and Smectic Elastomers Free-standing or on substrate, sheets or slabs Reactive to heat, light, electric field multi-actuation Spontaneous elongation (N), shear (SmC) Rotation of optical axis (and polarisation) makes strain cheaper Softer elasticity by director rotation Low cost elasticity in SmC microstructures (when constraints) SmC* soft, ferro-electric solid