Lecture II: Liquid Crystal Elastomers. Kent State University

Transcription

1 Lecture II: Liquid Crystal Elastomers Peter Palffy-Muhoray Liquid Crystal Institute Kent State University 1

2 Outline review elastomers liquid crystal elastomers & gels photoactuation, energy generation modeling & simulations summary 2

3 What to remember: order parameter ˆn lˆi 1 S Q =< (3 ˆˆ ll I) > 2 1 Q = S (3 nn ˆˆ I) 2 3

4 What to remember: free energy F L 1 T = A Q BQ + CQ + QEE o( 1).. Tc F L 1 T = a ( 1).. ( ˆ o S bs + cs + ε n E) 2 T c S T c ρu 5k B kt l NI 3 mol T 4

5 Liquid Crystal Elastomers ANISOTROPIC RUBBERS with combined features of LIQUID CRYSTALS & ELASTIC SOLIDS P.G. de Gennes, proposed by de Gennes produced by Finkelmann H. Finkelmann P.G. de Gennes, C.R. Seances Acad.Sci.218, 725 (1975) H. Finkelmann, H.J. Kock, G. Rehage, Makromol. Chem., Rapid Commun. 2, 317 (1981) 5

6 Why liquid crystals & elastic solids? both are soft liquid crystals: respond to variety of stimuli liquid (cannot support stress) elastic solids: solid (supports stress) respond to stress only -complementary! 6

7 Liquid Crystal Elastomers: Behavior monodomain nematic LCE 5cm x 5mm x 0.3mm lifts 30g wt. on heating, lowers it on cooling large strain! (400%) (H. Finkelmann) 7

8 Elastic solids: position of a material point before deformation: r position of a material point after deformation: r + R displacement vector: R strain tensor: e αβ 1 Rα = + 2 xβ R x β α 8

9 Elastic solids: for incompressible materials, the free energy density is η F = 1 2 ηe where is Young s modulus 2 η 3 2 ρckt and is the cross-link density*. ρ c 9

10 Elastic solids: for incompressible materials, the free energy density is η F ext = ηe σ e where is Young s modulus, and is the external stress. σ ext 6 η 10 Pa Theory of Elasticity, L.D. Landau and E.M. Lifshitz 10

11 Liquid crystal elastomer polymer network incorporating mesogens polymer: anisotropic random walk step length tensor: l + 2l 3 L= ( ) I+ ( l l ) Q 3 2 liquid crystal: aligning effect of polymer chain 11

12 Liquid Crystal Elastomers free energy density*: F Q.. ' = A + ε QEE γqe + ηe σ ext e sum of free energies of liquid crystal + elastic solid, γ plus new coupling term ρ Qe proportional to and to step length anisotropy c effect of strain on LC order is same as external field effect of LC order on strain is same as external stress *P.G. de Gennes, C.R. Seances Acad.Sci.218, 725 (1975) 12

13 What happens: F Q.. ' QEE Qe = A + ε γ + η changing Q applies stress, causing shape change heating causes contraction along director e σ ext e Note: γ / A ρ / ρ m c mechanical strain has same effect as strong E -field* director ˆn reorients, S changes. 13

14 Liquid Crystal Elastomers key feature: coupling between orientational order and mechanical strain f = f( Q, e ) αβ order parameter tensor αβ strain tensor 14

15 Free energy: another look F ext = aq bq + cq γqe + ηe σ e U' Qe o can also write F γ ( ) 2 = a' Q bq + cq + η e Q η SOFT ELASTICITY! 15

16 Soft Elasticity if S is constant, 1 γ 1 F = η( e S (3 nn ˆˆ I)) 2 η 2 changes in strain can be accommodated by director reorientation without energy cost stress 2 vibration damping strain L. Golubovic and T.C. Lubensky, Phys. Rev. Lett. 63, 1082 (1989) 16

17 LCE Samples 17

18 Structure If orientational order increases, expansion contraction director If orientational order decreases, contraction expansion 18

19 Composition of nematic LCE samples CH 3 Si H O n methylsiloxane monomer (main chain) O O C O OCH 3 mesogenic biphenyl (side group) O 9 9 O trifunctional crosslinker O 9 19

20 Sample preparation mix components in solvent centrifuge & evaporate solvent take out sample (partially polymerized) as solvent evaporates, polydomain nematic forms strain slightly to make sample monodomain 20

21 Appearance of nematic LCE samples birefringent sample between crossed polarizers 50mm x 5mm x.3mm samples from: H. Finkelmann, Freiburg now produced at the LCI 21

22 Strain changes optical properties changing sample shape changes Q and magnetic permeability, dielectric permittivity optical properties: cholesteric pitch cholesteric elastomer 3 λex =532nm, 35ps Light Intensity (a.u.) Wavelength (nm) -mechanically tunable PBG material -mirrorless rubber laser H. Finkelmann, S-T. Kim, A. Munoz, P. Palffy-Muhoray and B. Taheri, Adv. Mat. 13, 1069 (2001) 22

23 Effects of solvent vapors siloxane based side chain nematic LCE nematic single crystals solvent: chloroform effect: vapor reduces mesogen density: T c = ρu 5k 23

24 Effects of solvent vapors Sidechain nematic + RTV silicone bi-rubber RTV film cast on LCE films have equal thickness strong tendency to bend when exposed to solvent vapor solvent: chloroform T. Toth-Katona, P. Luchette, P. Palffy-Muhoray (unpublished) 24

25 Effects of solvent vapors hybrid aligned sample K. Harris, C. Bastiaansen, D. Broer, J. MEM Syst., 16, 480 (2007)

26 Light detection with LCEs order parameter depends on T causes strain T LCE is photomechanical transducer sensing light strain in LCE tunes Fabry-Perot cavity can be cascaded to increase sensitivity N. Dawson, M. Kuzyk, J. Neal, P. Luchette, P. P-M., Opt. Commun. 284, (2011) 26

27 Liquid Crystal Gels 27

28 LC Gels here: gel = elastomer + solvent scenarios for LC gels: LC elastomer + isotropic solvent isotropic elastomer + LC solvent LC elastomer + LC solvent 28

29 LC gels Kornfield group (Caltech) triblock copolymer long midblock with mesogenic sidechains short polystyrene endblocks dissolve in nematic LC (5CB) in isotropic phase, have isotropic solution in nematic phase, endblocks become insoluble, aggregate, forming physical crosslinks : physical gel 29

30 LC Gels isotropic nematic M.D. Kempe, N.R. Scruggs, R. Verduzco, J. Lal and J.A. Kornfield, Self-assembled liquid-crystalline gels designed from the bottom up, Nature Mat. 3, (2004) P. Palffy-Muhoray, R.B. Meyer, Liquid Crystal Gels: Bridging the experiment-theory gap, Nature Mat., 3, (2004). 30

31 LC Gels: electro optic effect 31

32 LCE Photoactuators 32

33 Mechanisms of Optomechanical Effects in LCE optomechanical coupling: light orientational order mechanical strain shape change 33

34 Effects of light on order parameter optical field changes order parameter via: direct heating absorption disruption of order photoisomerization direct optical torque angular momentum transfer from light laser p = _h λ ray indirect optical torque Landauer s blowtorch orientational Brownian ratchet no angular momentum transfer from light; light drives molecular motor table 34

35 Experimental Results (Warner et al.) azo-dye incorporated in network H. Finkelmann, E. Nishikawa, G. G. Pereira and M. Warner, Phys. Rev. Lett. 87, (2001) 35

36 Experimental Results (Warner et al.) 36

37 Experimental Results (Ikeda et al. ) Yanlei Yu,Makoto Nakano, Tomiki Ikeda, Nature 425, 125 (2003) LC + diacrylate network + functionalized azo-chromophore timescale: 10 s Yanlei Yu,Makoto Nakano, Tomiki Ikeda, Nature 425, 125 (2003) 37

38 Photoinduced Bending sample: nematic elastomer EC4OCH % dissolved Disperse Orange 1 azo dye 5mm 300µ m Response time: 70ms M. Chamacho-Lopez, H. Finkelmann, P. Palffy-Muhoray, M. Shelley, Nature Mat. 3, 307, (2004) 38

39 Dynamic Response 2.5 P = 0.6W d = 3mm 5mm 5mm 1 0 τ=75ms force (mn) log (force) time (ms) time (ms) 39

40 Photoinduced oscillations if sample bends > 90 o both sides are illuminated, producing oscillations nematic azo-elastomer sample size: 5 mm 0.8 mm 0.05 mm max. frequency = 270Hz S. Serak, N. Tabiryan, R. Vergara, T. White, R. Vaia, T. Bunning, Soft Matter 6, (2010) 40

41 Photoinduced oscillations if sample bends > 90 o both sides are illuminated, producing oscillations sunlight operation is possible! η = Pa T = C = C 8 o o 6 10, g 65, TNI 147 sample size: 5mm 0.8mm 0.05mm S. Serak, N. Tabiryan, R. Vergara, T. White, R. Vaia, T. Bunning, Soft Matter 6, (2010) 41

42 Photoinduced oscillations can it fly? -particle velocimetry to study lift of LCE wings ongoing work: T. White, AFOSR/WPAFB A. Altman, U. Dayton 42

43 Photoinduced oscillations it can swim! azo-doped nematic LCE pumps water sample size: 50mm 5mm 0.3mm J. Neal, P, Palffy-Muhoray (unpublished) 43

44 Swimming away from the light floating nematic LCE sample illuminated from above Laser beam Elastomer water container M. Chamacho-Lopez, H. Finkelmann, P. Palffy-Muhoray, M. Shelley, Nature Mat. 3, 307, (2004) 44

45 Swimming away from the light floating nematic LCE sample illuminated from above Laser beam Elastomer ethylene water glycol container M. Chamacho-Lopez, H. Finkelmann, P. Palffy-Muhoray, M. Shelley, Nature Mat. 3, 307, (2004) 45

46 Swimming away from the light floating nematic LCE sample illuminated from above Laser beam Elastomer water container M. Chamacho-Lopez, H. Finkelmann, P. Palffy-Muhoray, M. Shelley, Nature Mat. 3, 307, (2004) 46

47 the Puzzle: how does it work?? LCE is motor: motion is due to transfer of energy only, not momentum! 47

48 what happens: laser laser laser small displacement director force on water force on elastomer 48

49 Locomotion in batoid fishes Atlantic stingray. Swims by propagating waves down the pectoral fins from anterior to posterior. L.J. Rosenberger, J. Exp. Biol. 204, (2001). 49

50 Swimming dynamics elastomer swims like a fish intrinsic instability propagates wave-like deformation in elastomer system is a light-driven motor M. Chamacho-Lopez, H. Finkelmann, P. Palffy-Muhoray, M. Shelley, Nature Mat. 3, 307, (2004) 50

51 Light-driven artificial cilia non-reciprocal motion can drive current: UV & vis. responsive LC network can be printed via ink-jet technology (Fuji Dimatix) cilium in action: C. van Oosten, C. Bastiaansen and D. Broer, Nat. Mater (2009) 51

52 Thermal actuation continuous production via microfluidics uniform array of microactuators can accurately control size & cross-link density C. Ohm, C. Serra and R. Zentel, Adv. Mater. 21, (2009) 52

53 Responsive Helices tendrils of passiflora edulis liquid crystalline cellulosic fibers via electrospinning (note perversion) form adaptive non-woven mats H.M. Godinho, J. Canejo, G. Feioa and E. Terentjev, Soft Matter, 6, (2010) 53

54 Energy Conversion 54

55 Flexoelectricity the divergence of the dielectric tensor is a vector ε ~ P electric polarization if an isotropic rubber sample is deformed, ε P=0 55

56 Flexoelectricity the divergence of the dielectric tensor is a vector ε ~ P electric polarization if an isotropic rubber sample is deformed, ε P=0 if an LCE is deformed ε= ( ε I+ εq) P 0 i have giant ferroelectricity! 56

57 Giant flexoelectricity in banana LCEs banana elastomers P = ek e3 = 30 nc / m 3 J. Harden, M. Chambers, R. Verduzco, P. Luchette, J. Gleeson, S. Sprunt, A. Jakli, Appl. Phys. Lett. 96, (2010) 57

58 Solar to electrical energy conversion via LCEs dielectric tensor of LCs depends on orientational order ε= ε I+ εq i since the order parameter depends on temperature, capacitor with LCE* can act as a charge pump. V >> V 2 1 Vc low temperature Vc high temperature as T increases, ε & C decrease, Vc increases. charge is pumped from V1 to V2 ; efficiency 5%! * high dielectric breakdown T. Hiscock, M. Warner and P Palffy-Muhoray, J. Appl. Phys. (to appear). 58

59 Modeling the dynamics of nematic LCEs Order parameters: Displacement: R α () r R R ' r r ' Orientation: Q αβ () r 59

60 Strategy specify free energy density nematic + elastomer F = aβ α F( Q, R ) specify dissipation nematic + elastomer R = α ( R R Qαβ, ) x β 60

61 Strategy obtain dynamics from momentum conservation: d EKE δf δr dt R δr δr = α α α d r 0 non-conserved order parameter dynamics: δf δq αβ δr δq 3 + = αβ d r 0 61

62 Free energy: F( Q, R )? aβ α = mean field theory order parameters and vary in space Q aβ use symmetry allowed squared gradient terms R α squared gradient terms may be a problem! 62

63 Elastic free energy for isotropic polymers, distribution of separation of connected crosslinks is 2 3 Rs P( R s ) ~ exp( ) 2L L where is the chain length, and is the step length L the free energy of the polymer chain between the crosslinks is L F = kt ln P( R ) s 63

64 Elastic free energy* for anisotropic polymers, distribution of separation of connected crosslinks is the matrix of effective step lengths is anisotropic, for nematic LCEs 3 P R 2 R L R L T 1 ( s) ~ exp( s s ) L while initially, L= li+ lq L = li+ lq o o * Liquid Crystal Elastomers, M. Warner and E. Terentjev (Cambridge, 2003) 64

65 Non-local elastic free energy F 1 = ρ P( rr, ') g( r+ Rr, ' + R) d rd r' el o o is Lagrangian coordinate, r R= Rr () g( r+ Rr, ' + R) = kt ln P( r+ Rr, ' + R) 3kT g = r + R r R L r + R r R 2L ' ' 1 ' ' ( a α a α ) αβ ( β β β β ) Fel = Fel ( Rα, Qαβ ) 65

66 Non-local nematic free energy FLC = aq r bq r + cq r [ () () ().. + ( r)( ( r) ( r')) ] r r ' Q Q Q ρu d d ( r' + R' r R) Eulerian separation F = F ( R LC LC α, Q αβ ) 66

67 Rayleigh dissipation function 2R = TS = ν Q Q + (1) αβγδ αβ γδ R R ( Q Q γ + ) + x (2) α αβγδ γδ αβ xβ viscosities depend on. ν αβγδ ν Q ν αβ (3) αβγδ R x δ α β R x γ δ R = R ( R, Q LC ) α αβ 67

68 Dynamics for material points ρ Q R ν ν 2 δ F (2) γδ (3) γ α = + αβγδ + αβγδ δ Rα xβ xβ xδ R for nematic order parameter ν Q δ F = ν R (1) (2) γ αβγδ γδ γδαβ δqαβ xδ R. Ennis, L. Malacarne, P. Palffy-Muhoray, M. Shelley, 68

69 Dynamics for the surrounding fluid: Dv ρ Dt boundary conditions: = ( pi+ 2 ηd) v =0 σfl n= σel n V = v = v fl el on Ω 69

70 Simulations Mike Shelley & Wei Zhu (Courant Institute, NYU) numerical solution of coupled PDEs: spectral Chebyshev method Q ρr ν ν R 2 δf (2) γδ (4) γ α = + αβγδ + αβγδ δ Rα xβ xβ xδ ν Q δ F = ν R (1) (2) γ αβγδ γδ γδαβ δqαβ xδ 70

71 Bending 71

72 Bending 72

73 Bending 73

74 Bending 74

75 Bending 75

76 Bending 76

77 Saddle observed light induced saddle deformation want to simulate the dynamics simulation imposes temperature M. Camacho-Lopez, H. Finkelmann, P. Palffy-Muhoray, M. Shelley, Nature Mat. 3, 307, (2004) 77

78 SADDLE 78

79 SADDLE 79

80 SADDLE 80

81 SADDLE 81

82 SADDLE 82

83 SADDLE 83

84 SADDLE S y x 84

85 SADDLE 85

86 TWIST is it possible to induce spontaneous twist in a uniform achiral nematic sample with plane polarized light? 86

87 TWIST is it possible to induce spontaneous twist in a uniform achiral nematic sample with plane polarized light? illuminate (heat) along line in middle? 87

88 TWIST 88

89 TWIST 89

90 TWIST 90

91 TWIST 91

92 TWIST 92

93 TWIST 93

94 TWIST 94

95 Modelling recent papers: P. Cesana, A. DeSimone: Strain-order coupling in nematic elastomers: equilibrium configurations. Math. Models Methods Appl. Sci., 19, (2009). A. Fukunaga, K. Urayama, T. Takigawa, A. DeSimone, L. Teresi: Dynamics of electro-opto-mechanical eects in swollen nematic elastomers. Macromol. 41, (2008). T.C. Lubensky, Fangfu Ye: Elastic response and Ward identities in stressed nematic elastomers. Phys. Rev. E 82, (2010) R. Selinger, B. Mbanga, J. Selinger, Modeling liquid crystal elastomers; actuators, pumps and robots. In Emerging Liquid Crystal Technologies III, 69110A-5 SPIE (2008) Wei Zhu, M. Shelley, P. Palffy-Muhoray, Modeling and simulation on liquid crystal elastomers, Phys. Rev. E 83, (2011) 95

96 Summary 96

97 Summary LCEs combine features of LCs & elastomers key feature: coupling of orientational order & strain salient feature: responsivity temperature, light, chemicals modeling underway 97