Esteban Anoardo Universidad Nacional de Córdoba and IFFAMAF - CONICET, Córdoba Argentina

Transcription

1 NMR Relaxometry in mesogenic systems Esteban Anoardo Universidad Nacional de Córdoba and IFFAMAF - CONICET, Córdoba Argentina

2 Liquid crystals Thermotropics Lyotropics Biological mesophases

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4 Common thermotropic mesophases

5 SMECTIC A

6 Tilted smectic C phase

7 Source: Liquid Crystals: frontiers in biomedical applications. G. P. Crawford and F. J. Woltman

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9 Cyanobiphenyl homologous series: transition temperatures CN C5H11 Source: Liquid Crystals: frontiers in biomedical applications. G. P. Crawford and F. J. Woltman

10 Polymeric calamitic mesophases Source: Liquid Crystals: frontiers in biomedical applications. G. P. Crawford and F. J. Woltman

11 LYOTROPICS

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14 Lipids

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16 S < 1/3 S ~ 1 S > 1 S >1 Micela invertida Hexagonal invertida Fase L α Fase P β S ν la 0 S 1 S ~ 1 Cúbica Lamelar T Fase L β 1 1 S 3 2 Hexagonal Fase L β S < 1 Micelas

17 Liposomes

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19 How NMR relaxation became a relevant tool for the study of liquid crystals?

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21 Molecular dynamics NMR Relaxation Molecular order

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25 Dispersion law predicted by P. Pincus in 1969

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27 Field-cycling relaxometry as a sensitive tool for the study of molecular dynamics & order Bulk 8CB ISOTROPIC 323K NEMATIC 309K T 1 [ms] CB+Aerosil 8CB Bulk T 1 [ms] 10 υ 1/ K ν 0 [khz] ν 0 [khz] Anoardo-Grinberg-Vilfan-Kimmich (2004)

28 T 1 relaxation driven by ODF T 1-1 =f(j 1 (ω),j 2 (ω)) J K ( ω) ( τ ) i = Re G e ωτ dτ K CN K=1,2 C5H11 [ τ ϑ τ ] ( 0) * G = Y Y ( τ ) Y = g θ ( ), ( ) K K 0 2K 2K 2 g If n fluctuates around B: Y θ... Y θ G ( τ ) = n ( t) n ( t + τ) + n ( t) n ( t + τ) r r r r 1,,,, x x y y

29 Elastic and magnetic free energy 3 G ( τ ) = n ( q t) n * ( q t + τ ) n ( q t) n * ( q t + τ ) {,. ',,. ', } q, q ' n 1 :splay+bend n 2 :twist F 1 = K 2 { ( ) ( ) ( ) 2 } 2 2 K n + K n. n + n n 33 Magnetic orienting term: ( ) 2 F m = 1 2 χ µ 0 n.b F 2 1 = K 2V q α = 1 α ( q) n ( q) 2 α K 2 2 α = Kααq + K33q χ + B µ 0 2

30 The nematic ODF relaxation mechanism n t ( ) * q n ( q ) = ( q ) 2 α α δ qq n α n α ( q) = τ K = K = K Kα Kq Pincus Blinc (1969) α 33 1 ( q) n α ( q) J 1 τ α ( q) = α =1,2 η K α α 1 ( ω) ω 2 ( q) ( q)

31 Rotating-frame spin-lattice relaxation: T 1ρ π/2 P2: LOCK PULSE FID M M H 1 H 1

32 Differences between rotating and laboratoryframe spin-lattice relaxation 100 Bulk 8CB ISOTROPIC 323K NEMATIC 309K T 1 [ms] υ 1/2 ν 1 [khz] T 1ρ [ms] ν 0 [khz]

33 J K i ( ω ) = Re G ( τ ) e ωτ dτ K G = K Y * ( ) Y ( τ ) 2 K 0 2 K Small angle fluctuations

34 Dipolar spin-lattice relaxation: T 1D Z T 1 Lattice T M D T 1D

35 Jeener-Broekaert Pulse Sequence + field cycling H 0 H 1 90 x 45 y 45 y Dipolar Echo

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37 10 3 FC-JB 10 2 ν 0.5 T 1D [m ms] CB Nematic 36C ,01 0, Larmor Frequency [MHz]

38 Summarizing T 1 intra+inter T 1ρ Not sensitive to ODF T 1D Intra: ODF+rotations

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41 Smectic A phase

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45 Typical dispersion for Smectic A 0,1 T 1 [s] 0,01 ν 1 8CB Sm A 23C 1E-3 Cooling from isotropic phase Heating from 20hs at freezer temperature 1E-4 1E-3 0,01 0, ν[mhz]

46 10kH z 0,1 2.6kH z T 1 [s] 0,01 424H z 1E-3 11CB SmA 55C 1E-4 1E-3 0,01 0, ν[mhz]

47 Magnetiz zation [au] T 1 =( ± )ms kHz T 1 =0.101 (0.79%) 0,0 0,1 0,2 0,3 0,4 0,5 Evolution Time [ms]

48 CB SmA 55C Magneti ization [au] Pol=5MHz - Slew=4MHz/ms T 1 =( ± )s Hz T 1 = (47%) 0,00 0,02 0,04 0,06 0,08 0,10 0,12 Evolution Time [s]

49 Magnetization evolution including local field effects ( 1 K ) ( ) M ( ) M 0 exp τ Aexp τ τ B K cos( ωτ ) exp τ = A B T T CR T + D K: number of spin evolving in non-adiabatic way A: adiabatic spins subjected to cross relaxation B: adiabatic spins relaxing directly Tcr: cross relaxation time Td: damping time of the oscillations ω: characteristic frequency L. Aguirre and E. Anoardo, unpublished

50 False dispersions 11CB 328K 2x CB 295K a T 1 [s] CB 301K P=0 P=13.5 W/cm 2 P=22.5 W/cm 2 b E-3 B p =10MHz, S l =12MHz/ms B p =5MHz, S l =12MHz/ms B p =5MHz, S l =4MHz/ms 1E-4 1E T 1 [s] P=0 P=13.5 W/cm 2 P=22.5 W/cm 2 c ν[mhz] 326K 330,5K CB 323.3K P=0 P=13.5 W/cm 2 P=22.5 W/cm ν [MHz] Anoardo-Bonetto-Kimmich (2003) 294,5K 306,5K

51 Extreme conditions 0.1 Bulk 8CB T 1 [s] 0.01 ν 0.5 ISOTROPIC 323K NEMATIC 309K SMECTIC A 303K A ν 0 [khz] Magnetization [au] CB SmA 303K 30kHz 20kHz Evolution time [ms] B

52 Cross Relaxation between Zeeman and Dipolar systems in the rotating frame. P1: π/2 ( t) A P2: SPIN-LOCK PULSE FID Z M(0) B Z B eff C B Lz B Lz M(δt+T 2ρ ) M(δt) X B eff B 1 (π/2) Y X B 1 (Lock) M(δt) Y

53 T CR H z * H D * T Z T D Lattice H * z + H * D H z * H D * + T b T D T b T D eff Lattice Lattice

54 Experimental. The existence of the cross relaxation was verified in the nematic phase of two liquid crystals at different temperatures. The two free parameters are B L and a. The values of T are 100ms for 5CB and 120ms for 8CB. 1 1 Signal intensity [u.a.] 0,1 5CB T=25ºC B L =(4.3±0.2) khz, a=(150±75) T=29ºC B L =(3.7±0.2) khz, a=(500±300) T=33ºC B L =(3.6±0.2) khz, a=(250±140) 0,1 8CB T=34ºC B L =(5.2±0.1) khz, a=(90±20) T=36ºC B L =(4.7±0.1) khz, a=(300±114) frequency ν 1 [khz] frequency ν 1 [khz]

55 T 1 as an order sensor 0,1 8CB A ISOTROPIC Magnetization decay as exp ponential [s] NEMATIC 309K 0,01 ISOTROPIC 323K 1E-4 1E-3 0,01 0, B 0,1 T 1 region 0,01 8CB SmA 296K NEMATIC 1E-3 1E-4 1E-3 0,01 0, ν 0 [MHz] SMECTIC A

56 Fundamental point Molecular Order Molecular Dynamics Nuclear spin relaxation

57 The action of sound on a nematic

58 30 years later..

59 Acoustic-Director fields interaction V int = 1 Q ( n.q ) 2 a 2 n θ 1 Q. q 2 cos 2 ( θ α ) a = α 2 Q = ξρ 2 I v 0 3 q a Bonetto-Anoardo-Kimmich (2002) Selinger-Spector-Greanya-Weslowski-Shenoy-Shashidhar (2002)

60 Acoustic term: molecular reorientation 1 ( ) 2 1 χ F a = Q n.q ( ) 2 a F m = n.b 2 2 µ 0 F = 1 2V q 2 α = 1 n α ( ) 2[ ] q Kq 2 Q

61 9 mm Experimental SONOTRODE 3 mm MAGNET SAMPLE 5 mm 13 mm

62 Effect of sonication in standard nematics 2 1 No-sound P=13.5W/cm 2 P=22.5W/cm T 1 [s] 0.1 PAA 394 K k 100k 1M 5M 5CB 301 K k 1M 5M 100k 1M 5M Larmor Frequency [Hz] 8CB 310 K Bonetto-Anoardo-Kimmich (2003)

63 Magnetically ordered state 0,1 OFF ON ON-M 25Hz 5CB 303K T 1 [s] CASE I 0,01 0, ν 0 [MHz] F = nα ( q ) Kq Q 2V q α = 1

64 Acoustically ordered state 0,1 OFF ON ON-M 25Hz 5CB 300K MEMORY OF ACOUSTIC ORDER T 1 [s] CASE II Magnetization decay [ms] ν 0 [khz] OFF ON-M 25Hz 0,01 0,01 0, ν 0 [MHz]

65 Comparison with angle-dependent fieldcycling NMR relaxometry 3.25W/cm 2 f m =27Hz no sound Magn netization decay [ms] 10 5CB 27C 1 10 f [khz] Struppe - Noack (1996)

66 Relevant features Ultrasound mainly interacts with ODF T 1 dispersion is sensitive to the interaction Effects in the whole frequency window Efficient molecular reorientation

67 11CB 328K 0.1 T 1 [s s] 0.01 B p =10MHz, S l =12MHz/ms B p =5MHz, S l =12MHz/ms B p =5MHz, S l =4MHz/ms 1E-3 1E-4 1E ν[mhz]

68 Sonication effect at low frequencies 0.1 8CB 301K T 1 [s] 0.01 Pow er [W /cm 2 ] E CB 328.6K 1E ν [M Hz] Anoardo Bonetto Kimmich (2003)

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71 Effects of sound in the smectic A phase 6x Perpendicular 100 Smectic Model 10 2 Perpendicular 10 1 T 1 [a a.u.] 10 0 Simplified Model 6x T 1 [a a.u.] Parallel 10 2 Parallel ν [Hz] ν [Hz]

72 0.1 Smectic-model q a \\ n Model The sound allows to display ODF T 1 [s] CB 295 K P=0 P=13,5W/cm 2 P=22.5W/cm 2 10k 100k 1M 10M Larmor Frequency [Hz] 0.04

73 Lyotropic systems

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75 Lipids

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78 DMPC: 1,2-Dimyristoyl-sn-glycero-3-phosphocholine- 1:1 in D 2 O. Multilamellar

79 Order fluctuations (smectic) Translationally induced rotations (diffusion on curved surfce) 3 rotational terms (Lorentzian) Lateral diffusion (Vilfan s for smectic)

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81 Liposomes DMPC D 2 O 100nm