NMR Relaxometry in mesogenic systemsNMR Relaxometry in mesogenic systems

Esteban Anoardoanoardo@famaf.unc.edu.ar

Universidad Nacional de Córdoba and IFFAMAF - CONICET, Córdoba – Argentina

Liquid crystals

• Thermotropics

• Lyotropics

• Biological mesophases

Common thermotropic mesophases

SMECTIC A

Tilted smectic C phase

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

Cyanobiphenyl homologous series: transition temperatures

C5H11CN

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

Polymeric calamitic mesophases

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

LYOTROPICS

Lipids

Fase Lα

1S >

1S ≥ Cúbica

Hexagonal invertida

Micela invertida

S < 1/3 S ~ 1 S > 1

Sν≡

Fase Lβ

Fase Lβ´

Fase Pβ´

T

1 1

3 2S≤ ≤

1S < Micelas

Hexagonal

LamelarS ~ 10

Sla

ν≡

Liposomes

How NMR relaxation became a relevant tool for

the study of liquid crystals?the study of liquid crystals?

NMR Relaxation

Molecular dynamics

NMR Relaxation

Molecular order

Dispersion law predicted by P. Pincus in 1969

Field-cycling relaxometry as a sensitive tool for

the study of molecular dynamics & order

100

0.1 1 10 100 1000 10000

10

100

Bulk 8CB

υ1/2

ISOTROPIC 323K NEMATIC 309K

T 1[ms]

νννν0 [kHz]

1 10 100 1000 1000050

60

70

80

90

323K

8CB+Aerosil 8CB Bulk

T 1[ms]

νννν0[kHz]

Anoardo-Grinberg-Vilfan-Kimmich (2004)

T1 relaxation driven by ODFT1

-1=f(J1(ω),J2(ω))

( ) ( ) ττω ωτ deGJ iKK

−∞

∞−∫= Re

K=1,2

( ) ( )τ*0 YYG = ( ) ( )[ ]τϑτθ ,gY =

C5H11CN

( ) ( )τ*22 0 KKK YYG = ( ) ( )[ ]τϑτθ ,2 gY K =

If n fluctuates around B:2

2221 ....... θθ ∝∝ YY

( ) ( ) ( ) ( ) ( )τττ +++= tntntntnG yyxx ,,,,1 rrrr

Elastic and magnetic free energy

n1:splay+bend n2:twist( ) ( ) ( ){ }2

332

222

11 .2

1nnnn.n ∧∇∧+∧∇+∇= KKKF

( ) ( ) ( ) ( ) ( ){ }* *1 1 1 2 2

, '

3, . ', , . ',

2 q q

G n t n t n t n tτ τ τ= + +∑ q q q q

2

Magnetic “orienting” term: ( )2

02

1n.B

µχ∆−=mF

( ) ( )22

121

qnqq

αα

α∑∑=

= KV

F 2

0

233

2 BqKqKKµχ

ααα∆++=

⇑⊥

The nematic ODF relaxation mechanism

( ) ( ) ( ) 2

´* qq´q ααα δ nnn qq=1

2

3

( ) ( ) ( )qq

q αα

α τnn

t

1−=∂∂ ( ) ( )

( )qq

qα

αα

ητK

=

KKK ==3

4332211 KKK ==

2KqK ≈α

( ) 2

1

1

−∝ωωJ

2,1=α

Pincus – Blinc (1969)

Rotating-frame spin-lattice relaxation: T1ρππππ/2

P2: LOCK PULSE

FID

M

H1

M

H1

100

Bulk 8CB

ISOTROPIC 323K NEMATIC 309K

Differences between rotating and laboratory-frame spin-lattice relaxation

0.1 1 10 100 1000 10000

10

10

100

10 15 20 25 30 35

ν1 [kHz]

T1

ρ[m

s]

υ1/2

T1[

ms]

ν0 [kHz]

( ) ( ) ττω ωτ deGJ iKK

−∞

∞−∫= Re

( ) ( )τ*22 0 KKK YYG =

Small angle fluctuations

Dipolar spin-lattice relaxation: T 1D

ZLattice

T1

D

TM

T1D

Jeener-Broekaert Pulse Sequence + field cycling

H0

H1

45y90x 45y

Dipolar Echo

102

103

FC-JB

νννν0.5

[ms]

0,01 0,1 1 10 100100

101T1D

[ms]

Larmor Frequency [MHz]

8CB Nematic 36C

Summarizing

T1 intra+inter

TT1ρρρρ Not sensitive to ODF

T1D Intra: ODF+rotations

Smectic A phase

0,1

1

Typical dispersion for Smectic A

1E-4 1E-3 0,01 0,1 1 101E-3

0,018CB SmA 23C

ν1

Cooling from isotropic phase Heating from 20hs at freezer temperature

T1[s

]

ν[MHz]

0,1

2.6kHz

10kHz

[s]

1E-4 1E-3 0,01 0,1 1 101E-3

0,01

424Hz

11CB SmA 55C

T1[s

]

ν[MHz]

2000

2500

3000

3500

4000

T1=(0.10185±0.00123)ms

Mag

netiz

atio

n [a

u]

0,0 0,1 0,2 0,3 0,4 0,5

0

500

1000

1500

10kHzT

1=0.101 (0.79%)

Mag

netiz

atio

n [a

u]

Evolution Time [ms]

600

800

1000

1200 11CB SmA 55C

Pol=5MHz - Slew=4MHz/ms

T1=(0.00364±0.00176)s

Mag

netiz

atio

n [a

u]

0,00 0,02 0,04 0,06 0,08 0,10 0,120

200

400

100HzT

1=0.0036 (47%)

Mag

netiz

atio

n [a

u]

Evolution Time [s]

Magnetization evolution including local field effect s

( ) ( )( ) ( )0

1

1exp exp cos exp

CR D

KM M A B K

A B T T T

τ τ ττ ωτ − = − − + + − +

• K: number of spin evolving in non-adiabatic way

• A: adiabatic spins subjected to cross relaxation• A: adiabatic spins subjected to cross relaxation

• B: adiabatic spins relaxing directly

• Tcr: cross relaxation time

• Td: damping time of the oscillations

• ωωωω: characteristic frequency

L. Aguirre and E. Anoardo, unpublished

0.01

0.1

11CB 328K

T 1[s]

False dispersions

10-2

10-1

2x10-1

10-1

a8CB 295K

P=0 P=13.5 W/cm2

P=22.5 W/cm2

b8CB 301K

[s]

1E-4 1E-3 0.01 0.1 1 101E-3

Bp=10MHz, S

l=12MHz/ms

Bp=5MHz, S

l=12MHz/ms

Bp=5MHz, S

l=4MHz/ms

νννν[MHz]

10-2

10-3 10-2 10-1 100 10110-2

10-1

P=0

P=13.5 W/cm2

P=22.5 W/cm2

c

8CB 323.3K P=0

P=13.5 W/cm2

P=22.5 W/cm2

T 1 [s]

νννν [MHz]

Anoardo-Bonetto-Kimmich (2003)

326K – 330,5K

294,5K – 306,5K

1 10 100 1000 10000

0.01

0.1

ν [kHz]

A

ν0.5

Bulk 8CB

ISOTROPIC 323K NEMATIC 309K SMECTIC A 303K

T1 [

s]

Extreme conditions

0 50 100 150 200 250 3000.0

0.2

0.4

0.6

0.8

1.0

1 10 100 1000 10000

B

ν0 [kHz]

30kHz 20kHz

8CB SmA 303K

Mag

netiz

atio

n [a

u]

Evolution time [ms]

Cross Relaxation between Zeeman and Dipolar systems in the rotating frame.

P1: ππππ/2 (∆∆∆∆t)

P2: SPIN-LOCK PULSE

FID

A

Z

B BZ

C

YY

X

Beff

M (δt)

M (0)

B1(π/2)

BLz

B

M (δt)

M (δt+T2ρ)

B1(Lock)

BLz

Beff

X

C

Lattice

TZ TD

TCR

HHHHzzzz*

HHHHDDDD*

HHHHzzzz*

HHHHDDDD*++++

Lattice

TbTD

HHHHzzzz* HHHHDDDD

*++++

Lattice

Tb TDeff

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 BL and a. The values of T are 100ms for 5CB and 120ms for 8CB.

1

Sig

nal i

nten

sity

[u.a

.] 5CB

1

8CB

10 20 30 40

0,1

Sig

nal i

nten

sity

[u.a

.]

frequency νννν1 [kHz]

T=25ºC BL=(4.3±0.2) kHz, a=(150±75)

T=29ºC BL=(3.7±0.2) kHz, a=(500±300)

T=33ºC BL=(3.6±0.2) kHz, a=(250±140)

10 20 30 40

0,1

frequency νννν1 [kHz]

T=34ºC BL=(5.2±0.1) kHz, a=(90±20)

T=36ºC BL=(4.7±0.1) kHz, a=(300±114)

ISOTROPIC

T1 as an “order sensor”

0,01

0,1

Mag

netiz

atio

n de

cay

as e

xpon

entia

l [s]

A

8CB

NEMATIC 309K ISOTROPIC 323K

NEMATIC

SMECTIC A1E-4 1E-3 0,01 0,1 1 101E-3

0,01

0,1

1E-4 1E-3 0,01 0,1 1 10

0,01

B

8CB SmA 296K

Mag

netiz

atio

n de

cay

as e

xpon

entia

l [s]

νννν0 [MHz]

ISOTROPIC 323K

T1 region

Fundamental point

MolecularOrder

MolecularDynamicsOrder Dynamics

Nuclear spinrelaxation

The action of sound on a nematic

30 years later..

Acoustic-Director fields interaction

2int

2 2

1( )

21

. cos ( )2 a

V Q

Q q θ α

=

= −

an.qθ

α

n

. cos ( )2 aQ q θ α= − α

qa

Bonetto-Anoardo-Kimmich (2002)

Selinger-Spector-Greanya-Weslowski-Shenoy-Shashidhar (2002)

03

2 IQ

v

ξρ=

Acoustic term: molecular reorientation

( )2

2

1an.qQFa = ( )2

02

1n.B

µχ∆−=mF

( ) [ ]∑∑=

−=q

qn2

1

22

2

1

αα QKq

VF

Experimental 3 mm

9 mm

SONOTRODE

SAMPLE

MAGNET

13 mm

5 mm

1

2

0.1

0.2 T 1 [

s]

No-sound P=13.5W/cm2 P=22.5W/cm2

Effect of sonication in standard nematics

15k 100k 1M 5M0.04

0.1

100k 1M 5M 100k 1M 5M0.02

PAA394 K

5CB301 K

Larmor Frequency [Hz]

8CB310 K

Bonetto-Anoardo-Kimmich (2003)

Magnetically ordered state

0,1

5CB 303K

T1[s

]

OFF ON ON-M 25Hz

( )2

2 2

1

1

2F Kq Q

V αα =

= − ∑∑q

n q

0,01 0,1 1 10

CASE I

ν0 [MHz]

Acoustically ordered state

0,1

5CB 300K OFF ON ON-M 25Hz

MEMORYOF ACOUSTIC

ORDER

0,01 0,1 1 100,01

CASE II 1 10

10

Mag

netiz

atio

n de

cay

[ms]

ν0 [kHz]

OFF ON-M 25Hz

T1[s

]

ν0 [MHz]

Comparison with angle-dependent field-cycling NMR relaxometry

10

Mag

netiz

atio

n de

cay

[ms]

3.25W/cm2 fm=27Hz

no sound

1 10

5CB 27CMag

netiz

atio

n de

cay

[ms]

f [kHz]

Struppe - Noack (1996)

Relevant features

• Ultrasound mainly interacts with ODF

• T1 dispersion is sensitive to the interaction

• Effects in the whole frequency window

• Efficient molecular reorientation

0.1

11CB 328K[s

]

1E-4 1E-3 0.01 0.1 1 101E-3

0.01

Bp=10MHz, S

l=12MHz/ms

Bp=5MHz, S

l=12MHz/ms

Bp=5MHz, S

l=4MHz/ms

T 1[s]

νννν[MHz]

1E-3 0.01 0.1 1 100.01

0.1

8CB 301K

T1 [s

]

Pow er [W/cm 2] 0 13.5 22.5

Sonication effect at low frequencies

1E-3 0.01 0.1 1 10

0.1

1E-3 0.01 0.1 1 10

11CB 328.6K

ν [MHz] Anoardo – Bonetto –Kimmich (2003)

Effects of sound in the smectic A phase

101

102

103

6x103

Perpendicular

[a.u

.]

100

200

Perpendicular

Smectic Model

[a.u

.]

100

104 105 106 107

100

101

102

103

6x103

Parallel

Simplified Model

ν [Hz]

T1

[a.u

.]

10

103 104 105 106 107

4

10

100

200

Parallel

ν [Hz]

T1[a

.u.]

0.10.04

0.1

Model

T 1 [s]

• Smectic-model

•qa \\ n

The sound allows to display ODF

10k 100k 1M 10M0.04

P=0 P=13,5W/cm2

P=22.5W/cm2

8CB 295 K

Larmor Frequency [Hz]

Lyotropic systems

Lipids

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

• Order fluctuations (smectic)• Order fluctuations (smectic)

• Translationally induced rotations (diffusion on curved surfce)

• 3 rotational terms (Lorentzian)

• Lateral diffusion (Vilfan’s for smectic)

Liposomes DMPC – D2O 100nm