esteban anoardo [email protected] · cyanobiphenyl homologous series: transition temperatures...
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NMR Relaxometry in mesogenic systemsNMR Relaxometry in mesogenic systems
Esteban [email protected]
Universidad Nacional de Córdoba and IFFAMAF - CONICET, Córdoba – Argentina
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Liquid crystals
• Thermotropics
• Lyotropics
• Biological mesophases
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Common thermotropic mesophases
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SMECTIC A
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Tilted smectic C phase
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Source: Liquid Crystals: frontiers in biomedical applications. G. P. Crawford and F. J. Woltman
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Cyanobiphenyl homologous series: transition temperatures
C5H11CN
Source: Liquid Crystals: frontiers in biomedical applications. G. P. Crawford and F. J. Woltman
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Polymeric calamitic mesophases
Source: Liquid Crystals: frontiers in biomedical applications. G. P. Crawford and F. J. Woltman
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LYOTROPICS
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Lipids
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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≡
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Liposomes
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How NMR relaxation became a relevant tool for
the study of liquid crystals?the study of liquid crystals?
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NMR Relaxation
Molecular dynamics
NMR Relaxation
Molecular order
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Dispersion law predicted by P. Pincus in 1969
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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)
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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
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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∆++=
⇑⊥
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The nematic ODF relaxation mechanism
( ) ( ) ( ) 2
´* qq´q ααα δ nnn qq=1
2
3
q αα
α τnn
t
1−=∂∂ ( ) ( )
qα
αα
ητK
=
KKK ==3
4332211 KKK ==
2KqK ≈α
( ) 2
1
1
−∝ωωJ
2,1=α
Pincus – Blinc (1969)
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Rotating-frame spin-lattice relaxation: T1ρππππ/2
P2: LOCK PULSE
FID
M
H1
M
H1
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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]
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( ) ( ) ττω ωτ deGJ iKK
−∞
∞−∫= Re
( ) ( )τ*22 0 KKK YYG =
Small angle fluctuations
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Dipolar spin-lattice relaxation: T 1D
ZLattice
T1
D
TM
T1D
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Jeener-Broekaert Pulse Sequence + field cycling
H0
H1
45y90x 45y
Dipolar Echo
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102
103
FC-JB
νννν0.5
[ms]
0,01 0,1 1 10 100100
101T1D
[ms]
Larmor Frequency [MHz]
8CB Nematic 36C
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Summarizing
T1 intra+inter
TT1ρρρρ Not sensitive to ODF
T1D Intra: ODF+rotations
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Smectic A phase
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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]
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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]
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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]
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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]
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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
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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
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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]
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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
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Lattice
TZ TD
TCR
HHHHzzzz*
HHHHDDDD*
HHHHzzzz*
HHHHDDDD*++++
Lattice
TbTD
HHHHzzzz* HHHHDDDD
*++++
Lattice
Tb TDeff
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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)
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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
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Fundamental point
MolecularOrder
MolecularDynamicsOrder Dynamics
Nuclear spinrelaxation
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The action of sound on a nematic
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30 years later..
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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=
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Acoustic term: molecular reorientation
( )2
2
1an.qQFa = ( )2
02
1n.B
µχ∆−=mF
( ) [ ]∑∑=
−=q
qn2
1
22
2
1
αα QKq
VF
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Experimental 3 mm
9 mm
SONOTRODE
SAMPLE
MAGNET
13 mm
5 mm
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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)
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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]
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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]
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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)
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Relevant features
• Ultrasound mainly interacts with ODF
• T1 dispersion is sensitive to the interaction
• Effects in the whole frequency window
• Efficient molecular reorientation
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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]
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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)
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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.]
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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]
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Lyotropic systems
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Lipids
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DMPC: 1,2-Dimyristoyl-sn-glycero-3-phosphocholine- 1 :1 in D 2O.Multilamellar
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• Order fluctuations (smectic)• Order fluctuations (smectic)
• Translationally induced rotations (diffusion on curved surfce)
• 3 rotational terms (Lorentzian)
• Lateral diffusion (Vilfan’s for smectic)
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Liposomes DMPC – D2O 100nm