esteban anoardo anoardo@famaf.unc.edu · cyanobiphenyl homologous series: transition temperatures...
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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
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)
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
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