Transcript Diapositiva 1

6.1
Low Field Nuclear Magnetic Resonance
High Field (Resolution) NMR:
7.5 T < B < 37 T
Low Field (Resolution) NMR:
0.37 T < B < 2.43 T
Study of chemical structures,
reactions (only solution)
Study of physical structures
(solid, liquid, gel, solution,
suspension, emulsion)
Hydrogen
mi (permanent magnetic momentum)
B0 = 0
N
M   μi  0
i 1
B0 ≠ 0
n 0 = g B0
n0 = Larmor frequency (Hz)
g = hydrogen giromagnetic ratio
(2.67*108 rad/Ts)
N
M   μi  0
i 1
B0 ≠ 0
B0
Z
B1
t = t0 - - - > B1 >> B0
Y
N
M   μi  0
i 1
M XY  0
MZ  0
X
t = t1 > t0 - - - > B1 = 0
B0
Z
120
100
Relaxation (T1)
Mz/M0
M /M 0
80
X60
Mxy/M0 Relaxation (T2)
40
20
0
0
Y
500
1000
t (ms)
1500
2000
Determination of T2i
60
Discontinuous spectrum
50
A1
N
I   Ai * e
80
70
I
40
30
30
A3
20
A2
Data Fitting
i 1
50
T2i 
10
T2max
 a T e
t T2 
2
A4
0
dT2
0
500
1000 1500
T 2(ms)
2000
2500
T2min
20
10
Continuous spectrum
BA3
A
0.4
0
2000
4000
6000
time(ms)
8000
10000 12000
0.35
4
0.3
0.25
0.2
2
0
Intensity
a(T ) (a.u)
Intensity (%)
60
 t
Ak %
40
0.15
C D
A2
0.1
A1
0.05
0
10
100
1000
T 2(ms)
10000
Effect of environment on T2
PORES CONFINED WATER
x
x
HOMOGENEOUS
HYDROGEL
EXTERNAL
WATER
“Free” water molecules:
LONG RELAXATION TIME (T2)
T2 ~ 2200 ms (25°C)
WATER MOLECULE =
“Bound” water molecules:
SHORT RELAXATION TIME (T2)
T2 ≤ 300 ms
It can be demonstrated1 that T2 f(x)
TWO FRACTION – FAST EXCHANGE MODEL2
1) Diffusion between bulk and surface
much faster than relaxation
fb
fs
1


T2 T2b T2s
x
T2b
2) If fb ≈ 1 and fs ≈ 0
T2s
Water molecule
T2  kξ
3) T2 << T2b (≈ 2200
ms T = 25°C, B =
0.47 tesla)
f b  fs  1
(x > 10 nm)
1
1
1


T2 T2b kξ
 1
1
T2  1 
 
 T2b kξ 
2200
2000
1800
1600
k  T2av ξ av  500ms / 50mm
T2  kξ
 1
1
T2  1 
 
 T2b kξ 
T2(ms)
1400
1200
1000
  1
1  
  13ms / mm
k  1  ξ av 


  T2av T2b  
800
600
400
T2b = 2200 ms
200
0
0
100
200
300
x(mm)
400
500
600
700
k determination
kξ max
T2 max
T2 
 aT2 *T2 * dT2
T2 min
T2 max
 aT * dT
2
T2  kξ


kξ min
kξ max
k
2
 aξ * dξ
kξ
kξ min
T2 min
Mesh size distribution
10
9
8
7
6
5
4
3
2
1
0
P( x)
kT2 ξ
 aξ * ξ * dξ
k2
1
3
xnm)
5
7
ξ
B0
determination: gradient test
B1(p/2)
B1(p)
B0
Signal intensity
(A0)
t(ms)
t
B0
B1(p)
t
B1(p/2)
B1(p)
gradient
gradient
Signal intensity
(A)
t(ms)
t
d
D
d
B1(p/2)
n0 = g B(x) B0
n0 = g B(x) B0
phase shift
still present
phase shift
zeroed
B1(X)
B1(p)
NO H DIFFUSION
B1(X)
B1(p)
H DIFFUSION
n0 = g B(x)
n0 = g B(x)
phase shift
phase shift
It can be demonstrated that the following relation holds2:
Ln(A/A0) = -g2 D d2 (D - d/3) G2
A = signal intensity with gradients
A0 = signal intensity without gradients
D = water molecules self diffusion coefficient
g = hydrogen giromagnetic ratio
d = gradient duration
D = intergradient separation
G = gradient intensity (T/m)
D can be determined as a function of the diffusion time td = D-d/3
It can be demonstrated that the for small td, the following relation
holds3:
Dtd 
4
 1
D0
9 π
6
D0td
ξ
Dtd 
4
 1
D0
9 π
6
D0td  BD0t
ξ
td
= diffusion time (= D-d/3)
D(td) = water self diffusion coefficient inside the hydrogel at td
D0 = water self diffusion coefficient
Latour4 proposed the following expression holding for every td
 1  td
C t d  1  
Dtd 
θ
 1

 1  1  
D0
   1  1   C t  1  1  t d




d
 
 θ
C
4
9 π
6
D0td
ξ
= characteristic time
 = network tortuosity
2.60E-09
 =2
=1
2.40E-09
300 micron
30 micron
3 micron
0.3 micron
2.20E-09
D(m2s-1)
2.00E-09
1.80E-09
1.60E-09
1.40E-09
1.20E-09
1.00E-09
0
0.05
0.1
0.15
td 0.5(s0.5)
0.2
0.25
2.60E-09
 = 1.1
=1
2.40E-09
300 micron
30 micron
3 micron
0.3 micron
2.20E-09
D(m2s-1)
2.00E-09
1.80E-09
1.60E-09
1.40E-09
1.20E-09
1.00E-09
0
0.05
0.1
0.15
td 0.5(s0.5)
0.2
0.25
2.60E-09
teta 1
 =2
x = 30 m m
2.40E-09
teta 0.01
teta 0.001
2.20E-09
D(m2s-1)
2.00E-09
1.80E-09
1.60E-09
1.40E-09
1.20E-09
1.00E-09
0
0.05
0.15
0.1
td 0.5(s0.5)
0.2
0.25
Water diffusion coefficient (DH2O) dependence on temperature (T)5
1.00E-08
9.00E-09
8.00E-09
2
D H2O (m /s)
7.00E-09
6.00E-09
5.00E-09
4.00E-09
3.00E-09
2.00E-09
1.00E-09
0
20
40
60
T (°C)
80
100
120
REFERENCES
1) Brownstein K.R., et al. Physical Review A, 1979 19, 2446.
2) Brownstein K.R., et al., J. Magnetic Resonance, 1977, 26, 17
3) Mitra P.P., et al. Physical review B, 1993, 47(14), 8565.
4) Latour L.L. et al., J. Magnetic Resonance A, 1993, 101, 342.
5) Holz M. et al., Phys. Chem. Chem. Phys., 2000, 2, 4740.