Low Field Nuclear Magnetic Resonance

High Field (Resolution) NMR:7.5 T < B < 37 T

Study of chemical structures, reactions (only solution)

Low Field (Resolution) NMR:0.37 T < B < 2.43 T

Study of physical structures (solid, liquid, gel, solution, suspension, emulsion)

Hydrogen

H

i (permanent magnetic momentum)

H

H

H

H H

H

H

HH

H

B0 = 0

H0μ

1i

N

i

M

6.1

B0 ≠ 00 = B0

0 = Larmor frequency (Hz)

= hydrogen giromagnetic ratio (2.67*108 rad/Ts)

H

0μ1

i

N

i

M

HH

H

H

H

H

H

H

H

H H

H

HH

H

HH

H

HH

HH

B0 ≠ 0

H

t = t0 - - - > B1 >> B0

H

B0

B1

Z

X

Y 0μ1

i

N

i

M

0XYM 0ZM

t = t1 > t0 - - - > B1 = 0

H

B0Z

Y

X

0

20

40

60

80

100

120

0 500 1000 1500 2000

t (ms)

M/M

0

Mz/M0

Mxy/M0

Relaxation (T1)

Relaxation (T2)

0

10

20

30

40

50

60

70

80

0 2000 4000 6000 8000 10000 12000

time(ms)

Inte

nsi

ty (

%)

Data Fitting

2iT

1ii * t

N

eAI

Determination of T2i

2

T

T

2 da 2

2max

2min

TeTI Tt

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

10 100 1000 10000T 2(ms)

Intensity

(a.

u)

Continuous spectrum

a(T

2)

B

C D

A4A3

A2A1

0

10

20

30

40

50

60

0 500 1000 1500 2000 2500T 2(ms)

Ak

%

Discontinuous spectrum

A4

A3

A2

A1

EXTERNAL WATER

HOMOGENEOUS HYDROGEL

PORES CONFINED WATER

WATER MOLECULE =

“Free” water molecules:LONG RELAXATION TIME (T2)

T2 ~ 2200 ms (25°C)

“Bound” water molecules:SHORT RELAXATION TIME (T2)

T2 ≤ 300 ms

Effect of environment on T2

It can be demonstrated1 that T2 f()

TWO FRACTION – FAST EXCHANGE MODEL2

Water molecule

T2b

T2s

2s

s

2b

b

2

1

T

f

T

f

T

1) Diffusion between bulk and surface much faster than relaxation

1sb ff

2) If fb ≈ 1 and fs ≈ 0 ( > 10 nm)

ξ

111

2b2 kTT

ξ11

12b

2 kTT

3) T2 << T2b (≈ 2200 ms T = 25°C, B = 0.47 tesla) ξ2 kT

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

0 100 200 300 400 500 600 700

(m)

T2(

ms)

ξ11

12b

2 kTT

ξ2 kT

T2b = 2200 ms

mmsTk 50/500ξav2av

mmsTT

k /1311

ξ12b2av

av

k determination

ξ

dξ*ξ

dξ*ξ*ξ

d*

d**

max

min

max

min

2

max2

min2

max2

min2

ξ

ξ

ξ

ξ

2ξ

22

222

2 k

ak

ak

TTa

TTTa

T k

k

k

k

kT

T

T

T

T

ξ2Tk

0123456789

10

1 3 5 7nm)

P(

)

Mesh size distribution

determination: gradient test

B0

B1() B1(/2)

ξ

t(ms)

B0 B1(/2) B1()

Signal intensity(A0)

t(ms)

B0 B1(/2) B1()

gradient gradientSignal intensity

(A)

It can be demonstrated that the following relation holds2:

Ln(A/A0) = -2 D 2 ( - /3) G2

A = signal intensity with gradientsA0 = signal intensity without gradientsD = water molecules self diffusion coefficient = hydrogen giromagnetic ratio

D can be determined as a function of the diffusion time td = -/3

= gradient duration = intergradient separationG = gradient intensity (T/m)

B0

B1()

B1(X)

0 = B(x)

0 = B(x)

phase shift

phase shift zeroed

NO H DIFFUSION

B0

B1()

B1(X)

0 = B(x)

0 = B(x)

phase shift

phase shift still present

H DIFFUSION

It can be demonstrated that the for small td, the following relation holds3:

ξ

6

π9

41 d0

0

d tDD

tD

td = diffusion time (= -/3)D(td) = water self diffusion coefficient inside the hydrogel at td

D0 = water self diffusion coefficient

tBDtD

D

tD0d0

0

d

ξ

6

π9

41

Latour4 proposed the following expression holding for every td

θ1

11

1

θ1

11

11d

d

dd

0

d

ttC

ttC

D

tD

ξ

6

π9

4d0tDC

= characteristic time

= network tortuosity

1.00E-09

1.20E-09

1.40E-09

1.60E-09

1.80E-09

2.00E-09

2.20E-09

2.40E-09

2.60E-09

0 0.05 0.1 0.15 0.2 0.25

td0.5(s0.5)

D(m

2 s-1

)

300 micron 30 micron

3 micron 0.3 micron

= 2 = 1

1.00E-09

1.20E-09

1.40E-09

1.60E-09

1.80E-09

2.00E-09

2.20E-09

2.40E-09

2.60E-09

0 0.05 0.1 0.15 0.2 0.25

td0.5(s0.5)

D(m

2 s-1

)300 micron 30 micron

3 micron 0.3 micron

= 1.1 = 1

1.00E-09

1.20E-09

1.40E-09

1.60E-09

1.80E-09

2.00E-09

2.20E-09

2.40E-09

2.60E-09

0 0.05 0.1 0.15 0.2 0.25

td0.5(s0.5)

D(m

2 s-1

) teta 1

teta 0.01

teta 0.001

= 2 = 30 m

1.00E-09

2.00E-09

3.00E-09

4.00E-09

5.00E-09

6.00E-09

7.00E-09

8.00E-09

9.00E-09

1.00E-08

0 20 40 60 80 100 120

T (°C)

DH

2O(m

2 /s)

Water diffusion coefficient (DH2O) dependence on temperature (T)5

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.