T1 experiment - Inversion Recovery
M ( )  M (0)  1  2 exp( / T1 )
29-May-16
NMR Sampling
29-May-16
dM z M 0  M z

dt
T1
M n( z )  M n cos
dM z
t

M o  M z T1
M n1

M n(v )  M n sin 
Steady-state solution; Mn+1 =Mn =Mss
1  e t / T1
M ss  M 0
1  cos  e t / T1
29-May-16
M n( z )  M n cos
dM z
t

M 0  M z T1
Maximum signal for a given repetition time t = tp
M obs  M ss sin 
1  e t / T1
M0
sin 
t / T1
1  cos  e
Given t= tp, what is the maximum signal intensity obtainable?
M obs
0
t
cos  e t / T1
 2 M obs
0
2
t
29-May-16
Spin-lattice relaxation T1
Transition probabilities (see exersice 2.7)
Energy
Population Transition probability
N
W
W
N
Simple kinetics
dN 
dt
dN 
dt
 W N   W N 
 W N   W N 
29-May-16
d (N )
 (W  W )(N  N 0 )
dt
Since: M z  kN and M z 0  kN 0
We obtain :
dM z
 (W  W )(M z  M z 0 )
dt
We identifythe sum of transition probabilities :
1
(W  W ) as
T1
NMR SPECTROSCOPY - AN INTRODUCTION
CHEMICAL SHIFT AND COUPLING
29-May-16
How can we derive the frequency spectrum F()
from
the time-domain signal (FID) f(t)?
See Exercise 2.5.

F ( ) 

f (t )  e it dt
0
Show a FT-transform
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Int
f (t )  e
t / T2
FID
time
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F ( ) 
T2
1  (  0 ) 2 T22
i
(  0 )T22
1  (  0 ) 2 T22
FIRST OBSERVATION OF A NUCLEAR MAGNETIC RESONANCE SPECTRUM
PURCELL and BLOCH
NMR-SIGNAL OF WATER
 = gB
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1H-NMR
SPECTRUM OF ETHANOL, WHAT DOES IT LOOK LIKE ?
?
29-May-16
WHY DO WE OBSERVE THREE RESONANCE BANDS ?
THE ELECTRON MOTION GENERATES A MAGNETIC
FIELD AT THE NUCLEUS
B0
THE MAGNETIC FIELD SENSED BY THE NUCLEUS IS THUS
MODIFIED;
BNUCLEUS =B0-BEl
29-May-16
WE WRITE;
 = gB = gBnucleus = g(1-BEl/B0).B0 = g (1-s)B0
s defines the shielding constant
The electron densites around the three “groups” of protons in ethanol are different
Hence;
29-May-16
RESONANCE FREQUENCY OF A NUCLEUS IS ALWAYS
MEASURED RELATIVE TO SOME REFERENCE FREQUENCY
THIS REFERENCE IS CHOSEN TO BE TMS (FOR 1H- OG 13C)
CH3
CH3
Si
CH3
CH3
THE LARMOR FREQUENCY OF TMS IS DENOTED nREF
29-May-16
THE RELATIVE FREQUENCY OF A RESONANCE CAN THUS BE WRITTEN
n  nSAMPLE nREF
SINCE; n g/2p.(1s)B0
nSnREF  g/2p.(sREF  sS)B0
To obtain a magnetic field independent chemical shift we devide by n0 (= gB0/2p)

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n S   REF
 (s REF  s S )
0

n S   REF
0
H2O
TMS
Økende s
Avtagende frekvens
9
8
7
6
5
4
3
2
CHEMICALSHIFT () ppm
29-May-16
1
0
-1
s II
-C=O
f
^
^
CHEMICAL SHIFT
s
s
1
s1=s2=1
0,8
0,6
0,4
s1=0,2, s2=1
0,2
0
0
50
100
Orientation; f (o)
29-May-16
150
HOW CAN WE IRRADIATE A BROAD RANGE OF SPECTRAL FREQUENCIES?
ASSUME A RECTANGULAR Rf-PULSE
What will be the power distribution Vs frequency ?
29-May-16
FOURIER TRANSFORMATION
tp /2
F ( ) 
it
e
 B1dt
t p / 2
2 B1 exp( it p / 2)  exp( it p / 2)



2i
sin( t p / 2)
 B1
 /2
Strong B1  short 900-puls  short tp  broad band excitation
Weak B1  long 900-puls  long tp  selective excitation
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COUPLING CONSTANT
(Communication between nuclei via bonding electrons)
H
Hoe does the spectrum of
H
C
F
Chemical shift
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C
Cl
look like ?
Chemical shift
WHY ?
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The magnetic dipole moment m of spin-half (1/2) nuclei may have
two orientations in a magnetic field
This will be discussed later when introducing the quantum mechanical concept)
B0
”up”
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”down”
The spin-orientation of a neighbouring nucleus affects
the magnetic field seen by the other nucleus
Bseen = B0+
HB 
HA
(I)
C = C
Bseen = B0-
HB
HA

(II)
C = C
What will be the number of HA molecules in I and II ?
NA(I)  NA(II)
29-May-16
Boltzmann distribution
Exercise 3.0A
How will the 1H-NMR spectrum of the following molecular
fragments look like ? Discuss
b)
a)
-CH-Cd)
c)
-CH2 -CH
f)
CH3-CH-
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CH3-C=C-CH3
CH3-CH2
QUANTITATIVE NMR PUT SOME DEMANDS ON TH Rf-PULSE
The power of the pulse must be homogeneously distributed
throughout the frequency domain
Frequency
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METABOLISME I CELLER
31P - NMR
29-May-16