Transcript No Slide Title

Applications of spin-echo sequences
• Last time we had seen how spin-echoes could be used in the
the determination of T2 relaxation times by removing the
effects of Bo inhomogeneities and dephasing from the signal.
90y
180y (or x)
tD
tD
• We’ll now analyze how spin echoes affect chemical shifts and
coupled spin systems.
• One of the most annoying things in NMR is to get the right
phase of the spectrum. Why do we have the phase? We have
to look at the effects of chemical shift after a short period of
time on the different components of Mxy. This delay is placed
before acquisition after pulses to avoid burning the probe:
y
y
...
x
x

Spectrum phasing
• The phase of the lines appears due to the contribution of
absorptive or real (cosines) and dispersive or imaginary
(sines) components of the FID. Depending on the relative
frequencies of the lines, we’ll have more or less sine/cosine
components.
S(w)x = S cosines(w) - real spectrum
S(w)y = S sines(w) - imaginary spectrum
• What we want is the purely absorptive spectrum, so we
combine different amounts of the real (cosine) and the
imaginary (sine) signals obtained by the detector. The
combination depends on the frequency of the spectrum:
S(w) = S(w)x + [ fo + f1(w) ] * S(w)y
• fo is called the zero order phase and f1 the first order
phase.
• There is one experiment using spin-echoes that
theoretically allows us to avoid this. We’ll see later why it
is actually not that useful...
Spin-echoes on chemical shift
• Now we go back to our spin-echoes. The effects on elements
of Mxy with an offset from the B1 frequency are analogous to
those seen for dephased Mxy after the p / 2 pulse:
z
y
x
y
tD

x
f
x
y
weff
• After a time tD, the magnetization precesses in the <xy>
plane weff * tD (f) radians, were weff = w - wo. After the p pulse
and a second period tD, the magnetization precesses the
same amount back to the x axis.
y
y
180
f
x
tD
x

weff
• Apart from being upside down, we have no dephasing if we
start acquisition immediately after the second tD. In principle,
this sequence would give a purely absorptive spectrum...
Spin-echoes and heteronuclear coupling
• We now start looking at more interesting cases. Consider a
13C nuclei coupled to a 1H:
13C
ab
bb
J (Hz)
1H
1H
aa
ba
13C
I
• If we took the 13C spectrum we would see the lines split due
to coupling to 1H. These couplings are from 50 to 150+ Hz,
and make the spectrum really complicated and overlapped.
We usually decouple the 1H, which means that we saturate
1H transitions. The 13C multiplets are now single lines:
ab
13C
bb
1H
1H
aa
ba
13C
I
Spin-echoes and heteronuclear coupling (…)
• We modify a little our pulse sequence to include decoupling:
90y
180y (or x)
tD
13C:
tD
{1H}
1H:
• Now we analyze what this combination of pulses will do to
the 13C magnetization in different cases. We first consider a
CH (a methine carbon). After the p / 2 pulse, we will have
the 13C Mxy evolving under the action of J-coupling. Each
vector is said to be labeled by the states of the 1H it is
coupled to, a and b:
z
y
y
-J/2
(a)
x

tD
x
y
• Remember that under J-coupling f = p * tD * J.
f
x
(b)
J/2
Spin-echoes and heteronuclear coupling (…)
• We now apply the p pulse, which inverts the magnetization,
and start decoupling 1H. This removes the labels of the two
vectors, and effectively stops them. They collapse into one,
with opposing components canceling out:
y
y
x

y
x

x
• In this case the second tD under decoupling of 1H is there to
refocus chemical shift and get nice phasing…
• Now, if we take different spectra for several tD values and plot
the intensity we get something that looks like this:
tD= 1 / 2J
tD= 1 / J
tD
Spin-echoes and heteronuclear coupling (…)
• The signal intensity varies with the cosine of tD, is zero for tD
values equal to multiples of 1 / 2J and maximum/minimum
for multiples of 1 / J.
• If we are looking at a CH2 (methylene), the analysis is
similar, and we obtain the following plot of amplitudes versus
delay times:
tD= 1 / 2J
tD
tD= 1 / J
• Analogously, for CH3 (methyl), we have:
tD= 1 / 2J
tD= 1 / J
tD
Spin-echoes and heteronuclear coupling (…)
• Now, if we make the assumption that all CH J-couplings
are more or less the same (true to a certain degree), and
use the pulse sequence on the following molecule with a tD
of 1 / J, we get (don’t take the d values for granted…):
OH
5
3
2
4
7
6
1
6
HO
1,4
150
100
50
0 ppm
5
2,3
7
• The experiment can discriminate between C, CH, CH2, and
CH3, and we identify all the carbon types in the molecule.
• This experiment is called the attached proton test (APT).
It is one of the first multiple pulse sequences, and has been
superseded by the DEPT pulse sequence.
Spin-echo and homonulcear coupling
• Here we’ll see why spin echoes won’t work if we want to get
our perfectly phased spectrum. The problem is that so far we
have only used single lines (no homonuclear J-coupling) or
systems that have heteronuclear coupling.
• Lets consider a 1H that is coupled to another 1H, and that we
are exactly on resonance. After the p / 2 pulse of the spinecho sequence and the td delay we have evolution under the
effects of J-coupling. Each vector will be labeled by the state
of the 1H it is coupled to. We have:
z
y
y
J/2
(a)
x
y

tD
x
x
(b)
J/2
• The problem is that if we now put the p pulse, we invert the
populations of all protons in the sample. Therefore, we invert
the labels of our protons:
Spin-echo and homonulcear coupling (…)
• The p pulse flips the vectors and inverts the labels:
J/2
y
J/2
(a)
y
(b)
180y (or x)
x
x
(b)
(a)
J/2
J/2
• Now, instead of refocusing, things start moving backwards,
and we will have even more separation of the lines of the
multiplet during the second evolution period. If we then take
the FID, the signal will be completely dispersive (although
this depends on the length of the tD periods…):
y
tD
FID, FT
x
Spin-echo and homonulcear coupling (…)
• We see why this is not all that useful. For different td values
we get the following lineshapes for a doublet coupled with
a triplets (both have the same J value…):
tD = 0
tD = 1 / J
tD = 2 / J
• Despite of its patheticness, understanding how this works is
crucial to understand 2D J-spectroscopy. The phenomenon
is known as J-modulation.
Take-home message…
• Different combinations and uses of a very simple pulse
sequence allow us to investigate different things:
• Refocus chemical shift and coupling constant effects
in the rotating frame.
• Calculate T2 relaxation times.
• Identify carbon atom types in a molecule.
• With it we can study how a signal is modulated by coupling
to another spin, which will be useful in 2D spectroscopy.
• Despite its simplicity, sin-echoes are normally used as a
block of other more complex sequences to refocus Mxy.
Next class topics
• Polarization transfer
• INEPT - Insensitive nuclei enhanced by polarization transfer
• DEPT - Distortionless enhancement by polarization transfer