DETERMINATION OF T1 AND T2
OBJECT: An introduction to multiple-pulse NMR techniques which
yield values of the longitudinal (T1) and transverse (T2)
relaxation times. A rotational correlation time is obtained from
the relaxation times. A second value of the correlation time is
obtained from viscosity measurements. The two results are
compared.
REFERENCES:
FT hardware and measurement of NMR relaxation times: T. C. Farrar
and E. D. Becker, Pulse and Fourier Transform NMR, Academic Press,
New York, 1971, ch. 1, 2, 4.
NMR relaxation theory: A. Carrington and A. D. McLachlan,
Introduction to Magnetic Resonance, Harper and Row, 1967, Ch. 11.
(included with the lab manual)
Measurement of viscosity: D. P. Shoemaker, C. W. Garland, and J.
W. Nibler, Experiments in Physical Chemistry, 6th. ed., McGrawHill, New York, 1996.
EXPERIMENTAL:
Two afternoons are required to acquire the experimental data. The
NMR measurements will be made on one day and the viscosity
measurements on another. The two sets of measurements can be made
in either order provided that both be conducted at the same
temperature.
A) NMR Measurements.
For a variety of reasons, the NMR measurements will be made on
normal water (H2O) dissolved in oxygen-free perdeuterio
dimethylsulfoxide (DMSO). The mole fraction of the water in the
sample, a binary mixture of water and DMSO, is 0.010. The DMSO
gives a strong lock and the moderately high water concentration
yields a good signal-to-noise ratio. The two protons in normal
water form an A2 spin system which assures a uniquely defined value
of T1. With most proton spin systems, this is not the case. In
the oxygen-free sample provided, relaxation is dominated by the
intramolecular dipole-dipole interaction between the two protons.
The measurements will be made on a Bruker DPX 400 MHz pulsed
Fourier transform NMR spectrometer. Because of the high field
strength of the 9 Tesla magnet, special safety measures must be
taken. The room containing the spectrometer is strictly off
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limits to anyone with a pacemaker, neurostimulator, or metallic
implant. Those authorized to use the instrument must remove all
magnetic objects from their person before entering the room. The
magnet is also capable of erasing your credit cards. Please
refrain from walking in the vicinity of the magnet while an
experiment is in progress.
OUTLINE OF THE PROTOCOL FOR THE USE OF THE BRUKER
1) Logging on
a) Place your billfold in the rack. Do not bring any
magnetic materials into the room.
b) Log on to the student account on the SGI workstation ernst
whose full address is ernst.pomona.edu. The password is
sage_hen.
c) Open an Xwindows Unix shell and start the NMR program by
entering in lower case xwinnmr.
d) Load the file which defines the default values of the
spectrometer parameters for the experiment and the sample.
The file is T1_setup and the process is achieved by the
following set of mouse clicks:
File
Open
Datasets by Name
`
T1_setup
e) Create your own copy of the setup file with the following
set of input:
File
New
Provide a new, unique file name in the field
provided. All later changes will be made in
your file rather than T1_setup.
f) Open the Lock window using the following menu mouse
clicks:
Window
Lock
Do not close the Lock window in the standard SGI manner by
clicking on the minus sign in the upper left-hand corner of
the window. This action will create an error condition for
the next user. There is no need to close the window but if
you must, click on the Quit button at the bottom right of the
window.
2) Introduction of the sample.
a) Remove the black cap covering the sample port.
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b) Eject the sample already in the probe using the
spectrometer keypad.
c) Replace the tube in the rotor with the solution of H2O in
d6-DMSO. Do not touch the sides of the rotor. Use the depth
tool so determine the position of the tube in the rotor.
d) Place the tube in the sample port.
e) Drop the tube/rotor assembly into the probe using the
spectrometer keypad.
e) Cover the sample port with the black cap that keeps dirt
out of the magnet bore.
g) Using the spectrometer keypad, initiate spinning of the
sample at a rate of ca. 20 Hz.
3) Locking and shimming
a) Select a temperature for the experiment. Both the NMR and
the viscosity measurements will be made at this temperature
which must be less than the normal boiling point of water.
b) Turn on the air for the supplemental probe cooling and the
set the variable temperature unit for the temperature which
you selected. The command to access the temperature
controller is edte. Turn on the heater and wait until the
probe temperature reaches the set point.
c) The instructor will tune the probe for the solvent DMSO.
The relevant command is wobb.
d) Lock the spectrometer for the solvent by entering
lock dmso
(The generic command is lock solvent_name.)
e) Load the shim set for the spectrometer by entering
rsh bbi
f) Using the spectrometer keypad, manually shim the magnet.
Use only the z1, z2, and z3 shims. The sample must be
spinning during this step.
g) Initiate the simplex by entering command tune. Select the
autoshim-z1z2z3 suite.
When the shimming is completed (a
finished message will appear in the command line), proceed
with the rest of the experiment. The macro program turns on
the autoshim feature before exiting. The autoshim will
continue to adjust the shimming during the experiment.
During the experiment, be on the lookout for a degradation in
the shimming as indicated by a drop in the lock level or the
line shape. Report this to the instructor who will suggest a
remedy.
4) Setup for the measurement of the 90 or /2 pulse time.
a) The setup file selects the simplest, one-pulse experiment
whose name is zg. The pulse program waits d1 seconds (the
relaxation decay is set to 10 s), turns on the transmitter
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for p1 sec, waits 4.5 sec, and then samples the free
induction decay (fid). The transmitter power is set for 3
dB. At this level, a 90 pulse is ca. 7.6 sec.
b) To set for a series of runs, set p1 to 7.6 sec. Either
enter the command p1 and supply the value or provide the
value in the appropriate field of the menu of all
spectrometer parameters which is accessed by entering eda.
The former approach is simpler. For your information, eda
accesses the menu of processing parameters.
c) Set the spectrometer gain by entering rga.
d) Execute the pulse sequence by entering zg. Note that
Bruker uses the same name for the command which runs any
pulse sequence and the simplest pulse program.
e) Fourier transform the fid by entering ft.
f) Phase the spectrum by entering apk. apk determines the
phase angle and then uses the result to obtain a 100%
absorption signal. In later steps, you will use the phase
command pk which uses the phase angle determined by apk.
5) Determination of the 90 Pulse Time. At the temperature
selected, you will examine the intensity of the water peak as a
function of the pulse width. Since you will be comparing
intensities from one run to the next, you will run in absolute
value mode in which a constant scaling factor is used.
Furthermore, you will use the same phase angle which will be
determined in this setup phase of the experiment
a) You will vary p1, the length of the transmitter pulse, in
3 sec increments until you pass the second null. Plot the
height of the water peak versus the value of p1 in the
vicinity of the second null. The 360 pulse is obtained from
the value of p1 at the second null. You want to determine
the peak height in absolute value mode. Clicking on the YU
box on the left of the xwinnmr screen will turn the absolute
value mode on.
b) For each desired value of p1, execute the following
commands or steps:
p1 (Provide the value of p1 as prompted.)
zg (Answer OK to the request to overwrite old data.)
ft
pk (Use pk, not apk to phase)
(Determine the height of the water peak.)
6) Determination of T1. The following pulse sequence is used in the
determination of T1: d1-()-d7-(/2)-AT. With the exception of the
delay d7 which is varied, the same parameters and macro are used
as in step 5. The peak height of the water signal is measured as
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a function of the delay time d7 which for technical reasons cannot
be zero.
In measuring T1 you do not initially know the time scale
of relaxation. Hence, the delay d7 is varied in a initial set of
exploratory runs by powers of 10 from 1 s to 10 s, e.g. 1 s, 10
s, 100 s, 1 ms, 10 ms, 100 ms, 1 s, and 10 s. The 10 s delay is
a conservative estimate of ca. 5T1 and is long enough to insure
relaxation of the system back to equilibrium.
Examine the data from the exploratory set of runs and find the
shortest value of d7 that yields a significant change in the peak
height. Then sample the entire dependence of peak height on delay
by measuring the peak height in increments of this value. Note
that the peak height changes sign in this run and collect data on
both sides of the null. The peak height at a long delay, e.g. 10
s or ca. 5T1, yields the value of the equilibrium magnetization,
Ae. T1 is obtained by fitting the data to the equation:
ln[Ae - A(t)] = constant - t/T1 where t = d7.
a) Use command eda to select t1ir1d as the pulse program
(PULPROG). Set p1 to the value for a 90 pulse and p2 to the
value for a 180 pulse. The delay between the 180 and 90
pulse is determined by the variable d7. The lab manual
discusses how the values of this parameter are chosen.
b) For each desired value of the delay d7, execute the
following commands or steps:
d7 (Provide the value of d7 as prompted.)
zg
ft
pk
(Determine the height of the water peak.)
7) Determination of T2. The following pulse sequence is used in the
determination of T2: d1-(/2)-d7-()-d7-AT. Two pulses, a /2
pulse and a  pulse, are used. The measurements in this step are
made in the same manner as step e. However, the sample is NOT
spun during the determination of T2. The delay time is set by d7.
A value of T2 can be obtained by examining the height of the water
peak as a function of the delay and by fitting the data to the
equation: ln[A(t)} = constant -2t/T2 where t = d7. Note that the
peak height does not change sign in this experiment.
a) Turn off the spinner. Use the command eda to select t2cp
as the pulse program. The delay between the pulses is still
d7.
b) For each desired value of the delay d7, execute the
following commands or steps:
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d7 (Provide the value of d7 as prompted.)
zg
ft
pk
(Determine the height of the water peak.)
8) Shut down.
a) Turn off the variable temperature unit and wait until the
probe temperature is close to ambient temperature.
b) Eject the sample and insert the sample of neat d6-DMSO.
c) Exit the program.
d) Log off the work station.
e) Don't forget your wallet.
B) Determination of the viscosity of the DMSO-water mixture.
The mole fraction of the water in the sample used in the NMR
measurements is 0.010. Determine the viscosity of a normal waterDMSO solution with the same composition at the NMR probe
temperature. You will make time-of-fall measurements with a size
100 Ostwald viscometer. The relevant equation is  = Bt where 
is the viscosity of the fluid,  is its density, t is the time
required for the fluid to fall a fixed distance marked by the
lines on the viscometer, and B is the conversion factor of the
viscometer. To obtain the required viscosity, three measurements
are required:
a) the drop time t of the DMSO solution,
b) the drop time t of a calibration fluid, water (The
viscometer needs to maintained at the same temperature and
loaded with the same volume of fluid (10 ml) in parts a and
b.
c) the density of the DMSO mixture using a pycnometer
calibrated with water.
The density determination requires a set of three measurements:
a) the mass of the pycnometer when empty,
b) the mass of the pycnometer when filled with water, and
c) the mass of the pycnometer when filled with the DMSO
solution.
From these data, one calculates the volume of the pycnometer from
the published density of water and its mass. The required density
of the DMSO solution is obtained from the volume of the pycnometer
and the mass of the solution.
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CALCULATIONS:
Your report should include the report form, all graphs, printouts,
sample calculations, entries from your lab manual. The parameters
extracted from the NMR data, e.g. T1, T2, and c, should be
presented to the correct number of significant digits and should
be accompanied with the corresponding 95% confidence interval.
You will obtain a value of c, the rotational correlation time of
water, in DMSO from the NMR results. You will obtain an
independent value from the viscosity data. BOTH values should be
reported.
1) Calculation of c from the NMR measurements. The spectrometer
frequency for proton operation on the Bruker DPX is 400.13 MHz. c
will be calculated from the value of T1 which is more accurate.
Unfortunately the relationship between T1 and c is multivalued.
T2 was measured to resolve this dilemma. The value of T2 obtained
from the simple pulse sequence used is not very accurate but it is
good enough to determine whether c is very short (the motional
narrowing limit) or very long. In the motional narrowing limit, T1
= T2. In other words, the measured values should be comparable,
In the other extreme, T2 << T1. Determine which case applies and
use the appropriate formula from Carrington and McLachlan to
calculate c from T1. Perform these calculations in cgs units as
the cgs-esu system of units is implied by the equations in
Carrington and McLachlan. You will need the proton-proton
internuclear distance in water to complete the calculation.
2) Calculation of c from the viscosity measurements. Calculate an
independent value of c from the viscosity of the solution. You
will need the O-H bond length for this calculation.
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DETERMINATION OF T1 AND T2
NAME:______________________________
a) Temperature = ______________
Date expt. done:__________
Date report due:__________
Date submitted:___________
90 pulse time = ______________
b) Determination of T1
peak height
delay time, d7
c) Determination of T2
peak height
delay time, d7
regression of ln[Ae-A(t)] versus t
regression of ln[A(t)] versus t
slope = _________________________
slope = ______________________
T1 = ____________________________
T2 = __________________________
d) viscosity measurements
volume of the pycnometer = ___________________
density of the DMSO-water solution = __________________
drop time of water = ____________
viscosity of water = __________
drop time of the solution = ________________
viscosity of the solution = ________________
e) rotational correlation time of water
from the NMR data: _____________________
from the viscosity data: ____________________