Physical Measurements Goux Spring 2016 Daniel Gonzalez
NMR analysis of Ethylbenzene
Physical Measurements
Goux Spring 2016
Daniel Gonzalez
Partner: Dorothy N.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
ABSTRACT:
An HNMR experiment was performed on ethylbenzene using a JEOL System with DELTA
software. A regular 90o pulse experiment was run to produce a typical spectrum with
deuterated chloroform as the solvent system. Peaks were recorded at 7.3ppm 2.7ppm and
1.3ppm with multiplicities of 6,4, and 3 respectively. A 1800 pulse experiment was performed
and the minimum intensity was used to calculate the optimal pulse width of a 90o pulse which
was determined to be 13.75 μs. Subsequently, using a double pulse experiment with a 180o
followed by a 90o pulse a variable time τ was used to calculate three T1 values, one for each
NMR peak on the ethylbenzene spectrum. T1’s were recorded as 4.216, 4.567, 5.191 seconds
with T1 max being 5.191 seconds. The relaxation delay corresponding to 95% peak intensity
was determined to be 15.57 seconds, with a total delay time D of 16.57 seconds. Optimum flip
angles were calculated for the peak at 7.3ppm and a plot of D, total delay time verses φ was
made. A linear positive relationship was evident in the said plot with y intercept laying around
40o.
INTRODUCTION:
Proton NMR is a spectroscopic technique that takes advantage the magnetic properties
of hydrogen nuclei to create spectra with peaks corresponding to particular proton
environments. The positively charged hydrogen nuclei are in continuous rotation, and as a
charged particle spins, a magnetic moment is formed. This magnetic moment denoted as μ is
related to the angular momentum by the equation:
μ=γJ (1)
where J is the angular momentum and γ is the gyromagnetic ratio.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
The gyromagnetic ratio is simply a measure of how well molecules will interact with a magnetic
field, much like εo , the molar extinction coefficient, is simply a measure of how well molecules
absorb light in Beer’s law. γ will very amongst different molecules and will change in different
chemical environments.
The energy E, of a magnetic field interaction is given by the equation
E=-μB (2)
Where B is the magnetic field strength.
When considering the proton nucleus, there are only two possible spin states as predicted by
quantum mechanics, that is ½ and – ½ . These states are simply solutions to quantum numbers
in Schrodinger’s equation. The ½ and – ½ state can be described respectively as the α and β
states.
Figure 1[1]. Splitting of α and β states
The α spin state is nearly equally occupied as the beta spin state and in the presence of an
external magnetic field, it is possible to separate the two states with the degree of separation
being proportional to the strength of the external magnetic field. If the magnetic fields of the
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
two spin states are vectorily summed, the result is a net magnetic moment M in the direction of
the alpha states.
Figure 2: Net Magnetic Moment
The net magnetic moment then will point towards the positive Z axis and is spinning at a
frequency in the MHz region. The diagram in figure 2 represents all magnetic dipole
orientations rotating as a conical surface. As the nuclei spin they can be perturbed by external
fields to produce a wobble in the nuclei spin as the net magnetization vector is thrown off the z
axis. The common analogy used to describe this movement is that of a spinning top wobbling
about its axis. However, unlike the top eventually falling over, M will return to equilibrium on
the z axis; given the magnetic field stays constant.
When viewing the spinning nuclei, if a rotating frame of reference is used to move with the
rotation, then any movement of M from the z axis will appear as a rotation downwards towards
the XY plane by an angle φ the flip angle
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Figure 3
A coil can be placed perpendicular to the magnetic field vector B, and as M wobbles an induced
magnetic field will occur in the coil which can be measured by a computer. This IMF will appear
as a sinusoidal wave that decays as the vector M returns to its equilibrium position of Mo which
can be Fourier transformed to produce peaks in an NMR spectra.
Figure 3: IMF and Signal for NMR
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
As the pulse angle changes, more nuclei switch between the alpha and beta state with 90˚
being where the two states are nearly equal in population. As more nuclei flip to the beta state
the angle approaches 180˚ where there are nearly twice as many beta states than alpha states.
Similarly, approaching 0˚ there are nearly twice as many alpha states than beta states.
Figure 4: Population of α and β states at different flip angles.
Clearly the acquisition of signal is dependent upon the degree of flip angle and the amount of
time it takes for the net magnetization vector M to return to the position Mo, also known as the
relaxation delay. As a 90˚ pulse is applied, M will lay parallel and coplanar to the YX axis. As time
progresses though, the M will relax back towards the Z axis position Mo.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Figure 5: Relaxation of the net magnetic moment M after a 90˚ pulse
The relaxation of M is different for each hydrogen nucleus due to different electronic and
magnetic environments contributed by neighboring bonded atoms. This unique delay time is
known as the variable T1 which is simply a time constant.
(K)= 1T 1 (3)
In this case, the rate of relaxation K, is inversely proportional to T1.
When performing an NMR experiment then, it is of interest to pulse the sample and perturb M,
and then depending upon T1, (which is dependent upon unique electronic environments) the
time taken to relax will produce a IMF that can be transformed to intensities in a frequency
domain. This frequency domain will have peaks that correspond directly to unique differences
in T1’s of different protons and thus allows for identification of particular groups of hydrogens
on an NMR spectra.
To measure T1 a 180o pulse followed by a delay , and then a 90o read pulse experiment can be
used. This essentially forces M towards the negative Z axis ,allows for M to start recovering
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
towards the positive Z axis, and then forces M back down to the XY plane, thus allowing one to
measure how quickly M can recover between the two pulse periods. When is very short M
has very little time to recover and the 180o pulse and 90o pulse essential combine yielding a
270o pulse, which is opposite the detecting coil, and will produce an inverted spectrum. As
lengthens M begins to relax along the z-axis to its equilibrium value which is expected as τ is
simply a delay time and given long enough, M will always return to Mo.
M o−M z=2M o e−τ /T1
(4)
Using equation 4 τ can be solved for algebraically.
MM o
=(1−2e−τT 1 )
Recovery% ¿1−2e− τT 1
If 95% recovery is assumed,
(.95-1)/2 =-e− τT 1
τ = -ln(.025)T1
where T1 can be automatically obtained from the JOEL NMR Software.
It is important to consider that there is a relationship between resolution, the number of scans
one performs, the pulse angle, and the acquisition time it takes to perform each h NMR run.
The more scans one does, the longer the acquisition time. Also, if the recovery time of the M is
too long before the next subsequent pulse, resolution and signal will be lost because M can not
return to its equilibrium position. With these factors in mind, it is possible to acquire an optimal
pulse width for each T1 of the sample and used these values to acquire a better spectrum.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
The purpose of this experiment then is to first, take a regular NMR of the sample of
ethylbenzene and analyze the peaks to confirm it is indeed ethylbenzene. Second, run a single
180o pulse NMR and extrapolate the optimal pulse width for a 900 pulse that gives a maximum
signal. Third, to use a double pulse experiment to measure the T1s of each peak in ethyl
benzene. Fourth and finally, to measure the optimum flip angle at 3 different values of D, the
total duration.
METHODS:
All methods were carried out at the University of Texas at Dallas’ undergraduate teaching
laboratory in Berkner Hall under the guidance of Dr. Warren Goux. A JEOL FT-NMR was used to
acquire all data and spectra were printed and analyzed. Procedural details can be found in
appendix C and were provided by Dr Goux and his team of graduate TA’s.
1) A normal NMR spectrum was run by placing a sample of ethylbenzene in deuterated
chloroform in n NMR tube and subsequently after turning on the nitrogen gas, placing
the sample in the magnet. The sample was lowered, the auto lock was adjusted
accordingly the pulse angle was set to 90o the relaxation delay was set to 25[s] and the
receiver gain was 11. The NMR was run, the peaks were labeled, and the spectrum was
printed.
2) A single pulse experiment was run however the auto gain was turned off and the scans
were adjusted to 4. The pule was set to 45o and the listed values next to the pulse were
set to start at 5[us] and end at 35[us] with 5[us] increments. The relaxation value was
then changed to 25[s] and the NMR was run. Choosing the spectra once finished the
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
spectrum was analyzed using the DELT curve fit analysis software. The spectra was
transferred over, the peaks were phased up, and the graph of intensity vs time was
printed and used to calculate the value of the 90o pulse width.
3) T1s were measured by the inversion recovery method where a 180o pulse was followed
by a 90o pulse . A double pulse experiment was performed in which the receiver gain
was set to 11 and a 90o pulse was optimized using a pulse width of 13.75 as determined
form part 2. The τ values were arrayed and set to start at .05s and to end at 25s. 8 scans
were performed, and the relaxation delay was set to 25[s]. The experiment was then
submitted and the spectra were collected for each of the 3 T1 peaks. The JEOL software
was used to calculate and fit the T1 data by using the curve analysis function and
applying an unweighted T1 for the function . the Data was fit to equation 4 and the
spectra were printed.
4) To measure the flip angle a single pulse experiment was run. The receiver gain was set
to 11 and the acquisition time was set to 1 second automatically after the number of
data points was set to 4096. The pulse with was set to 13.75 and the relaxation delay
was set to .1 sec. the Pulse angle was arrayed by setting the parameters to linear and
setting the start angle to 30 and end angle to 90 with 15 increments. The experiment
was submitted and the spectra were analyzed using the Delta software with the angle
measured at with d1 set to 2sec and 4 sec.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
RESULTS:
Figure 6 HNMR of Ethylbenzene
Table 1 NMR Analysis of Ethylbenzene
Peak Multiplicity Intensity (millions) Character 1.3ppm Triplet 14.8 -CH3
2.7ppm quartet 4.5 -CH2-7.32ppm Sextet 6 Shielded Aromatic
hydrogen7.39ppm Aromatic hydrogens
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Figure 7: Measurement of a 90o pulse width from minimal 180o signal
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Figure 8: T1 at 7.3ppm
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Figure 9: T1 at 2.7ppm
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Figure 10: T1 at 1.3ppm
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Figure 11: Flip Angle φ at D= 1.1 sec.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Figure 12: Flip Angle φ at D= 3 sec.
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60 degrees
Physical Measurements Goux Spring 2016 Daniel Gonzalez
Figure 13: Flip Angle φ at D= 5 sec.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Table 2. T1 and optimal Flip angle at Values of D
Peak ppm
intensity (mil) T1 (S)
d1 for95%
Intensity3(T1)
(s)
Total DelayAT+d1
for 95% intensity
(S)
K1/T1
D(AT+d1)
ΦFlip angle
1.4 14.8 4.21612 12.64836 13.65 0.237185 5 752.8 4.5 4.56756 13.70268 14.70 0.218935 3 607.3 6 5.19108 15.57324 16.57 0.192638 1.1 45
Figure: 14 Optimal Pulse Angle vs total Duration
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50
10
20
30
40
50
60
70
80
Pulse Angle vs D
D = total delay time [AT+ d1] (s)
optim
al P
ulse
Ang
le D
egre
es
DISCUSSION:
Overall this experiment was indeed successful. The HNMR of Ethylbenzene was taken and when
compared to spectra obtained by others [2], peak values of 7.3ppm, 2.7ppm and 1.3ppm with
multiplicities of 6, 4, and 3 aligned neatly with their results.
Upon determining the optimal pulse width of a 90o pulse, it was determined that 13.75
microseconds seemed to appear as the correct value as determined graphically.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
The T1 values collected of 4.216, 4.56756, 5.19108 seconds all appear to be reasonable.
According to Dr. Hu form the University of Massachusetts, typical T1 values of proton NMRs will
lay between 1-5 seconds, which agree well with results obtained.
The value of d1 to obtain 95% intensity should be such that d1 > 3(max T1)[5]. In this case the
largest T1 was 5.191 (s) which yields a d1 of 15.5732 (s) for 95% integration. D, or total delay
would be 16.5732 seconds given that acquisition time was set to 1 second.
It was noted that upon adjusting the τ values in the acquisition of T1 values, that if τ was too
small, the spectra would appear inverted. This could be explained by the fact that by decreasing
τ there is less time for relaxation between the 180o and 90o pulses, essentially resulting in the
two pulses nearly adding to create a 270o pulse. A 270o pulse orients M opposite relative the
detecting coils, which results in an EMF verses time graph in the opposite direction than a 900
pulse would create. The spectrum will thus appear inverted, and as τ increases, the pulse will
act more as the subsequent 90o one, which should produce a normal upright spectrum.
Upon research of T1 values for ethylbenzene it was noted that T1 vales are dependent on
temperature and concentration in addition to the character of the species being analyzed. In
this particular instance however, the temperature of the sample, nor the connection of the
ethyl benzene were noted as the sample was prepared by a graduate teaching assistant and
this information was not provided.
It was determined that when plotting the flip angle yielding max intensity verses different
values of total delay time D, a linear plot (figure 14) was obtained. According to this plot,
extrapolating backwards to the y axis where delay time is 0 seconds, the flip angle would
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
appear to lay around 40 degrees. This is expected though as typical NMR experiments are run
using multiple scans, and if a pulse of 90 is used with a sample having a particularly long T1,
signal could be lost if M does not have enough time to recover to Mo before the next pulse.
With this in mind, adjusting the time intervals between each pulse to accommodate a long T1
will result in an experiment that will take a long time to complete. Instead, if the pulse is
somewhere less than 90, perhaps 75[5], the time to recover will be less and more scans can be
completed in a shorter amount of time without losing much signal and therefore could be more
practical than running an NMR for multiple hours.
REFFERENCES:
1) Prof.N.L.Bauld, Final Exam, University of Texas at Austin, 2002 http://research.cm.utexas.edu/nbauld/ex4_key.htm (accessed Apr, 23,2016)
2) Gravitywaves.com. H NMR of Ethylbenzene http://www.gravitywaves.com/chemistry/CHE303L/OxidationArene_10.htm (Accessed Apr, 23, 2016)
3) University of Illinois. NMR Basic Concepts, http://scs.illinois.edu/nmr/handouts/getting_started/NMR_basic_theory.pdf (Accessed Apr, 23, 2016)
4) Weiguo, Hu, Introduction to 1D and 2D NMR Spectroscopy, university of Massachusetts http://nmrwiki.org/wiki/images/8/8e/NMRcourse2009.4.pdf (accessed Apr,24,2009)
5) Zhou, H. ;Optimal Pulse Width and Recycle Delay in a Single Pulse Experiment, Oct 20106) Goux,Warren; NMR Experiment/Report CHEM 4473 Spring 2015 (accessed Apr, 21,
2016)
APPENDIX:
-A- Rough Spectra
-B- Notebook Pages
-C- Procedural Instructions for Data Acquisition
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