8/23/02 clc

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NMR - ESR Experiment

 

            In this experiment you will study the resonant absorption of radio-frequency (RF) E-M radiation by samples containing protons (NMR) or unpaired electrons (ESR or EPR)  when the samples are in a magnetic field (B).  The resonance occurs at a frequency, f, such that hf matches the difference in energy of a proton (or electron) aligned "with" or "against" the field.  The absorption is observed by sweeping B at 60 Hz around its average value Bo, while an oscilloscope is used to display a signal proportional to the energy absorbed from a coil surrounding the sample and driven with the RF.  If B passes through the resonant value during the sweep, a blip will appear on the scope. Your apparatus includes:

§         1 AL Magnet (3 kg Max)

§         Regulated power supply

§         NMR Probe, ESR Probe

§         2 Sweep modulation supplies

§         Various fluxmeters

§         515A Tektronix Scope

§         Sets of samples for NMR and ESR

 

 

            The basic NRM process can be described either in terms of classical processing magnetic moments (section 7.7.2 in Melissinos and Napolitano) or in terms of the absorption of "photons" of energy hf  by a system of energy levels split by DE = gBh/2p, where g is the gyromagnetic ratio (MN section 7.7.1*; see below). The appearance of a resonant absorption signal requires that the sample be able to absorb energy from the RF oscillator.  This happens through "spin-lattice" coupling, which is characterized by a time constant T1,  and which is enhanced by the presence of paramagnetic ions in a water sample (See MN section 7.3.1) . If T1 is too long (few ions), little absorption occurs.  If T1 is short enough, it will begin to affect the line width through DET1 = h/2p , the uncertainty principle.

            A second time constant characterizes the spreading of the energy levels by the interaction of spins of neighboring nuclei.  This will spread the line with a characteristic time T2 or

DE = h/(2pT2).  The mechanism does not absorb energy from the RF field, however.  It just destroys the "coherence" of the magnetic moments of different precessing nuclei.  (MN section 7.3.2).  T2 measures the length of time the magnetic moments of different nuclei will precess "in step" after they are resonantly excited.  These precessing nuclei themselves give rise to an RF signal which "beats" with the applied signal and produce "wiggles" in the signal trace following passage through resonance .

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*There seems to be a problem in section 7.2.1 of MN. The equations either have errors or misleading notations. This text takes I to be the angular momentum in units of hbar. That is, I is dimensionless. Then the gyromagmetic ratio g is indeed in units of (sT)-1 and most of the rest of the equations are correct. However, the gyromagnetic ratio of the proton ( gp  ) is  5.586 mN divided by hbar.  It has a value of 2.6 x 108 rad./sT.  When divided by 2p, this results in the resonance frequency for the proton which is given correctly as 42.58 MHz/T. The authors either seem to take an aberrant definition of the nuclear magneton or confused themselves by a factor of hbar several times in this discussion.

 

 For the record, the values in SI units of  some relevant constants are:

mB           =  0 .92 x 10 -23

mN           =  0 .505 x 10 -26

gN           =  4.8  x 10 7

gp            =  5.586 x 4.8  x 10 7

 

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            Do at least the following experiments:

1)  Measure f versus B and determine g for protons.  Also determine the magnetic moment,  m,  of the proton, in units of the nuclear magneton mN .  Use water doped with CuCl.  Check the frequency calibration chart provided by using the oscilloscope and a coil antenna which can replace the sample (do not insert it too far into the coil or it will affect the oscillator tank circuit) to measure the RF frequency.

2)  Measure the magnetic moment of 19F, using the teflon sample.

3)  Measure T2 using a doped CuCl water sample.  Follow MN section 7.4.3.  Determine from this the energy spread due to spin-spin interactions.

4)  Measure the width (in gauss and eV) and height of the signal for different ion concentrations.  Calculate T1 and discuss the effect of ion concentration on the signal.

 

Q:  Are field inhomogeneities important?

 

5)The EPR experiment operates on exactly the same principle as the NMR.  Use this apparatus to measure the magnetic moment of the electron. Use the DDPH sample.

 

Q:  What should be the ratio of m (electron) to m (proton) if both were rotating charged spheres?

 

Q:  Why is the ESR magnet smaller than the NMR one?

 

            For a classical charge distribution, the angular momentum J is related to the magnetic moment m of a system by m = g ( q/2m) J, where q and m are the charge and mass

and the “g-factor”  g = 1.  For quantal systems , g is not unity.

 

Q:  What is your measured g for the proton?  The electron?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MANUFACTURER’S MANUAL

 

               Nuclear Magnetic Resonance Spectrometer

                                      (Cat. No. 71898)

 

Introduction

 

            Nuclear Magnet Resonance (NMR) is an effect which allows the analysis of magnetic fields at the sites of nuclei.  It is very useful for the study of the structure of nuclei, atoms and molecules, and it has extensive technical application for the measurement of magnetic fields to a high accuracy.

 

Theory

 

            At first suggested by Pauli in 1924, some nuclei possess a magnetic moment.  This is now explained in terms of the magnetic moments of protons and neutrons, which are of opposite sign and may add to zero.  Because of the results of observation, nuclei are also said to possess a (mechanical) angular momentum.  This has led to a very simple description of the phenomena which shall be outlined.  Consider the nucleus to be something like a top, spinning at high speed about its axis.  If we apply a constant torque on this axis, the nucleus will precess about the normal to both the axis and the torque.  If the torque is due to a magnetic field, the precession shall be about the direction of the field.  An increase in the field only increases the rate of precession.  In a sample with many equal nuclei all will be precessing at the same rate.

            Apply now an alternating magnetic field normal to the d.c. magnetic field and of much smaller intensity.  For simplicity consider the a.c. magnetic field as equally spaced "kicks" in opposite directions.  Recalling how hard it can be to tilt a fast spinning bicycle wheel, the student must realize that normally nothing would happen.  However, if the frequency is "right", i.e. if it coincides with that the precession, the spinning nuclei will be tilted with respect to the d.c. field.  At the risk of using too many images, the effect of well-timed pushes on a pendulum may be recalled.

            This change of relative inclination demands some energy for its production, and, conversely, releases energy when "relaxed".  The experiment consists in producing, measuring and interpreting these energy variations.

            We have used several classical pictures for this description because of the impossibility of "directly" observing the process.  Consequently, the image formed in the students' minds is incorrect in several details.  Quantum mechanics provides a simpler description which is more correct (in the sense that this description is in agreement with that of phenomena ranging in size from galaxies to subnuclear particles, according to present experience) and has served to predict new phenomena.

 

The quantum description:  It has been observed that the measurable component of an angular momentum in any one direction is always an integral multiple of h.  The maximum value of this component is IS, which defines I, the "spin quantum number".  The symbol I, particularly, is reserved for the spin of nuclei.  Along any one direction, the component of the angular momentum can be

 

            I, I-1, I-2...-I+1, -I

 

The magnetic moment of nuclei has been found to be parallel to J.  Calling ì the maximum observable component of the magnetic moment along the chosen direction, the possible observed values are:

0

 

0

We may relate these quantities by their ratio ã.

 

     ì = ã(IS)

 

ã is called the gyromagnetic ratio.

 

            Our main concern in this experiment is with the magnetic moment.  As is generally known, magnetic dipoles tend to aline themselves with the magnetic field in which they are immersed.  Consequently, any magnetic dipole (or "moment") forming an angle with the H at its position has some potential energy.  If the zero corresponds to the parallel alignment, this energy is:

 

            -  A

 

If  defines our Z-direction,  = H, and the energy is -ìzH, and because of what we have said about the only possible values of the projection of ì, we have 2I+1 possible values of the energy, equally separated,

0

The separation is ìH/1.  By comparison to the similar phenomenon encountered with electron energy levels, this is called "nuclear Zeeman splitting".

            The basis of NMR is the possibility of forcing the nuclei to go from one level to another, thus absorbing and emitting definite amounts of energy or integral multiples.

            The quantum "selection rules" - confirmed by experience - further restricts these transitions to occur only between neighboring levels.  From the Bohr frequency condition,

 

     ÄE = hv = ìH/I

 

It follows that if one "shines" a band of frequencies, energy shall only be absorbed at the value:

 

     v = ìH/Ih = ãH/2Ð

 

Because of several minor effects and equipment restrictions, one observes absorption in a small region centered approximately at the v.

 

                         Block Diagram of the NMR Master Oscillator-Detector-Amplifier Unit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

There are no fuses in the NMR system except for the Magnetic Sweep Unit.  Battery life is approximately 500 hours of use.  Batteries are Burgess 2NG 9V cell and a Burgess non-leak flashlight cell.

 

Description of the Equipment

 

            For convenience, the D.C. magnetic field is modulated by a small, low frequency field.  This is done by the two black coils in the probe.  The high frequency (R.F.) magnetic field is provided by a coil surrounding the sample and fed by R.F. electric current.  As the (modulated) d.c. magnetic field goes through the resonance value, the load of the oscillator changes because of the absorption of energy.  As can be seen from the oscillator diagram, this will result in a signal visible in the oscilloscope.  Since the modulation is sinusoidal, two signals are seen: one when Hdc is increasing, and one when decreasing.

            The sample probe consists of a 7mm tube containing water with copper chloride in solution.  The sample tube is removable so that NMR of different samples may be demonstrated.

            A D.C. Power Supply and A.C. Voltage Regulator must be used.  A filter consisting of a choke and capacitor is recommended as part of the power supply to the electromagnet in order to see the correct line shape and eliminate hum in the signal.  The effect of the filter is to reduce 120 cycle ripples in the magnet current.  Ripple causes distortion of the NMR signal.  The filter can be omitted, but is strongly recommended.  A schematic of the recommended filter is given in Figure 1.

            The spectrometer proper consists of a calibrated transistor marginal oscillator and a transistor detector and amplifier system powered by two self contained batteries (one 9 volt cell and one 1? volt cell).  The only controls are:

 

            1)  An on-off battery switch

            2)  A bias (sensitivity) control

            3)  A frequency control which is calibrated

            4)  A sweep control for changing the amplitude of the 60 cycle sweep on the coils surrounding the sample.

 

            The apparatus is connected as follows:  The sample probe is attached to the oscillator-detector-amplifier unit, and the end of the probe is inserted in the center of the magnet.  The display output connector is connected to the Y input of an oscilloscope.

            The cable from the 60 cycle modulator coil is attached to the output of the 60 cycle/second A.C. sweep circuit which is simply a rheostat and a small transformer with a maximum voltage output of about three volts.

            Copper sulphate and ferric nitrate are provided, plus an empty sample holder.

 

Observations of Nuclear Spin Resonance; Setting Up

 

            Turn on the oscilloscope and focus the beam so that it is clearly visible.  The oscilloscope display unit vertical gain should be adjusted for about 1 volt per inch A.C. sensitivity and the horizontal sweep selector turned to the internal 60 c.p.s. line voltage sweep.  The horizontal sweep gain and centering should be adjusted so that the entire trace is visible on the screen (a 2 inch horizontal sweep amplitude is sufficient for most purposes).  The magnet power supply unit is switched on and the A.C. sweep is turned up, to only about 25% for the probe provided.  (More sweep makes the line so sharp that it is difficult to see on the scope.)  If the filter is not used, the base line may be distorted.  Try removing all possible sources of noise from the vicinity of the magnet.

            The oscillator frequency should be set at the low end and the current control on the oscillator-detector-amplifier unit should be adjusted as far counter-clockwise as possible but so the oscillator operates.  (Oscillator operation is indicated by the generation of noise or "grass" when the current control is adjusted.)  If grass is not readily noticeable when the oscillator is adjusted, it may be necessary to use more oscilloscope vertical gain.  Slowly increase the magnet d.c. current from zero.  A resonance signal should cross the oscilloscope at about 40 to 50 percent of the d.c. current.  If the magnet current is increased too rapidly, the signal may zip across the screen too fast to be noticed.  Even with very careful adjustments, it may be necessary to raise and lower the current several times before the signal can be stopped in the sweep field range.  When the signal appears, it will be well to adjust the phasing control on the scope until the two resonance lines coincide as the field sweeps back and forth through the resonance.  The A.C. sweep may be decreased until it sweeps only about 5 to 10 times the line width.  (The phasing and d.c. current or frequency may have to be readjusted also.)  After a good pattern is obtained, the oscillator may be adjusted for the best signal to noise ratio.  This is done by varying both the oscillator current with readjustment of frequency as needed, and the scope vertical gain.  The best signal to noise ratio is not necessarily at the setting where the greatest signal amplitude is obtained.  The oscillator frequency can be varied from about 6 to 12 megacycles by the tuning control.  As the tuning is adjusted, the oscillator current may need readjusting.  Both the signal amplitude and signal to noise ratio may vary somewhat over this tuning range.

            There is normally a vertical displacement of the oscilloscope display pattern when the oscillator current control is varied.  It is best to wait a few seconds for equilibrium conditions before changing the oscillator current control again.

 

Sensitivity

 

            The sensitivity of this instrument is determined by the background noise level.  Most NMR spectrometers are evaluated in terms of the number of nuclear spins which can be detected.  Using the oscilloscope display, this model can detect the protons in less than 0.1 gram of water.

            The instrument is much more sensitive when used with a phase detector and pen recorder due to the fact that much noise is eliminated in this method of operation.  Phase detection attachments can be added to the model if additional sensitivity for research is needed.  Your inquiry is invited.

 

Frequency of Operation

 

            The operating frequency of the NMR system is approximately 6 to 12 megacycles/second.  Both the static magnetic field and the r.f. oscillator-detector system are variable.  The feature of r.f. tunability is helpful for measuring absorption line widths in frequency units, and for illustrating the frequency dependence of the resonance.

 

Experiments

 

Experiment 1:  Measurement of ã for protons in water

 

            Place a water sample in the holder.  Measure carefully the frequency and magnet current for resonance.  Do this at various frequencies, repeating each measurement at least five times.

            From 2ðv = ù = ãHo, where v is found in the spectrometer calibration chart and Ho in that of the magnet, it is possible to calculate several values of ã.  These should be averaged, and the probable error should be estimated.

            If the frequency is measured in Mc/s and the field in k gauss, then for protons in water:

     v = 4.26 H

This relation is also found in the form:

     Sù = gìoH

where g is the "spectroscopic splitting factor" which characterizes the nucleus studied, and ìo is the nuclear magneton: ìo = eS/2Mc = 0.51 H 10-23 erg/gauss.

            The proton moment is 2.79 ìo.

 

Experiment 2:  Precise measurement of magnetic fields

 

            This experiment is different from the preceding only in emphasis.  Given that the proton resonance is very well known and that frequencies can be measured to very high precision, it follows that NMR provides a very good method of measuring fields.

            Set the magnet current at some pre-selected value.  Allow to stabilize.  Find the frequency at which resonance occurs in different regions of the magnetic field.  For fairly high fields it shall be possible to observe resonances away from the region between the pole pieces.

            The field values are calculated from

     v Mc/sec = 4.2577 H kgauss

using the proton resonance in water.

            Another effect shall be evident, the broadening of the resonance line.  This broadening is due to the increase of inhomogeneity of the field over the volume of the sample.  As the latter is moved away from the center of the space between the pole pieces, the field is increasingly inhomogeneous.  Hence resonance occurs at different places in the sample for different magnet currents.

            The x-axis of the oscilloscope display can be calibrated in terms of magnetic field.  For this, change the magnet current and measure the shift in position of the resonance peak.  This calibration is valid for only one setting of the oscilloscope controls; consequently, it is worthwhile only for measuring small inhomogeneities.

            For a better determination of the frequency, such as required for precise calculation of fields, the R.F. signal generator should be calibrated with crystal markers.  These have well known frequencies and are available on request.

 

Experiment 3:  Determination of the effect of paramagnetic ions on the relaxation time of protons in water.

 

            Relaxation means, in general, the process of adaptation of a system to a sudden change in conditions.  The relaxation time mentioned above is a parameter which gives an indication of the ability of nuclei to adapt themselves to the A.C. variation of the magnetic field.

            The effect of paramagnetic ions is to decrease the relaxation time.  Relaxation is normally brought about by the varying magnetic fields of nearby moving nuclei.  If there are present paramagnetic ions - even in small concentration - with large magnetic moments due to "uncompensated" electrons, field strengths shall change rapidly at each resonating nucleus, and relaxation times tend to be short.

            If water is now used to which ferric chloride or copper sulphate has been added, for example, the relaxation time decreases.  This results in a more prompt response of the system to the value of the magnetic field, thus sharpening the line.

            An interesting phenomenon which depends strongly upon the relaxation time is the appearance of "wiggles" in the tail of the resonance curve.  When the D.C. magnetic field changes too rapidly in terms of the relaxation time of the sample, the moments shall be predominantly ordered in a non-equilibrium direction.  These moments then precess as a whole about the D.C. field with diminishing amplitude.  The beats between this varying frequency and the R.F. appear as damped oscillations in the screen.  If two or more very close resonances were to occur, the beats between the wiggles themselves would allow one to study this "hyperfine" structure of the resonance line.

            We will concern ourselves with a total relaxation time.  It is usual to study spin-lattice and spin-spin relaxations.

            To measure a relaxation time:

 

            1.  Verify that the sample is well centered, and the field is as homogeneous as possible.

            2.  Calibrate the horizontal scale in the oscilloscope screen in terms of frequency.

            3.  Measure the frequency separation between points of half amplitude in the signal.

            4.  The total relaxation time is the inverse of one half of this frequency difference.

 

            This experiment can be repeated with samples of increasing molarity of impurities, and the corresponding decrease in relaxation time plotted versus concentration.

 

Other Experiments:  Resonances in other substances should be tried.  For example, proton resonance in kerosene; F19 resonance in solid KF (in which case v = 4.006H).

            Also, the "chemical shift" of the proton resonance in a series of compounds such as water, methylene chloride, benzene, chloroform, and sulfuric acid.  The effect of having different sets of non-equivalent protons, which therefore resonate at different external fields, can be tried in pure dry ethyl alcohol.

            Field homogeneity is very important in any experiment where more than one line is searched.  It may be necessary to remove all field-producing objects several feet away.

 

References:

 

G.E. Pake; "Magnetic Resonance"; Scientific American; August 1945; page 58.

G.E. Pake; American Journal of Physics; 18, 438 and 473; 1950.

J.A. Pople; "High-Resolution Nuclear Magnetic Resonance"; McGraw-Hill; 1959.

Bloch, Hansen and Packard; Phys. Rev. 79, 474; 1946.

W.B. Fretter; "Introduction to Experimental Physics"; Prentice-Hall; 1954.

K.K. Darrow; "Magnetic Resonance"; Bell Telephone System; Monograph No. 2065 (A very comprehensive and readable survey.  It includes M.R. of electrons.)