Table Of ContentNMR AND EPR
SPECTROSCOPY
Papers presented at Variants Third Annual Workshop
on Nuclear Magnetic Resonance and Electron Paramagnetic
Resonance, held at Palo Alto, California
by
THE NMR-EPR STAFF
OF VARIAN ASSOCIATES
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INTRODUCTION
IT IS the annual practice of Varian Associates to hold in October an inter
national gathering of scientists who share a common interest in acquiring,
expanding or exchanging their knowledge of Nuclear Magnetic Resonance
and Electron Paramagnetic Resonance Spectroscopy. The fundamental pur
poses of this "NMR-EPR Workshop" are twofold: first, to provide new
workers with an opportunity to attend introductory, intermediate, and
advanced lectures and laboratory sessions in these fields of spectroscopy;
and second, to offer experienced workers a meeting ground for keeping abreast
of recent developments.
As has been the case with so many other facets of the brief history of
Varian Associates (less than twelve years), much of the spirit of the NMR-
EPR Workshop can be traced to the inspiration and atmosphere established
from the beginning by the late Russell H. Varian. This unusual man proved
beyond all doubt that basic and applied science can mix compatibly and
beneficially with the necessities and objectives of private enterprise. We join
the world-wide scientific community in mourning the passing, in Alaska on
July 28, 1959, of this extraordinary scientist and humanitarian.
This book covers in large part the material presented by the NMR-EPR
staff of the Instrument Division of Varian Associates at the Third Annual
Workshop, held October 19-23, 1959.
The 1959 Workshop was divided consecutively into three parts. The first
day was devoted to an introduction to NMR and EPR. The content of this
session was tailored specifically to persons approaching these subjects for the
first time. The second and third days were devoted exclusively to intermediate
and advanced topics in the High Resolution form of NMR Spectroscopy ; the
content of this part included a number of laboratory sessions designed to
supplement and complement the lectures. Finally, the fourth and fifth days
were devoted to lecture and laboratory sessions in.EPR Spectroscopy. All
of the lectures presented during the Workshop week have been included
herein in necessarily more formal fashion than originally delivered; on the
other hand, several laboratory sessions have been omitted completely in the
compilation because they did not lend themselves readily to a written pre
sentation.
The 1959 registration figures show that 160 scientists from a wide variety
of disciplines in chemistry, physics, biology, and medicine converged on
Palo Alto for the Third Annual Workshop. Of this number, eighteen came
from thirteen foreign countries.
vi Introduction
Several acknowledgments should be made. First, we are grateful to Gerard
Piel, publisher of Scientific American, who provided a thought-provoking
after-dinner speech—"The Economics of Disarmament"—at the Workshop
banquet. We must also pay our tardy respects in print to Professor Bryce
Crawford, Chairman of the University of Minnesota Chemistry Department,
for having, in the summer of 1957, reminded us of just the precise word—
"Workshop"—for describing our proposed gathering of scientists. John
Marling, James Shoolery, and Robert Rempel served tirelessly and enthusi
astically as the chairmen of the three Parts of the 1959 Workshop. Mr.
Marling also merits thanks for having helped compile and check all of the
papers which have been reproduced herein. The 1959 Workshop Registrar,
Miss Frances Demma, deserves special commendation for her efforts, as does
also Edward Vopat,. wBo was in charge of many advance arrangements and
the extracurricular programs associated with the Workshop. The wives of
Varian participants were hostesses for several of these events ; it was their
considerable pleasure to meet and entertain the wives of visitors. Finally,
we can only express gratitude anonymously and profusely to all of the other
persons whose names cannot appear here for space reasons, but whose efforts
contributed vitally to the success of the Workshop.
MARTIN E. PACKARD, Director
Instrument Division Research
EMERY H. ROGERS, Chairman
NMR-EPR Workshop
1
BACKGROUND AND FUNDAMENTALS OF
NMR-EPR SPECTROSCOPY AND
SPECTROMETERS
EMERY H. ROGERS
Varian Associates, Palo Alto, California
NUCLEAR Magnetic Resonance (NMR for short) depends for its existence
upon the fortunate and useful fact that most isotopes of the elements possess
gyromagnetic properties. By this it is meant that they behave like tiny spin
ning bar magnets.
When a sample containing nuclei exhibiting this immutable gyromagnet-
ism is placed in an appropriate d.c. magnetic field and is simultaneously
irradiated by just the right kind of a much weaker rotating radio-frequency
magnetic field, the nuclei can be compelled (a) to reveal their presence,
(b) to identify themselves, and (c) to describe the nature of their surroundings
—all by means of minute radio signals which they transmit to a receiver coil
coupled closely to the sample. It can well be imagined that these significant
revelations, which can be elicited painlessly and nondestructively from nuclei,
can be of immense importance to, among others, the organic chemist, the
physical chemist, the analytical chemist, the spectroscopist, the nuclear
physicist, the solid-state physicist, the nuclear isotope spectroscopist, the
polymer physicist, the biochemist, the biophysicist, and the medical research
worker. By a fortunate inverse mechanism which will be explained later, it
turns out that any worker interested in making a precise measurement of a
d.c. magnetic field is also indebted to NMR for simplifying his endeavors and
expanding their precision.
Electron Paramagnetic Resonance (EPR for short) is basically similar to
NMR in that it depends upon gyromagnetic properties of sub-atomic particles
for its existence. However, in the case of EPR, it is the population of un
paired electrons in the samples which is subjected to the above-described d.c.
magnetic field and simultaneously-applied radio-frequency field, and which
then responds with transmitted revelations of its own. Because the gyro
magnetic constant associated with the spinning electron is some hundreds
of times greater than that associated with nuclei, the experimental apparatus
1
0 EMERY H. ROGERS
necessary for detecting EPR signals is usually comprised of microwave
components, such as wave-guide, cavities and klystron tubes; while on
the other hand in NMR the detecting apparatus is replete with lumped
inductances and capacitors, wires for conducting the conventional frequency
r.f. energy from one place to another, and the standard sort of vacuum tubes
which you would encounter in your TV set. But, stripped of the differences in
outward experimental trappings, NMR and EPR have many similarities, and
the one may be much more readily understood once the other is mastered.
In fact, many workers in the wide range of scientific disciplines enumerated
above move back and forth between NMR and EPR studies, depending
upon which tool offers the most effective means of getting a given job done.
Thus, for convenience, I will develop the subject of NMR first and then con
clude with EPR, utilizing much of the groundwork built up for the former to
explain the latter.
The first successful NMR experiments were performed essentially simul
taneously and independently at two American universities, Stanford and
Harvard, in the winter immediately following the end of World War II. The
co-discoverers—Felix Bloch at Stanford and E. M. Purcell at Harvard—
were rewarded for their achievements with the 1952 Nobel Prize in Physics.
Significant though these historic experiments were, it is surely true that the
co-discoverers would have been pleasantly surprised if they could have en
visioned then the vast range of subsequent usefulness to which the original
ideas were nurtured and expanded by themselves and thousands of other
workers. For an indication of the accomplishments and developments in just
the first decade after the initial discovery, the reader is referred to two excel
lent review articles.* Improvements and discoveries came so rapidly during
the years after the first experiments that it is only recently that compre
hensive textbooks on the various aspects of magnetic resonance are beginning
to appear.f Workers in the field were simply too well aware of the fact that
any book which appeared today would inevitably be disastrously obsolete
tomorrow.
In order for us to understand the basic principles and instrumentation of
NMR, we must first realize that man's quest for this mechanism was bolstered
considerably by earlier knowledge. Long before the first NMR experiments
were performed, it was well known that nuclear isotopes with non-zero spin
also possessed a coupled magnetic moment. Through secondary effects, such
as observation of hyperfine structure in the Zeeman Effect, and through
atomic and neutron beam experiments, the proof was conclusive even though
* H. S. Gutowsky, Ann. Rev. Phys. Chem., 5, 1954; and J. N. Shoolery and H. E.
Weaver, Ann. Rev. Phys. Chem., 6, 1955.
t Good examples: Roberts, Nuclear Magnetic Resonance, McGraw-Hill (1959); Pople,
Schneider and Bernstein, High-Resolution Nuclear Magnetic Resonance, McGraw-Hill
(1959); and for EPR: Ingrain, Free Radicals as Studied by Electron Spin Resonance,
Butterworths (1958).
Background and Fundamentals 3
the measurements of the moments themselves were crude insofar as accuracy
was concerned. But the real trick was recognized as the measurement of this
property in a direct and precise fashion in bulk material. Once nuclei could
be forced to reveal themselves directly, a valuable new tool for, at the very
least, identification purposes would have been devised. This thought followed
from evidence that each isotopic species of non-zero spin had not only an
immutable gyromagnetic constant, but also one which would be expected to
differ from the gyromagnetic constants associated with all the other non
zero-spin isotopic species. Thus, just as the mass spectrometer distinguishes
on the basis of mass, an NMR device would be expected to distinguish on the
basis of gyromagnetism. Now how was this thought brought to reality?
The success of the 1945-46 experiments was first of all dependent upon a
classical theorem enunciated at the turn of the century. J. Larmor showed
in effect that a spinning bar magnet, free of all frictional forces, would, when
placed in a d.c. magnetic field, precess like a top about the direction of the
magnetic field. He further showed that the frequency of precession was
directly proportional to the strength of the magnetic field, and that the
constant of proportionality was the ratio of the magnetic moment of the
spinning bar magnet to its angular momentum. This constant of propor
tionality is now called y, the "gyromagnetic ratio" for the spinning magnet.
(Since the constant γ is the ratio of magnetic moment to angular momentum
rather than the reverse, several workers have rightfully proposed that the
constant be called the "magnetogyric ratio". Unfortunately, this literally
more accurate nomenclature has not been generally adopted.) Thus, the
Larmor Precession Theorem can be stated as follows :
ω = γΗ
where ω = 2π times the precession frequency, y is the gyromagnetic constant
appropriate for the spinning bar magnet, and H is the d.c. magnetic field in
which the precession is taking place.
Now if we expand the original Larmor concept to include the inevitable
existence of frictional forces, it is evident that the spinning bar magnet will
sooner or later come into alignment with the d.c. magnetic field, depending
upon the strength of those forces. The time associated with re-alignment is
generally called the "relaxation time", or more specifically, the "longitudinal
relaxation time". When the frictional forces are large, the time is short, and
vice versa. At the point of alignment, the precession ceases, but at all times
up to this point, regardless of the angle between the precession field and the
spinning magnetic moment, the frequency of precession is given by the basic
Larmor expression.
Taking the simple model of a hydrogen nucleus as a rotating charged sphere,
we can visualize how its spin might give rise to an associated magnetic mo
ment. We must realize that a spinning charge is the equivalent of a small
4 EMERY H. ROGERS
current loop, and remember that such a loop can be represented by an equiva
lent magnetic moment. Thus, the hydrogen nucleus fits the model of the spin
ning bar magnet, having both a magnetic moment and an angular momentum
due to its well-known quantized spin. The ratio of these two quantities, y,
is of course the gyromagnetic constant for the proton.
Since we are dealing with particles subject to the rules of quantum mech
anics, we should be able to derive the basic Larmor Equation from these
principles.
Equating the Planck quantum of energy, hv, with the energy of reorienta
tion of a magnetic dipole with magnetic moment fiina magnetic field H, we
have
2μΗ = hv
Rearranging, we find that
o W μ „
ω = 2πν = = X H
Α/2π £(λ/2π)
Now the angular momentum of the proton is equal to its spin value (i) multi
plied by Α/2π. Thus
— xH = γΗ
ω
ang. mom.
i.e. the Larmor Equation.
While a single nucleus is treated according to quantum mechanical laws
here, a great ensemble of nuclei, such as one would find in, say, \j cm3 of
T
some liquid sample containing hydrogen, can be looked upon as obeying the
laws of classical dynamics in the aggregate. This time-honored duality of
viewpoint—the classical and quantum mechanical—has so far caused few,
if any, nervous breakdowns on the part of countless workers in the various
fields of physics and chemistry, and for convenience of understanding mag
netic resonance, the alternative viewpoints appear frequently in its literature.
For countless eons, hydrogen nuclei (and all the other non-zero-spin iso
topes) have been precessing transiently, according to Larmor's equation,
in whatever magnetic field they found themselves. Of course, these nuclei
are subject to frictional forces provided by coupling to their environment,
and the only way that they can experience brief precessional motion is for
their axes to be tilted somehow with respect to the magnetic field in which
they are immersed.
Let us consider a simple example. The protons in an undisturbed glass of
water are aligned along the earth's magnetic field. During a brief period after
a small magnet has been momentarily brought near this glass of water, hydro
gen nuclei therein are wrenched around and thereby experience a tilt with
respect to the earth's magnetic field. Accordingly they will precess at a fre-
Background and Fundamentals 5
quency determined by the earth's field, until they relax back into alignment
again. If there had been an ice cube floating in the water, the time for re
alignment of the protons in the ice would have been shorter by many orders
of magnitude than that for the protons in water, but in either case the pre
cession frequency would have been the same. To give specific numbers, the
constant y for hydrogen nuclei is such that, in the earth's field of approxi
mately 0.5 gauss, the Larmor precession frequency is something like 2000 c/s.
Of course the O17 nuclei in the glass of water would also have experienced a
transient precession, but their y is such that, in the earth's magnetic field of
0.5 gauss, their precession frequency would have been more like 300 c/s.
All other non-zero-spin nuclei in the glass-water combination would have
also obeyed the Larmor Precession Theorem immediately after tilt had been
introduced.
Our glass of water subjected to a momentary small additional magnetic
impulse over and beyond the steady earth's field would of course have re
vealed nothing to our human senses, feeble detectors insofar as magnetism
is concerned, or to any artificially contrived detecting mechanism which
might have been placed in the vicinity of the glass. In addition to the highly
transient nature of the phenomenon, two other factors militated against any
apparent observable results. The first additional factor is the one of random
ness. Looking at the event in a simplified way, we might say that all of the
protons making up the ensemble were without phase reference to one another
during the transient precession. Thus, not having coherence, there was no
way in which they could combine their forces to produce an effect multiplied
by their great number. Unfortunately, and here is where the second additional
negative factor comes in, even if they had somehow acquired phase coherence,
all of their population would not have contributed to the resultant effect.
This arises from the Boltzmann condition which tells us that, due to the
competing process of thermal agitation within the sample, there is almost the
same probability that the protons will be pointing along the field direction
as in opposition to it; and furthermore that whatever excess population is
pointing along the direction of the field must be directly proportional in
magnitude to the precession field strength. Because of the cancellation of
opposing vectors, it is only the excess population pointing along the field
direction which can be considered in any dynamical event in which the whole
population participates. An analysis of the Boltzmann distribution of gyro-
magnetic particles in a d.c. magnetic field yields the sad news that at room
temperature only one proton out of each ten billion contributes to any effect
at the earth's field, whereas 20,000 protons out of each ten billion serve a
useful purpose at a strong field of 10,000 gauss. Even if the effect had not
been transitory and even if phase coherence had been miraculously introduced
and retained, the effective participating population would have been so small
as to produce only the feeblest of effects.
6 EMERY H. ROGERS
Thus, a successful NMR experiment requires {a) some mechanism for
replenishing the precessing population in opposition to the frictional relaxing
forces, (b) some means for introducing phase coherence so that a great effec
tive multiplication of the individual precession occurs, and (c) a precession
field much stronger than that of the earth in order to obtain a useful working
population. It is exactly these three ingredients which Bloch applied to the
water sample when he and co-workers performed the first successful ''nuclear
induction' ' experiment.
In order to understand how the first two ingredients were supplied in the
Bloch experiment, we must refer to Fig. 1, a greatly simplified diagram of an
^ fi S-
R-F
R-F RECEIVER
TRANSMITTER
a DETECTOR
9 9
■fi
SWEEP RECOROER
GENERATOR U J
TO
r rr , MAGNET
FIG. 1. How an NMR spectrometer works.
NMR detector of the "crossed-coil" type. Our water sample has been placed
in a small test tube located at the air gap center of a large magnet with field
H of, say, 10,000 gauss. Reality has been blithely ignored in the diagram :
the magnet is shown with a very unfavorable pole-diameter-to-air-gap ratio,
and, as a consequence, the magnetic field gradient at the sample position
would in actual practice seriously impair chances of obtaining a signal
successfully.
At right angles to the field direction in the air gap of this mythical magnet
has been placed a radio-frequency transmitter coil, which in turn is excited
by r.f. energy supplied from the r.f. transmitter. The master oscillator in this
r.f. transmitter has been set precisely at 42.577 megacycles to correspond,
through the Larmor relation ω = γΗ, to the assumed 10,000 gauss magnetic
field in the air gap. At right angles to both the d.c. magnetic field and the
radio-frequency transmitter coil, a receiver coil has been wound tightly
around the sample tube. The leads from this receiver coil proceed to a radio-
frequency receiver, tuned to the same frequency as the transmitter. An r.f.
