Table Of ContentHigh Resolution NMR
of Macromolecules
F R A NK A. B O V EY
BELL LABORATORIES
MURRAY HILL, NEW JERSEY
ACADEMIC PRESS New York and London
COPYRIGHT © 1972, BY BELL TELEPHONE LABORATORIES, INCORPORATED
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PREFACE
The study of polymers by nuclear magnetic resonance can be roughly
divided into two fields: (1) the measurement of nuclear (usually proton)
relaxation by pulse methods or by direct observation of "wide-line" spectra;
and (2) the study of high resolution spectra. The first of these commonly
employs polymers in the solid state with the object of obtaining information
concerning morphology and molecular motion. The second, which is the
province of this book, deals (with rare exceptions) with polymers in solution
and is directed toward the elucidation of the structure and stereochemistry of
polymer chains. It is the younger field of the two. The first studies of solid
polymers were reported only about a year after the original observations of
NMR in bulk matter in 1946; by 1958 there was a sufficient accumulation of
data to justify a lengthy review.1 In 1957, the first proton spectrum of a natural
polymer (lysozyme) was published, and in the following year the first report of
a synthetic polymer spectrum (polystyrene) was published. Since that time
the field has expanded rapidly, partly as the result of the observation in 1960
that NMR is a powerful means for the investigation of the stereochemistry of
vinyl polymers.
Chapter I is a description of the fundamentals of NMR, very similar to that
in Chapter I of my more general book.2 This discussion is intended to make the
book more or less self-contained. For more detailed descriptions of spectral
1 W. P. Slichter, Fortsch. Hochpolym. Forsch. 1, 35 (1958).
2 F. A. Bovey, "Nuclear Magnetic Resonance Spectroscopy," Academic Press, New
York, 1969.
ix
χ Preface
analysis and the dependence of chemical shifts and / couplings on structure,
one may wish to consult the treatises listed at the end of Chapter I (this is a very
partial list, in both senses of the word). Chapter II is a discussion of isomerism
in polymer chains without special reference to NMR. Chapters III-XII
describe the interpretation of synthetic polymer spectra in terms of structure,
stereochemical configuration, conformation, and chain growth mechanism.
The last three chapters (XIII-XV) deal with biopolymers (excluding carbo
hydrates) and their model compounds. This is the most exciting area of applica
tion of NMR to polymer science and is at present growing with explosive
rapidity, largely as the result of the more general accessibility of instruments of
high magnetic field (50 kG and upwards). Indeed, it may be said that in general
the fruitfulness of the NMR study of polymers has paralleled the development
of instruments of increasing field strength. For biopolymer studies, 50-kG
instruments have proved virtually indispensable.
A CKNO WLEDGMENTS
I wish to thank Mrs. Anne I. Brewster for running a number of spectra
obtained specifically to illustrate this book. I am grateful also to Dr. R. G.
Shulman and Dr. W, D. Phillips for critically reading Chapters XIII and XIV
and Dr. Tetsuo Yamane and Dr. Dinshaw Patel for performing a similar
service with respect to Chapter XV. Thanks are also due to many others,
particularly Dr. Dennis Torchia, for helpful discussions.
xi
Chapter I
FUNDAMENTALS OF
NUCLEAR MAGNETIC RESONANCE^
1. Introduction
The phenomenon of nuclear magnetic resonance depends on the fact that
some atomic nuclei possess (in addition to charge and mass, which are of
course common to all nuclei) spin, or angular momentum. A spinning charge
generates a magnetic field, and so there is associated with this angular momen
tum a magnetic moment. Nuclear spin was first proposed by Pauli1 as an
explanation for certain hyperfine structural features of atomic spectra. The
phenomenon of nuclear magnetic resonance has long been known in molecular
beams and has yielded much fundamental information on nuclear properties.2
This information was of little significance to chemists, however, until the
observation of nuclear magnetic resonance in bulk matter. This was achieved
by two independent groups in 1945—one with Purcell at Harvard and the
other with Bloch at Stanford. Purcell et al} reported resonance in solid
paraffin while Bloch et al.4 reported it in liquid water. With the observation
of three magnetically nonequivalent types of protons in ethyl alcohol,5 nuclear
magnetic resonance began to be primarily the province of the chemist, as it
is today.
t As noted in the Preface, much of the material in this chapter is similar to that in
Chapter I of the author's more general book "Nuclear Magnetic Resonance Spectroscopy,"
Academic Press, New York, 1969.
1
2 I. Fundamentals of Nuclear Magnetic Resonance
2. Nuclear Spin
The angular momentum of a nucleus possessing a spin (or of any particle
or system having angular momentum) is a half-integral or integral multiple
of Λ/27Γ, where h is Planck's constant. The maximum value of the angular
momentum is /, which is called the spin quantum number or more commonly
simply "the spin." Each nuclear ground state is characterized by just one
value of I. If /= 0, the nucleus has no angular momentum and no magnetic
moment. If / is not zero, the nucleus will possess a magnetic moment /χ,
which is taken as parallel to the angular momentum vector. The permitted
values of the vector moment along any chosen axis are described by means of
a set of magnetic quantum numbers m given by the series:
m = h (7-1), (7-2), -/ (1-1)
Thus, if I is \, the possible magnetic quantum numbers are and — \. If
/is 1, m may take on the values 1,0, and —1 and so on. In general, then, there
are 21 + 1 possible orientations or states of the nucleus. In the absence of a
magnetic field, these states all have the same energy. In the presence of a
uniform magnetic field H, they correspond to states of different potential
0
energy. For nuclei for which I is ^, the two possible values of w, and —
describe states in which the nuclear moment is aligned with and against the
field H, respectively, the latter state being of higher energy. The detection
0
of transitions of magnetic nuclei (often themselves referred to as "spins")
between these states is made possible by the nuclear magnetic resonance
phenomenon.
The magnitudes of nuclear magnetic moments are often specified in terms
of the ratio of the magnetic moment and angular momentum, or magnetogyric
ratio y, defined as
y -ψ ™
A spinning spherical particle with mass Μ and charge e uniformly spread
over its surface can be shown to give rise to a magnetic moment ehjAnMc,
where c is the velocity of light. For a particle with the charge, mass and spin
of the proton, the moment should be 5.0493 χ 10~24 erg/G on this model.
Actually, this approximation is not a good one even for the proton, which is
observed to have a magnetic moment about 2.79 times as great as the over
simplified model predicts. No simple model can predict or explain the actual
magnetic moments of nuclei. However, the predicted moment for the proton
serves as a useful unit for expressing nuclear moments and is known as the
nuclear magneton; it is the analog of the Bohr magneton for electron spin.
2. Nuclear Spin 3
Observed nuclear moments can be specified in terms of the nuclear magneton
by
P = g (1-3)
A 4πΜA/f c
ν
where M is the proton mass and g is an empirical parameter called the nuclear
p
g factor. In units of nuclear magnetons, then,
μ-gl (1-4)
In Table 1-1, nuclear moments are expressed in these units. It will be noted
that some nuclei have negative moments. This is of no great practical signific
ance to NMR spectroscopists; its theoretical meaning will be evident a little
TABLE 1-1
NUCLEI OF MAJOR INTEREST FOR POLYMER NMR SPECTROSCOPY
NMR frequency
Abundance (Hz) in 10 kG Relative Magnetic Spinc
Isotope (percent) field sensitivity0 moment (μ)5 (I)
Ή 99.9844 42.577 1.000 2.7927 *
2H(D) 0.0156 6.536 0.0096 0.8574 1
io 18.83 4.575 0.0199 -1.1774 3
B
nB 81.17 13.660 0.165 1.8006 §
13C 1.108 10.705 0.0159 0.7022 \
I4N 99.635 3.076 0.0010 0.4036 1
15N 0.365 4.315 0.0010 -0.2830 i
19p 100 40.055 0.834 2.6273 *
3ip 100 17.235 0.0664 1.1305
a For equal numbers of nuclei at constant H.
0
b In multiples of the nuclear magneton, eh!4nMc.
p
c In multiples of Α/27Γ.
later. It should also be noted that the neutron, with no net charge, has a sub
stantial magnetic moment. This is a particularly striking illustration of the
failure of simple models to predict /x. Clearly, the neutron must contain
separated charges (for at least a part of the time) even though its total charge
is zero.
Although magnetic moments cannot be predicted exactly, there are useful
empirical rules relating the mass number A and atomic number Ζ to the
nuclear spin properties:
1. If both the mass number A and the atomic number Ζ are even, 1=0.
2. If A is odd and Ζ is odd or even, / will have half-integral values: \,
h h etc-
3. If A is even and Ζ is odd, / will have integral values: 1, 2, 3, etc.
4 I. Fundamentals of Nuclear Magnetic Resonance
Thus, some very common isotopes, such as 12C, 160, and 32S, have no
magnetic moment and cannot be observed by NMR. This is fortunate in a
way, however, for if these nuclei did have magnetic moments, the spectra of
organic molecules would be much more complex than they are.
3. The Nuclear Magnetic Resonance Phenomenon
Nuclei with spins of such as protons, are often likened to tiny bar magnets.
But because of their small size and because they spin, their behavior differs
in some ways from the ordinary behavior of macroscopic bar magnets. When
placed in a magnetic field, the spinning nuclei do not all obediently flip over
and align their magnetic moments in the field direction. Instead, like gyro
scopes in a gravitational field, their spin axes undergo precession about the
field direction, as shown in Fig. 1-1. The frequency of this so-called Larmor
FIG. 1-1. Nuclear moment in a magnetic field.
precession is designated as ω in radians per second or v in cycles per second
0 0
or hertz, abbreviated Hz (ω = 2πν). If we try to force the nuclear moments
0 0
to become aligned by increasing H, they only precess faster. They can be
0
made to flip over, however, by applying a second magnetic field, designated
as H at right angles to H and causing this second field to rotate at the
u 0
precession frequency v. This second field is represented by the horizontal
Q
vector in Fig. 1-1, although in practice (see Section 4) it is actually very much
smaller in relation to H than this figure suggests. It can be seen that if Hi
0
rotates at a frequency close to but not exactly at the precession frequency, it
will cause at most only some wobbling or nutation of the magnetic moment μ.
If, however, H is made to rotate exactly at the precession frequency it will
x
3. The Nuclear Magnetic Resonance Phenomenon 5
cause large oscillations in the angle between μ and H. If we vary the rate of
0
rotation of H through this value, we will observe a resonance phenomenon
}
as we pass through v.
0
One might suppose that the Larmor precession of the nuclear moments
could itself be detected by some means without the need to invoke a resonance
phenomenon. This, however, is not possible because each nucleus precesses
with a completely random phase with respect to that of its neighbors and there
is therefore no macroscopic property of the system which changes at the
Larmor frequency.
By a well-known relationship, the Larmor precession frequency is given by
ω = γΗ (1-5)
0 0
or, from Eq. (1-2),
Ην = μΗΙΙ (1-6)
0 0
The result of this classical treatment can also be obtained by a quantum
mechanical description which is in some ways a more convenient way of
regarding the resonance phenomenon. It is best, however, not to try to adopt
either viewpoint to the exclusion of the other, since each provides valuable
insights. In quantum mechanical terms the quantity hv is the energy separation
0
ΔΕ between the magnetic energy levels in a magnetic field H, as shown in
0
Fig. 1-2. For a nucleus of spin ΔΕ will be 2μΗ, and, as we have seen, only
0
H
0
m =-ι, τ +//H
m = -i/2 j +μΗ 0
/ 0 / ·
/ ",H°
i 2//H 5ΐΞ£^-' 1
\ \ ι» 0 0
\ ι
\ *
m =+i/2 ^ 1 μΗ0 m =+i\ < ** //H0
I i =i 1=1
FIG. 1-2. Magnetic energy levels for nuclei of spin \ and 1.
two energy levels are possible. For a nucleus of spin 1, there are three energy
levels, as illustrated in Fig. 1-2. The quantum mechanical treatment gives us
an additional result for such systems with / > 1 which the classical treatment
does not: it tells us that only transitions between adjacent energy levels are
allowed, i.e., that the magnetic quantum number can only change by ±1.
Thus, transitions between the m = — 1 and m = 0 levels and between the
m = +1 and m = 0 levels are possible, but transitions between the m = — 1
and the m = +1 levels are not possible.
