High Field DNP NMR Probe Design and
Application in Crystalline Solids
by
Christopher Blake Wilson
Submitted to the Department of Physics
in partial fulfillment of the requirements for the degree of
MASSACHUSETTS INSYffWE
OF TECHNOLOGY
Bachelor of Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2013
@ Christopher Blake Wilson, MMXIII. All rights reserved.
The author hereby grants to MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document
in whole or in part in any medium now known or hereafter created.
A uth o r ............. .........................................
......
Department of Physics
May 10, 2013
r~ r
C ertified by ........
..
.
.. ... ............
....................
Professor Robert G. Griffin
Department of Chemistry
Thesis Supervisor
A ccepted by .......................
I...v ..............................
Professor Nergis Mavalvala
Senior Thesis Coordinator, Department of Physics
SEP 0 4 2013
IBRARIES
2
High Field DNP NMR Probe Design and Application in
Crystalline Solids
by
Christopher Blake Wilson
Submitted to the Department of Physics
on May 10, 2013, in partial fulfillment of the
requirements for the degree of
Bachelor of Science
Abstract
Dynamic nuclear polarization (DNP) is a valuable tool which can be used to enhance
nuclear magnetic resonance (NMR) signal intensities in a variety of biological and
materials science systems, by transferring polarization from unpaired electrons to
nuclei. In this thesis, the mechanical design and radio frequency NMR circuit for
a triple channel magic angle spinning (MAS) DNP NMR probe for operation at 5
Tesla are developed, and the construction of the probe is detailed. The probe carries
15
1
13
out NMR in three frequency ranges, corresponding to the H, C, and N Larmor
1
2
frequencies at 5 T, but can be tuned to other nuclei as well, in particular H. A H
cross effect DNP enhancement of 40 on 1 3C labeled urea, using 10 mM TOTAPOL, is
reported after cross polarization to 13 C. As of writing, the probe is undergoing further
optimization to improve the enhancement.
The dynamics and interactions of water molecules are studied in lanthanum mag2
nesium nitrate hydrate (La 2 Mg 3 (NO 3 ) 12 24H 2 0) (LMN) using a variety of H and
170 NMR techniques. Variable temperature 2 H spectra are studied to characterize
water dynamics in LMN, and the 170 quadrupole interaction is studied in an attempt
to resolve crystallographically distinct water sites. 170 MQMAS is performed.
Gadolinium is explored as a polarizing agent for DNP enhanced NMR. LMN
crystals doped with Gd are synthesized, with the goal of using the enhancement from
DNP to allow further characterization of crystalline solids. Polarization transfer to
1
H in LMN doped with 3% Gd through the solid effect at 5 T is observed, and an
15
2
NMR enhancement of 2.5 is recorded at 85 K. Planned future work on H and N
DNP in LMN, using the MAS DNP NMR probe described here, is outlined.
Thesis Supervisor: Professor Robert G. Griffin
Title: Department of Chemistry
3
4
Acknowledgments
I have been extremely fortunate to work with a great many excellent scientists and
friends at the MIT Francis Bitter Magnet Lab. Thank you Professor Bob Griffin, for
your advice, your help, and your patience, as well as your confidence in me, without
which none of this work would have been possible. Thank you Dr. Vlad Michaelis,
Dr. Bj6rn Corzilius, and Ta-Chung Ong for teaching me everything I know about
NMR spectroscopy. Vlad, thank you for being patient with me, and thank you for
taking me under your wing last summer- I have learned an incredible amount in the
last year. Bj6rn, thank you for your help with the design and early testing of the
probe. Most of the data presented here was collected with the help of Vlad and TC,
and for their help in that respect I am doubly grateful. In addition, without a great
deal of work from Jeffery Bryant, the probe described here would not exist. Finally,
thanks to the entire Bitter crew for their support and friendship over the past two
years.
5
6
Contents
1
Introduction
17
2
Overview of Solid State Nuclear Magnetic Resonance Spectroscopy
19
2.1
2.2
2.3
3
. . . . . . . . . . . . . . .
20
2.1.1
Density Matrix Formalism . . . . . .. . . . . . . . .
20
2.1.2
Nuclear Spin in a Static Magnetic Field . . . . . . .
23
2.1.3
Nuclear Spin in a Radio Frequency Magnetic Field
24
2.1.4
Relaxation . . . . . . . . . . . . . . . . . . . . . . .
25
Solid State NMR Spectroscopy
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.2.1
Dipolar Coupling . . . . . . . . . . . . . . . . . . . . . . . . .
27
2.2.2
Chemical Shielding and Chemical Shifts
. . . . . . . . . . . .
28
2.2.3
Quadrupole Interaction . . . . . . . . . . . . . . . . . . . . . .
29
Solid State NMR Techniques . . . . . . . . . . . . . . . . . . . . . . .
31
2.3.1
Bloch Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
2.3.2
Hahn Echo
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
2.3.3
Magic Angle Spinning
. . . . . . . . . . . . . . . . . . . . . .
32
2.3.4
Decoupling
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
2.3.5
Cross Polarization
. . . . . . . . . . . . . . . . . . . . . . . .
35
2.3.6
Multiple Quantum MAS . . . . . . . . . . . . . . . . . . . . .
35
Interactions
37
Dynamic Nuclear Polarization
3.1
DNP at High Magnetic Fields . . . . . . . . . . . . . . . . . . . . . .
38
3.2
Gyrotrons as Microwave Sources for DNP . . . . . . . . . . . . . . . .
38
7
3.2.1
Polarization Mechanisms . . . .
39
3.3
Theory of DNP . . . . . . . . . . . . .
39
3.4
The Solid Effect . . . . . . . . . . . . .
40
3.4.1
Static Electron and Nucleus . .
41
3.4.2
Microwave Hamiltonian
. . . .
42
The Cross Effect and Biradicals . . . .
43
3.5
4
Probe Construction and Design
45
4.1
. . . . . . . . . . .
45
4.1.1
NMR Coil . . . . . . . . . . . .
47
4.1.2
M AS . . . . . . . . . . . . . . .
48
4.1.3
Sample Eject
. . . . . . . . . .
48
. .. . . . . . . . . . . . .
49
Mechanical Design
4.2
RF Circuitry
4.3
Microwave Waveguide
. . . . . . . . .
50
4.4
Performance . . . . . . . . . . . . . . .
50
4.4.1
4.5
4.6
'H and
13
C 7B 1 . . . . . . . . .
Cross Effect DNP with TOTAPOL
51
. .
51
4.5.1
DNP Enhancement . . . . . . .
51
4.5.2
Polarization Buildup . . . . . .
52
4.5.3
Microwave Power Dependence .
53
Discussion . . . . . . . . . . . . . . . .
53
5 NMR and DNP NMR Investigation of Lanthanum Magnesium Nitrate
55
5.1
Lanthanum Magnesium Nitrate Hydrat e
5.2
Methods ...
5.3
.......
... . .....
5.2.1
Synthesis
5.2.2
Deuterium NMR
.
. . . . . . . . . . . . .
5.2.3
Oxygen NMR
5.2.4
170
.. . . . . . . . .
MQMAS
. . . . . . . . .
56
. . . . . ..
58
. . . . . . . . .
58
. . . . . . . . .
59
. . . . . . . . .
60
. . . . . . . . .
61
Solid Effect Dynamic Nuclear Polarization with Gadolinium
8
..
. . . . .
63
D NP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
64
5.3.1
5.4
A Supplementary Figures
67
9
10
List of Figures
2-1
Zeeman interaction of an I = 1/2 nucleus. (Reference [29])
2-2
The Zeeman, first, and second order quadrupolar interactions, for an
I= 9/2 nucleus. (Reference [29])
2-3
. . . . . .
. . . . . . . . . . . . . . . . . . . .
24
30
Schematic representations of Bloch (a) and Hahn echo (b) pulse sequences. (Reference[29])
. . . . . . . . . . . . . . . . . . . . . . . . .
2-4
NMR signal observed after a Hahn Echo pulse sequence. (Reference [30])
2-5
The anisotropic chemical shielding interaction, for (a) a static sample,
32
32
(b-d) increased spinning speeds at the magic angle, and (e) in the limit
of infinite spinning. (Reference [29]) . . . . . . . . . . . . . . . . . . .
3-1
DNP of 'H, followed by cross polarization to
of
3-2
13
C (or
13
C (or
15
34
N). NMR signal
15
N) is detected, under 'H decoupling. . . . . . . . . . . . .
38
Electron-nuclear spin system, with EPR and NMR transition energies
and couplings calculated to first order. DNP transitions corresponding
to positive and negative enhancements are indicated by the solid and
dashed lines, respectively (Reference [18]) . . . . . . . . . . . . . . . .
4-1
Triple channel MAS DNP NMR probe, view of the tuning box at the
top .
4-2
42
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
Triple channel MAS DNP NMR probe, view a) the sample eject, b)
the magic angle adjust, c) the stator housing, d) the drive and bearing
gas posts, e) the microwave waveguide, f) the bearing gas transfer line,
g) the drive gas transfer line, and h) the exhaust and eject gas transfer
lin e.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
47
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-3
Sam ple Eject
4-4
13 C-CP signal of
where
1
13
49
C-urea from the enhanced 'H polarization at 92 K,
H was polarized via the cross effect at 5 Tesla, with 8.5W of
microwave power. The sample contained 10mM TOTAPOL, and was
rotated at a MAS frequency of 8.3 kHz. . . . . . . . . . . . . . . . . .
4-5
Buildup of
13
C-CP signal of
13
C-urea from the enhanced
1
52
H polariza-
tion during a delay while under microwave irradiation. The buildup
time constant TB 6.2s. The sample contained 10 mM TOTAPOL, and
was rotated at a MAS frequency of 5.8 kHz.
4-6
Microwave power dependence of cross effect DNP
measured through
quency of 5.8 kHz.
5-1
. . . . . . . . . . . . . .
13
1
52
H enhancement,
C-CP, for 10 mM TOTAPOL under a MAS fre. . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
Lanthanum Magnesium Nitrate Hydrate. Yellow is lanthanum, purple
is magnesium, grey is hydrogen, red is oxygen, and blue is nitrogen.
The four crystallographic water sites are labeled 1-4. Crystallographic
parameters taken from Reference [3].
5-2
. . . . . . . . . . . . . . . . . .
57
Spectra a) and b) feature jagged lines which arise from small single
crystals which were not finely enough ground. Spectrum c) is a powder
line spectrum from a properly ground sample. The sharp peak at 0
kHz arrises from residual mobile water, and is not part of the crystal
structure.
5-3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
NMR spectrum of the
170
59
central transition at 18.8 T for LMN syn-
thesized in 40% 170 enriched H 2 0. Simulated spectra on top, observed
spectra bellow. Left: under MAS, with 18 kHz spinning frequency.
Right: Under static conditions, with no decoupling.
5-4
. . . . . . . . . .
60
NMR spectrum of the 170 central transition at 21.1 T for LMN synthesized in 90%
170
enriched H 2 0, (a) with a MAS frequency of 20 kHz,
(b) non-spinning, with 83 kHz 1H decoupling, and (c) non-spinning
with no decoupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
61
5-5
MQMAS spectrum of 170 at 18.8 Tesla, with a MAS frequency of 16
kHz. The horizontal axis is the MAS dimension, and the vertical axis
is the isotropic dimension. a) and b) are spinning sidebands. . . . . .
5-6
62
Direct detect 'H spectra of LMN-Gd, 3% Gd doped, taken at 85K with
4.2 kHz MAS spinning, with microwaves on (top) and off (bottom),
showing a DNP enhancement E = 2.5. A recycle delay of 90s was used.
63
A-1 Observed and simulated 2 H spectra taken at 9.4 Tesla, at variable temperatures. Spectra were simulated using a simple two-site hop model,
from which hoping rates were calculated to be (from the top): 6.1 x 108
Hz, 6.3 x 107 Hz, 2.5 x 107 Hz, 1.0
x 107
Hz, 1.6 x 106 Hz, and 6.5 x 105
Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
A-2 The 'H channel transmission line branching off from the main transmission line. The branching point is adjustable, and is set at the location
of a 1H channel voltage node
. . . . . . . . . . . . . . . . . . . . . .
69
A-3 Schematic representation of the radio frequency circuit of the NMR
probe. ........
...................................
13
70
14
List of Tables
5.1
Calculated hopping frequency of D 2 0 in LMN. . . . . . . . . . . . . .
15
64
16
Chapter 1
Introduction
Solid state nuclear magnetic resonance (NMR) spectroscopy is an extremely valuable
tool for studying a variety of biological, inorganic, and materials science systems. By
understanding the interactions between intrinsic nuclear spins and magnetic fields,
spectroscopists can extract valuable information about molecular structure and dynamics. However, NMR is limited in its usefulness by weak signal intensities arising
from the small values of nuclear gyromagnetic ratios.
NMR spectroscopy in the solid state is further limited by strong anisotropic couplings between nuclei and their environment, leading to broad, weak lines that obscure
information about the sample. A variety of techniques, such as magic angle spinning
(MAS), isotopic enrichment, decoupling, and cross polarization, have made it possible to obtain high resolution spectra of solid samples. Resolution has been further
improved as higher and higher magnetic field strengths have become available to
spectroscopists.
Despite advances in techniques, the sensitivity of solid state NMR is still limited.
Over the past two decades, dynamic nuclear polarization (DNP) as a method to
improve the sensitivity of solid state NMR experiments has been developed. DNP
can improve the sensitivity of NMR spectroscopy by two to three orders of magnitude,
dramatically reducing signal acquisition times, and allowing NMR to be applied to
systems where low sensitivity made traditional NMR prohibitively expensive or time
consuming.
17
DNP increases NMR sensitivity by transferring electron polarization from unpaired electron spins to nuclear spins, resulting in a theoretical NMR enhancement
of -660 for 1H, and -2600 for
13
C. Polarization transfer occurs through a variety
of mechanisms, and is driven by microwave radiation near the electron Larmor frequency. Polarizing agents are added to NMR samples to increase the number of
unpaired electron spins and to optimize polarization transfer.
Chapters 2 and 3 give an overview of solid state NMR and DNP NMR, outlining the methods used to obtain high sensitivity, high resolution spectra, and the
mechanisms through with polarization transfer occurs in solid dielectrics.
There are several challenges to designing spectrometers for DNP enhanced NMR.
High resolution solid state DNP NMR probes must be able to sustain MAS at temperatures below 90 K, and must be able to deliver high powered microwaves to the
NMR sample. At high magnetic fields, where NMR resolution is improved, a source
of high powered microwaves in the hundreds of GHz range must be used. The development of new polarizing agents for DNP which can efficiently transfer polarization,
are soluble in aqueous media, and may be applied to a wide range of systems is an
area of active research.
Chapter 4 details the design and construction of a MAS DNP NMR probe, operating at 5 T at the MIT Francis Bitter Magnet Lab. The performance of the probe is
presented along with preliminary DNP results. Chapter 5 outlines the investigation,
using NMR spectroscopy, of lanthanum magnesium nitrate hydrate (LMN). LMN
crystals doped with gadolinium are explored spectroscopically, with the aim of developing self-polarizable crystals for DNP NMR. Solid effect DNP of 'H in Gd doped
LMN is carried out, and future DNP experiments on LMN using the probe described
in Chapter 4 are outlined.
18
Chapter 2
Overview of Solid State Nuclear
Magnetic Resonance Spectroscopy
The interactions between nuclear spins, electron spins, and magnetic fields are described by the theory of magnetic resonance. This chapter outlines the basic theory of
pulsed NMR spectroscopy, and highlight techniques of particular importance to the
application of NMR to the solid state. In addition, a formalism is developed which
will by applied in Chapter 3 to describe various dynamic nuclear polarization (DNP)
mechanisms.
NMR was discovered in 1946 [33, 8], and was initially hailed as a new method for
accurately measuring nuclear magnetic moments. Nuclei with intrinsic spin, when
placed in a large magnetic field, became polarized along the direction of the field.
By applying additional magnetic fields at right angles and in short pulses to the
constant field, this polarization could be rotated away from the static field, leading to
a coherent magnetization that rotated about the static field at the Larmor frequency,
given by the product of the nucleus' gyromagnetic ratio, -y, and the magnitude of the
static magnetic field, B 0 .
In 1950, Hahn [14] showed that the observed NMR frequency of a given nucleus
varied depending on the molecular environment experienced by the nucleus.
This
effect, known as the chemical shift, led to the development of NMR as a technique
for studying molecular structure. In addition to the chemical shift, a wide range of
19
spin-spin and spin-environment interactions [37, 16] have been characterized, further
increasing the power of NMR spectroscopy as a tool for studying systems in biological
and materials science.
However, in its infancy, NMR spectroscopy was limited as a useful tool to liquid
samples [15]. This is because many spin-spin and spin-environment interactions are
anisotropic, and depend strongly on molecular orientation. In liquids, molecular motion quickly averages out these anisotropic interactions, leading to narrow absorption
lines and well defined NMR spectra. In solid samples, however, any molecular motion
is usually too slow to average out these anisotropic interactions, leading to broad lines
that reveal little of interest to physicists or chemists.
Section 2.1 describes methodologies that have allowed solid state NMR to achieve
high sensitivity, such as magic angle spinning, decoupling, and multiple quantum
techniques.
2.1
Solid State NMR Spectroscopy
A typical pulsed NMR spectroscopy experiment involves four components- a large,
static magnetic field, a sample of interest, a source of time-varying magnetic field,
and a coil to detect the NMR signal. Typically, the time-varying magnetic field is
supplied by pulsing a current through the same coil that is used for detection. Here, a
formalism for describing theoretically the behavior of nuclear spins in the presence of
static and oscillating magnetic fields is developed. The same formalism also describes
electron spins.
2.1.1
Density Matrix Formalism
Developing a theory of magnetic resonance, one inevitably encounters statistical mixtures of states. The density matrix formalism allows for the treatment mixed of states,
20
such as arise in a thermal distribution. The density matrix p of a system is given by
P= Z
Pk
(2.1)
K1
?/)k
k
where
Pk
is the probability the system is in state
10k).
The expectation value of an
operator is given by the trace of the operator with the density matrix,
(0) = Tr (Op)
(2.2)
The time evolution of the density matrix follows from the Schr6dinder equation,
P k Pk(+dIVk
d
'kI
k
O
(2.4)
1
k
d
1
-= -[ H,p]
dt
ih
(2.5)
Equation 2.5 has a simple solution when H is time independent. Setting h = 1,
the solution is given by
p(t) = e-iHtp(O)eiHt
(2.6)
The time evolution of expectation values can be then be calculated as follows,
(0) = Tr (Oe-iHtp(O)eiHt)
Tr (eiHtO-iHtp(O))
(2.7)
When H depends on time, the situation is more complicated, and in general no
simple analytic solution p(t) exists.
However, for certain classes of Hamiltonians,
analytic solutions do exist. In some cases, the dynamics of a system governed by a
time varying Hamiltonian can be calculated by transforming the system into a frame
where the Hamiltonian is time independent.
21
Consider the density matrix p',
p' = UpUt
(2.8)
related to p by a unitary transformation U. The time evolution of p' is given by
+ Up+Uft + UUt
'pU,
(2.9)
Using Equation 2.10 and defining a new Hamiltonian H', Equation 2.9 reduces to
Equation 2.11, where H' is give by Equation 2.12.
d
-(UUf)
= Out + U(Tf = 0
(2.10)
' = -i[H', p']
(2.11)
H'= UHUt - iUUt
(2.12)
For a time dependent H', the solution to Equation 2.11 is given by
p'(t)
e-iH'tp/(O)eiH't
(2.13)
Therefore, for a time varying Hamiltonian H related to a static Hamiltonian H' by
Equation 2.12, the solution to Equation 2.6 is given by
p(t) = ep(o)et
(2.14)
E
(2.15)
= Ut e-iH'tU
and expectation values are given by
(0) = Tr (Ot0Op(0))
(2.16)
This formalism is quite powerful, and can by applied to many systems that appear
22
in the context of NMR, from the most basic, to quite complex systems involving
multiple interacting spins and time varying fields.
Nuclear Spin in a Static Magnetic Field
2.1.2
The simplest system involving nuclear magnetic moments and magnetic fields is a
singe nuclear spin coupled to a static magnetic field. The Hamiltonian governing this
system is the Zeeman Hamiltonian,
Bo
Hz-
(2.17)
where ' is the magnetic moment of the spin, and Bo is the magnetic field. Aligning
BO along the 2 axis in the laboratory frame, Hz is given by
Hz = -hwol
where
1
(2.18)
z is the nuclear spin along the z-axis, and wo = yBo is the Larmor frequency
of nucleus.
The Zeeman Hamiltonian splits nuclear spin states with different values of spin
along the 2 axis. The energy splitting is proportional to the magnetic field, and for a
nucleus with spin I, splits the degenerate spin states into 21+1 levels, with a splitting
of energy
Em = -hymBo
where -I < m <I. H,
13
(2.19)
C, and "N, to name a few, are all nuclei with spin I = 1/2,
giving rise to two Zeeman states and one transition, where nuclei such as 2 H (I = 1)
and "0 (I = 5/2) split into three and six Zeeman states, respectively, giving rise to
several single quantum transitions, as well as multiple quantum (MQ) transitions.
In thermal equilibrium, the density matrix describing the system is given by
eHNkBT
p=Tr(e-HN~kBT
23
m =+
B.*0
B.=0
Magnetic Field Increases
Figure 2-1: Zeeman interaction of an I = 1/2 nucleus. (Reference [29])
where T is the temperature and kB is Boltzmann's constant.
For a spin- 1/2 transition, the polarization P is given by the expectation value of
Iz. Using Equation 2.2, P is the fractional population difference between the up and
down quantum states,
(2.21)
P = tanh
Detected NMR signals are proportional to I.
In thermal equilibrium, the NMR
signal is zero. In order to observe a signal, a time varying magnetic field must be
applied.
2.1.3
Nuclear Spin in a Radio Frequency Magnetic Field
A nuclear spin interacting with an oscillating magnetic field linearly polarized along
the x axis is governed by the Hamiltonian given in Equation 2.22, setting h = 1. In
a pulsed magnetic resonance experiment, short radio frequency pulses are applied,
separated by periods of free evolution.
H = Hz
+ HRF = -w 0 Iz + 2w1 cos(wt)Ix
(2.22)
Equation 2.5 can be solved in this in the rotating frame, by applying unitary transformation U = exp(-iwtIz). In the rotating (primed) frame, the Hamiltonian H' is
24
given by
H' = (w - wo)Iz + w1I1 + wi ( cos(2wt)I + sin(2wt)Iy)
(2.23)
Near resonance, where w ~ wo, the terms oscillating at 2w can be ignored, and H'
reduces to
H'
wi 1
(2.24)
Given an initial density matrix, Equation 2.14 describes the evolution of p, where
e
eiwtIze-iwt e-wtIz. Assuming the spin is initially at thermal equilibrium in a
static magnetic field BO, the polarization P and the expectation value of I, evolve in
the rotating frame according to Equations 2.25 and 2.26, respectively.
P(t) = cos(wit) tanh
W)
(kBT
(2.25)
(I'(t)) = sin(wit) tanh (kWO)(2.26)
kBT)
By applying an RF magnetic field on resonance for a time wit = 7r/2, the populations of the up and down quantum states are equalized, and the Boltzmann polarization manifests as a coherence in the x-y plane which nutates at the nuclear Larmor
frequency. By applying a pulse of time wit = 7r, the population is inverted, leading
to an inverted polarization and no coherences.
2.1.4
Relaxation
7r/2 and 7r pulses of radio frequency magnetic fields form the building blocks of most
experiments in NMR spectroscopy. A typical experiment involves a thermal population of spins in a static magnetic field BO, interacting with a time varying magnetic
field Bi perpendicular to BO which is pulsed for a short time in order to change the
populations of spin up and spin down states, and generate coherences perpendicular
to BO.
These coherences nutate in the x-y plane, producing a rotating transverse
magnetization and inducing a current in the NMR coil [23].
The transverse magnetization which produces a measurable NMR signal decays
25
through multiple mechanisms. Populations of spins which are out of thermal equilibrium relax back to equilibrium though interactions with other nuclei, with electrons,
and with the lattice, with a time constant T 1. This longitudinal relaxation or "spinlattice" relaxation time varies from a few milliseconds, to many minutes for highly
ordered solid samples, and is usually temperature dependent [24].
In addition to longitudinal relaxation, interactions between spins (spin-spin relaxation) leads to dephasing, which manifests as a decay of the transverse magnetization.
This dephasing occurs with a time constant T 2 , the transverse relaxation time [23].
Measurements of T and T 2 can provide important information about the properties of a material. In addition to being temperature dependent, T is affected by the
presence of unpaired electron spins, and by molecular motion [12]. The amount of order in a solid sample can also affect T 1 , as highly ordered crystals often display much
longer longitudinal relaxation times than disordered solids. T 2 is affected by magnetic
field inhomogeneities, as well as the amount of order in solids, and is temperature
dependent as well [23].
Extremely short relaxation times can make NMR spectroscopy difficult, since the
rapid magnetization decay can make it difficult to acquire a signal. Extremely long
spin-lattice times are also detrimental to NMR sensitivity, since a long recycle delay
must be used between experiments to allow the Boltzmann polarization to reform
[26].
2.2
Interactions
The full Hamiltonian describing magnetic resonance includes the Zeeman interaction,
the interaction of spins with an oscillating magnetic field
(HRF),
as well as several
other interactions. The full NMR Hamiltonian is given by
H = HZ + HRF + HD + HCS +HJ+HKS +HQ
26
+He +Hne
+Hmw
(2.27)
where HD is the dipole interaction between neighboring nuclear spins, Hcs is the
chemical shielding interaction that gives rise to the chemical shift, Hj and HKS describe J-coupling and the Knight Shift, respectively, HQ is the nuclear quadrupole
interaction, He is the Zeeman Hamiltonian for electrons, He is the hyperfine interaction, and Hmw governs the interaction of electron spins with a microwave field
[23, 17].
Of particular importance in solid state NMR are chemical shielding, dipolar coupling, and the quadrupole interaction.
All three of these anisotropic interactions
are often not averaged within solids, resulting in a NMR spectrum that is spectrally
broad, but rich with structural information.
Please note, He, Hne, and Hmw are important interactions for DNP, and are treated
in Chapter 3.
2.2.1
Dipolar Coupling
The interaction between two magnetic dipoles fl1 and
spins I1 and
12
separated by a distance r, is given by
HD =
Y
72
47r
1 I1-3
2
-
r3
3(
1 )(2
3(I )5f
*)
Both homonuclear (y
- ))
(2.28)
r
where 71 and -y2 are the gyromagnetic ratios of j1 and
1.
associated with nuclear
/2,
= -y2) and heteronuclear (-y
/2,
respectively, and h
# -y2) dipolar couplings are
observed, in the form of a small energy splitting that broadens NMR spectra.
27
Expanding in polar coordinates, HD can be written in the Zeeman basis as
HD -
[C0112
47
(A+ B+C+D+E+F)
A = (3 cos 2
-
C = - 2 sin 0 Cos Oe-
2
(11+122
sin 0 cos Oe i
E = - 3sin2 Oe-2
F = -
where 1±
=
(2.30)
1)11Z12Z
(3cos 2 0 - 1) -11+12- +11-12+
B = -
D = -
(2.29)
\
I2z +
(2.31)
(2.32)
11z12+
(2.33)
11z12_
(2.34)
(11+12+
sin2
(2.35)
11-12_)
Im ± 1) (mI connects Zeeman states with quantum numbers m and m± 1.
Terms C, D, E, and F are normally neglected, as their effect on the spectrum is
negligible [17].
Chemical Shielding and Chemical Shifts
2.2.2
Chemical shielding is caused by interactions between a nucleus, the local electron
density, and the external magnetic field. A secondary induced magnetic field, created
by electrons circulating in the external field, shields the nucleus, changes the net magnetic field felt by the nucleus. Nuclei surrounded by different electron configurations
and densities will experience different degrees of shielding.
The chemical shielding interaction is given by
Hcs =I-
where
(2.36)
o-BO
- is the shielding tensor. The shielding tensor can be represented as the sum
of an isotropic, a symmetric, and an antisymmetric tensor, - = 0-iso +
However,
7anti
U-sym
+ Uanti.
has no measurable effect on spectrum, and can be neglected [23]. o-iso
gives rise to a shift in the resonance peak away from the Larmor frequency, and Usym
determines the line shape.
In the principle axis system, a- is given by a diagonal
28
matrix, with elements (by convention)
-a
!
-2 2
U33 .
Measured shifts 6 are known as chemical shifts, and are given by
6
=
)
\W -
where the measured peak is at w, and
Wref
(2.37)
refU
\
reref
-0ref/
is the frequency of the reference [29, 23].
the span of the anisotropy Q, and the skew K are
The isotropic chemical shift 6j,
given by
Q
K
2.2.3
(2.38)
611 + 622 + 633)
6iso =
(2.39)
= 611 - 633
(622
(2.40)
-iso
Quadrupole Interaction
Nuclei with spin greater than 1/2 have an electric quadrupole moment, which interacts
with the local electric field gradient (EFG) through the quadrupole interaction. [32,
23]. Roughly 72% of nuclei with intrinsic spin are quadrupolar nuclei [28].
A nuclear electric quadrupole moment eQ in an electric potential V(r) couples
to the local EFG Vij = 0 2 V/i&
3 through HQ. In the principle axis system (PAS)
of the EFG, Vij is given by a diagonal matrix with elements V,,,
Vyy,
IVxxj < JVyyj < lVzzl by convention. Using Laplace's equation V2V
0, the EFG in
V,,
with
the PAS is described by Vzz and r, given by
where 0 <
- V
XVY
Xz
(2.41)
< 1 [28]. The quadrupole interaction HQ is then given by
HQ =
where C
V
T1= V
(312 - I(I + 1) +
(2.42)
= eQVz [23, 29]. The shape of the observed NMR spectrum is characterized
by C and q, with Cq ranging between 0 Hz to hundreds of MHz [28].
29
In the presence of the Zeeman interaction, HQ is treated as a perturbation, with
first and second order terms H(1) and H
Q
3 eQV
4 2I(2I
Q
(2.43)
312 - I(I + 1)
H()
WQ
1(1) is given by
Q
1 )(3
cos 2 0 - 1 + rsin2/ cos 2a)
(2.44)
are the first two Eular angles of B 0 in the PAS of the EFG [28], and
where oz and
H is given by
2 V 2 ,v 2 , 1 (41(I + 1)
H2) =,_
Q 2wo (2I(2 -- 1))(_8Z_1
-
8I
-
1)
+ V2,-2V2,2 (21(I + 1) - 21 - 1)i,)
where %,j are the components of the EFG, expressed as a rank 2 spherical tensor
[28], and wo is the Larmor frequency of the nucleus.
No B.
Strong B.
Zeeman Interaction
Ist Order
Quadrupolar
Interaction
2nd Order
Quadrupolar
Interaction
m
-9/2
-7/2
-5/2
-3/2
3/2
5/2
7/2
Figure 2-2: The Zeeman, first, and second order quadrupolar interactions, for an
I = 9/2 nucleus. (Reference [29])
30
HQ) generates small shifts in the Zeeman energy levels, which are even functions
of the quantum number m (Equation 2.19).
Quadrupolar nuclei with half- integer
spin have a central transition (m = -1/2
m = 1/2), who's energy levels shift by
++
the same amount. These central transitions are not affected by HQ to first order,
while all other transitions are shifted [28, 231. Nuclei with integer spin, such as
2H,
have no central transition, and all transitions are first order shifted. The central
transition of half-integer quadrupolar nuclei is shifted from wo by the second order
quadrupolar interaction H(.
2.3
2.3.1
Solid State NMR Techniques
Bloch Pulses
A Bloch pulse is perhaps the simplest NMR experiment (see Section 2.1.3). After waiting for an ensemble of spins to come to thermal equilibrium in an external magnetic
field BO, a second field B 1 is applied which oscillates in time at the Larmor frequency
wo of the spins to be interrogated. B1 is applied for a time woAt =7r/2, producing
a net transverse magnetization which nutates at the Larmor frequency. After the
pulse, the magnetization undergoes free nutation, and decays with a characteristic
time constant T2*, shorter than T or T 2 (discussed bellow). The free induction decay
(FID) is detected in the current induced in the NMR coil. Spectroscopic information
is extracted from the Fourier transform of the FID [23].
2.3.2
Hahn Echo
After a Bloch pulse, the transverse magnetization decays with time constant T2*, which
is observed in the FID. This decay primarily results from the fact that each nuclear
spin experiences a slightly different magnetic field, due to inhomogeneities in the Bo
and to varying molecular environments, and so nutates at a rate W = wo t±W. The
individual coherences quickly dephase, leading to a loss of transverse magnetization.
The transverse magnetization can be recovered, however, by applying a second
31
=T2
a
Trn2
b
Figure 2-3: Schematic representations of Bloch (a) and Hahn echo (b) pulse sequences.
(Reference[29])
RF pulse after time -r for time wAt = 7r which applies a phase of -1 to each spin.
The coherences continue to nutate at their individual Larmor frequencies, but with
the accumulated phase differences precisely reversed.
Now, the effects which lead
to dephasing lead to a refocusing of the coherences and a reemergence of the net
transverse magnetization, which reaches a maximum after time -r.
90* RF Pulme
180* RF Pul
spin Echo
Fee Induction Decay (FID)
Figure 2-4: NMR signal observed after a Hahn Echo pulse sequence. (Reference [30])
2.3.3
Magic Angle Spinning
NMR spectroscopy as it was originally developed suffers from extremely poor resolution when applied to solid samples. This is a consequence of the fact that a great
many of the interactions between nuclei and between nuclei and unpaired electrons
are anisotropic, or have anisotropic components [15].
The dipolar interaction (Section 2.2.1), in the secular approximation, includes
32
only the terms A and B from Equation 2.29, which are both proportional to the
second order Legendre polynomial P 2 (cos 0) = (3 cos 2 0
-
1)/2. In liquid or gas sam-
ples, molecular motion and reorientation lead to a much reduced dipolar interaction,
because the integral of P 2 (cos 0) over the sphere vanishes [15].
In solid samples, motional averaging often does not occur, since molecular motion
and reorientation are severely restricted. However, by spinning a solid sample along
an orientation inclined by an angle a from Bo such that P 2 (cos a) = 0, the mean
value of P 2 (cos 0) for all nuclei vanishes [4, 25, 26].
Consider a sample rotating as described above, at a frequency W'.
The angle 0
between the axis defined by a pair of nuclei and B 0 is given by
3 cos 2
-
1 COS2
(3
-
3-1)
1)(3 cos 2
1) + - sin a sin 2
1(3 cos2 a - 1)(3 cos 2/_
2
cos(2w't)
1) + R(a, ,w', t)
(2.45)
(2.46)
where 3 is the angle between the axis of rotation and the pair of nuclei [15]. Since the
time average over one rotor period of R(a, /, w', t) is zero, the time average of P 2 (cos 0)
vanishes as well, independent of molecular orientation, as long as P 2 (cos a) = 0. The
angle a has the value of 54.73', and is known as the magic angle.
In addition to dipolar coupling, other interactions which transform as secondrank spherical harmonics, such as the chemical shielding anisotropy and the first
order quadrupolar interaction, vanish under magic angle spinning (MAS), leading to
a narrowing of resonance lines for quadrupolar nuclei as well as for I = 1/2 nuclei [26].
In the limit of infinitely fast spinning, these anisotropic interactions are completely
averaged out, and an isotropic spectrum, as would appear in a liquid, is obtained.
For finite spinning speeds, the modulation of the interactions caused by R(a, /, W', t)
introduces spinning sidebands, signals equidistant from the isotropic line by integer
multiples of the spinning frequency [26].
One interaction that is not averaged out by MAS is the second order quadrupolar
coupling, which has components that transform as second-rank spherical harmonics,
and components that transform as higher rank spherical harmonics [22, 2].
33
As a
d
C
a
150 100 50
0
-100
ppm
Figure 2-5: The anisotropic chemical shielding interaction, for (a) a static sample,
(b-d) increased spinning speeds at the magic angle, and (e) in the limit of infinite
spinning. (Reference [29])
of H 2 ) .
result, no single spinning axis can cancel out the anisotropic components
Q.
However, under MAS second order quadrupolar broadening are reduced by up to a
factor of three [2, 26].
2.3.4
Decoupling
Dipolar coupling between 1H and other nuclei in solids is often very large, and is often
a source of significant line broadening even under MAS [26]. However, the effects of
1
H heteronuclear dipolar coupling can be removed by irradiating the sample with a
radio frequency magnetic field while measuring the spectrum of the nuclei of interest.
In a strong transverse RF field B 1 oscillating at the 1H Larmor frequency, 'H spins
undergo Rabi oscillations with a frequency -7B 1 , where 7 is the proton gyromagnetic
ratio. yB
1
is referred to as the decoupling frequency. As the 'H spins flip, the effects
of heteronuclear dipolar coupling are averaged to zero.
necessary for the high resolution of biological solids [7].
34
1
H high-power decoupling is
2.3.5
Cross Polarization
In solid samples, NMR spectroscopy of dilute nuclei is often difficult for two reasons.
First, their induced polarization is low since there are relatively few of them, and
second, they often exhibit long spin-lattice relaxation times [26].
In samples with
both dilute nuclei n and abundant nuclei m with nuclear spins In and 1'i,
these
problems can be overcome using cross polarization, a spin transfer technique whereby
polarization may be transferred to n from m.
Cross polarization involves two radio frequency magnetic fields Bin and Bin at
the Larmor frequency of n won and at the Larmor frequency of m, wom, transverse
In-magnetization and I, -magnetization are created. When the RF powers satisfy
the Hartmann-Hahn condition
ynBin = 7mBim
(2.47)
the transverse polarizations are spin-locked, and Im-polarization is transferred to the
In population through heteronuclear dipolar coupling [26].
After joint irradiation,
the RF power is removed, and NMR pulse sequences are applied to n, often with m
decoupling.
Cross polarization both increases the signal strength of dilute nuclei, and allows
for shorter recycle delays, since the experiment is limited by m spin-lattice relaxation
times, not n spin-lattice relaxation times.
2.3.6
Multiple Quantum MAS
High resolution spectra of the central transition of half integer quadrupolar nuclei may
be obtained using a variety of other techniques. One technique, known as double rotation (DOR), involves spinning the sample along two axes, while another technique,
known as dynamic-angle spinning (DAS), involves spinning the sample along an axis
who's direction varies in time [2]. A third technique, multiple- quantum MAS (MQMAS), involves generating multiple quantum (e.g. m = 3/2
++ m
= -3/2) coherences
to perform an averaging procedure in conjunction with magic angle spinning [2] (see
35
Section 2.3.6). MQMAS has the advantage that it can be implemented on an ordinary
MAS probe, where DOR and DAS require specially designed spinning NMR probe
technology.
Bloch pulses, as described in Section 2.3.1, are used in most pulsed NMR experiments to generate single quantum (Am = 1) coherences. The NMR signal read
out as an FID depends on single quantum coherences (see Equation 2.26). However,
forbidden multiple quantum (Am > 1) coherences may also be generated by strong
RF pulses, and may be used to average out the anisotropic second order quadrupolar
interaction [2].
MQMAS is a two-dimensional technique which takes advantage of the fact that
symmetric transitions are not broadened by the first order quadrupolar interaction,
and the fact that the second order quadrupolar interaction is an odd function of m, to
average out the anisotropies of the second order interaction. Schematically, a MQMAS
experiment can be used to obtain isotropic spectra of the central transition of a half
integer spin quadrupolar nuclei as follows. First, multiple quantum coherences are
generated by a strong RF pulse P1 , and then evolve freely for a period ti. Then, a
second hard RF pulse converts the desired multiple quantum coherence into single
quantum coherence, which is then read out in an echo after a delay.
By properly phase cycling the RF pulses, the top of the echo, recorded at t 2 = kt 1 ,
is isotropic, where k depends on I and the coherence pathway [2, 29]. An isotropic
spectrum can by obtained by carrying varying the delay times, taking the isotropic
peak of the echoes, and creating a two dimensional spectrum, where one dimension
is the regular MAS spectrum and the other is the isotropic spectrum.
36
Chapter 3
Dynamic Nuclear Polarization
NMR spectroscopy, especially of solid samples, suffers from an inherently weak signal.
This is doubly the case for nuclei such as
15
N (I = 1/2), which appear in low natural
abundance (0.1% natural abundance), and triply the case for low natural abundance
quadrupolar nuclei such as 170 (I
=
5/2, 0.038% natural abundance).
In 1953, Overhauser [31] proposed that by saturating the EPR transition of unpaired electrons in a material, the Boltzmann polarization of the electrons could be
transferred to neighboring nuclei, increasing dramatically the nuclear polarization
and thus increasing the NMR signal by a factor of roughly -y,/N, where -ye is the
electron gyromagnetic ratio and 7, is the nuclear gyromagnetic ratio. For protons,
this corresponds to a factor of
-
660, and for
13
C, a factor of ~ 2600.
In the past two decades, novel use of high frequency high power microwave sources,
and the development of various radicals and biradicals for use as polarizing agents,
have made it possible to carry out DNP at high magnetic field (up to 18.8 Tesla).
Since 1953, there have been a number of polarization mechanisms proposed beyond
the Overhauser effect. Of particular relevance to solid state NMR at high magnetic
fields are the solid effect (SE) [1, 18], the cross effect (CE) [20, 21, 42, 18], and
thermal mixing (TM) [39, 5] mechanisms. In this chapter, a brief description of the
three mechanisms is given, followed by an introduction to the theory of the solid
effect. In addition, the experimental requirements of high field DNP are outlined.
37
3.1
DNP at High Magnetic Fields
DNP experiments are typically done at cryogenic temperatures (~
80 K) in order
to increase longitudinal relaxation times and improve spin diffusion [18]. Polarizing
agents must be added to in order to achieve efficient electron-nuclear polarization
transfer. In addition, high power microwaves at the electron Larmor frequency (140
GHz at 5 Tesla) are necessary in order to drive DNP processes.
3.2
Gyrotrons as Microwave Sources for DNP
Advances in DNP as a tool for increasing the sensitivity of solid state NMR at high
magnetic field have been dependent on high power, high frequency microwave sources.
At high magnetic fields, the EPR frequency is in the hundreds of GHz range (-140
GHz at 5 Tesla, ~ 250 GHz at 9 Tesla, ~"10460 GHz at 16.4 Tesla), where few high
power microwave sources are available. In the last two decades, cyclotron resonance
masers (gyrotrons) have been developed to operate as continuous wave microwave
sources for DNP enhanced NMR [6, 27]. Such gyrotrons drive DNP with -10 W of
microwave power.
er/2
1H
13
C/15N
Figure 3-1: DNP of 1H, followed by cross polarization to
of 13 C (or 15N) is detected, under 'H decoupling.
13
C (or
15
N). NMR signal
A typical DNP enhanced NMR pulse sequence, utilizing dynamic 'H polarization,
38
followed by cross polarization to
is aquired on
13
C (or
15
13
C (or
15
N), is shown in Figure 3-1. The NMR signal
N), while two pulse phase modulation (TPPM) [7] decoupling
is applied to 1H.
3.2.1
Polarization Mechanisms
There are three principle polarizing mechanisms for DNP in solid dielectric sample
which are driven by microwave saturation of EPR transitions. They are the solid
effect, the cross effect, and thermal mixing.
These mechanisms are characterized
microscopically by the number of electrons involved, and macroscopically by the relationship between the nuclear Larmor frequency wc0 , and the homogeneous linewidth
6 and inhomogeneous breadth A of the EPR spectrum of the polarizing agent [18].
The solid effect involves a single electron, the cross effect involves two, and thermal
mixing involves many, while the solid effect dominates when 6, A <
w 01 , and the
cross effect or thermal mixing dominate when A > woi.
3.3
Theory of DNP
An unpaired electron spin S in an external magnetic field B 0 is described by the
Hamiltonian
-g - S
He =
.1)
(3.o
where g is in general a tensor. Free electrons have an isotropic g tensor, but radicals
have g tensors with varying degrees of anisotropy. In order to perform DNP enhanced
NMR, radicals with nearly isotropic g tensors are typically used [181.
The physics of a system of electron and nuclear spin ensembles in contact with a
lattice is governed by the Hamiltonian
H = He + Hee + Hn + Hnn + Hen + HeL + HnL + HL
(3.2)
where H, is the nuclear Zeeman interaction, Hee, Hen, and Hnn are the inter-electron,
electron-nuclear, and inter-nuclear couplings,
39
HeL
and HnL are the electron and nu-
clear spin-lattice interactions, and HL describes the generalized lattice interactions.
He, Ha, Hen, and Hee are the largest contributors to DNP as they mediate polarization transfer, while the efficiency of polarization transfer is regulated by electron
and nuclear relaxation. In addition to H, a microwave field is necessary to drive
polarization transfer [1, 17, 18].
Unpaired electrons interact with nuclei in their immediate vicinity, shifting the
nuclear Larmor frequency and effectively isolating them from the bulk nuclei through
strong electron-nuclear coupling. The region where this effect dominates is known as
the diffusion barrier, and typically covers the region within roughly 3
[41].
A of the electron
The electron polarization is transferred to the bulk both directly [1] through
hyperfine coupling to nuclei outside the diffusion barrier [17, 36], and indirectly, as
polarized nuclei enhance the polarization of neighboring nuclei through spin diffusion
[1, 17]. Recent results (see Reference [36]) indicate that the role of spin diffusion is
less than was previously thought, with the polarization primarily transported directly
from electrons to bulk nuclei.
The enhancement E is related to the nuclear polarization P by
P
=(3.3)
eq
where Peq is the nuclear polarization at thermal equilibrium. E grows as the duration
of microwave irradiation increases, following an exponential saturation-recovery curve
with time constant T 1 , the nuclear spin-relaxation time [17].
3.4
The Solid Effect
The solid effect involves one unpaired electron spin coupled to a nuclear spin, in the
presence of microwave radiation. In addition, the homogeneous and inhomogeneous
EPR linewidth of the polarizing agent must be narrower then the Larmor frequency
of the nucleus to be polarized [18].
40
3.4.1
Static Electron and Nucleus
Considering only the electron Zeeman interaction He, the nuclear Zeeman interaction
Ha, and the hyperfine interaction Hen, the Hamiltonian describing the system in the
absence of time varying fields is
Ho = He + Hn + Hen = wosSz - woIIz +
, SAkIk
(3.4)
j,k
where S is the electron spin, I is the nuclear spin, wos is the electron Larmor frequency,
wo, is the nuclear Larmor frequency, and Aj,i are the coefficients of the hyperfine
interaction. In the high field approximation, keeping only terms that include S, , Ho
reduces to
HO = wosSz - woiz + A 1 SzIz + B 1 SzI
(3.5)
where A 1 and B 1 are the coefficients of secular and pseudo-secular hyperfine interactions, respectively, and h = 1.
Following the formalism developed in Chapter 2, HO can be diagonalized in the
Zeeman basis by applying a unitary transformation U, given by
U = exp (i(70 - r7)SzIV + 2(n"' +
)Iy)
(3.6)
H6, given by
HO = UHoUt
(3.7)
is diagonal in the Zeeman basis, and is given by
HO = wcOSz - w'r-z + A'SzIz
(3.8)
where
W/01 =
22 (Cos 77 + cosqi8)
A,
4 (cos 7
41
_ cos 7)
)
B (sin TI - sin T8)
(3.9)
i= -wo
and the angles
A1
(cosrj 0 - cos Ip)+ -(cos rQ
I,
B1
+ cosmo) + -(sinq
-+ sin rT8)
(3.10)
and q,3 are given by
r/, = tan-
(AB
A,
f-
B
1
)
r/3 = tan- 1 (A
(A, + 2wmor
)
2wOr
,
(3.11)
(see Reference [18]). The energy eigenstates and transitions of H are shown in Figure
3-2.
E
t1>131>
14>12>-
i2
-2
Coupling
NMR
EPR
E12=OS +
E 3 12= wo-
E34=wOS-A
E42=
2
o+61
H 13 = H31 = 4
H24
=H42
,
Figure 3-2: Electron-nuclear spin system, with EPR and NMR transition energies
and couplings calculated to first order. DNP transitions corresponding to positive
and negative enhancements are indicated by the solid and dashed lines, respectively
(Reference [18])
3.4.2
Microwave Hamiltonian
The interaction HM between an electron and nuclear spin system and a microwave
field oscillating at frequency wm is given by
HM
=
2wis cos(wmt)S.,
42
(3.12)
and in the primed frame by
H4 = UHMUt
(3.13)
= w1s cos(wMt) (2S, cos %O - (S+I- + SI+) sin qafl + (S+I++ SI_) sin
,a)
(3.14)
where 7,B = (na - 7,)/2. The solid effect is mediated by either the zero quantum
term (S+I- + S-I+) or the double quantum term (S+I+ + S_11), depending on the
microwave frequency [18]. Applying a second unitary transformation U1 = exp(iHOt)
to the combined Hamiltonian H' =
H6 + Hj, the zero quantum and double quantum
terms become
U1 (S+I- + S_1+)Ult
Ui(S+I+ + S_ -)Ut
exp(i (wos + w' 1)t) + c.c.
(3.15)
= S+I+ exp(i(wos - wo1)t) + c.c.
(3.16)
S+I-
When wM = WoS -~w',, a positive enhancement is observed, and when WM = Wos +W,
a negative enhancement is observed [18].
The solid effect is mediated by forbidden transitions, and therefore exhibits a W-2
dependence. In order to produce an enhancement, the polarizing agent must have
an EPR linewidth smaller then the nuclear Larmor frequency. Narrow line organic
radicals with a g ~~2 such as trityl are typically used, as well as high spin transition
metal ions such as Mn2+ and Gd 3 + [11].
3.5
The Cross Effect and Biradicals
The cross effect is a polarization transfer mechanism involving two coupled electrons
and one nucleus. The EPR spectrum of the system is homogeneously broadened by
inter-electron dipolar coupling, and inhomogeneously broadened by the electron g
tensor anisotropy. For a theoretical treatment of the cross effect, see Reference [18].
Under the cross effect matching condition
jwos 1
43
-
WOS 2
=
wO1 ,
where
Wos
and wos 2 are
the electron Larmor frequencies of the coupled electrons, certain energy levels become
degenerate, and polarization enhancement can be driven using microwave radiation.
In order to satisfy the cross effect matching condition, two electron spins must experience homogeneous broadening. The number of spins which satisfy the cross effect
matching condition increases linearly with w0j; therefore, the cross effect exhibits a
Wc-
1
dependence.
In order to satisfy the cross effect matching condition, two electron spins must homogeneously and inhomogeneously broadened, by electron dipole-dipole interactions
and by g anisotropy.
Organic nitroxide-based radicals such as TEMPO (2,2,6,6-
tetramethylpiperydin-1-oxyl) can be used to produce a cross effect enhancement due
to their reasonably broad inhomogeneous EPR linewidth [18].
The cross effect is
optimized when the two participating electrons couple to each other, but couple only
weakly to other unpaired electrons. This is difficult to achieve at low radical concentrations, where inter-electron dipolar coupling is extremely weak.
However, by
using two tethered radicals as a polarizing agent, this difficulty can be overcome. The
two unpaired electrons in a biradical experience dipolar coupling, and while at low
concentrations experience negligible interactions with other unpaired electrons [19].
One biradical particularly useful as a cross effect polarizing agent is TOTAPOL
1-(TEMPO-4-oxy)-3-(TEMPO-4-amino)propan-2-ol),
(
which consists of two TEMPO
radicals tethered with a three carbon chain. TOTAPOL can be used to polarize a
wide range of samples, ranging from small molecules to proteins, and is soluble in
aqueous media [38].
44
Chapter 4
Probe Construction and Design
In this chapter the design and optimization of a triple channel magic angle spinning
DNP probe for operation at 5 T is described. The probe was constructed an tested
over the last year at the Francis Bitter Magnet Lab, and is currently being optimized
to improve DNP enhancements.
The probe is designed to carry out cryogenic MAS NMR on 'H,
13
C, and
15
N,
corresponding to frequencies of 211 MHz, 53 MHz, and 21 MHz at 5 T, and deliver
microwaves at 140 GHz to drive DNP, as part of a DNP/EPR spectrometer [6]. The
probe operates at a range of temperatures, from room temperature to -80K, where
DNP is carried out.
The design of the probe is presented, followed by an overview of the probe performance.
Finally, preliminary DNP results are presented.
Figures of the probe,
transmission line, and sample ejection system were made using Inventor Autodesk.
4.1
Mechanical Design
Structurally, the probe consists of three sections: a "head" or "top" containing the
NMR coil and MAS housing, a body consisting of a coaxial transmission line, a
microwave waveguide, and MAS gas transfer lines, and a tuning box, containing an
RF circuit for capacitive tuning and matching (See Figures 4-1 and 4-2). The probe
is designed to study samples packed in 3.2 mm diameter MAS rotors, which can be
45
spun in excess of 18 kHz at room temperature.
The probe head is inserted downwards into a 5 Tesla NMR magnet, lowering the
NMR coil into the region of high magnetic field homogeneity. The tuning box sits
on top of the magnet, and is connected to the probe head by the transmission and
transfer lines. Keeping the tuning circuit outside of the magnet allows the probe to
be tuned both at room temperature and at cryogenic temperatures. The tuning box
forms a seal over the top of the magnet dewar, allowing temperatures at the NMR
coil to drop to ~80 K.
Figure 4-1: Triple channel MAS DNP NMR probe, view of the tuning box at the top.
46
Figure 4-2: Triple channel MAS DNP NMR probe, view a) the sample eject, b) the
magic angle adjust, c) the stator housing, d) the drive and bearing gas posts, e) the
microwave waveguide, f) the bearing gas transfer line, g) the drive gas transfer line,
and h) the exhaust and eject gas transfer line.
4.1.1
NMR Coil
The NMR coil was made out of six turns of 22 gauge copper wire (0.643 mm diameter)
with spacings between turns of 0.643 mm. The diameter of the coil is slightly larger
than 3.2 mm, the diameter of a MAS rotor. The coil is housed in a Revolution NMR
3.2 mm MAS stator. A fixed capacitance is added in series with the coil, and used to
set the voltage nodes of the channels.
47
4.1.2
MAS
Magic angle spinning facilitated using a Revolution NMR MAS stator, which uses
streams of pressurized nitrogen gas to both hold the NMR rotor in place (bearing
gas), and to spin the sample (drive gas) as air flows over the rotor's finned drive cap.
Two vacuum coated transfer lines feed nitrogen gas to the stator, and a third vacuum
coated exhaust line vents gas back up out through the back of the tuning box.
The gas lines are vacuum coated to allow gas just above the boiling point of liquid
nitrogen to be blown over the sample. This cools the sample for DNP while keeping
the rotor spinning. The MAS spinning speed is monitored using two fiber optic cables
which fit into grooves cut in the sample eject.
The orientation of the MAS sample can be changed during operation by adjusting
the hight of a rod which extends from the probe head and out through the tuning
box. The axis of rotation is adjusted by measuring the
79
Br signal in KBr, using
either the ratio of spinning sidebands or the number of echoes observed within the
FID. With the angle properly set, echoes appear in the FID for >9 ms.
4.1.3
Sample Eject
A sample ejection system is incorporated in the probe in order to facilitate quick
sample changes. Without a sample ejection system, the entire probe must be removed
from the magnet to change samples. This is extremely time consuming, especially
when operating at cryogenic temperatures, when the probe must be removed, warmed
with dry nitrogen gas before samples can be changed, then returned to the magnet
and re-cooled.
The sample eject was designed using Inventor Autodesk, and manufactured by out
of VeroGrey or VeroBlue (an ABS-like plastic) by AGS 3D. MAS rotors are inserted
at through the top of the tuning box, down through a tube, and land in the eject
piece (see Figure 4-3), where they turn and slide into the MAS stator. To remove a
rotor, high pressure nitrogen gas is blown down through the main eject line, forcing
the rotor back up through the tube.
48
The sample eject system has been demonstrated to work at room and at cryogenic
temperatures.
Figure 4-3: Sample Eject
4.2
RF Circuitry
The radio frequency circuit was designed using APLAC. The NMR coil couples to a
transmission line with an impedance, which leads from the probe head to the tuning
box. Part way up the main transmission line, a second transmission line branches
off from the inner conductor, makes a 90 degree turn and continues up to the tuning
box. The height of the branching line is adjustable, and is set so that it connects
to the inner conductor at a voltage node of the 1H (211 MHz) channel (see Figure
A-2). The remaining two channels are branched off from the main transmission line
at the probe box. Each channel is tuned and matched capacitively with two Polyflon
variable capacitors.
The main transmission line was constructed in two parts, with the part closest to
the probe head made of copper and the part connecting to the tuning box made of
stainless steel to act as a thermal break. The outer conductor has an inner diameter
49
of 3.13 inches, and the inner conductor has an outer diameter of 1.5 inches. Teflon
spacers at the probe head and at the tuning box hold the inner conductor in place.
A schematic of the RF circuit is shown in Figure A-3.
Using the variable tuning circuit, the three channels have a good deal of tuning
range, which can be extended greatly by adjusting the fixed capacitance in the tuning
box. In particular, the
to do 2 H and
170
15
N channel can be tuned as high as 32 MHz, making it possible
NMR, as well as several other nuclei. The
tuned to a variety of nuclei, including
79
C channel can also be
Br.
The mechanical design was based on an existing triple channel MAS/DNP NMR
probe operating at 5 Tesla at the Francis Bitter Magnet Lab, with modifications to the
transmission line, RF circuit, and MAS system. That probe was built to hold 4 mm
MAS rotors, and was tuned with the help of "sausage," a variation in the diameter of
the inner conductor of the coaxial transmission line. No branching transmission line
for the 'H channel was used.
4.3
Microwave Waveguide
The hollow inner conductor of the main coaxial RF transmission line is used as a
circular microwave waveguide. Microwaves enter through the top of the tuning box
from an external circular waveguide, and are coupled to a 0.375 inch diameter corrugated waveguide running down to the probe head, where a miter bend directs the
microwaves at the NMR coil where they irradiate the sample for DNP.
4.4
Performance
The probe operates successfully when channels one, two, and three are tuned to
1
13
C,
H, and 2 H, respectively. All three channels tune to an attenuation of >-30 dB at
room temperature and at cryogenic temperatures.
50
4.4.1
1H
and
13 C
7B 1
Cross polarization from 'H and
3
C has been demonstrated, and used to determine the
RF power available from the NMR coil, tuning circuit, and spectrometer amplifiers.
First, the Hartman-Hahn condition is roughly found, and the sample is irradiated
for a period allowing for polarization transfer from 'H to
3
C. Then, the nutation
frequencies (Rabi oscillations) for 'H were found by varying the power for a given
pulse duration of applied RF radiation at the 'H Larmor frequency and observing the
size of thei3 C FID. Then, with optimized 'H microwave powers, the same procedure
was carried out for carbon.
'H and
3
C microwave powers capable of producing Rabi oscillations in excess of
160 kHz are available at this time, as well as 'H decoupling at 100 kHz.
4.5
Cross Effect DNP with TOTAPOL
In order to test microwave powers and DNP enhancements, a sample of
3
C labeled
urea (CO(NH 2 )) 2 with 10 mM TOTAPOL was prepared in a 60% glycero-ds, 30%
D 2 0, and 10% H 2 0 solution, and sealed in a 3.2 mm sapphire MAS rotor. DNP of 'H
was performed with the main NMR magnetic field optimized for positive cross effect
mechanism using TOTAPOL at 92 K, with a variety of microwave powers. Enhancements were measured on 13C after cross polarization, and under 'H decoupling.
4.5.1
DNP Enhancement
A maximum NMR enhancement of 40 was reported, using 8.5 W of microwave power
at 92 K, with a MAS frequency of 8.3 kHz. Figure 4-4 shows the DNP enhanced
1C
spectrum compared to the 13C spectrum obtained under the same experimental
conditions, but with no microwave power.
51
40
pw on
pw off
-0
200
250
6
16o
150
3C
Chemical Shift (ppm)
Figure 4-4: '3 C-CP signal of 13 C-urea from the enhanced 1H polarization at 92 K,
where 'H was polarized via the cross effect at 5 Tesla, with 8.5W of microwave power.
The sample contained 10mM TOTAPOL, and was rotated at a MAS frequency of 8.3
kHz.
E
0.8
.6
N
0
0.4
0.2
0
0
10
20
30
40
50
60
70
Time (s)
Figure 4-5: Buildup of 13 C-CP signal of "C-urea from the enhanced 'H polarization
during a delay while under microwave irradiation. The buildup time constant TB
6.2s. The sample contained 10 mM TOTAPOL, and was rotated at a MAS frequency
of 5.8 kHz.
4.5.2
Polarization Buildup
The recycle delay between experiments was varied in order to obtain a 'H polarization buildup curve (see Figure 4-5). A polarization buildup time TB = 6.2s was
52
found, which also corresponds to the 'H spin-lattice relaxation time measured without
microwaves.
4.5.3
Microwave Power Dependence
The microwave power dependence for this probe using TOTAPOL was obtained by
varying the power of the microwave radiation and recording the enhancements. Results presented here were obtained at an earlier phase of probe development, when
lower enhancements were reported (see Figure 4-6). The NMR enhancement is found
to increase linearly with applied microwave power between the range of 5 W and 12
W.
50
-40
0D
E
a 30
W 20
Q_
z
= 2.4278x + 2.1311
0
R2
0
.
0
.
.
2
.
4
.
.
.
.
.
.
10
6
8
Microwave Power (W)
=
0.9976
.
.
12
.
.
14
Figure 4-6: Microwave power dependence of cross effect DNP 'H enhancement, mea-
sured through "3 C-CP, for 10 mM TOTAPOL under a MAS frequency of 5.8 kHz.
4.6
Discussion
The NMR circuit performs adequately at room temperature and at cryogenic temperatures, and very high 'H and
3
C frequency RF power is accessible. Few NMR
experiments have been done as of now to test the effectiveness of the third channel.
53
However, the measured tuning range,
2
H -yB
1
(~60 kHz), and isolation are quite
satisfactory.
MAS and the ability to exchange samples using the sample eject have both been
repeatably demonstrated, both at room temperature and at cryogenic temperatures.
As an NMR probe, performance has been extremely good.
As a DNP probe, however, there is a great deal of room for improvement. A 1H
enhancement of 40, while a significant improvement in signal to noise, is far bellow
the expected enhancement, by at least a factor of three. This is likely caused by
poor microwave coupling to the sample, a conjecture supported by the measured microwave power dependence of cross effect enhancements. Experiments reporting DNP
enhancements of three orders of magnitude [6, 19, 36] typically show an enhancement
dependence on microwave power that follows an exponential saturation-recovery curve
for TOTAPOL 'H cross effect.
Poor microwave coupling is likely related to one or more of the following: low
microwave power reaching the sample coil due to dispersion as microwaves leave
the miter bend, low microwave transmission through the coil or through the rotor
wall, and anomalies in the microwave waveguide. Currently, the probe is undergoing
modifications designed to improve the microwave coupling. The preliminary results
of these modifications are the jump in observed NMR enhancement from c = 30 at
10 W of microwave power to E = 40 at 8.5 W of microwave power. However, further
modification will be necessary in order to improve the effectiveness of DNP.
54
Chapter 5
NMR and DNP NMR
Investigation of Lanthanum
Magnesium Nitrate
Lanthanum Magnesium Nitrate (LMN) presents an extremely interesting system for
the study of water molecules in crystal hydrates. The high degree of hydration and
the ease with which the crystal may be synthesized make LMN an ideal test system for
testing various NMR spectroscopy techniques, including lineshape calculations, and
pulse sequences, and 'H DNP. In this chapter, the dynamics of water molecules in
crystalline LMN are characterized through measurements of the 2 H quadrupolar coupling at variable temperatures. The oxygen spectrum is characterized in an effort to
resolve the four crystallographically distinct water sites through the 170 quadrupolar
interaction, and experimental results of MQMAS are presented.
Solid State NMR spectroscopy of 2 H and "70 is limited by the weakness of their
respective NMR signals.
Both are quadrupolar nuclei, and experience significant
line broadening through quadrupolar coupling to local electric field gradient (EFG).
2
H has nuclear spin I
=
1, and therefore has two transitions which are first order
broadened by the quadrupole interaction (see Section 2.2.3). The only stable oxygen
isotope accessible to NMR is 170, which has a natural abundance of 0.037 %, severely
reducing the NMR signal [26].
170
has nuclear spin I = 5/2, and as a result has a
55
central transition (m = 1/2 ++ m = -1/2)
which is not broadened by the first order
quadrupolar interaction, but which does experience second order broadening.
The NMR sensitivity for both nuclei improves at higher magnetic fields, since the
Boltzmann polarization and therefore the NMR signal increases (see Section 2.1.2).
In addition, the second order quadrupolar broadening of the
170
central transition is
inversely proportional to the magnetic field.
Dynamic nuclear polarization of single crystals of LMN was explored in the 1960's
and 70's [35, 10, 34] at low magnetic fields and at liquid helium temperatures. Here,
high field dynamic nuclear polarization as a method to improve the sensitivity of
solid state NMR in crystal hydrates is explored.
Protons in LMN crystals doped
with gadolinium are polarized through the solid effect at 5 Tesla, and sensitivity
enhancements are reported, with a view towards 2 H,
5.1
170,
and "N DNP experiments.
Lanthanum Magnesium Nitrate Hydrate
LMN is a rare earth double nitrate crystal with a history of use as a proton spin polarized target for nuclear physics and polarized neutron diffraction studies [3, 35, 10].
LMN (La 2 Mg 3 (NO 3 ) 12 - 24H 2 0) is a trigonal rhombohedral (R3) crystal consisting of
(Mg(H 20)6 ) 2 + and (La(N0 3 )6 ) 3- ions linked by hydrogen bonds from both the metal
complex and from "free" water molecules [3].
The motion of water molecules in solids can be studied using
2
H NMR experi-
ments [13, 24]. Water molecules in crystal hydrates exhibit a flipping motion, where
molecules jump between two degenerate orientations, which can be characterized by
studying the lineshape of the 2 H first order quadrupole interaction in powder samples. The
2
H quadrupole interaction is 170-250 kHz broad, much larger then other
interactions such as the dipole interaction or chemical shift, and dominates the lineshape. At room temperature, the fast flipping of water molecules partially averages
out anisotropies in the 2 H spectrum, producing a large isotropic peak. At lower temperatures, however, this flipping rate decreases, an is eventually frozen out, resulting
in an 'r = 0 powder pattern spectrum [24].
56
2
3
AOLA~k k
i
;
I
4
-
Figure 5-1: Lanthanum Magnesium Nitrate Hydrate. Yellow is lanthanum, purple is
magnesium, grey is hydrogen, red is oxygen, and blue is nitrogen. The four crystallographic water sites are labeled 1-4. Crystallographic parameters taken from Reference
[3].
The
2
H lineshape in powder samples does depend, however, on the size of the
powdered crystal grains.
Coarse-ground samples with crystal grains hundreds or
thousands of microns across exhibit a coarse structure with many sharp peaks, while
finely ground crystals exhibit a smoother structure and a single peak.
There are four crystallographically distinct water sites in LMN. These in principle
can be resolved by comparing quadrupolar lineshapes with simulated spectra; however, since the strength of the 10 quadrupole interaction depends strongly on the
covalency of the X-0 bond [26], three of the four sites are difficult or impossible to
distinguish using this method.
57
5.2
Methods
Several LMN samples were synthesized, and were studied at multiple magnetic fields.
2
H spectra were taken at 9.4 Tesla, and
170
spectra were taken at 9.4, 16.4, 18.8,
and 21.1 Tesla. In order to carry out high field DNP, a polarizing agent within the
sample is necessary. Here, gadolinium(III) complexes in LMN crystals doped with
3% gadolinium are self polarized via the solid effect at 5 Tesla.
5.2.1
Synthesis
Separate samples were prepared for NMR spectroscopy of 2 H and 170. For 2 H NMR,
single crystals of LMN-24D 2 0 were grown by slow evaporation of a saturated solution
of lanthanum nitrate (La(N0 3 )-6H 2 0) and magnesium nitrate (Mg(N0
3 ).6H 2 0)
in
D 2 0 at room temperature. The dried crystals were crushed into a powder, which was
sealed in a sample tube.
For oxygen NMR, the low natural abundance of 170 made it necessary to synthesize isotopically enriched LMN. Two samples for oxygen NMR were grown as single
crystals by slow evaporation of a saturated solution of lanthanum nitrate and magnesium nitrate, one in 40%
170
enriched H 2 0 and the other in 90% 170 enriched H2 0,
at room temperature. The dried crystals were crushed into a powder and sealed in
3.2 mm MAS rotors.
Three generations of gadolinium doped LMN crystals were made.
In all three
generations, lanthanum nitrate, magnesium nitrate, and gadolinium nitrate were dissolved in solution, but the concentration of gadolinium and the solvent used varied for
each generation. The first generation was grown with an amount of gadolinium nitrate
equal to 0.1%, 0.3%, and 1% of the mass of the lanthanum nitrate, and was dissolved
in H 20. The second generation was also made with 0.1%, 0.3%, and 1% gadolinium,
but was dissolved in D 2 0. The third generation was made with 3% gadolinium, and
was dissolved in an 80% D 2 0
/
20% H 2 0 mixture. The third generation sample was
used for tests of DNP, and the second generation samples were used to measure
2H
transverse and spin-lattice relaxation times at variable temperatures in the presence
58
of paramagnetic impurities.
b
150
50
-50
-150
Frequency (kHz)
Figure 5-2: Spectra a) and b) feature jagged lines which arise from small single
crystals which were not finely enough ground. Spectrum c) is a powder line spectrum
from a properly ground sample. The sharp peak at 0 kHz arrises from residual mobile
water, and is not part of the crystal structure.
5.2.2
Deuterium NMR
The deuterium quadrupolar interaction was characterized using a static quadrupole
echo experiment at 9.4 Tesla, where the 2 H Larmor frequency is 61.05 MHz. NMR
measurements were performed using quadrature detection, and spectra were taken
at temperatures ranging from 164 K to room temperature. Simulated spectra were
produced using the lineshape simulator TURBOPOWDER, with a simple two-site hop
model describing exchange between degenerate orientations [24, 40].
and simulated spectra are shown in Figure A-1.
59
Experimental
Spectra of crystals which were not finely enough ground were also taken. These
produced spectra that varied from smooth powder patterns to spectra with several
jagged peaks. The jagged peaks are a result of preferred single crystal arrangements
(see Figure 5-2).
5.2.3
Oxygen NMR
Oxygen NMR experiments were done at multiple magnetic field strengths, in order
to characterize the
17
0 central transition which has a wo 1 dependence, where wo is
the Larmor frequency. Spectra presented here were taken at 18.8 T and at 21.1 T
( 108 MHZ and 122 MHz 170 Larmor frequency, respectively), using a Hahn echo
pulse sequence (see Section 2.3.2) under three conditions: static, static with proton
decoupling, and under MAS (Figure 5-4).
Static spectra are broadened by the second order quadrupole interaction, by the
chemical shift anisotropy (CSA), and by heteronuclear dipolar coupling to protons.
By applying continuous wave proton decoupling at the proton Larmor frequency
(900 MHz), the proton-oxygen dipolar coupling can be removed, yielding a spectrum
broadened by the second order quadrupole interaction and by the CSA. Finally, under
MAS, heteronuclear dipolar coupling and the CSA are removed, producing a line
broadened only by the second order quadrupole interaction.
A-
I
I
I
I
50
0
-50
-100
ppm
200
100
0
-100
I
-200
ppm
Figure 5-3: NMR spectrum of the 170 central transition at 18.8 T for LMN synthesized in 40% 170 enriched H 2 0. Simulated spectra on top, observed spectra bellow.
Left: under MAS, with 18 kHz spinning frequency. Right: Under static conditions,
with no decoupling.
60
Spectra of the '"0 central transition taken at 18.8 T using LMN synthesized in
40% 170 enriched H 2 0 are presented in Figure 5-3. To achieve higher resolution,
LMN synthesized in 90% 170 enriched H 2 0 were taken at 21.1 T (see Figure 5-4).
a
21.1 T
=20 kHz
Cow/2rr
b
C
=0 kHz
+CAw12TT
YB, (H)
C
w/27T =0 kHz
yB, C'H) = 0 kHz
C, +CS A+Di polar
300
=83kHz
200
100
170
0
-100
-200
-300
Frequency (ppm)
Figure 5-4: NMR spectrum of the 17 0 central transition at 21.1 T for LMN synthesized in 90% 170 enriched H 2 0, (a) with a MAS frequency of 20 kHz, (b) non-spinning,
with 83 kHz 1H decoupling, and (c) non-spinning with no decoupling.
Static experiments with decoupling were done using RF power, to produce proton Rabi oscillations of 83 kHz.
Simulated spectra were produced using parame-
ters calculated from the MAS spectra, which were fitted and provided an average
CQ = (7.2 ± 0.3) MHz, q = 0.95 ± .05, and J3,, = (-10 ± 3) ppm.
5.2.4
170 MQMAS
In an effort to resolve the crystallographically distinct water sites in LMN, MQMAS
was used to improve the resolution of the oxygen spectrum. MQMAS suffers from
61
a high degree of signal attenuation during the MQ evolution, and as a result, signal
averaging must be carried out over many days to produce good signal to noise while
high fields are essential for good resolution. In order to increase the signal to noise,
highly 170 enriched LMN was used to provide a larger oxygen signal.
ppm
*
'
~
-
-
'C
a,6.
9.
,,D
*
e0
*e.
'
-- 50
'
0
-
bes
C'SP
-
50
-
100
150
I
150
100
50
0
-50
-100
-150
PPM
Figure 5-5: MQMAS spectrum of 170 at 18.8 Tesla, with a MAS frequency of 16
kHz. The horizontal axis is the MAS dimension, and the vertical axis is the isotropic
dimension. a) and b) are spinning sidebands.
The two dimensional MQMAS 170 spectrum of LMN is shown in Figure 5-5. The
MQ pulse sequence used consisted of a hard pulse to excite triple quantum coherences,
an evolution time, a second hard pulse to convert 3Q coherences into single quantum
coherences, and a third soft refocusing pulse.
62
5.3
Solid Effect Dynamic Nuclear Polarization with
Gadolinium
The EPR spectrum of Gd3 + in LMN was studied 1960's [9]. In LMN, Gd3 + has a
nearly isotropic g tensor close to 2 (gll = 1.9917 ± 0.0001 and gI
=
1.9922 ± 0.0001).
Here, at a concentration of 3% by weight, Gd 3+ is shown to polarize 1H in LMN at 5
1
Tesla (211 MHz
5.3.1
H Larmor frequency) through the solid effect mechanism.
DNP
DNP experiments were done on powdered 3% gadolinium doped LMN crystals (see
Section 5.2.1) sealed in a 4 mm MAS rotor. 'H polarization was measured directly,
using a Hahn echo with a recycle delay of 90 s, with a MAS frequency of 4.2 kHz at a
temperature of 80 K. DNP off signals were collected under the same conditions, but
with no microwave irradiation. Results are shown in Figure 5-6.
E = 2.5
t= 8
mw on
MW off
40
-20
20
-40
1H Frequency (kHz)
Figure 5-6: Direct detect 1H spectra of LMN-Gd, 3% Gd doped, taken at 85K with
4.2 kHz MAS spinning, with microwaves on (top) and off (bottom), showing a DNP
enhancement 6 = 2.5. A recycle delay of 90s was used.
63
5.4
Results and Discussion
The motion of water molecules in LMN was characterized using 2 H NMR spectroscopy,
and compared to spectra simulated using a two-site hop model. The calculated flipping rates are shown in Table 5.1. Well resolved spectra were impossible to obtain for
temperatures below 164 K, likely due to extremely long spin-lattice relaxation times
and extremely short transfers relaxation times.
Table 5.1: Calculated hopping frequency of D 2 0 in LMN.
Temperature (K)
Flipping Frequency (Hz)
108
x 107
x 107
x 10 7
287
237
222
197
6.1
6.3
2.5
1.0
176
1.6 x 106
6.5 x 105
164
x
Resolving multiple crystallographic water sites in LMN was beyond the sensitivity
of the one dimensional 170 techniques used at 21.1 Tesla. However, the highly 170
enriched LMN sample provided a much larger oxygen signal than is typically accessible, and proved to be extremely valuable as a tool for calibrating and optimizing
pulse sequences for other samples.
A MQMAS two dimensional spectrum of the 170 central transition was collected
at 18.8 Tesla, providing improved resolution. Using the highly 170 enriched LMN
sample, calibration of the MQMAS pulse sequence was possible in four days. However,
multiple water sites were not resolved. The isotropic component could only reveal a
35 ppm broad resonance, likely limited by short 170 spin-spin (T2) relaxation times.
The inability to utilize 'H decoupling on the probe used at 18.8 T may have
resulted in shorter spin-spin relaxation times. To test the effects of decoupling, spinspin relaxation times were measured under MAS conditions, with and without 83
kHz
1
H decoupling. Measured T 2 's were nearly identical, suggesting the lack of 'H
decoupling was not a limiting factor for MQMAS resolution. Performing MQMAS
64
at cooler temperatures will likely result in longer T 2 's, and may be advantageous for
obtaining higher resolution.
A solid effect 1H DNP enhancement of 2.5 was measured directly, corresponding to
a signal to noise enhancement of a factor of -8 from room temperature measurements.
This is comparable to recent results [11] obtained using Gd3 + and other high-spin
transition metal ion complexes.
Detecting 'H polarization directly has the disadvantage that the proton signal is
broadened by dipolar coupling. It is possible to obtain higher signal enhancements
of other nuclei by first polarizing the 1H reservoir, and then cross polarizing to other
nuclei. To that end, Gd doped LMN samples enriched with
15
N have been prepared
in the last month, and indirect and direct DNP of nitrogen and 2 H will be explored
in the near future, utilizing the 3.2mm MAS DNP NMR probe described in Chapter
4.
65
66
Appendix A
Supplementary Figures
67
Experimental
Simulation
287 K
6.1x10 8 Hz
237 K
6.3x1 07 Hz
222 K
2.5x10 7 Hz
197 K
1.0x10 7 Hz
176 K
1.6x10 6 Hz
164 K
6.5x10 5 Hz
150
50
-50
Frequency (kHz)
150
-150
50
-50
Frequency (kHz)
-150
Figure A-1: Observed and simulated 2 H spectra taken at 9.4 Tesla, at variable temperatures. Spectra were simulated using a simple two-site hop model, from which hoping
rates were calculated to be (from the top): 6.1 x 108 Hz, 6.3 x 107 Hz, 2.5 x 107 Hz,
1.0 x 107 Hz, 1.6 x 106 Hz, and 6.5 x 105 Hz.
68
Figure A-2: The 1H channel transmission line branching off from the main transmission line. The branching point is adjustable, and is set at the location of a 'H channel
voltage node
69
output-n
y_check-n
L n
i check
n
v-check-c
c
Oup
c
i check
i
e
coax2_top_2
acc
V2
V chek h
0
-utut
co
i-check-h
-:top_1
coax-top_teflon
coax opz2
Ta
hh[
co0
Ott
07_I
coaxbottom-veflon
cobottom2_2
coil
C
V-coil
Figure A-3: Schematic representation of the radio frequency circuit of the NMR
probe.
70
Bibliography
[1] A. Abragam and M. Goldman. Principles of dynamic nuclear polarisation. Reports on Progress in Physics, 41(3):395, March 1978.
Opti[2] Jean-Paul Amoureux, Christian Fernandez, and Lucio Frydman.
mized multiple-quantum magic-angle spinning NMR experiments on half-integer
quadrupoles. Chemical Physics Letters, 259(34):347-355, September 1996.
[3] M. R. Anderson, G. T. Jenkin, and J. W. White. A neutron diffraction study of
lanthanum magnesium nitrate La 2-Mg 3 (NO 3 ) 12.24H 2 0. Acta Crystallographica
Section B, 33(12):3933-3936, Dec 1977.
[4] E. R. Andrew, A. Bradbury, and R. G. Eades. Removal of dipolar broadening
of nuclear magnetic resonance spectra of solids by specimen rotation. Nature,
183(4678):1802-1803, June 1959.
[5] V. A. Atsarkin. Dynamic polarization of nuclei in solid dielectrics. Soviet Physics
Uspekhi, 21(9):725, September 1978.
[6] L.R. Becerra, G.J. Gerfen, B.F. Bellew, J.A. Bryant, D.A. Hall, S.J. Inati, R.T.
Weber, S. Un, T.F. Prisner, A.E. McDermott, K.W. Fishbein, K.E. Kreischer,
R.J. Temkin, D.J. Singel, and R.G. Griffin. A spectrometer for dynamic nuclear
polarization and electron paramagnetic resonance at high frequencies. Journal
of Magnetic Resonance, Series A, 117(1):28-40, November 1995.
[7] Andrew E. Bennett, Chad M. Rienstra, Michle Auger, K. V. Lakshmi, and
Robert G. Griffin. Heteronuclear decoupling in rotating solids. The Journal
of Chemical Physics, 103(16):6951-6958, October 1995.
[8] F. Bloch. Nuclear induction. Physical Review, 70(7-8):460-474, October 1946.
[9] H. A. Buckmaster, J. C. Dering, and D. J. I. Fry. Anomalous electron paramagnetic resonance angular spectra of gadolinium in rare earth double-nitrate single
crystals. Journal of Physics C: Solid State Physics, 1(3):599, June 1968.
Dynamic nuclear polarization in
[10] Charles E. Byvik and David S. Wollan.
samarium-doped lanthanum magnesium nitrate. Physical Review B, 10(3):791800, August 1974.
71
[11] Bjrn Corzilius, Albert A. Smith, Alexander B. Barnes, Claudio Luchinat, Ivano
Bertini, and Robert G. Griffin. High-field dynamic nuclear polarization with
high-spin transition metal ions. J. Am. Chem. Soc., 133(15):5648-5651, 2011.
[12] R. Freeman. Spin lattice relaxation. In A Handbook of Nuclear Magnetic Resonance. Longman, 1988.
[13] Robert G. Griffin. [8] solid state nuclear magnetic resonance of lipid bilayers. In
John M. Lowenstein, editor, Methods in Enzymology, volume Volume 72, pages
108-174. Academic Press, 1981.
[14] E. L. Hahn. Spin echoes. Physical Review, 80(4):580-594, November 1950.
[15] Jacek W. Hennel and Jacek Klinowski. Magic-angle spinning: a historical perspective. In Jacek Klinowski, editor, New Techniques in Solid-State NMR, number 246 in Topics in Current Chemistry, pages 1-14. Springer Berlin Heidelberg,
January 2005.
[16] Ulrike Holzgrabe. Quantitative NMR spectroscopy in pharmaceutical applications. Progress in Nuclear Magnetic Resonance Spectroscopy, 57(2):229-240, August 2010. WOS:000280033700004.
[17] Kan-Nian Hu. Polarizing agents for high-frequency Dynamic Nuclear Polarization : development and applications.Thesis, Massachusetts Institute of Technology, 2006.
[18] Kan-Nian Hu, Galia T. Debelouchina, Albert A. Smith, and Robert G. Griffin.
Quantum mechanical theory of dynamic nuclear polarization in solid dielectrics.
The Journal of Chemical Physics, 134(12):125105-125105-19, March 2011.
[19] Kan-Nian Hu, Hsiao-hua Yu, Timothy M. Swager, and Robert G. Griffin. Dynamic nuclear polarization with biradicals. Journal of the American Chemical
Society, 126(35):10844-10845, September 2004.
[20] Chester F. Hwang and Daniel A. Hill. Phenomenological model for the new effect
in dynamic polarization. Physical Review Letters, 19(18):1011-1014, October
1967.
[21] Chester F. Hwang and Daniel A. Hill. Phenomenological model for the new effect
in dynamic polarization. Physical Review Letters, 19(18):1011-1014, October
1967.
[22] F. Lefebvre, J.-P. Amoureux, C. Fernandez, and E. G. Derouane. Investigation
of variable angle sample spinning (VASS) NMR of quadrupolar nuclei. i. theory.
The Journal of Chemical Physics, 86(11):6070-6076, June 1987.
[23] Malcolm H. Levitt. Spin Dynamics: Basics of Nuclear Magnetic Resonance.
Wiley, 2 edition, April 2008.
72
[24] Joanna R. Long, Rainer Ebelhuser, and R. G. Griffin. 2H NMR line shapes and
SpinLattice relaxation in ba(Cl03)22H20. The Journal of Physical Chemistry
A, 101(6):988-994, February 1997.
[25] I. J. Lowe. Free induction decays of rotating solids. Physical Review Letters,
2(7):285-287, April 1959.
[26] Kenneth J. D. MacKenzie and M. E. Smith. Multinuclear Solid-State Nuclear
Magnetic Resonance of Inorganic Materials, Volume 6. Pergamon, 1 edition,
May 2002.
[27] Thorsten Maly, Galia T. Debelouchina, Vikram S. Bajaj, Kan-Nian Hu, ChanGyu Joo, Melody L. MakJurkauskas, Jagadishwar R. Sirigiri, Patrick C. A.
van der Wel, Judith Herzfeld, Richard J. Temkin, and Robert G. Griffin. Dynamic nuclear polarization at high magnetic fields. The Journal of Chemical
Physics, 128(5):052211-052211-19, February 2008.
[28] Pascal P. Man. Quadrupole couplings in nuclear magnetic resonance, general. In
Encyclopedia of Analytical Chemistry. John Wiley & Sons, Ltd, 2006.
[29] Vladimir K. Michaelis. Nuclear Magnetic Resonance Studies of Disorder and
Local Structure in Borate and Germanate Materials. PhD thesis, University of
Manitoba, December 2010. February 2011.
[30] MIT Department of Physics. Pulsed Nuclear Magnetic Resonance: Spin Echoes,
March 2013.
[31] Albert W. Overhauser.
Polarization of nuclei in metals.
Physical Review,
92(2):411-415, October 1953.
[32] R. V. Pound.
Nuclear electric quadrupole interactions in crystals.
Physical
Review, 79(4):685-702, August 1950.
[33] E. M. Purcell, H. C. Torrey, and R. V. Pound. Resonance absorption by nuclear
magnetic moments in a solid. Physical Review, 69(1-2):37-38, January 1946.
[34] J Ramakrishna. Nuclear spin-lattice relaxation in neodymium-doped lanthanum
magnesium nitrate. Proceedings of the Physical Society, 92(2):520-521, October
1967.
[35] T. J. Schmugge and C. D. Jeffries. High dynamic polarization of protons. Phys.
Rev., 138:A1785-A1801, Jun 1965.
[36] Albert A Smith, Bjrn Corzilius, Alexander B Barnes, Thorsten Maly, and
Robert G Griffin. Solid effect dynamic nuclear polarization and polarization
pathways. The Journal of Chemical Physics, 136(1):015101-015101-16, January
2012.
73
[37] S 0 Smith and R G Griffin. High-resolution solid-state NMR of proteins. Annual
Review of Physical Chemistry, 39(1):511-535, 1988. PMID: 3075467.
[38] Changsik Song, Kan-Nian Hu, Chan-Gyu Joo, Timothy M. Swager, and
Robert G. Griffin. TOTAPOL: a biradical polarizing agent for dynamic nuclear
polarization experiments in aqueous media. Journal of the American Chemical
Society, 128(35):11385-11390, September 2006.
[39] R.A. Wind, M.J. Duijvestijn, C. van der Lugt, A. Manenschijn, and J. Vriend.
Applications of dynamic nuclear polarization in 13C NMR in solids. Progress in
Nuclear Magnetic Resonance Spectroscopy, 17:33-67, 1985.
[40] R. J. Wittebort, E. T. Olejniczak, and R. G. Griffin. Analysis of deuterium
nuclear magnetic resonance line shapes in anisotropic media. The Journal of
Chemical Physics, 86(10):5411-5420, May 1987.
[41] J. P. Wolfe. Direct observation of a nuclear spin diffusion barrier. Physical Review
Letters, 31(15):907-910, October 1973.
[42] David S. Wollan. Dynamic nuclear polarization with an inhomogeneously broad-
ened ESR line. i. theory. Physical Review B, 13(9):3671-3685, May 1976.
74