Applications of the bloch-siegert shift in solid-state proton-dipolar-decoupled 19F MAS NMR

Article abstract of DOI:10.1006/jmra.1996.0012

In solid-state proton-dipolar-decoupled ¹⁹F MAS NMR spectroscopy, ¹⁹F chemical-shift data need to be corrected for the BlochSiegert shift. Assigning the single sharp ¹⁹F resonance of 2-fluoroadamantane to its proton-coupled ¹⁹F shift of -174.4 ppm results in chemical-shift referencing that is independent of the amplitude of the proton-decoupling field. The Bloch-Siegert shift is also a useful tool to characterize the amplitude and homogeneity of the proton-decoupling field, H_1H, and to monitor probe performance. Considerable inhomogeneity in H_1H along the long axis of the rightcylinder sample rotor was detected. In our commercial 7 mm H-F MAS probe, the proton field strength, A _HH_1H, decreases to 25% of the maximum value across the usable sample volume. Measurement of the Bloch-Siegert shift revealed that the proton-decoupling field strength decreases during the first few scans of an acquisition. Reductions in the proton field strengths can exceed 10%, and they are explained by the heating of the RF coil circuitry which is caused by high-power proton decoupling. The extent of reduction in field amplitude is a function of the decoupling duty cycle. Losses in A _HH_1H can be avoided by tuning the probe proton RF circuitry at the operating temperature of the probe, using the Bloch-Siegert shift as an optimization parameter.

Full text of DOI:10.1006/jmra.1996.0012

JOURNAL OF MAGNETIC RESONANCE, Series A 118, 84–93 (1996)
ARTICLE NO. 0012
Applications of the Bloch –Siegert Shift in Solid-State
19
Proton-Dipolar-Decoupled F MAS NMR
¨
S
TEPHANIE A. VIERKOTTER
*
Chemical and Analytical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6201
Received May 10, 1995; revised October 5, 1995
In solid-state proton-dipolar-decoupled 19F MAS NMR spectros-
copy, 19F chemical-shift data need to be corrected for the Bloch–
Siegert shift. Assigning the single sharp 19F resonance of 2-fluoro-
adamantane to its proton-coupled 19F shift of 0174.4 ppm results
in chemical-shift referencing that is independent of the amplitude
of the proton-decoupling field. The Bloch–Siegert shift is also a
useful tool to characterize the amplitude and homogeneity of the
proton-decoupling field, H1H , and to monitor probe performance.
Considerable inhomogeneity in H1H along the long axis of the right-
cylinder sample rotor was detected. In our commercial 7 mm H–
F MAS probe, the proton field strength, H H1H , decreases to 25%
of the maximum value across the usable sample volume. Measure-
ment of the Bloch–Siegert shift revealed that the proton-decoupling
field strength decreases during the first few scans of an acquisition.
Reductions in the proton field strengths can exceed 10%, and they
are explained by the heating of the RF coil circuitry which is caused
by high-power proton decoupling. The extent of reduction in field
amplitude is a function of the decoupling duty cycle. Losses in
H H1H can be avoided by tuning the probe proton RF circuitry at
the operating temperature of the probe, using the Bloch–Siegert
shift as an optimization parameter. ᭧ 1996 Academic Press, Inc.
(
gobs H1 )2
D
Å
,
[1]
v20
0
v2
where gobs is the gyromagnetic ratio of the observed nucleus,
H1 is the decoupling field in gauss, v0 is the Larmor fre-
quency of the observed nucleus, and
quency of the decoupled nucleus. Reference (2) gives the
Bloch–Siegert shift for the off-resonance case as v21 /(v20
2 ). The examples given on p. 227 in this reference show
that v1 is taken as H1 with as the gyromagnetic ratio of
the decoupled nucleus. This was found to give Bloch–
Siegert shifts which are too large compared to shifts mea-
sured by Webb and Zilm (4) and ourselves. Correct values
v is the Larmor fre-
0
v
g
g
are obtained when
g is taken as the gyromagnetic ratio of
the observed nucleus. Using the gyromagnetic ratio of the
observed nucleus makes sense since the Bloch–Siegert shift
expresses the interaction between the H1 field and the field
of the moment of the observed nucleus. By use of the rela-
tionships
as
v
Å
2
pn and
Å
g
/(2p), Eq. [1] can be written
obs H1 )2
INTRODUCTION
(
D
Å
.
[2]
n20
0
n2
It is well known that the resonance frequency of a nucleus,
n0 , shifts when a second, off-resonance RF field is applied
(1, 2). This effect, the Bloch–Siegert shift, is a contribution
to H0 that arises from the off-resonance component of the
oscillating RF irradiation field (3). In the context of this
work, the second irradiation field is a heteronuclear dipolar
decoupling field, hereafter referred to as the ‘‘decoupling
field,’’ H1 . The effect is manifested as a shift in the Larmor
frequencies of the observed nuclei. For the off-resonance
case where the difference between the Larmor frequencies
of the decoupled and the observed nuclei is much larger than
Equations [1] and [2] show that the Bloch–Siegert shift is
proportional to the square of the decoupling field, H1 , and
inversely proportional to the difference between the squared
Larmor frequencies of the observed and the decoupled nu-
clei. The amplitude of the proton decoupling field, in hertz,
is calculated by multiplying H1 (gauss) from Eq. [2] by
of the proton nucleus, i.e., H H1H .
In {1H}13C NMR spectroscopy of liquids or dissolved
solids, where the proton decoupling field H1H serves to re-
move scalar coupling, the required decoupling-field strengths
are relatively small, e.g., 10 kHz. For this decoupling field,
the frequency of the decoupling field,
É
v
0
v0É ӷ v1 , the
the Bloch–Siegert shift is very small, 6.7
1
1004 ppm at a
Bloch–Siegert shift, , is described by (4)
D
static magnetic field, H0 , of 2.35 T (see Table 1). In solid-
state proton-dipolar-decoupled 13C, [1H]13C, MAS NMR
* Current address: Department of Chemistry, Louisiana State University,
Baton Rouge, Louisiana 70803-1804.
1
spectroscopy, the H decoupling fields employed are typi-
84
1064-1858/96 $12.00
Copyright
᭧ 1996 by Academic Press, Inc.
All rights of reproduction in any form reserved.

PROTON-DECOUPLED MAS NMR
85
TABLE 1
RF coil circuitry under actual measurement conditions using
the Bloch–Siegert shift is described.
Magnitudes of the Bloch –Siegert shift in Proton-Decoupled
Carbon and Fluorine NMR Spectroscopy for Different Proton-
Decoupling Amplitudes, HH1H , and Different Static Magnetic-
Field Strengths, H0
EXPERIMENTAL
General
19F solid-state NMR experiments with and without proton
decoupling were performed on a Bruker MSL-100 spectrom-
eter using a H–F double-tuned probe that allows magic-
HH1H
(kHz)
H0 (T)
D
(ppm)
{1H}13C
[1H]13C
[1H]19F
2.35
2.35
2.35
2.35
1.41
10
100
50
100
100
6.7
6.7
1
1
1004
1002 angle spinning speeds up to 7–8 kHz (Doty Scientific Inc.).
1.9
The right-cylinder sample rotor is placed inside of the dou-
ble-tuned, four-turn RF coil (105 nH). The coil is made
from gold-plated Cu foil (5 mm Au) and is 13.2 mm long.
7.7
21.4
Note. {1H} designates proton decoupling in solution NMR (removal of
The copper foil is 1.7 mm in width. The coil is wrapped
scalar coupling only), and [1H] stands for dipolar proton decoupling as such that the gap between the start and the end points of the
applied in solid-state NMR experiments.
foil for the first turn is 0.5 mm, 1.85 mm for the second and
third turns, and 0.5 mm for the forth turn. The coil is wrapped
about the stator which has an o.d. of 8.25 mm. The right-
cylinder sample rotors are made from zirconia or silicon
nitride and have an outer diameter of 7.0 mm and a length
cally 50–70 kHz since such field strengths are necessary to
remove the heteronuclear C–H dipolar interactions. Even
for a 100 kHz proton decoupling field, the Bloch–Siegert
of 22.1 mm. Maximum sample volume (about 360
ml) is
shift in [1H]13C NMR is only 6.7
1
1002 ppm (1.7 Hz).
achieved with use of two short end caps that leave 16.1 mm
of length of the rotor for the sample. Several experiments
described in this paper employed smaller sample volumes.
In these cases, the remaining volume was taken up by spacers
made from boron nitride. The NMR experiments involve
1
In solid-state H-dipolar-decoupled 19F, [1H]19F, MAS
NMR spectroscopy, the difference between the Larmor fre-
quencies of the observed and decoupled nuclei is 6 MHz at
2.35 T (rather than 75 MHz as in the case of proton-decou-
pled 13C NMR), and large Bloch–Siegert shifts are ob-
served. In [1H]19F NMR spectroscopy at 2.35 T, a proton
decoupling field of 50 kHz leads to a shift of 1.9 ppm (181
Hz) and a decoupling field of 100 kHz produces a shift of
7.7 ppm (725 Hz; Table 1). It is apparent that valid compari-
sons of 19F chemical shifts measured in the solid state in the
presence of proton decoupling are possible only if the re-
ported values are independent of the amplitude of the proton
decoupling field. The correction for the Bloch–Siegert shift
becomes even more important at lower static magnetic fields,
H0 , where the Bloch–Siegert shift is larger (Eqs. [1] and
[2]). At 1.41 T (60 MHz 1H Larmor frequency), the Bloch–
Siegert shift in a [1H]19F NMR experiment using a 100 kHz
decoupling field is 21.4 ppm (1209 Hz; Table 1).
a
19F Bloch-decay pulse sequence with or without proton
decoupling. A 3.3 m
s 19F excitation pulse was used. Acquisi-
tion times were 10 ms unless cited otherwise. The recycle
delay was 4 s. The magic-angle spinning speed was 4 kHz
for the experiments shown in Figs. 2, 3, and 6 and 6.3 kHz
for the spectra presented in Figs. 1 and 5. Digital resolution
was 6 Hz.
2-Fluoroadamantane, 1, was prepared from 2-hydroxyada-
mantane (Aldrich) via a procedure similar to that described
by Olah et al. (6). Five grams of 2-hydroxyadamantane in
ether/hexane were added dropwise to 30 ml of HF-pyridine
(70/30) at 0ЊC. After the addition was completed, the reac-
tion mixture was stirred at room temperature for two hours.
The mixture was poured onto tossed ice and the aqueous
layers were extracted with ether. The combined organic lay-
ers were washed twice with 50 ml of 10% Na2CO3 solution
and with water. After drying over MgSO4 , the organic phase
was concentrated and the material was purified by column
chromatography (neutral alumina in hexane). A total weight
of 3.1 g of pure 2-fluoroadamantane was obtained. Alterna-
tively, 1 can be prepared from 2-hydroxyadamantane by
reaction with diethylaminosulfur trifluoride (DAST) as re-
ported by Adcock (7).
In this paper, the Bloch–Siegert shifts observed in solid-
state [1H]19F NMR spectroscopy are discussed from several
perspectives: (1) a method for correcting solid-state 19F chemi-
cal shifts for the Bloch–Siegert shift is reported; (2) H1H field
amplitudes are determined from the measurement of the Bloch–
Siegert shift; (3) the observation of the Bloch–Siegert shift is
used to evaluate the homogeneity (4, 5) of the proton-decou-
pling field throughout the sample volume; (4) the inhomogene-
ity in H1H across the sample is used to observe the sublimation
of 2-fluoroadamantane, 1, within the sample rotor; (5) heating
of the RF coil circuitry by application of proton decoupling
and its influence on the measurement of the Bloch–Siegert
Chemical-Shift Referencing
Chemical-shift referencing in [1H]19F NMR experiments
shift are discussed; and (6) a procedure for tuning the proton was achieved by blending 2-fluoroadamantane, 1 (structure

¨
STEPHANIE A. VIERKOTTER
86
shown on the right in Fig. 1), into the sample of interest. (b) was performed using buffered acquisition so that all data
The chemical shift of 1 was set to 174.4 ppm { (CFCl3 ) could be acquired in a single experiment.
0
d
Å
0 ppm} which corresponds to the 19F chemical-shift value To test whether the 19F chemical shift of 1 is temperature
of this compound in solution (CDCl3 ) (8) in the absence of dependent, a 20.5 ms heating pulse (proton-decoupling field,
1H decoupling, i.e., in the absence of a Bloch–Siegert shift. 112 kHz) was applied on the proton RF channel prior to the
2-Fluoroadamantane can be easily removed from precious 19F excitation pulse. The excitation pulse was followed by
samples by room-temperature sublimation.
acquisition of the fluorine signal in the absence of proton
decoupling. The chemical shift of 1 measured in this experi-
ment was compared to the proton-coupled 19F shift that was
recorded without any prior RF heating pulses.
Measurements of the Proton Field Amplitude
2-Fluoroadamantane, 1, was used neat or mixed into a
sample uniformly. The Bloch–Siegert shift, measured as the
difference in the chemical shifts of the proton-coupled and
the proton-decoupled 19F resonances, gives the proton field
1
Tuning and Matching of the H RF Coil Circuitry under
Measurement Conditions
A rotor packed with 1 in the middle third of the rotor
volume (cf. Fig. 2d) was used in this procedure. The spec-
trometer was programmed to continuously record one scan
of a proton-decoupled 19F spectrum of this sample, to auto-
matically process the FID, and to display the frequency of
the fluorine resonance. The tuning and matching capacitors
for the proton RF circuitry were adjusted to maximize the
Bloch–Siegert shift of the observed fluorine resonance of 1.
This experiment was performed under conditions identical to
those intended for use in the actual measurements following
sample change (same recycle delay and acquisition time,
same RF filters in the proton RF line, etc.). The 19F RF
channel was tuned and matched in the conventional, off-line
manner which involves sending a low-power fluorine signal
into the circuit and adjusting the tune and match for the least
amount of reflected power. The tuning and matching of the
proton and fluorine channels were performed in an iterative
manner.
H1H by Eq. [1] or [2]. H1H (gauss) is multiplied by
gH /(2 ) to obtain the proton field amplitude, H H1H .
Å
H
p
H1H Homogeneity Measurements
For the measurement of the profile of the H1H field (5)
along the long axis of the rotor, boron nitride spacers were
used to hold a thin sample slice, a right-cylinder volume,
0.38
{
0.03 mm thick, in place, with the sample disk face
orthogonal to the rotor axis. The Bloch–Siegert shift was
measured for 11 different positions (see Figs. 3 and 4) of
this slice of 1 along the axis of the rotor.
For the evaluation of radial H1H homogeneity, the volume
of the middle sample slice and an end sample slice were
subdivided further into an annulus of sample (i.d.
mm, o.d. 5.4 mm) and an on-axis inner core (o.d.
mm), again using boron nitride spacers. The Bloch–Siegert
shifts that arise from 1 packed in these two volumes (annulus
and inner core) were compared.
Å
2.7
2.7
Å
Å
RESULTS AND DISCUSSION
Measurement of the Sublimation Behavior of 1
(a) Chemical-Shift Referencing
2-Fluoroadamantane, 1, 3.8 wt%, was blended with 3-
fluoro-4-methoxybenzoic acid, 2, to give a uniform physical
mixture. The powder mixture was hand packed in a rotor,
filling the entire volume that is available when using short
end caps. [1H]19F spectra were recorded as a function of
time. Each spectrum was acquired with 300 transients. At
the end of this experiment, the sublimation of 1 was con-
firmed by visual inspection of the sample.
The differences in the Bloch–Siegert shifts of all reso-
nances in a given solid-state proton-dipolar-decoupled 19F
MAS NMR spectrum are small. For fluorine resonances sep-
arated by 20 kHz (212.3 ppm at 2.35 T), the difference is
only 2.4 Hz for a proton-decoupling field amplitude, H H1H ,
of 100 kHz. Thus, correct chemical shifts can be obtained
by simply referencing one of the resonances in the proton-
decoupled 19F spectrum using its known proton-coupled
chemical-shift value. This referencing procedure leads to 19F
chemical shifts that correspond to the values that would be
Heating of the RF Coil Circuitry through Proton
Decoupling
Heating of the RF coil circuitry caused by proton decou- measured in the absence of proton decoupling. These chemi-
pling was studied (a) by observing the Bloch–Siegert shift cal shifts are automatically corrected for the Bloch–Siegert
for a range of proton-decoupling duty cycles (proton-decou- shift and can be compared between different investigators
pling pulses of 2.5 to 40.5 ms width with a recycle delay of without knowledge of the proton-decoupling field strengths
4 s) and (b) by measuring the Bloch–Siegert shift for a employed. A convenient way to accomplish this experiment
given proton-decoupling pulse width (20.5 ms, recycle delay is to blend 1 into the sample of interest to get a uniform
4 s) as a function of the number of transients. Experiment physical mixture and set its 19F resonance to
0
174.4 ppm,

PROTON-DECOUPLED MAS NMR
87
Figure 1 shows the solid-state 19F MAS NMR spectrum
for 3-fluoro-4-methoxybenzoic acid, 2, mixed with 1 (3.8
wt%) recorded without proton decoupling (Fig. 1a) and with
proton decoupling using fields of 54.2 kHz (Fig. 1b) and
1
110.4 kHz (Fig. 1c). The H-coupled spectrum shows the
sharp 19F resonance of 1 at
0
174.4 ppm and a much broader
resonance (n1/2
Å
1.5 kHz) for 2 at 133.2 ppm. The fluo-
0
rine in 2 is attached to an aromatic carbon, a bonding con-
figuration that produces a highly anisotropic electron density
about the fluorine atom. This is manifested as a large chemi-
cal-shift anisotropy which gives rise to two sets of spinning
1
side bands at a MAS speed of 6.3 kHz (9). The H-decou-
pled spectra show that all 19F resonances are shifted upfield
by the same amount with respect to their chemical shifts in
the 1H-coupled spectrum. This shift increases with increasing
proton-decoupling field strength (Figs. 1b and 1c). By set-
ting the 19F resonance of 1 in the proton-decoupled spectra
to
0
174.4 ppm, the chemical shifts in the spectra shown in
Figs. 1b and 1c become independent of the strength of the
proton-decoupling field.
The asymmetry that is seen in the lineshape of 1 (Fig.
1c; see also Fig. 2c) is caused by a nonuniform proton-
decoupling field which produces differential Bloch–Siegert
shifts in different volume elements within the RF coil. This
field inhomogeneity and its impact on chemical-shift refer-
encing are discussed in detail in part (c) of this section.
(b) Characterization of the Amplitude of the H1H Field
The measurement of the Bloch–Siegert shift is useful
for a rapid characterization of the H1H field amplitude and
provides an alternative to the use of an external antenna
which monitors the forward and reflected power of the RF.
A few weight percent of 1 is blended into the sample of
interest to give a uniform physical mixture, and the chemical
shift of the 19F resonance of the reference is measured with
and without proton decoupling. The Bloch–Siegert shifts
observed for the relatively sharp 19F resonances of 1 in con-
nection with Eq. [2] give the proton field H1H . The field
amplitude is obtained by multiplying H1H by H . The preci-
sion of this determination depends on the digital resolution
of the measurement and on the amplitude of the decoupling
field. A digital resolution of 6 Hz gives a maximum uncer-
FIG. 1. Solid-state 19F MAS NMR spectra of 3.8 wt% of 2-fluoroada-
mantane 174.4 ppm) mixed with 3-fluoro-4-methoxybenzoic acid
133.2 ppm) to give a uniform physical mixture. (a) H coupled; (b, c)
with HH1H 54.2 and 110.4 kHz, respectively. The magic-angle spinning
rate is 6.3 kHz.
(
0
1
(
0
Å
i.e., the chemical shift observed in solution (CDCl3 ) (8)
when no proton decoupling is employed. One advantage of
using 1 as a reference compound is its relatively narrow
19F resonance (for sample slice in middle of rotor: 460 Hz
1
linewidth at half-height without H decoupling, 90 Hz with
tainty in H H1H of
{
0.8 kHz (
{
1.6%) for a 50 kHz field
126 kHz H H1H ; slice is 0.38
{
0.03 mm thick; see under
and 0.4 kHz ( 0.4%) for a 100 kHz field. The citation
{
{
Experimental). The narrow resonance is the result of the
high molecular-reorientation rate of this substance in the
solid state which reduces heteronuclear dipolar interactions
by motional averaging. Thus, the resonance of this com-
pound does not obscure a large portion of the spectral win-
dow. The chemical shift of 1 can be set with higher accuracy
than the shifts of typical, more rigid 19F-containing com-
pounds that give rise to resonances with linewidths at half-
height of a kilohertz or more.
of H H1H to higher precision is not warranted since the
inhomogeneity in the H1H field exceeds these ranges, except
for highly spatially constrained samples, as shown in the
next section.
(c) Characterization of H1H Field Homogeneity
Figure 2 shows expansions of 19F spectra of 1 (full rotor,
short end caps) recorded with (a) no proton decoupling and

¨
STEPHANIE A. VIERKOTTER
88
middle of the rotor while slices 1 and 11 are positioned at
opposite ends of the sample rotor using short end caps (see
under Experimental). The spectra of 1 in slices 5, 6, and 7
(Fig. 3) in the center of the rotor show the largest Bloch–
Siegert shifts,
D, and the highest signal-to-noise-ratios. The
D
values of these slices correspond to H H1H of 125, 126,
and 127 kHz, respectively. Slices of 1 that were positioned
further removed from the center of the rotor show a drastic
decrease both in their Bloch–Siegert shifts and in their sig-
nal-to-noise ratios. Slices 1 and 11 give rise to such poor
signal sensitivity that the number of scans for these spectra
was increased 8- and 23-fold, respectively.
The data from Fig. 3 are plotted in Fig. 4 as the proton field
strength, H H1H, calculated from the measured
D, versus the
positions of the sample slices along the long axis of the
rotor. The graph shows that the H1H field along the long axis
of the rotor drops off drastically toward either end of the
rotor. The maximum field strength, H H1H max , of 127 kHz
near the center of the rotor is reduced to about 32 kHz at
FIG. 2. Solid-state 19F MAS NMR spectra of 1 (a) 1H coupled and (b–
1
d) H decoupled as indicated. Spectra (a–c) were recorded with 1 packed
into the entire rotor volume (using short end caps). Spectrum (d) is ob-
tained from 1 restricted to the middle third (on long axis of rotor) of the
rotor volume.
(b) proton decoupling of 49 kHz, and (c) 115 kHz. In the
absence of proton decoupling, the full width at half-height,
n1/2 , of the 19F resonance is 460 Hz (Fig. 2a). This linewidth
decreases when proton decoupling is employed (10) (Fig.
2b). The 19F signal is strikingly asymmetric in experiments
using high proton-decoupling fields (Fig. 2c). The increase
in asymmetry and overall width of the signal upon increase
in proton-decoupling field amplitude indicates that the H1H
field is not homogeneous throughout the sample volume.
Inhomogeneity in H1H causes the sample in different loca-
tions in the rotor to experience different Bloch–Siegert
shifts, leading to the observed asymmetric lineshape.
The inhomogeneity along the long axis of the rotor was
investigated by packing a 0.38
{
0.03 mm thick disk of 1
in the sample rotor with the sample disk face orthogonal to
the rotor axis. The remainder of the volume in the rotor
was filled with boron nitride spacers. This sample slice was
moved incrementally to 11 different positions in the rotor,
and the Bloch–Siegert shift was measured. The result of this
experiment using a proton-decoupling field strength of 127
kHz is shown in Figs. 3 and 4. Figure 3 presents the spectra
obtained from the 11 slices of 1. The positions of these slices
FIG. 3. Solid-state [1H]19F MAS NMR spectra of 1 packed as a thin
disk, 0.38
{
0.03 mm thick, with the sample disk face orthogonal to the
rotor’s long axis. The 11 spectra are derived from this sample slice being
placed in 11 different positions within the rotor as indicated in Fig. 4. The
within the rotor are indicated in Fig. 4. Slice 6 is in the maximum HH1H is 127 kHz (slice 7).

PROTON-DECOUPLED MAS NMR
89
with the same proton-decoupling field strength. The Bloch–
Siegert shifts measured using the peak maxima in Figs. 2c
and 2d give field strengths of 115 and 116 kHz, respectively,
i.e., values that agree within 1%. Consequently, it is not
necessary to restrict 1 to the center of the rotor to get an
accurate measure of H H1H max . Instead, 1 may be mixed
uniformly with the sample and the Bloch–Siegert shift deter-
mined using the frequency of the 2-fluoroadamantane reso-
nance at highest peak intensity.
The H1F field will show the same inhomogeneity over the
rotor volume as H1H . A 19F excitation pulse that leads to a
90
a 23
spins give rise only to 40% of their integrated intensity in
the spectrum, relative to that observed using a 90 pulse
excitation (Fig. 2c). Despite this underrepresentation, the
1H inhomogeneity in 1 is visible as an asymmetric, hetero-
Њ
rotation for those spins in the center of the rotor generates
Њ
rotation for 19F spins at the rotor ends. The latter 19F
Њ
H
geneously broadened signal. This observation of H1H inho-
mogeneity in [1H]19F MAS spectra by lineshape analysis is
exceptional since most fluorine resonances are broad enough
FIG. 4. Profile of the proton field amplitude, H H1H , along the long
rotor axis. The plot is based on the data shown in Fig. 3. The x axis shows
the 11 positions of the sample disk along the rotor’s long axis in fractions
of the rotor length (the length refers to the usable rotor length, i.e., excluding
the portion that is taken up by the short end caps). Zero on the lower x
axis indicates the midpoint of the rotor axis. The upper x axis is marked
off in millimeters. The horizontal line drawn through each data point repre-
(
n1/2
§
1 kHz) to obscure this effect (see the spectrum of
2 in Fig. 1). Differential Bloch–Siegert shifts for samples
packed in the entire rotor volume become visible when the
19F linewidth is exceptionally narrow. This situation applies
for compounds with high degrees of mobility, e.g., 1, and
for large monofluorinated molecules that have slow 19F– 19F
spin diffusion.
sents the thickness of the sample disk, 0.38
{
0.03 mm.
Radial inhomogeneity in the H1H field was also investi-
gated. For this purpose, the Bloch–Siegert shift was remea-
sured for thin slices of 1 in the center and at one end of the
rotor (slices 6 and 1) as described above, except in this
experiment each of these sample slices was subdivided fur-
ther into an annulus and an inner core of sample (see under
Experimental). It was found that the sample in annulus and
inner core of slice 6 exhibited equal Bloch–Siegert shifts to
within 1%. Thus, radial inhomogeneity in H1H at the center
of the rotor (coil) is negligible. However, when this experi-
ment was repeated for slice 1, marked differences in the
Bloch–Siegert shifts for 1 in the annulus and in the inner
core were observed. The H1H field amplitude found in the
annulus is weaker than in the core by about a factor of
two, indicating that radial inhomogeneity is dramatic for the
sample at the rotor ends.
While a detailed profile of the radial inhomogeneity has
not been measured, these experiments show that radial inho-
mogeneity is increasingly significant as the sample location
is further removed from the center of the rotor (coil). The
linewidths in the spectra of the 11 sample slices of 1 (Fig.
3) could be indicative of the extent of radial inhomogeneity
at those 11 positions along the long axis of the rotor. How-
ever, these linewidths are not influenced solely by radial
the ends of the rotor. This is a reduction to 25% of HH1H max
.
The data in Fig. 4 indicate that only about 40% of the rotor
volume centered about the position of slice 7 (0.7 mm offset
from the middle of the rotor) may be filled with sample if
the decrease in H1H field amplitude across the sample should
not exceed 10% of H H1H max . If an H1H homogeneity of
20% is acceptable, 60% of the rotor volume may be filled
with sample. The slight deviation of the data points from
the quadratic function in Fig. 4 shows that the reduction of
the H1H field amplitude is not quite symmetrical about
H H1H max . The slice experiment shown in Figs. 3 and 4 was
repeated for lower proton-decoupling fields with maximum
field amplitudes of 56 and 94 kHz (data not shown). The
decrease in H H1H , in percent of the maximum, is about the
same in each case as for the example shown in Figs. 3 and
4 (the amplitude drops from the maximum at slice 7 to 52–
53% of the maximum value at slice 10 in all cases).
Figure 2d shows the proton-decoupled 19F MAS spectrum
of a sample of 1 which was constrained to the middle third
of the rotor volume (using BN spacers) rather than being
packed in the entire rotor volume (Fig. 2c). The comparison
of Figs. 2c and 2d clearly shows the improvement in H1H
homogeneity upon using a significantly reduced rotor vol- inhomogeneity but also by axial inhomogeneity since the
ume centered within the rotor. These spectra were recorded sample slices are of finite thickness and the drop in field

¨
STEPHANIE A. VIERKOTTER
90
strength across the slice thickness is much more drastic for
slices close to the end caps than for those near the center of
the rotor (Fig. 4). A minor error contribution to the line-
widths is the uncertainty in the reproducibility of the sample
slice thickness for the 11 slice positions (see under Experi-
mental).
Figure 2d shows that packing the sample in the middle
third of the rotor volume results in a more homogeneous
H
1H field over the sample dimensions. The 19F spectrum does
not show the characteristic low-field asymmetry seen in Figs.
1c and 2c. Restricting the sample to a fraction of the rotor
volume centered about the middle of the rotor significantly
reduces both axial and radial inhomogeneities. Uniformly
blending 1 into the sample has the advantage of providing
both the minimum and the maximum H H1H over the sample
volume in experiments performed with large decoupling
fields (see Fig. 1c). This method allows one to determine
rapidly the minimum and maximum proton field strengths
over the chosen sample volume with one experiment instead
of having to perform a more tedious study involving several
samples slices as shown in Figs. 3 and 4.
Close inspection of the 19F lineshape of 1 recorded with
high proton-decoupling power (Figs. 1c, 2c, and 5a) reveals
that two portions of the downfield ‘‘tail’’ of the lineshape
have somewhat higher intensities than the remainder of the
tail. As discussed above, the width of the lineshape indicates
the spread in proton-decoupling field strengths across the
sample. The intensities of the individual resonances that lead
to the observed lineshape are proportional to the amount of
sample that experiences a given field strength, and they are
also weighted by the H1F field profile across the sample. To
accurately account for the detail of the lineshape including
the fine structure, several additional factors must be taken
into account. The spinning of the sample often causes some
repacking of the sample within the rotor, leading to small
cone-shaped voids near the ends of the rotor. Higher resolu-
tion in the profile of the proton-decoupling field strength
across the long axis of the sample might reveal ripples in
FIG. 5. (I) [1H]19F MAS NMR spectra of 3.8 wt% of 1 uniformly
blended into 2, recorded as a function of time H H1H max 110.4 kHz;
6.3 kHz). Only the signals of 1 are shown. Each spectrum
represents 300 scans. (II) Cross section of the rotor. In the beginning of
the experiment, the concentration of 1 is constant throughout the sample
volume x (y indicates the rotor end caps). After 88 h, 1 has accumulated
at the ends of the rotor (z). (III) The ratio of I/I0 , i.e., the intensity of the
Å
(
MAS rate
Å
fluorine resonance at
in Ia) at time t over the initial intensity of this resonance, versus the
0
183.8 ppm (resonance with highest peak intensity
experimental evolution time.
the profile that correspond to the gaps between the turns of decoupled 19F MAS spectra of a uniform physical mixture
the coil. Furthermore, the radial inhomogeneity needs to be of 1 (3.8 wt%) and 2 as a function of time. In the beginning
considered to predict the lineshape correctly in detail. The of the experiment, the asymmetric lineshape is indicative of
detailed simulation of the lineshape is, however, not neces- 1, being distributed evenly throughout the rotor volume (cf.
sary for the determination of the strength and the inhomoge- Fig. 2c). The 19F resonance of the highest peak intensity in
neity of the H1 field. This information is readily extracted Fig. 5 (I.a) at
0
183.8 ppm exhibits a Bloch–Siegert shift
from the observed lineshapes as described above.
of 9.4 ppm corresponding to a value for H H1H max of 110.4
kHz. Over time, the intensity of this resonance decreases
(Fig. 5, I and III) as a narrow (n1/2
with a symmetric lineshape at 175.2 ppm grows in inten-
sity. Eventually, all resonance area is represented in this line.
Å
140 Hz) resonance
(d) Sublimation Behavior of 1 within the Rotor in Long-
Term Experiments
0
The inhomogeneity in H1H that was discussed in the previ- This chemical shift corresponds to a Bloch–Siegert shift of
ous section has a surprising consequence in experiments only 0.8 ppm, i.e., a proton field amplitude of 32 kHz. This
using 1 as a chemical-shift reference in long-term experi- field amplitude represents only about 30% of the value that
ments. Figure 5 (I) shows the 19F signals of 1 in the proton- was measured in the beginning of the experiment. The spec-

PROTON-DECOUPLED MAS NMR
91
tra in Fig. 5 reveal that 1 physically moves toward the ends
of the rotor where it accumulates. The movement of 1 occurs
via sublimation. The compound collects at the ends of the
rotor, possibly due to cooling from the bearing gas which
impinges on the rotor at the points where 1 condenses (see
Fig. 5, II).
The ability to observe the sublimation behavior of 1 is an
interesting consequence of the inhomogeneity in H1H . From
a practical point of view, the sublimation behavior of 1
places a minor limitation on its use for chemical-shift refer-
encing and for the determination of H1H field strengths. It
was found that the rate with which 1 accumulates at the ends
of the rotor decreases when the rotor is packed tightly as
was the case for the experiments shown in Fig. 5. But even
when the material is packed loosely, the sublimation of 1
becomes a problem only if the 19F resonance of 1 is used for
chemical-shift referencing and field strength determinations
several hours after the experiment is started. This is usually
not a restriction since the 19F resonance of 1 is visible in the
spectrum after one transient. For long-term experiments that
involve measurements at several different proton-decoupling
field strengths, one can, after initially referencing with 1,
use any peak in the spectrum as a secondary reference. One
can also avoid the problems arising from sublimation of 1
by mixing only some of the sample with 1 and packing this
material in the center region of the rotor where H H1H is
within 10% of H H1H max . The rest of the rotor is filled with
neat sample. A disk of weighing paper of the same diameter
as the inner diameter of the rotor, placed at both interfaces
of mixture and neat sample, effectively stops the sublimation
of 1 out of the center region of the rotor.
FIG. 6. Plot of the Bloch–Siegert shift of 1 as a function of the number
of transients, in a [1H]19F MAS NMR experiment. The data were recorded
using buffered acquisition. The proton pulse length was 20.5 ms, and the
recycle delay was 4 s.
field strength which was reached after about 40 transients is
113 kHz, 4% less than the observed field amplitude after
the first scan, 118 kHz.
The observed effect possibly could be due to a temperature
dependence of the 19F chemical shift of 1. To investigate
this possibility, heating pulses were applied on the proton
RF channel prior to the fluorine-excitation pulse. The proton-
coupled 19F chemical shift measured with and without heat-
ing pulses were identical. These data prove that the depen-
dence of the Bloch–Siegert shift on the proton RF duty cycle
is not due to a temperature dependence of the 19F chemical
shift of 1.
Experimentally, different T2 relaxation times for various
samples require different 19F acquisition times and different
proton-decoupling pulse lengths. The influence of the decou-
pling duty cycle on the H1H field strength means that the
experimental protocol should involve a sufficient number of
discarded scans prior to acquisition of the desired spectrum
so that the coil circuit can reach thermal equilibrium. Second,
the value of the H1H field strength needs to be redetermined
when the duty cycle of the proton decoupling is changed.
These considerations are of little concern when routine
[1H]19F NMR spectra are acquired. They are important when
it is necessary to know the H1H field amplitude and when it
is important that the field strength remains constant through-
out the experiment. A procedure for tuning and matching of
the proton RF coil circuit under measurement conditions is
(e) The Influence of the Proton-Decoupling Duty Cycle
on the H1H Field Strength
The proton-decoupling duty cycle is an important experi-
mental parameter in quantitative [1H]19F NMR spectros-
copy. In experiments that involve only a few transients, it
was observed that the Bloch–Siegert shift decreases as the
proton-decoupling duty cycle increases (data not shown).
For a given proton-decoupling duty cycle, the Bloch–Siegert
shift and the H1H amplitude decrease as more and more scans
are acquired until a plateau value is reached. This behavior
is shown in Fig. 6 for the resonance of 1. A rationale for these
observations is that high-power proton decoupling leads to
an increase in the coil circuitry temperature relative to typical
probe-tuning conditions and thereby causes a reduction in
performance. After a number of scans, thermal equilibrium
is reached. The amplitude of the equilibrium H1H field for a
given RF input and the rate at which this equilibrium is
reached depend on the decoupling duty cycle. The data
shown in Fig. 6 were acquired with a duration of the proton
pulse of 20.5 ms and a 4 s recycle delay. The equilibrium H1H described below.

¨
STEPHANIE A. VIERKOTTER
92
1
(f ) Tuning and Matching of the H RF Coil Circuitry
under Measurement Conditions
with similar Larmor frequencies can show significant Bloch–
Siegert shifts, depending on the H1 amplitudes employed
(Eqs. [1] and [2]). For example, in 15N-decoupled 13C NMR
experiments at 2.35 T, a decoupling field amplitude of 30
kHz (69.5 G) gives rise to a Bloch–Siegert shift of 10.4
ppm (263 Hz). [19F]1H MAS NMR spectroscopy is another
example in which the Bloch–Siegert shift is a useful tool.
In this case, the Bloch–Siegert shift is comparable to the
range of proton chemical shifts.
In some of our [1H]19F solid-state NMR experiments,
proton-decoupling fields as large as 158 kHz were employed.
As the proton amplifier was used at higher and higher power
levels, an increasingly severe loss of signal-to-noise at the
fluorine observe frequency (94.2 MHz) occurred. This S/N
loss was traced to the proton frequency synthesizer that was
producing a small 94 MHz artifact. In the extreme case,
the ‘‘contamination’’ of the frequency synthesizer led to
overloading of the receiver. Significant improvements in the
signal-to-noise ratio were achieved by using RF filters de-
signed to eliminate the 19F frequency from the signal coming
out of the high-power proton amplifier. Use of these RF
filters leads to a 1 dB attenuation of the proton RF voltage
measured at the probe. Importantly, it was found that the
proton field strengths measured when using these RF filters
were reduced by 10–20% compared to experiments not us-
ing the filters, but at the same probe RF voltage. The reason
for this difference is that the impedance of the RF circuit is
changed by insertion of the filters, and this change is not
compensated for in our routine tuning procedure. This tuning
and matching procedure involves sending a low-power sig-
nal into the circuit and then adjusting the tuning and match-
ing capacitors to give minimum power reflection. This proce-
dure does not simulate the same conditions under which the
actual experiment is performed since the RF filters that are
used in the experiment are not in the tuning circuit. Further-
more, the impedance of electronic components in the circuit
changes with temperature (see previous section) which in
turn is sensitive to the power levels and the duty cycles
employed. An on-line tuning procedure that is implemented
under actual measurement conditions eliminates these short-
comings. The performance of the circuit is optimized by
adjusting the tuning and matching capacitors while the elec-
tronic components of the circuit are at their actual operating
temperature, i.e., the equilibrium temperature of the circuit
for a given decoupling duty cycle.
CONCLUSIONS
Bloch–Siegert shifts in [1H]19F MAS NMR spectroscopy
need to be considered when citing fluorine chemical shifts.
A simple way to obtain 19F chemical shifts independent of
proton field is by setting the fluorine resonance of an internal
reference material, e.g., 1, to its proton-coupled 19F chemi-
cal-shift value. The measurement of Bloch–Siegert shifts
provides the experimental data to directly evaluate the ampli-
tude of the proton H1 field and the extent of its inhomogene-
ity throughout the sample volume. The impact of the inho-
mogeneity in H1H is experiment dependent. In [1H]19F NMR
experiments, the inhomogeneity in the proton-decoupling
field is usually not visible as distortions in the lineshapes
since linewidths at half-height of
É
1 kHz are typical. How-
ever, even in such experiments, the portion of the sample
that is packed at the ends of the rotor experiences insufficient
proton decoupling if the entire rotor volume is used. The 19F
RF field amplitude profile will show a position dependence
analogous to the H1H amplitude. If a 19F pulse is applied that
corresponds to a 90
the rotor, the excitation of the 19F spins at either end of the
rotor can be much less (a 23 tip angle for the probe used
Њ
rotation for 19F spins in the center of
Њ
in this study). Measurements of spin–lattice relaxation times
in the rotating frame, T1r(1H) or T1r(19F), can give drasti-
cally different results for samples that are packed in the
middle third of the rotor versus samples that are packed in
an outer third of the rotor. If the entire rotor is filled with
sample, the observed relaxation time is an average over the
range of the different H1 field amplitudes.
The Bloch–Siegert shift has proven to be a sensitive mon-
itor of the temperature-dependent electronic performance of
standard solid-state NMR probes. Characterization of this
dependence may be important in many rotating-frame relax-
ation-time measurements and in variable-temperature NMR
studies. The measurement of the Bloch–Siegert shift also
provides a convenient way to tune and match the proton RF
circuit in the probe under actual measurement conditions,
thereby optimizing the impedance of the circuit at its op-
A convenient way to accomplish on-line tuning in proton-
dipolar-decoupled 19F MAS NMR uses the Bloch–Siegert
shift. One-scan [1H]19F spectra were taken of 1 (see under
Experimental). The tune and match capacitors of the proton
RF channel are adjusted while the frequency of the 19F reso-
nance is monitored. Improvements in the coil performance
are observed as an upfield shift of the 19F resonance of 1
since an optimized tune leads to greater H1H field and thus
a greater Bloch–Siegert shift. This method is a fast way to
obtain optimum performance of the probe’s 1H RF circuitry
under actual measurement conditions.
The applications of the Bloch–Siegert shift presented in
this paper are not limited to [1H]19F MAS NMR spectros- erating temperature and also taking into account the effect
copy. Double-resonance experiments involving two nuclei that RF filters may have on the impedance.

PROTON-DECOUPLED MAS NMR
93
ACKNOWLEDGMENTS
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The author gratefully thanks Dr. Edward W. Hagaman (Oak Ridge Na-
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support and many helpful discussions concerning this work. The author
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