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Robust Parahydrogen-Induced Polarization at High Concentrations
L. Dagys,1M. C. Korzeczek,2A. J. Parker,1J. Eills,3J. W. Blanchard,4
C. Bengs,5M. H. Levitt,5S. Knecht,1I. Schwartz,1, ∗and M. B. Plenio2, †
1NVision Imaging Technologies GmbH, Wolfgang-Paul Straße 2, 89081 Ulm, Germany
2Institut für Theoretische Physik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany
3Institute of Bioengineering of Catalonia, 08028 Barcelona, Spain
4Quantum Technology Center, University of Maryland, MD 20742, United States
5University of Southampton, Southampton, United Kingdom, SO171BJ
Parahydrogen-Induced Polarization (PHIP) is a potent technique for generating target molecules
with high nuclear spin polarization. The PHIP process involves a chemical reaction between parahy-
drogen and a target molecule, followed by the transformation of nuclear singlet spin order into
magnetization of a designated nucleus through magnetic field manipulations. Although the singlet-
to-magnetization polarization transfer process works effectively at moderate concentrations, it is
observed to become much less efficient at high molar polarization, defined as the product of po-
larization and concentration. This strong dependence on the molar polarization is attributed to
interference from the field produced by the sample’s magnetization during polarization transfer,
which leads to complex dynamics and can severely impact the scalability of the technique. We
address this challenge with a pulse sequence that negates the influence of the distant dipolar field,
while simultaneously achieving singlet-to-magnetization polarization transfer to the desired target
spins, free from restrictions on the molar polarization.
Introduction – Nuclear Magnetic Resonance (NMR),
one of the most widespread spectroscopic techniques with
a broad range of applications, extending from chemical
analysis and drug discovery to medical imaging, is in-
trinsically limited by its low sensitivity. This limitation
is rooted in the weak nuclear spin polarization in thermal
equilibrium, typically amounting to a few parts per mil-
lion. Thermal-equilibrium polarization and detection can
be improved by increasing magnetic field strength which
may not be easily achievable. A promising alternative
to address the sensitivity challenge involves hyperpolar-
ization methods, which can enhance nuclear spin polar-
ization by orders of magnitude compared to the level at
thermal equilibrium [1–18].
Parahydrogen-Induced Polarization (PHIP) [8–18] is
a hyperpolarization method that offers a high level of
polarization and fast throughput of polarized samples.
PHIP involves an irreversible hydrogenation reaction be-
tween a substrate and para-enriched hydrogen (parahy-
drogen) gas which is used to embed the nuclear singlet or-
der of parahydrogen in newly formed product molecules.
Upon completion of the reaction, the singlet order is then
transformed into observable magnetization using a vari-
ety of methods, e.g., coherence transfer by NMR pulse
sequences or adiabatic transfer schemes [15–27]. Conse-
quently, PHIP can generate samples with molar polar-
ization, defined as the product of the spin polarization
and the concentration of target nuclei, reaching reported
values of around 50–100 mM molar polarization for 13C
in fumarate [13].
∗ilai@nvision-imaging.com
†martin.plenio@uni-ulm.de
The NMR signal is proportional to molar polarization,
which is a better figure of merit than polarization alone
for many applications such as metabolic imaging or fun-
damental physics experiments, for which high polariza-
tion alone is insufficient and high target concentrations
are also desired [13,14,28]. Additionally, it may un-
lock applications that inherently benefit from high sam-
ple magnetization, such as microscale NMR [29,30] or
the nuclear Overhauser effect methods in liquid samples
[4–6,15]. Hence, it is pertinent to inquire to what extent
achievable molar polarization can be increased.
In this context it is important to note that high molar
polarization can introduce adverse effects. For example,
a sample of 1Hwater only yields about 3mM of 1Hmo-
lar polarization at 9 T magnetic field and room temper-
ature (111 M 1Hconcentration at 0.003% polarization),
but this is sufficient intrinsic magnetization to act back
on the sample itself. After rf excitation, such magnetiza-
tion in a tuned rf coil induces a current that generates an
additional transverse field that rotates sample magneti-
zation out of phase and causes radiation damping [31,32].
This typically leads to line broadening, phase distortions
and other effects often associated with 1H- and 19F-rich
samples.
A less pronounced phenomenon does not require cou-
pling to a tuned coil, and emerges from the (small) nu-
clear spin contribution to the magnetic flux density of
the sample [33–37]. A cylindrical 100 mM sample of 1H
spins at 50% polarization (50 mM molar polarization)
can generate a magnetic flux density of 180 nT corre-
sponding to an 8 Hz resonance shift, while the previous
example of water placed in a 9 T magnetic field would
result in a 0.5Hz shift [33–35]. The backaction of these
internal fields is known to induce chaotic dynamics even
arXiv:2401.07243v1 [physics.chem-ph] 14 Jan 2024
2
in highly symmetric samples with uniform initial polar-
ization distribution, as even minute inhomogeneities can
be amplified rapidly [7,34,35,38,39].
In this work we show that this phenomenon, previ-
ously associated with the excitation of multiple echoes
and experimental artifacts, can be sufficiently strong to
interfere with polarization-transfer sequences in hyper-
polarized samples. We obtained high 1Hmolar polar-
ization using the hydrogenation reaction of [1-13C,d6]-
dimethyl acetylenedicarboxylate with parahydrogen as
shown in Fig. 1. This reaction produces [1-13C,d6]-
dimethyl maleate in which the two 1Hspins from parahy-
drogen remain entangled in a nuclear singlet state, but
are no longer magnetically equivalent due to different J-
couplings to the 13Csite. This inequivalence enables
conversion of the singlet spin order into magnetization
by ramping the amplitude of a transverse magnetic field
oscillating in resonance with the 1Hnuclei as shown in
Fig. 2(a). This method is known as adiabatic Spin-Lock
Induced Crossing (adSLIC) and it can induce complete
conversion of singlet order to transverse 1Hmagnetiza-
tion [16,21,23,24].
Figure 1. Hyperpolarization of [1-13C,d6]-dimethyl maleate
using PHIP. Top - hydrogenation reaction of [1-13C,d6]-
dimethyl acetylenedicarboxylate using parahydrogen yields
[1-13C,d6]-dimethyl maleate with two protons in a nuclear
singlet state. J-couplings are indicated and taken from [25].
Deuterons and their couplings are ignored in the theory and
simulations. Bottom - the nuclear singlet state is transformed
to magnetization of the protons using the magnetic inequiva-
lence caused by non-symmetric coupling to the 13Csite.
At low [1-13C,d6]-dimethyl maleate concentrations
(<100 mM) we consistently observe approximately 47%
1Hpolarization following the hyperpolarization process,
a factor of ∼2 below the theoretical 100% limit, pre-
sumably because of imperfect transfer from adSLIC and
losses due to spin relaxation. However, if the product
concentration is increased beyond this value, the corre-
sponding increase in molar polarization becomes highly
nonlinear, and reaches a limit at ∼60 mM of 1Hmolar po-
larization, as shown in Fig.2(b). Constant molar polar-
ization independent of product concentration means that
in this regime the polarization is inversely proportional to
the concentration of the polarized target. We hypothesize
that this limit is due to a large dipolar field that emerges
Figure 2. (a) The magnetic field sequence employed for the
adSLIC polarization experiments. The procedure begins by
hydrogenating a solution of [1-13C,d6]-dimethyl acetylenedi-
carboxylate at 96 µT and under continuous wave irradiation
at 1HLarmor frequency. Polarization transfer is performed by
ramping up the amplitude of an on-resonant rf field (adiabatic
SLIC). The magnetization is rotated to B0by ramping down
both the amplitude and frequency of the B1field, with the fre-
quency shift which is depicted as color shading. The sample
is then transported to a benchtop NMR magnet (indicated as
high-field - HF) where signal is acquired after a hard rf pulse.
(b) 1Hmolar polarization of hyperpolarized target [1-13 C,d6]-
dimethyl maleate as a function of concentration achieved by
the adSLIC sequence. The amplitude sweep duration was set
to 2 seconds. The dashed line represents a fixed polarization
level of 47%, and polarization levels are shown in parentheses
next to the data points.
during the transformation of the singlet state into observ-
able magnetization, which disrupts the adSLIC polariza-
tion transfer step. This is not a radiation damping effect,
as the untuned and large excitation coil used for these
low-field experiments couples too weakly to the nuclear
spins to induce any appreciable radiation damping, and
we have seen a similar limit is encountered using mag-
netic field cycling, a simpler polarization transfer method
not requiring a transverse (B1) field [19]. Our observa-
tion presents a substantial obstacle for achieving high
molar polarization, and likely holds relevance for many
other hyperpolarization techniques involving high sample
concentrations or polarization, such as dynamic nuclear
3
polarization or spin-exchange optical pumping [1].
Here we propose a solution to overcome this challenge
by implementing a Lee-Goldburg decoupling sequence
which is commonly used in solid-state NMR to aver-
age out strong dipolar interactions [40,41]. We explain
how to combine this with suitable periodic modulation
to re-establish a polarization transfer equivalent to ad-
SLIC that we refer as LG-adSLIC. In our experimental
work we verify the principle and demonstrate that the
application of this pulse sequence leads to an order of
magnitude improvement over the previous limit, yielding
up to ∼450 mM 1Hmolar polarization. The achieved im-
provement is primarily limited by coil inhomogeneities in
our device and can in principle be enhanced further. This
should enable new PHIP applications involving high mo-
lar polarization, and may help to mitigate distant dipolar
field effects in other areas of hyperpolarized NMR.
Dipolar fields and Lee-Goldburg decoupling– Let us first
consider the dipolar field generated in an ensemble of sin-
gle spin-1/2 nuclei in the presence of off-resonant, Lee-
Goldburg (LG) decoupling [40,41]. We may then eas-
ily extend our considerations to the case of a heteronu-
clear three-spin system incorporating polarization trans-
fer during the said decoupling.
The Hamiltonian of an isolated single nuclear spin en-
semble subject to external fields provided by magnetic
coils and internal dipolar fields generated by the spin en-
semble can be written in three terms:
HI(t) = H0,I +HLG,I (t) + HDF,I (1)
=−γIB0Iz−γIBLG(t)Ix+HDF,I ,
where γIis the nuclear gyromagnetic ratio, B0is an ex-
ternal static magnetic field, BLG(t)is an external trans-
verse field and HDF,I takes into account internal mag-
netic field flux component due to all dipolar field contri-
butions from distant nuclear spins.
Under most NMR conditions, the last term is negligible
and can be ignored. At high concentrations or large po-
larization levels, however, dipolar fields can significantly
impact the system’s dynamics as it scales with number of
spins. This interaction between each spin and the sample
is complex and may be described either microscopically,
accounting for the dipolar interaction between all spins
explicitly [42], or by adopting a mean-field description,
which defines the dipolar field generated by a spatially
homogeneous sample [35]. For our purposes, these two
descriptions yield equivalent results, and we use the mean
field approach.
Expressing HDF,I in the frame rotating at frequency
ωof the continuous-wave transverse field BLG(t)and
discarding rapidly oscillating terms gives the state-
dependent Hamiltonian (cf. Eq. (16) from [43])
H′
DF,I = ∆DF [⟨I⟩ · I−3⟨Iz⟩Iz](2)
where ⟨I⟩=⟨ψ(t)|I|ψ(t)⟩and the over-bar indicates an
average over the spin ensemble. Assuming a spatially
homogeneous sample, we have
∆DF = ∆DF(rl) = X
k=l
µ0γ2
I
4π
1−3(ezrkl)2/|rk l|2
|rkl|3(3)
with rkl =rk−rlwhere rldenotes the position of nu-
cleus l. While in the general case ∆DF(rl)depends on
the position of spin land of all the other molecules and
their diffusive motion in the sample relative to spin l, the
general structure of Eq. 2remains independent of it with
time dependence suppressed as well. The contribution
to ∆DF(rl)from nearby spins is suppressed by molecu-
lar diffusion because Eq. 3vanishes when rkl is averaged
over a spherically symmetric volume [34,38,39]. Hence,
only distant nuclei contribute to the dipolar field.
In order to minimize the influence of the dipolar field
we make the BLG field off-resonant with respect to the
Larmor frequency such that:
−γIBLG(t)=2ωLG sin θcos(ωt),(4)
ω=ω0,I −ωLG cos θ ,
where ω0,I is the Larmor frequency of spin Iand factor
of 2 takes into account the average power of the linearly
oscillating transverse field. The total Hamiltonian HIin
the rotating frame then becomes:
H′
I=H′
1,I +H′
DF,I (5)
=ωLG(cos θIz+ sin θIx) + H′
DF,I ,
where ωLG and θdefine amplitude and orientation of a
new effective field. The eigenbasis of H′
1,I leads to the
tilted operators
˜
Ix=−sin θIz+ cos θIx,
˜
Iy=Iy,(6)
˜
Iz= cos θIz+ sin θIx.
Rewriting the Hamiltonian in this basis, moving to a sec-
ond interaction frame of H′
1,I establishes what we hence-
forth refer to as the effective field frame. Neglecting
rapidly oscillating terms, we find that dipolar field Hamil-
tonian in this frame becomes
H′′
DF,I (θ)=∆DF
(3 cos2θ−1)
2⟨˜
I⟩˜
I−3⟨˜
Iz⟩˜
Iz,(7)
which vanishes at the magic angle θM= arccos p1/3.
Note that at the magic angle is exactly Lee-Goldurg de-
coupling condition which is used to miminize the effects
of dipolar coupling.
Polarization transfer in the effective field frame– An
extension of our off-resonant decoupling to singlet-to-
magnetization transfer to achieve 1Hmagnetization in
[1-13C,d6]-dimethyl maleate (Fig. 1) may be given as fol-
lows. First, the total Hamiltonian of coupled heteronu-
clear 3-spin system may be given by extending Eq. 1to
a modified form:
H(t) = Hspin +Hrf (t) + HDF.(8)
4
The dipolar field Hamiltonian HDF inherits the same
structure as HDF,I by using substitution Ii→IΣ
iwith
IΣ
i:= I1,i+I2,i . Note that we do not consider correspond-
ing terms from the Sspins as these remain unpolarized
throughout the experiment while merely experiencing a
Zeeman shift from the I-induced dipolar field, and this
shift does not contribute to the dynamics of the Ispins.
In the present case Iand Sspins are 1Hand 13Cnuclei,
respectively. Here, Hspin now includes Zeeman interac-
tion for all spins Iand Sas well as J-couplings between
them:
Hspin =H0+HII
J+HIS
J,(9)
H0=−γIB0IΣ
z−γSB0Sz,
HII
J= 2πJ I1·I2,
HIS
J= 2π(J1I1,z +J2I2,z)Sz.
Hamiltonian Hrf describes the external transverse
fields that are applied to Ispins and is given by
Hrf (t) = −γI(BLG(t) + Bmod (t)) ·IΣ
x.(10)
The transverse field is now decomposed into two terms.
The first term is the LG decoupling field BLG(t)as writ-
ten in Eq. 4and is used to mitigate dipolar field by se-
lecting appropriate effective field angle. The singlet-to-
magnetization transfer using adSLIC is performed dur-
ing the said decoupling. Therefore, a second and lesser
component Bmod is applied which slightly modulates the
decoupling field. The modulation field is given by
−γIBmod(t) = −2 sin(ωt)·2ω2(t) cos(ωmod t+ϕ),(11)
where ωmod is the modulation frequency and the time-
dependent amplitude ω2(t)is needed for adiabatic po-
larization transfer. The second factor of 2 is added to
further compensate for linear polarization of the applied
field.
Combining the terms and expressing the total Hamil-
tonian (Eq. 8) in the Zeeman interaction frame we obtain
H′(t) = HII
J+HIS
J+H′
DF
+ωLG(cos θIΣ
z+ sin θIΣ
x)
+2ω2(t) cos(ωmodt+ϕ)IΣ
y(12)
which simplifies with tilted operators in Eq.6to
H′(t) = HII
J+HIS
J+H′
DF
+ωLG ˜
IΣ
z
+2ω2(t) cos(ωmodt+ϕ)˜
IΣ
y.(13)
It is evident that the last two terms in Hamiltonian
mimic the case of Ispins being exposed to a static field
of amplitude ωLG and an oscillating transverse field with
amplitude 2ω2. Therefore, if the modulating field is in
resonance with the effective field such that ωmod =ωLG
we can further simplify the Hamiltonian by expressing
it in the doubly-rotating frame and discarding rapidly
oscilating terms:
H′′(θ, t) = ˜
HII
J+ cos θ˜
HIS
J+H′′
DF(θ)(14)
+ω2(t)(cos ϕ˜
IΣ
y−sin ϕ˜
IΣ
x)
where we find that heteronuclear J-coupling Hamiltonian
is scaled by the cosine of effective angle. The tilde indi-
cates the use of tilted operators retaining the structure
of Eq.9. For θ=θM, the dipolar coupling H′′
DF is par-
tially suppressed compared to the original HDF (cf. Eq. 2)
whereas at the magic angle we get H′′
DF = 0 and recover
the dipolar-field-free Hamiltonian where at phase ϕ= 0
it leads to:
H′′
θM(t) = ω2(t)˜
IΣ
y+˜
HII
J+1
√3
˜
HIS
J.(15)
As a result of LG decoupling, the adSLIC sequence
achieving magnetization on Ispins (1Hin the present
case) can be implemented in the effective field frame or
exactly at LG frame via Bmod(t)without obstruction by
dipolar fields. As the derivation relies on the scale hier-
archy ω0≫ωLG ≫∆DF, ω2, we use an adiabatic SLIC
[16,21,23,24] to achieve robust transfer. It is impor-
tant to stress that while the level anti-crossing condition
for SLIC does not change (ω2= 2πJ ) the transfer rate
and thus adiabaticity is scaled by 1/√3as a consequence
of tilted effective field. This approach is also suited for
implementing other homonuclear NMR sequences by se-
lecting phase and time-dependent amplitude in Eq.14.
Methods– The precursor solution for [1-13C,d6]-
dimethyl maleate was prepared by dissolving 5mM
[Rh(dppb)(COD)]BF4catalyst (CAS number: 79255-71-
3) into acetone-d6. For the experiments with varied [1-
13C,d6]-dimethyl maleate concentrations, precursor con-
centrations were prepared in this order: 20, 40, 80, 160,
320, 640, 1080 mM. Two precursors concentration were
used in Fig. 4,20 mM and 300 mM for the blue and black
points in, respectively.
Parahydrogen was produced by ARS parahydrogen
generator packed with an iron monohydrate catalyst,
running at 22 K temperature and producing gas with
a para-enrichment level of ∼93 %.
Figure 2and Each experiment starts by injecting
500 µL of solution into a tube and bubbling para-enriched
hydrogen gas through the solution at 10 bar pressure at
a bias field of 96 µT. This is followed by nitrogen bub-
bling at 10 bar to stop the reaction proceeding further.
To avoid fast singlet order decay, resonant 1Hdecoupling
is provided throughout the entire bubbling period which
in all experiments was fixed to 30 seconds [16,17].
Polarization transfer was performed following two dif-
ferent protocols as displayed in Fig. 2(a) and Fig. 3(a).
The first one consisted of a transverse field swept up from
5
Figure 3. (a) A modified magnetic field sequence LG-adSLIC
that includes Lee-Goldburg decoupling. Polarization transfer
is performed with a modulation field (Eq. 11) mimicking the
adSLIC transfer in Fig.2(a) while under strong continuous
irradiation with a resonance shift. To rotate the magneti-
zation to align with B0, first the amplitude and frequency
of the Bmod field was ramped down to rotate the magneti-
zation along the effective field, and then the amplitude and
frequency of the BLG field were ramped down to rotate the
magnetization along B0. (b) 1Hmolar polarization of hy-
perpolarized target [1-13 C,d6]-dimethyl maleate as a function
of concentration achieved by the LG-adSLIC sequence (black
dots) compared to the previous results when LG decoupling
was omitted (blue dots). The amplitude sweep duration was
set to 2 s in both cases and the Lee-Goldburg effective field
amplitude was set to ωLG = 2π600 Hz (more details in Meth-
ods). The shaded area indicates the nonphysical region in
which 1Hpolarization exceeds 100%. A scaled inset plot is
provided for clarity.
0 to (2π)25 Hz in amplitude (with respect to 1H), fol-
lowed by an adiabatic flip pulse. The flip pulse was ar-
ranged by ramping the transverse field amplitude down in
1second with gradual carrier frequency shift (ω0+ ∆ω0)
of ∆ω0=−(2π)200 Hz. No decoupling was applied dur-
ing the polarization transfer.
The second method included an off-resonant (Lee-
Goldburg) decoupling (cf. Eq. 4) during the polarization
transfer to minimize the influence of the dipolar field.
Figure 4. (a) 1Hspin polarization and (b) 1Hmolar po-
larization of hyperpolarized [1-13 C,d6]-dimethyl maleate as a
function of effective angle θused in the LG-adSLIC sequence
(Fig. 3(a)). Data points acquired at [1-13C,d6]-dimethyl
maleate concentrations of 17 mM and 223 mM are shown in
blue and black, respectively. The amplitude sweep duration
was set to 4 s and the effective field amplitude was set to
ωLG = 2π400 Hz (see Methods for more details). Dashed lines
indicates the level of polarization acquired with the adSLIC
sequence in Fig. 2(a) at high and low product concentrations.
The magic angle value is shown as a vertical line.
The effective field amplitude ωLG was set to (2π) 600 Hz
and (2π) 400Hz for experiments in Fig. 3and Fig. 4, re-
spectively. After the polarization transfer, a flip pulse
was performed by ramping the transverse field ampli-
tude down in 1second with a gradual decoupling field
frequency shift (ω+ ∆ω) of ∆ω=−(2π)200 Hz. Po-
larization transfer during LG decoupling was initiated
by ramping modulation field (Eq.11) amplitude from 0
to (2π)25 Hz (with respect to 1H). The modulation
frequency was set to match the effective field ampli-
tude (ωmod =ωLG). To perform adiabatic pulse to
flip magnetization along the effective field, the mod-
ulation amplitude was ramped down in 1second with
gradual modulation frequency shift (ωmod + ∆ωmod ) of
∆ωmod =−(2π)200 Hz.
The 1Hfree-induction decays were excited by a small
flip angle pulse of (2π)20 kHz rf amplitude and recorded
with 131 k point density at a spectral width of 400 ppm.
Additional 1Hdecoupling was used for all experiments.
6
Thermal equilibrium 1Hspectra were recorded at room
temperature with a recycle delay of 90 s and with a 90
degrees flip angle pulse. Polarization levels were calcu-
lated by comparing the 1Hsignals of hyperpolarized and
thermally polarized samples. When estimating polariza-
tion level, the scaling factor of different excitation pulses
was taken into account. The concentration of [1-13C,d6]-
dimethyl maleate was determined by comparing the ther-
mal equilibrium signal to the signal of an external stan-
dard of known-concentration measured under the same
conditions. The molar polarization was calculated as the
product of the concentration, the spin-polarization, and
the number of 1Hsites in the molecule (two in the present
case).
Results – Implementing LG decoupling into the polar-
ization process leads to a significant improvement in the
molar polarization that can be obtained at high sample
concentrations. The experimental sequence and results
are shown in Fig. 3. Operating under the same experi-
mental conditions and getting two contrasting outcomes
using adSLIC and LG-adSLIC is a strong indication that
the limited molar polarization is not related to chemical
impurities disrupting the polarization process. The linear
scaling of molar polarization with product concentration
(as indicated by the dashed line in Fig. 3) persists to
higher concentration values when LG decoupling is used.
There is still a decrease in sample polarization at molar
polarizations above ∼300 mM, and we attribute this to
insufficient LG decoupling at such high sample magneti-
zation. In principle this could be remedied by employing
a stronger LG decoupling field, but this additionally re-
quires higher B1field homogeneity which was impractical
to implement on our equipment.
The efficacy of LG decoupling on 1Hpolarization is
investigated further by varying the effective field angle θ,
and the results are shown in Fig. 4. At low concentration
of [1-13C,d6]-dimethyl maleate (17 mM) no dependence
on the angle θwas observed as the sample dipolar field is
negligible and so the LG decoupling does not affect the
polarization. This was not the case at higher concentra-
tion of [1-13C,d6]-dimethyl maleate (223 mM) where LG
decoupling is important for obtaining high polarization.
The maximum polarization was achieved when setting
the effective angle to the magic angle θ=θMwhich is
consistent with prediction from Eq. 7. We reiterate that
radiation damping is not expected to play a role in these
experiments as the sample-coil coupling is negligible since
low excitation frequencies were used and the large coil
volumes result in a low filling factor.
Conclusions – In this work we observe that the achiev-
able molar polarization in PHIP-polarized samples is lim-
ited to approximately 60 mM, independent of the prod-
uct concentration above a threshold of approximately
100 mM. This limit was observed in samples of [1-13C,d6]-
dimethyl maleate following the application of a low-field
adiabatic spin-lock induced crossing (adSLIC) sequence
to induce 1Hsinglet-to-magnetization conversion. Our
findings suggest the limited molar polarization is due
to a distant dipolar field originating from the polarized
1Hspins as the sample becomes magnetized. The inter-
nal magnetic field along the cylinder axis in a sample of
1Hspins at 60 mM molar polarization is approximately
214 nT which would contribute 9 Hz to the Zeeman in-
teraction. This value is comparable to the amplitude of
the transverse field used and spin-spin couplings in the
molecule and thus disrupts the adSLIC pulse sequence ef-
fectively. We have seen that a similar limit is encountered
using simpler singlet-to-magnetization sequences such as
adiabatic magnetic field cycling (MFC) as the bias field
inducing the polarization transfer is in sub-microtesla
regime as well.
To negate this adverse effect we implemented Lee-
Goldburg decoupling, leading to an improvement in the
achievable molar polarization by an order of magnitude.
Our work highlights that further improvements in hy-
perpolarization can lead to circumstances where NMR
pulse sequences can be disrupted by high internal sample
magnetization and could complicate interpretation. Se-
quences which incorporate averaging of the dipolar inter-
action can help to reduce and diagnose this phenomenon.
This is crucial, as hyperpolarization methods that pro-
duce highly-polarized solutions have become increasingly
prevalent in recent years.
Acknowledgements – The authors acknowledge finan-
cial support by the German Federal Ministry of Edu-
cation and Research (BMBF) under the funding pro-
gram quantum technologies - from basic research to
market via the project QuE-MRT (FKZ: 13N16447) as
well as the EIC Transition project MagSense (grant
no. 101113079). We acknowledge support received
from EPSRC, UK by the grants EP/V055593/1 and
EP/W020343/1. This project has received funding from
the European Union’s Horizon 2020 Research and Inno-
vation Programme under the Marie Skłodowska-Curie
Grant Agreement 101063517. MBP and MK addition-
ally acknowledge financial support by the ERC Synergy
grant HyperQ (grant no. 856432).
7
Appendix
Figure A1. The vector representation of Lee-Goldburg (LG)
frame. On the left - consider a frame rotating with Larmor
frequency of spin I. The off-resonant nature of Lee-Goldburg
decoupling leads to a new field BLG tilted in XZ-plane with
transverse component representing the amplitude of decou-
pling and longitudinal component reflecting resonance mis-
match. On the right - the original rotating frame is now
tilted-back such that BLG is a principal axis in a so-called
LG frame. To set up a pulse in this frame, additional field
Bmod oscillating with frequency ωLG =−γIBLG needs to be
applied. Such component along Iy(note that ˜
Iy=Iy) can be
generated by phase-shifting the LG decoupling by 3π/2which
becomes a sine-wave as shown in equation 11.
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