Dendritic polarizing agents for DNP SENS

Article abstract of DOI:10.1039/C6SC03139K

Dynamic Nuclear Polarization Surface Enhanced NMR Spectroscopy (DNP SENS) is an effective method to significantly improve solid-state NMR investigation of solid surfaces. The presence of unpaired electrons (polarizing agents) is crucial for DNP, but it has drawbacks such as leading to faster nuclear spin relaxation, or even reaction with the substrate under investigation. The latter can be a particular problem for heterogeneous catalysts. Here, we present a series of carbosilane-based dendritic polarizing agents, in which the bulky dendrimer can reduce the interaction between the solid surface and the free radical. We thereby preserve long nuclear T′₂ of the surface species, and even successfully enhance a reactive heterogeneous metathesis catalyst.

Full text of DOI:10.1039/C6SC03139K

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Dendritic polarizing agents for DNP SENS†
Wei-Chih Liao,a Ta-Chung Ong,a David Gajan,b Florian Bernada,c Claire Sauvee,c
´
Cite this: DOI: 10.1039/c6sc03139k
Maxim Yulikov,a Margherita Pucino,a Roman Schowner,d Martin Schwarzwalder,a
¨
Michael R. Buchmeiser,d Gunnar Jeschke,a Paul Tordo,c Olivier Ouari,c Anne Lesage,b
e
a
*
Lyndon Emsley and Christophe Coperet
´
Dynamic Nuclear Polarization Surface Enhanced NMR Spectroscopy (DNP SENS) is an effective method to
significantly improve solid-state NMR investigation of solid surfaces. The presence of unpaired electrons
(polarizing agents) is crucial for DNP, but it has drawbacks such as leading to faster nuclear spin
relaxation, or even reaction with the substrate under investigation. The latter can be a particular problem
for heterogeneous catalysts. Here, we present a series of carbosilane-based dendritic polarizing agents,
in which the bulky dendrimer can reduce the interaction between the solid surface and the free radical.
We thereby preserve long nuclear T02 of the surface species, and even successfully enhance a reactive
heterogeneous metathesis catalyst.
Received 15th July 2016
Accepted 19th August 2016
DOI: 10.1039/c6sc03139k
www.rsc.org/chemicalscience
surface, resulting in a signicant sensitivity increase of their
NMR resonances. With sensitivity gains of one to two orders of
Introduction
magnitude, the signal averaging time needed is dramatically
reduced, and the detailed characterization of surface species
becomes possible. Notably, the improvement in sensitivity
enables advanced two-dimensional (2D) NMR experiments
that are not practicable using conventional solid-state NMR
spectroscopy.6,13–20
Solid-state nuclear magnetic resonance (NMR) spectroscopy is
one of the most powerful tools used to probe surface structures
at the atomic level.1 However, the application of NMR is
impeded by its inherently low sensitivity, which is compounded
by the small fraction of sites of interest present on solid
surfaces. Dynamic Nuclear Polarization Surface Enhanced NMR
Spectroscopy (DNP SENS) has recently emerged as an effective
method greatly increasing sensitivity for surface species.2–7 It
relies on a transfer of the large electron polarization of a para-
magnetic dopant to the nearby nuclei.8 A persistent radical, e.g.
a nitroxide biradical, is typically used as the polarizing agent
(PA). The PA is usually dissolved in a glass-forming solvent and
then introduced onto the solid under analysis by incipient
wetness impregnation.2 The sample is then usually cooled to
100 K or lower, and microwaves are applied to saturate the
electron paramagnetic resonance (EPR) transition, which
induces, predominantly through the cross effect mechanism,9–11
the transfer of the electron polarization to the protons of the
surrounding solvent molecules. This is typically followed by
a cross-polarization12 (CP) step to the heteronuclei on the solid
Over the last decade, much effort has been devoted to
developing free radicals that yield larger DNP enhancements. In
2004, Hu et al.21 demonstrated that binitroxide radicals were
highly efficient for cross effect DNP due to large intramolecular
dipolar couplings between the two tethered nitroxide radicals.
In 2012, Zagdoun et al.22 showed that binitroxide radicals could
be engineered to have longer T1e, based on bulky, rigid skele-
tons,23 and that this led to unprecedented DNP enhancements.
Michaelis et al.,24 Kubicki et al.25 and Sauvee et al.26 have recently
´
reported comprehensive studies, in which many binitroxide
radicals were investigated in order to rationalize the effect of
biradical structures on DNP performances. Note that hydro-
phobic radicals have been solubilized successfully in aqueous
solutions by incorporating them into cyclic oligosaccharides or
micelles.27,28 Using the most recently developed binitroxides,
including TEKPol- and AMUPol-like biradicals, DNP enhance-
ments of between 200 and 300 have been achieved in bulk
solutions at 9.4 T and 100 K. These PAs have been successfully
employed to polarize solutions to characterize the surfaces of
a wide range of materials including single-site catalysts,16 silica-
based materials,29–31 zeolites,14,32,33 metal oxides,19,20 supported
nanoparticles34 and colloidal nanoparticles.35
a
¨
Department of Chemistry and Applied Biosciences, ETH Zurich, Vladimir-Prelog-Weg
¨
1-5, 8093 Zurich, Switzerland. E-mail: ccoperet@inorg.chem.ethz.ch
b
`
`
Centre de RMN a Tres Hauts Champs, Institut de Sciences Analytiques (CNRS/ENS
´
Lyon/UCB Lyon 1), Universite de Lyon, 69100 Villeurbanne, France
cAix-Marseille Univ, CNRS, ICR UMR 7273, Marseille, 13013, France
dInstitut fur Polymerchemie, Universitat Stuttgart, Pfaffenwaldring 55, D-70569
¨
¨
Stuttgart, Germany
e
´
´ ´
Institut des Sciences et Ingenierie Chimiques, Ecole Polytechnique Federale de
In this approach, however, free radicals are inevitably in
proximity to the surface, which potentially leads to para-
magnetic quenching of the NMR signal, to faster transverse
Lausanne (EPFL), 1015 Lausanne, Switzerland
† Electronic supplementary information (ESI) available. See DOI:
10.1039/c6sc03139k
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relaxation of the surface nuclei, or most problematically to
reaction with the substrate.36,37 Most DNP studies reported so
far have focused on relatively stable materials, with only a few
targeting the characterization of reactive surface species.16,29,34,38
In particular, in the eld of heterogeneous catalysis, Lewis
acidic metal centers can interact with the free radicals.39–43 For
instance, bulky PAs are needed to probe the structure of active
sites in zeolites because they cannot enter the porous network
and interact with the active sites.33 It would thus be desirable to
develop polarizing agents that are compatible with non-porous
and large-pore-size reactive materials.
Here we present the syntheses (Scheme 1) and EPR char-
acterization of dendritic PAs combining a monoradical,
2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO), or biradicals
(bTUrea and PyPol)44 with core-functionalized hydrophobic
carbosilane dendrimers.45,46 We show in particular that the
dendritic PA with the bulkiest and most rigid structure
displays the minimum interference with the surface sites, and
preserves the coherence life time (T02) and has the best DNP
Results and discussion
General description of syntheses
A convergent synthetic route for the dendritic PAs was adopted,
in which the monoradical or biradical is introduced onto the
dangling OH or NH2 functionalities at the core of the dendrimer
(Scheme 1). For the radical, commercially available 4-carboxy
TEMPO was used, and the biradicals bTUreaB and PyPolB were
prepared by adapting the previously reported procedure.44
For the dendrimer, carbosilane dendritic backbones were
chosen due to their apolar and inert nature. A divergent repeti-
tive Pt(0)-catalyzed hydrosilylation and Grignard displacement
strategy45,46 was utilized to construct the dendrimers (Scheme 2).
Two dendrimer designs were explored: D1 with two dendritic
wedges and D2 with three dendritic wedges (Scheme 1 and 2a).
From allylbenzyl ether, D1 was built by repetitive hydro-
silylation with (dichloro)phenylsilane catalyzed by Karstedt's
catalyst48 followed by reaction with allylmagnesium bromide.
Trideuteriomethyl-magnesium iodide (CD3MgI) was used to
install the end groups to prevent fast electron and nuclear
relaxations promoted by the rotations of methyl groups (–CH3)
at 100 K.25,49,50 The benzyl group was then removed by homo-
geneous oxidative cleavage to generate the OH anchor group
(Scheme 2b). We note that the typical Pd/C catalyzed reductive
cleavage failed, suggesting the inaccessibility of the benzyl ether
13C CP
SENS performance (3
¼ 128). We also illustrate the
advantage of dendritic PAs by characterizing a reactive mate-
rial, a recently developed cationic heterogeneous alkene
metathesis catalyst.47 Notably, for this particular catalyst, the
currently favored “conventional” biradical, TEKPol, showed no
DNP enhancement.
Scheme 1 Convergent synthetic route of the dendritic PAs.
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Scheme 2 (a) Divergent synthetic route of the dendrimers. (b) Syntheses of the anchor groups on the dendrimers.
on the dendrimer to the Pd/C surface. D1 with generation 3 and
generation 4 (D1[G3]/[G4]) were synthesized, and their respec-
tive hydrodynamic diameters are around 1.7 nm and 2.3 nm as
measured by DOSY NMR (ESI†).
EPR properties
Obtaining good DNP enhancements requires a homogeneous
distribution of PAs in the frozen glassy matrix. Aggregation or
crystallization can generate an inhomogeneous distribution of
free radicals leading to a lower DNP efficiency.8,52 As macro-
molecules are known to self-assemble/aggregate,53 the EPR line
widths and relaxation time constants (T1e and T2e) of the
dendritic PAs were measured. First, the dendritic monoradicals
For D2, the same divergent synthetic strategy was utilized.
Trichlorosilane was used instead of dichlorophenylsilane to
afford three branches at the diverging points. Since allylbenzyl
ether was reduced by silyl hydride at the oxygen site, 3-chloro-1-
propene was thus used instead, and Lukevic's catalyst51 was
used to catalyze the hydrosilylation. The alkyl chloride at the
core of D2 was found to exchange with CD3MgI and result in an
insoluble gel product. Benzylmagnesium chloride was thus
used instead to form the end groups of D2. Further azide
substitution and Staudinger reduction afforded the NH2 anchor
group (Scheme 2b). Notably, the substitution step took days to
complete, indicating that the amine site is probably buried
inside the dendrimer. D2 with generation 3 (D2[G3]) was
synthesized, and its hydrodynamic diameter is around 2.3 nm
(ESI†), which is larger than D1[G3].
(TEMPO-D1[G3]/D1[G4]/D2[G3])
and
the
non-dendritic
analogue (TEMPO-C3, Fig. S1†) were separately prepared as 30
mM 1,1,2,2-tetrachloroethane (TCE) solutions. Their EPR
proles (Fig. S2†) were measured on a Bruker X band contin-
uous wave (CW) EPR spectrometer at 100 K. The average inter-
radical distances were estimated by measuring the EPR line
widths, which were found to be the same for all samples (11.7
Gauss), suggesting an average interradical distance of at least
1.8 nm in the frozen matrix.54 Secondly, we investigated the
electron relaxation time constants (T1e and T2e) as an alternative
probe of the distribution of biradicals since their EPR proles
were signicantly perturbed by strong intramolecular electron–
electron dipolar couplings. The dendritic biradicals (bTUreaB-
D1[G3]/D1[G4]/D2[G3] and PyPolB-D2[G3]) and the non-
dendritic analogue (bTUreaB-C3 and PyPolB-C3, Fig. S1†) were
separately prepared as 16 mM TCE solutions. T1e and T2e were
Finally, dendritic PAs were readily formed via conventional
ester/amide bond couplings. However, we noted that PyPolB
could not be connected to OH-anchored dendrimers (D1[G3]/
[G4]) possibly due to the large steric hindrance of the dendrimer
and lower reactivity of OH group.
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Table 1 T1e and T2e of the dendritic and non-dendritic PAsa
T1e (ms)
same as of the non-dendritic biradicals in TCE.25 We conclude
that the dendrimer does not adversely affect the biradical
conformations or glass forming properties of the solvent. In
particular the dendritic PA, PyPolB-D2[G3] is found here to
perform at least as well as AMUPol in TCE.25 Additionally, we
noted the presence of 13C NMR signals of the dendrimer in bulk
solutions (Fig. S7†). This is presumably due to the large size of the
dendrimer, some part of the dendritic structure experiencing less
or no paramagnetic bleaching by the unpaired electrons.
T2e (ns)
bTUreaB-C3
bTUreaB-D1[G3]
bTUreaB-D1[G4]
bTUreaB-D2[G3]
PyPolB-C3
26
25
25
28
82
82
411
431
410
424
1518
1607
PyPolB-D2[G3]
a
Errors were estimated to be approximately 5% as spectra with good
signal-to-noise ratio were recorded for all samples. See ESI for details.
Using dendritic PAs in DNP SENS on representative solid
materials
Table 2 MAS DNP properties of dendritic PAs in bulk solutionsa
In order to assess the effect of the dendrimer in preventing close
approach of the free radical to surface sites, well-dened
phosphonate-graed silica nanoparticles (P@SiO2, Fig. 1a) were
a (400/600 MHz)
TDNP (s) (400/600 MHz)
13C CP
3
TEMPO-D1[G3]
bTUreaB-D1[G3]
bTUreaB-D1[G4]
bTUreaB-D2[G3]
PyPolB-D2[G3]
6/—
41/10
45/10
48/13
128/29
2.5(1)/—
1.5(1)/—
1.5(1)/—
1.5(1)/4.6(1)b
2.2(1)/2.5(1)
a
The error is within 8% calculated based on the signal-to-noise ratio.
Presumably due to poor glass formation.
b
measured on a Bruker W band pulsed EPR spectrometer at 100
K. All biradicals had similar T1e and T2e (Table 1). Both the
measured line widths and relaxation time constants indicate
similar average inter-monoradical and -biradical distances in
dendritic and non-dendritic PAs, suggesting the absence of
signicant aggregation induced by the dendrimers.
Magic-angle-spinning (MAS) DNP performance
The MAS DNP performance of the dendritic monoradical
TEMPO-D1[G3] was assessed as a 30 mM solution in TCE.
The mixture was frozen at 100 K, and the solvent enhancement
)
55 was found to be 6, with a proton build-up time (TDNP
)
13
(3
C CP
of 2.5 s on a Bruker 400 MHz (9.4 T) DNP spectrometer (Table
2). A possible explanation to this low enhancement is that
since the cross effect is the most efficient DNP mechanism at
100 K, and requires strong dipolar coupling between two
unpaired electrons, the steric hindrance of the dendrimer
likely decreases the probability of free radical pairs to be at an
optimal distance (ꢀ1.3 nm)21 to fulll the matching condition
of the cross effect. However, this difference in free radical
distance distribution is seemingly hard to be detected from
their EPR line widths (11.7 Gauss on the X band CW EPR
spectrometer). The dendritic biradicals were separately
prepared as 16 mM solutions in TCE and frozen at 100 K. On
Bruker 400 MHz and 600 MHz DNP spectrometers, the
enhancement values for the dendritic PAs with bTUreaB were
around 45 and 10, respectively; and for PyPolB-D2[G3], the
values were 128 and 29, respectively (Table 2). TDNP for bTUr-
eaB PAs were about 1.5 s on a 400 MHz spectrometer, and
around 2.2 s and 2.5 s for PyPolB-D2[G3] on 400 MHz and
600 MHz DNP spectrometers, respectively (Table 2). The
Fig. 1 DNP (a) 31P CP Hahn-echo spectra of P@SiO2, (b) 119Sn
reconstructed CP-CPMG spectra of 10 wt% Sn-beta zeolite and (c) 13
C
CP spectra of a single-site tungsten TBP metallacycle with microwaves
on (top) and off (bottom). All samples were impregnated with a 16 mM
solution of PyPolB-D2[G3] in TCE. Asterisks mark spinning side bands.
enhancements of dendritic biradicals were essentially the NMR acquisition details are given in the ESI.†
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Table
P@SiO2
3 MAS DNP properties of bTUreaB PAs impregnated on
a
b
c
T02
(ms)
31
31P CP
P
31P
q
3
TDNP (s)
bTUreaB-C3
7
9
9
8
1.6(1)
2.2(1)
2.0(1)
2.3(1)
6.7(2)
7.6(2)
7.8(3)
8.9(2)
0.43(4)
0.42(4)
0.42(4)
0.51(5)
bTUreaB-D1[G3]
bTUreaB-D1[G4]
bTUreaB-D2[G3]
a
See ESI for more details. b The estimated errors are within 2.5% based
on the signal-to-noise ratios. c 31P contribution factor ¼ [MW OFF with
radical]/[MW OFF without radical] per unit mass. See details in ESI.
impregnated with polarizing solutions containing either non-
dendritic or dendritic bTUreaB PAs. The surface enhancements
(3 P CP), the proton DNP build-up time (TDNP), the 31P coherence
31
56
life time (T02 P) and the contribution factors (q
)
at the
31
31
P
surface were measured. The results, which were recorded on
a Bruker 600 MHz (14.1 T) DNP spectrometer, are summarized
in Table 3. The enhancements at the surface are roughly the
same, which suggests that the bTUreaB PAs, dendritic or not,
exhibit essentially the same DNP efficiency, as was the case in
bulk solutions. Similar TDNP (ꢀ2 s) was also observed for all
31
bTUreaB PAs. More interestingly, the P T02 increases as we
Fig. 2 DNP 13C CP spectra of W C@SiO2 impregnated with (a) 16 mM
PyPolB-D2[G3] (inset shows the enlarged region between 250 and 350
ppm) and (b) 16 mM TEKPol solutions in TCE with microwaves on (top)
and off (bottom) on a 400 MHz (9.4 T) DNP spectrometer. MAS ¼ 12
kHz, recycle delay ¼ (a) 4 s; (b) 4.5 s, contact time ¼ 0.5 ms, number of
scans ¼ (a) 2048 (for MW ON), 1024 (for MW OFF); (b) 616. Asterisks
mark spinning side bands.
13
move from C3 (non-dendritic) to D1[G3] z D1[G4] to D2[G3],
indicating that the free radical centers are further away from the
surface as the dendritic structure becomes larger. A similar
31
trend was observed for the P contribution factor,56 for which
we observed a signicant increase with D2[G3]. This suggests
that paramagnetic bleaching is reduced at the surface of the
material with larger dendritic PA. Thus, D2[G3] with 3 dendritic
wedges and a hydrodynamic diameter of ꢀ2.3 nm appears to
prevent close approach of the biradical to the surface. In
contrast, the results suggest that the D1[G3]/[G4] dendrimers
may atten on the surface, leading to a relatively stronger
interaction between the free radical and the surface.
We then evaluated the DNP SENS efficacy of PyPolB-D2[G3]
on several representative materials (Fig. 1). First, we impreg-
nated P@SiO2 with a 16 mM solution of PyPolB-D2[G3] in TCE.
The 31P enhancement measured at 600 MHz (14.1 T) was 17
(Fig. 1a). As was the case for bulk solutions, this enhancement is
much higher than those obtained with the bTUreaB PAs
(Table 3). Secondly, we tested PyPolB-D2[G3] on a hydrated Sn-
beta zeolite14 sample by acquiring the 119Sn CP spectra with
Carr-Purcell Meiboom-Gill (CPMG) echo train acquisition.57 The
119Sn enhancement was found to be around 4 (Fig. 1b). Notably,
Dendritic PA on a highly reactive heterogeneous catalyst
Furthermore, to validate the hypothesis that PyPolB-D2[G3]
prevents contact of the radical with the surface sites, we studied
a highly reactive single-site cationic alkene metathesis hetero-
geneous catalyst (W C@SiO2),47 for which conventional binitr-
13
oxide radicals do not yield to any DNP effect. This is illustrated
in Fig. 2b where no DNP enhancement was observed at the
surface when the material was impregnated with a 16 mM
TEKPol TCE solution (Fig. 2b). We postulate that TEKPol reac-
ted or coordinated upon contact with the tungsten center. Using
a
13C-labeled surface complex to speed up the exploration, we
observed a 13C enhancement of around 10 at the surface
13
(Fig. 2a) for W C@SiO2 impregnated with a 16 mM solution of
PyPolB-D2[G3] in TCE on a Bruker 400 MHz (9.4 T) DNP spec-
trometer. The results suggest that the dendritic structure largely
reduces the interaction between the free radical and the reactive
surface site, albeit not fully as evidenced by the observation of
29Si NMR signals from the dendritic backbone (Fig. S8a†),
whereas we barely observed such signal when the PA was
impregnated on pure silica (Fig. S8b†).58 Despite a relatively low
enhancement (3 ꢀ 10), under these conditions we could observe
all the expected resonances including the isotropic peaks of the
alkylidene carbon at 296 ppm and of the N-heterocyclic carbene
˚
given the pore size of the Sn-beta (ꢀ7 A), PyPolB-D2[G3] does
not enter the pores. Hence, the DNP enhanced polarization is
transferred through proton spin diffusion via the TCE mole-
cules and the adsorbed water on the inner-pore surface, which
may explain an overall low enhancement.14,17,32 Finally, the
performance of PyPolB-D2[G3] was evaluated on the recently
reported metallacyclobutane metathesis intermediates,16 and
a surface 13C enhancement of 8 was obtained. We note that the
13C CP
higher enhancement reported with TEKPol (3
14.1 T) originates from the intrinsic different efficiency between
ꢀ 23, at
at 184 ppm aer
a short period of signal averaging
(ꢀ15 minutes) (also see Fig. S9†).59 It is worth mentioning that
PyPol and TEKPol.
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the 13C signal of the surface alkylidene is typically very difficult
to observe even with 13C enrichment, mostly due to its large
chemical shi anisotropy (CSA),60 usually over 500 ppm, and it
typically requires hours or even days of acquisition with
conventional solid-state NMR.
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Conclusion
In summary, a series of mono- and bi-nitroxide radicals with
bulky hydrophobic carbosilane dendrimers were designed and
synthesized. EPR results suggest that there is no signicant
aggregation between dendrimers in frozen solutions at 100 K.
As expected, the dendritic monoradical shows poor DNP
enhancement in the bulk solution due to the spatial separation
between two nitroxide radicals. On the contrary, the dendritic
biradicals are as good PAs as their molecular analogues.
Furthermore, the most rigid and bulky molecule D2[G3] effec-
tively reduces signicant interaction between the free radical
and silica surface sites, reducing the fast relaxation of surface
substrates induced by the unpaired electrons. More impor-
tantly, PyPolB-D2[G3] is found to be signicantly less reactive
and more shielded than TEKPol, making possible the detection
here of a highly reactive heterogeneous metathesis catalyst due
to its large steric hindrance hampering the interaction between
the free radical and the surface site.
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Author contribution
13 D. Lee, G. Monin, N. T. Duong, I. Z. Lopez, M. Bardet,
¨
V. Mareau, L. Gonon and G. De Paepe, J. Am. Chem. Soc.,
WCL, AL, LE and CC designed research. WCL, TCO, DG and MY
performed research. FB and CS provided binitroxide radicals.
MP, RS and MS provided analytes. WCL, TCO, DG, MY, MRB, GJ,
PT, OO, AL, LE and CC analyzed data. WCL, TCO, AL, LE and CC
wrote the paper.
2014, 136, 13781–13788.
14 P. Wolf, M. Valla, A. J. Rossini, A. Comas-Vives, F. Nunez-
´
Zarur, B. Malaman, A. Lesage, L. Emsley, C. Coperet and
I. Hermans, Angew. Chem., Int. Ed., 2014, 53, 10179–10183.
15 M. Valla, A. J. Rossini, M. Caillot, C. Chizallet, P. Raybaud,
M. Digne, A. Chaumonnot, A. Lesage, L. Emsley, J. A. van
´
Bokhoven and C. Coperet, J. Am. Chem. Soc., 2015, 137,
10710–10719.
Acknowledgements
We acknowledge Patrick Wolf for providing the Sn zeolite
16 T.-C. Ong, W.-C. Liao, V. Mougel, D. Gajan, A. Lesage,
´
sample. We thank Dr Rene Verel for the technical support in the
´
L. Emsley and C. Coperet, Angew. Chem., Int. Ed., 2016, 55,
LAC NMR facility at ETHZ and fruitful discussions. We thank
4743–4747.
´
Lenaic Leroux for his technical support for the experiments
17 A. J. Rossini, A. Zagdoun, M. Lelli, J. Canivet, S. Aguado,
conducted on the 400 MHz DNP spectrometer in Lyon. We
acknowledge nancial support from the SNF for the 600 MHz
´
O. Ouari, P. Tordo, M. Rosay, W. E. Maas, C. Coperet,
D. Farrusseng, L. Emsley and A. Lesage, Angew. Chem., Int.
Ed., 2012, 51, 123–127.
DNP
spectrometer
(206021_150710)
and
for
WCL
(200020_149704), and ERC Advanced Grant No. 320860, the
University of Aix-Marseille and the CNRS. MRB acknowledges
nancial support by the Deutsche Forschungsgemeinscha
(DFG, BU 2174/19-1). The EU COST action TD1103 Euro-
hyperpol is gratefully acknowledged for stimulating interac-
tions and travel funds.
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