Stuart J Elliott

Lynda J Brown

Jean-Nicolas Dumez

Malcolm H Levitt

Long-lived nuclear spin states in monodeuterated methyl groups

Keywords: long-lived states, singlet state, methyl group, rotamer

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Introduction

Long-lived states (LLS) are configurations of nuclear spins which are protected against relaxation in nuclear magnetic resonance (NMR) experiments . Long-lived state lifetimes exceeding the conventional relaxation time T 1 by a factor of 50 have been observed, with a lifetime exceeding 1 hour in room-temperature solution in one case [22]. The combination of LLS phenomena with hyperpolarization techniques is particularly promising. Techniques such as dissolution-DNP (dynamic nuclear polarization) [23] offer large NMR signal enhancements, with wide-ranging implications, including the characterization of cancer in human patients [24]. However, the range of hyperpolarization applications is restricted by the finite lifetime of the enhanced magnetization, which is normally limited by T 1 . The use of LLS offers a promising means to transcend this limitation [9,[25][26][27][28].

In systems of spin-1/2 pairs, the LLS is called singlet order. This consists of the population imbalance between the spin-0 singlet state and the spin-1 triplet states [1,2]. The decay time constant of singlet order is denoted T S . Access to nuclear singlet order is provided by a chemical shift difference between the participating spins, or by differences in spin-spin couplings to spins outside the pair [13].

LLS have also been observed in the 3-spin-1/2 systems of rapidly rotating methyl groups in solution [29][30][31]. In this case the LLS is given by the imbalance in populations between spin states spanning different irreducible representations of the C 3 permutation group [START_REF] Bunker | Molecular Symmetry and Spectroscopy[END_REF]. Some materials, such as γ-picoline, display quantum-rotor induced polarization (QRIP) effects, in which a large polarization of the methyl LLS is induced by dissolution of the material from cryogenic conditions [29,[START_REF] Icker | [END_REF][34][35]. However, the hyperpolarized LLS only gives rise to observable NMR signals through an incoherent crossrelaxation mechanism involving a fourth nuclear spin, which greatly reduces the available signal enhancement [29][30][31].

Since methyl groups are ubiquitous in nature, the exploitation of methyl LLS is potentially attractive. In this communication we show that in certain cases, it is possible to achieve coherent access to a methyl LLS with a high conversion efficiency into observable NMR signals. The conditions are: (i) the methyl group is monodeuterated, and therefore contains a proton pair; (ii) the local environment is chiral, and (iii) the three methyl rotamers have sufficiently different populations, so that a small chemical shift difference is induced between the CH 2 D protons after averaging over all populated states. We show that the small chemical shift difference allows coherent (and therefore efficient) access to the long-lived singlet order of the proton spin pair, using known radiofrequency pulse techniques [11,12,19,20].

Chemical inequivalence of CH 2 D protons has been observed in several molecular systems, most of which contain a N-CH 2 D group in a chiral environment [36][37][38]. In this communication we report the observation of a proton LLS in the N-CH 2 D group of N-CH 2 D-2-methylpiperidine (Figure 1). We observe singlet lifetimes T S with values between 20 and 55 seconds (dependent on temperature). The ratio of singlet relaxation time T S to longi-2 tudinal relaxation time T 1 is found to be remarkably constant over a wide range of conditions, and equal to 3.1 ± 0.1. This result shows that is feasible to exploit methyl LLS without relying on weak cross-relaxation effects, in suitable cases. We provide evidence that singlet relaxation in this system is dominated by the dipolar interactions between the CH 2 D protons and the CH 2 D deuteron, and show that the singlet relaxation times cannot be explained by a model in which the three hydrogen nuclei are localised at the vertices of an equilateral triangle. We propose a modified geometrical model which is consistent with the experimental data.

Experiments

Proton Spectra

The methyl region of the proton NMR spectrum of (N-CH 2 D)-2-methylpiperidine is shown in Figure 1. This spectral region has a quartet-like appearance in the absence of deuteron decoupling (Figure 1a). The characteristic AB spectral pattern of an inequivalent proton pair appears when a deuteron decoupling field is used to remove the 2 J HD splittings (Figure 1b). This spectrum is consistent with a J-coupling of 2 J HH = 11.7 ± 0.2 Hz and a chemical shift difference of ∆δ = 13.5 ± 0.4 ppb between the CH 2 D protons, as reported previously [36].

The existence of a small chemical shift difference has been attributed to (i) hyperconjugation between the nitrogen lone pair and the anti -methyl C-H(D) σ-bond, which allows the zero-point vibrational energies of the anti CH and CD bonds to influence the rotamer energies; as a result, the rotamer with the CD bond anti to the nitrogen lone pair is less populated than the other two rotamers in thermal equilibrium, and (ii) the chiral environment associated with the neighbouring methyl group, which causes a significant chemical shift difference between the two protons in each rotamer [36,38]. In these circumstances, there remains a significant chemical shift difference between the CH 2 D protons after averaging over all methyl rotamers. The observed chemical shift difference decreases as the temperature is increased, as shown in Figure 2a. This is consistent with the Boltzmann populations of the three rotamers becoming more similar at higher temperatures.

Singlet NMR

The small chemical shift difference allows access to the long-lived singlet order between the CH 2 D protons by using the M2S [11,12] or SLIC [19] pulse 3 interactions between the three magnetic nuclei of the CH 2 D group, there are also chemical shift anisotropy contributions, magnetic dipole-dipole interactions with other nuclei in the same molecule, and intermolecular dipole-dipole interactions. The quadrupolar relaxation of the deuterium nuclei might also contribute to proton relaxation through mechanisms such as scalar relaxation of the second kind [START_REF] Abragam | Principles of Nuclear Magnetism[END_REF][START_REF] Pileio | [END_REF]. Furthermore, spin-rotation relaxation is known to be significant for many rotating methyl groups [45][46][47][48], and contributes to the LLS relaxation of γ-picoline in solution [29,30]. Singlet relaxation may also be caused by state mixing due to a finite chemical shift difference between the participating protons, or by asymmetric J-couplings to other magnetic nuclei ("singlet-triplet leakage") [14].

The excellent correlation between the T S and T 1 values shown in Figure 5 strongly supports the hypothesis that the longitudinal and singlet relaxation of the CH 2 D proton pair is driven by a common mechanism, with a common correlation function. This suggests that the mechanisms that dominate the T 1 and T S relaxation of the CH 2 D protons are internal to the CH 2 D group. This conclusion is supported by the following observations: (i) Deuteration of the 2-methyl group leads to only a small change in the relaxation times even though the protons of the 2-methyl group approach to within 229 pm of the CH 2 D protons; (ii) a large change in the deuteration level of the solvent only has a small influence on the relaxation times (see Figure 5 and the data in the Supporting Information).

In addition, one may discount major contributions from the spin-rotation, scalar relaxation, chemical shift anisotropy and singlet-triplet leakage mechanisms, for the following reasons:

1. Spin-rotation. The experimental finding that T S increases with increasing temperature (Figure 2b) speaks strongly against a significant contribution from spin-rotation, since that mechanism usually increases in strength with increasing temperature [45][46][47][48]. Presumably, in the current case, the methyl rotation is too strongly hindered to permit a significant spin-rotation relaxation contribution. 2. Scalar relaxation of the second kind. The existence of a resolved deuteron splitting in the proton spectrum (Figure 1a), as well as direct measurements of deuteron relaxation (see section 2.3) indicate that deuteron relaxation is too slow to induce significant scalar relaxation of the coupled protons. Furthermore, the two 2 J HD couplings are identical to a good approximation, which precludes a scalar contribution to singlet 8 relaxation [START_REF] Pileio | [END_REF]. 3. Chemical shift anisotropy. The weak dependence of T 1 and T S on magnetic field indicates a relatively small contribution from CSA. 4. Singlet-triplet leakage. Singlet-triplet leakage induced by the small chemical shift difference between the CH 2 D protons can be a significant contribution to the singlet relaxation rate constant T -1 S [14]. However, in the current experiments, this contribution is suppressed very effectively by the application of a resonant radiofrequency field during the singlet relaxation interval (see the Supporting Information).

We therefore postulate that both the singlet and the longitudinal relaxation of the proton pair in the monodeuterated methyl group of N-CH 2 D-2methylpiperidine are dominated by the 1 H-1 H and 1 H-2 D dipole-dipole interactions within the methyl group itself, modulated by the internal rotation of the methyl group with respect to the rest of the molecule, and by the rotation of the molecule as a whole. A relaxation model is therefore constructed based on (i) a simplified description of the motion of the methyl group and the molecule as a whole, and (ii) a description of the vibrationally-averaged spin-spin interactions within the rotating methyl group.

Motional Model

A plausible motional model for the monodeuterated methyl group in N-CH 2 D-2-methylpiperidine consists of a hindered 3-fold rotor attached to a sphere undergoing isotropic rotational diffusion (Figure 6). Although the existence of a finite chemical shift difference between the CH 2 D protons implies that the methyl rotamers have slightly unequal populations, we ignore this effect in the relaxation analysis, for the sake of simplicity. The thermally activated jumps between the methyl rotamers are assumed to be described by a rate constant κ, while the overall rotational diffusion of the molecule is described by a correlation time τ c . Both κ and τ c are in general temperaturedependent. We also assume that the correlation time τ c is short enough relative to the nuclear Larmor period to invoke the extreme narrowing approximation [START_REF] Abragam | Principles of Nuclear Magnetism[END_REF].

Dipole-Dipole Interactions

The three magnetic nuclei in the CH 2 D group interact by the magnetic dipole-dipole interaction. In general these dipole-dipole interactions are described by traceless second-rank tensors, and are subjected to averaging over local molecular vibrations and librations on a timescale fast compared to the methyl 3-fold jumps or the molecular tumbling. Spin relaxation is caused by motional modulation of the vibrationally-averaged dipole-dipole interaction tensors.

In general, the vibrationally-averaged tensors differ, both in magnitude and in orientation, from tensors derived from a naive geometrical model, for which point-like nuclei are located at the vertices of an equilateral triangle, with the magnitudes of the dipole-dipole interactions in exact proportion to the product of the gyromagnetic ratios, since the internuclear distances are all equal. As discussed below, this naive equilateral model of the CH 2 D group is inconsistent with the experimental results.

To maintain high generality, the relaxation theory is developed using three different interaction tensors for the vibrationally-averaged dipole-dipole interactions, leaving the magnitudes and orientations of the tensors as adjustable parameters. The two 1 H-2 D interaction tensors are assumed to have the same principal values, by symmetry. For the sake of simplicity, the vibrationallyaveraged interaction tensors are assumed to be axially symmetric, with the unique principal axes perpendicular to the N-C rotor axis. The angle between the unique principal axes of the two vibrationally-averaged 1 H-2 D interaction tensors is denoted 2θ. This angle defines the cross-correlation of the two 1 H-2 D interaction tensors, and is therefore important for the proton singlet relaxation. By symmetry, the unique principal axis of the vibrationally-averaged 1 H-1 H interaction tensor is perpendicular to the bisector of the two 1 H-2 D principal axes (see the Supporting Information). A point-nucleus equilateral geometry model would lead to the angle 2θ = 60

Physical Chemistry Chemical Physics Accepted Manuscript

assumed in the following discussion.

Rate Expressions

As shown in the Supporting Information, the motional and intra-methyl interaction models described above lead to the following expressions for the proton longitudinal and singlet relaxation rate constants:

T -1 1 (CH 2 D) = (4 + 3κτ c ) 24 (1 + 3κτ c ) 16ω 2 HD + 9ω 2 HH τ c , (1)
T -1 S (CH 2 D) = 8 sin 2 2θ 1 + 3κτ c ω 2 HD τ c . (2)
The following expressions apply to the relaxation of the 13 C nuclei in the CH N groups on the six-membered ring (with N = 1 or 2), and for the 2 H relaxation of the deuteron in the monodeuterated methyl group:

T -1 1 ( 13 CH N ) = N ω 2 CH τ c , (3)
T -1 1 ( 2 H) = 3 32 + 33κτ c + 9κτ c 4 cos(2θ Q ) + 3 cos(4θ Q ) 64 (1 + 3κτ c ) ω 2 Q τ c . (4)
Here ω CH is the dipole-dipole coupling constant for the interaction between the proton and carbon nuclei, ω Q is the quadrupole coupling frequency of the deuteron, and θ Q is the angle between the 3-fold jump axis and the dominant principal axis of the 2 D electric field gradient (EFG) tensor (assumed to be along the CD bond vector). For a tetragonal geometry of the CH 2 D group:

T -1 1 ( 2 H) = (3 + κτ c ) 2 (1 + 3κτ c ) ω 2 Q τ c . (5)
These equations assume rigid-body rotational diffusion of the whole molecule (including the ring) and 3-fold jumps of the methyl group, with 13 C-1 H dipolar and quadrupolar relaxation dominating the 13 C and 2 D relaxation, respectively.

For the simple case of point nuclei (ignoring vibrational averaging), the coupling constants are defined as follows:

ω CH = -µ 0 /4π γ( 1 H)γ( 13 C) r -3 CH (6) ω Q = e 2 qQ 2 (7)
11 where r HC is the internuclear distance, Q is the electric quadrupolar moment of the deuterium nucleus, and eq is the electrical field gradient at the deuterium nucleus [49]. This relaxation model leads to the following expression for the ratio of T S to T 1 :

T S T 1 = (4 + 3κτ c ) 16ω 2 HD + 9ω 2 HH 192ω 2 HD sin 2 2θ . ( 8
)
In general the ratio T S /T 1 depends on the jump rate κ and rotational correlation time τ c , and is expected to depend on temperature, solvent, and other factors. However, in the "slow-jump regime" κτ c ≪ 1, the ratio of T S to T 1 becomes independent of κ and τ c , and only depends on interaction parameters within the CH 2 D group:

T S T 1 ≃ 16ω 2 HD + 9ω 2 HH 48ω 2 HD sin 2 2θ ≃ 3ω 2 HH 16ω 2 HD sin 2 2θ (9)
The fact that 1 H-1 H dipolar couplings are about 6 times stronger than 1 H-2 D dipolar couplings (at equal distances) has been invoked in the last approximation. The observed direct proportionality of T S to T 1 is consistent with the validity of the slow-jump regime over the explored range of experimental conditions.

Relaxation analysis

The 13 C and 2 H relaxation data allow an estimate of the rotational correlation time τ c and 3-fold jump rate κ. The following analysis refers to data obtained on 0.1 M N-CH 2 D-2-methylpiperidine in degassed CD 2 Cl 2 solution, at 500 MHz and 25 • C.

The overall rotational correlation time τ c was estimated by analysing the experimental T 1C relaxation time constants for 13 C nuclei in the CH N groups on the six-membered ring, using Equation 3 which applies for extremenarrowing isotropic rotational tumbling, dominated by the 13 C-1 H dipolar relaxation mechanism [START_REF] Kowalewski | Nuclear Spin Relaxation in Liquids: Theory, Experiments, and Applications[END_REF]. By assuming an internuclear 13 C-1 H distance of 108.9 pm, which corresponds to a dipole coupling constant of ω CH /2π = -23.4 kHz, we obtain the following estimate of the rotational correlation time: τ c = 3.8 ± 0.6 ps.

The 3-fold jump rate constant κ may be estimated from the 2 D T 1 relaxation time constant, by using Equation 5. The deuteron quadrupole coupling constant ω Q /2π = 83.5 kHz has been estimated by solid-state NMR [START_REF] Beshah | [END_REF]52].

The unique principal axis of the deuteron quadrupole coupling tensor is assumed to be along the C-D bond, at an angle of 70.5 • with respect to the 3-fold jump axis. From comparing the experimental relaxation time T 1 ( 2 H) = 0.75 ± 0.01 s with Equation 4, which was derived for the case of a hindered 3-fold rotor attached to a molecule undergoing isotropic rotational diffusion, and assuming that the quadrupolar mechanism dominates the deuteron relaxation, we estimate an upper limit on the 3-fold jump rate: κ 3.2 × 10 10 s -1 . The product of the rotational correlation time and the 3-fold jump rate constant is therefore given by κτ c 0.12, which supports the validity of the slow-jump regime and hence Equation 9. Now consider the case where the three hydrogen nuclei of the CH 2 D group are considered to be points, located at the vertices of an equilateral triangle. In this case 2θ = 60 • , the internuclear distances are all equal, and the dipolar couplings are in the ratio of the magnetogyric ratios ω HH /ω HD = γ( 1 H)/γ( 2 D) = 6.51. This "equilateral triangle model" predicts the following relaxation time ratio: T S /T 1 △ = 10.5. However, the observed value is quite different: T S /T 1 obs = 3.1 ± 0.1.

How can this discrepancy be explained? One approach would be to call into question the intra-methyl relaxation model: However, as discussed above, the evidence for the dominance of intra-CH 2 D interactions in the 1 H and 2 D relaxation is very strong. An alternative approach is to maintain the local intra-methyl relaxation model, but to modify the relative magnitudes and geometries of the dipole-dipole interactions within the rotating CH 2 D group, to take into account differential vibrational averaging on a faster timescale than the molecular rotation or 3-fold jumps.

A detailed analysis of the effect of rapid vibrational motions on the dipolar interaction tensors in the CH 2 D group would be a major project. For the sake of simplicity we employ a naive picture, in which the nuclei are still regarded as localized points, but with the 2 D nucleus displaced from its original position, in order to account for differential vibrational averaging of the 2 D and 1 H interactions. In order to maintain symmetry, we consider a model in which the 2 D nucleus is moved in the CH 2 D plane along the line bisecting the 1 H-1 H vector (Figure 7a). This adjustment changes the internuclear distances as well as the angle θ. The dependence of the theoretical relaxation rate ratio T S /T 1 on the deuterium displacement is shown in Figure 7b. There is a strong sensitivity to the deuterium displacement, with the observed ratio T S /T 1 = 3.1 being consistent with a displacement of 38.7 pm towards the 13 2-methylpiperidine, where a hyperconjugation effect involving the nitrogen lone pair perturbs the vibrational energies and hence the rotamer populations, while the neighbouring methyl group provides a chiral environment.

In this system, the ratio of singlet relaxation time T S to longitudinal relaxation time T 1 is found to be 3.1 ± 0.1 over a wide range of conditions, with the longest observed value of T S approaching 1 minute at elevated temperature. The observation of a constant ratio of T S to T 1 supports a relaxation model in which dipolar interactions between the CH 2 D protons and deuteron dominate the singlet relaxation. However, a naive model in which the 1 H and 2 D nuclei of the CH 2 D group are viewed as point-like magnetic dipoles fixed at the vertices of an equilateral triangle predicts a much larger ratio of T S to T 1 . We explore the effects of a geometric distortion in which the 2 D nucleus is displaced towards the centre of the triangle and find that a displacement of 38.7 pm is needed to explain the experimental data. This adjustment should not be viewed as a realistic structural proposal, but as a crude attempt to represent the differential effects of vibrational averaging and nuclear wavefunction delocalization within a simplistic point-nucleus geometric model.

The observed relaxation time ratio of T S /T 1 ≃ 3.1 is probably too small for most feasible applications. However, it should be noted that equation 8 permits a much larger ratio T S /T 1 in the case of fast 3-fold jumps, i.e. κτ c 1. This does not occur in N-CH 2 D-2-methylpiperidine, where the rotational barrier appears to be relatively large. Nevertheless it may arise in other compounds displaying inequivalence of the CH 2 D proton pair. It remains to be seen whether it is possible to maintain a sufficient differential between rotamer populations while still having a sufficiently low barrier to permit fast 3-fold jumps. We are currently exploring some other chemical candidates.

We have also attempted to observe long-lived singlet states in other chiral CH 2 D systems, such as derivatives of 3-2 D-lactic acid, and also (N-CH 2 D)-3-methylpiperidine (similar to the substance used above, but with a more remote CH 3 group). We failed to access the CH 2 D singlet state in both of these cases: the chemical inequivalence of the CH 2 D protons is presumably too small to exploit. Apart from unusual circumstances [53], hyperconjugation between a lone pair on a neighbouring atom (such as N) and the methyl C-H/D bonds seems to be a requirement for obtaining a sufficient chemical shift difference of a few ppb or more. At the time of writing we have not attempted these experiments on other chiral compounds containing a X-CH 2 D moiety, where X is an atom other than N possessing a long pair, such as P, O or S.

It should be noted that many interesting chiral molecules do contain a tetrahedral N-methyl group of suitable type. Examples include the psychoactive agents lysergic acid, codeine, morphine, cocaine, heroin, and methamphetamine. It is not yet known whether the methyl-monodeuterated versions of these systems possess an accessible long-lived singlet state.

Figure 6 :

 6 Figure 6: The relaxation of the CH 2 D protons in N-CH 2 D-2-methylpiperidine is governed by the three-fold jump rate κ and overall rotational correlation time τ c .

10 Page 10 of 20 Physical Chemistry Chemical Physics

  • , but this value is not

Acknowledgements

This research was supported by the Engineering and Physical Sciences Research Council (UK), grant codes EP/N002482 and EP/L505067/1, and also the Wolfson Foundation, the Royal Society/CNRS exchange scheme and by Bruker Biospin (USA). The authors thank Daniel J. O'Leary (Pomona College) for discussions, Jim Kempf and Robert Krull (Bruker Biospin) for assistance with temperature dependent measurements, and Marcel Utz and Soumya Singha Roy for experimental help.


Hamza Menaceur

Dr Olivier Cuisinier
email: olivier.cuisinier@univ-lorraine.fr

Farimah Masrouri

Hossein Eslami

Impact of monotonic and cyclic suction variations on the thermal properties of a stabilized compacted silty soil

The soil stabilisation is employed to construct geostructures as embankments, river levees, road subbases or to backfill excavations, improving the mechanical behaviour and reducing the consumption of extracted primary aggregates. This study is focused on the use of lime/cement treated soils to backfill trenches where high power line cables are buried. Indeed, under these circumstances not only the mechanical properties but also the thermal characteristics of the treated soil are of primary importance.

The effect of changes in suction (soil water content) on the thermo-mechanical properties was investigated on lime-treated and lime-hydraulic binder treated silty soils in the laboratory. The relationship between the Soil Water Retention Curve (SWRC) determined by suction control and measurement techniques, and the thermal properties along the drying path from the Optimum Proctor point (initial state) was analysed. Moreover, to investigate the successive heating/cooling periods induced by the cable, several drying/wetting cycles were applied to analyse their effect on the thermal properties and mechanical behaviour of compacted treated soils. The obtained data showed that increasing the suction from initial state to 3.5 MPa induces a decrease in the thermal conductivity (), this diminution becomes more important below 3.5 MPa of suction. An inverse trend was however observed in the change of the thermal capacity (C) with increasing section. The drying/wetting cycles appeared to have a significant impact on the mechanical performances and smaller effect on the thermal properties of the studied compacted treated silty soil.

Introduction

The use of soil stabilisation is a convenient way to enhance the mechanical behaviour and to build geostructures as embankments, river levees, road subbases or to backfill excavations, reducing the consumption of extracted primary aggregates [START_REF] Correia | A review of sustainable approaches in transport infrastructure geotechnics[END_REF][START_REF] Puppala | Sustainability in Geotechnical Engineering -general report of TC307[END_REF]. Soil stabilisation thus permits to limit the environmental impact of earthwork. The performances of the treated soil need to be tailored as a function of the context of application of the treated soils. This paper is focused on the thermal properties of compacted treated soils that are relevant in several applications like the installation of underground high-power line cables. Indeed, such cables are often buried in the ground, installed within a trench of 1 to 2 m depth and about 1 m wide, most of the time underneath existing low traffic roads. The cables are installed at the bottom of the trench and embedded in concrete. A significant part of the excavated soil is used to backfill the trench, and the road structure is then rebuilt. The backfill is most of the time treated with lime and/or cement to improve its bearing properties to meet the design requirement of the road structure to be rebuilt above. Once the electric cables are operational, their temperature may increase by Joule effect, the energy released varying over the year. The temperature increase of the cables must be limited under a given threshold to minimize the risk of cables failure. The efficient dissipation of the generated energy depends mainly on the thermal properties of the materials around the cables [START_REF] Emeana | The thermal regime around buried submarine high-voltage cables[END_REF][START_REF] De | Experimental study of thermal field deriving from an underground electrical power cable buried in non-homogeneous soils[END_REF][START_REF] Bai | Modeling deepwater seabed steady-state thermal fields around buried pipeline including trenching and backfill effects[END_REF], including the treated soils installed in the trench. However, the thermal properties of a given soil depend on their moisture content (w%) and density. Some studies showed that the cable temperature increase induces a drying of the soil [START_REF] Chatzipanagiotou | Influence of soil humidity on the thermal impedance, time constant and structure function of underground cables: A laboratory experiment[END_REF][START_REF] Eslami | Modelling of coupled heat and moisture flows around a buried electrical cable[END_REF], that phase being followed by a progressive rehydration when the temperature of the cable decreases.

Thermal conductivity () and volumetric thermal capacity (C), which describe the ability of a material to conduct heat and its ability to store thermal energy respectively are affected by soil mineralogy, dry density, water content, and particle arrangement [START_REF] Brandl | Energy foundations and other thermo-active ground structures[END_REF][START_REF] Mitchell | Fundamentals of Soil Behavior[END_REF]. Solid particles have a thermal conductivity significantly higher than water, but water has a thermal conductivity of approximately 30 times of those of air. Consequently, the thermal conductivity of soils increases with their water content for a given density. Similarly, when the dry density of a given soil increases, a significant increase in the thermal conductivity is observed [START_REF] Abu-Hamdeh | Soil thermal conductivity effects of density, moisture, salt concentration, and organic matter[END_REF][START_REF] Balland | Modeling soil thermal conductivities over a wide range of conditions[END_REF]. Ekwue et al. investigated the simultaneous effects of dry density and water content of several compacted soils on thermal conductivity along the compaction curve [START_REF] Ekwue | Thermal Conductivity of Some Compacted Trinidadian Soils as affected by Peat Content[END_REF]. They showed that thermal conductivity exhibits a similar behaviour with maximum values reached at water contents slightly higher than the optimum water content. Available literature data on the thermal conductivity of compacted treated materials are scarce, while treatments with lime or hydraulic binders modify significantly the soil mineralogy [START_REF] Locat | Laboratory investigations on the lime stabilization of sensitive clays : shear strength development[END_REF][START_REF] Metelková | Maturation of loess treated with variable lime admixture: Pore space textural evolution and related phase changes[END_REF]. The microstructure of treated soil is also significantly different from the microstructure of the untreated soil [START_REF] Wang | Changes in thermal conductivity, suction and microstructure of a compacted lime-treated silty soil during curing[END_REF][START_REF] Cuisinier | Microstructure and hydraulic conductivity of a compacted lime-treated soil[END_REF] and is impacted by temperature [START_REF] Al-Mukhtar | Behaviour and mineralogy changes in limetreated expansive soil at 50°C[END_REF][START_REF] Silva | Two-staged kinetics of moduli evolution with time of a lime treated soil under different curing temperatures[END_REF]. Moreover, the hydro-mechanical behaviour of treated soils is highly time-dependent due to the processes induced by the presence of lime and/or binder. Wang et al. [START_REF] Wang | Changes in thermal conductivity, suction and microstructure of a compacted lime-treated silty soil during curing[END_REF] studied the changes in the thermal conductivity of a compacted lime treated silty soil during curing. They showed that the thermal conductivity of samples compacted on the dry side of the compaction curve decreases slightly with increasing curing time. For the samples compacted on the wet side of optimum, they showed that the effect of curing time on the thermal conductivity is not significant.

In the long term, fluctuations of the cable temperature will induce successive drying/wetting cycles of the soil surrounding the cable. It is well known that successive wetting and drying can alter the characteristics of treated soils [START_REF] Behnood | Soil and clay stabilization with calcium-and non-calcium-based additives: A state-of-the-art review of challenges, approaches and techniques[END_REF][START_REF] Cuisinier | Alteration of the Hydromechanical Performances of a Stabilized Compacted Soil Exposed to Successive Wetting-Drying Cycles[END_REF], this alteration being associated to a progressive modification of the treated soil microstructure. Tang et al. [START_REF] Tang | Effects of the maximum soil aggregates size and cyclic wetting-drying on the stiffness of a lime-treated clayey soil[END_REF] studied the cyclic wetting/drying effects of the stiffness of a lime-treated clayey soil by using bender elements. They indicated that an intensive cyclic wetting-drying induces micro-cracks resulting in a decrease in the small shear strain modulus, associated to a decrease of the mechanical performances. Cuisinier et al. [START_REF] Cuisinier | Alteration of the hydro-mechanical performances of a stabilised compacted soil exposed to successive wetting-drying cycles[END_REF] also showed the harmful effects on strength and hydraulic conductivity of wetting and drying cycles on cement treated soil performances. Despite this information on the influence of climatic conditions and cyclic variations of water content on the hydro mechanical performances of treated soils, knowledge on their effect on the thermal properties of soil is still limited.

In this context, the first objective of the study is to provide insights about the changes in the soil thermal properties along the drying path. Several conditions were considered for the soil: untreated, lime-treated or lime-hydraulic binder treated silty soils. The modification of the thermal conductivity, water content and mechanical performances at various curing times were also investigated to complement the analysis. The second objective was to evaluate the possible alteration of the thermal properties after successive wetting/drying cycles.

Materials and methods

Tested materials

The soil tested in this study is a silt taken from the experimental site of Gray, France. Natural soil was first air-dried, grounded and then passed through the target sieve of 2.5 mm. The grain size distribution of the used soil (Figure 1) was determined by the sieving method for particles larger than 80 m and by the hydrometer method for particles smaller than 80 m. This silt has a fine fraction (<80 m) of 40 %. The main geotechnical properties are listed in Table 1.

According to the Unified Soil Classification System, this soil is a silt of low plasticity (ML).

Lime and hydraulic binder were used as treatment products. As indicated above, treatment is essential to improve the soil mechanical properties. Lime and/or hydraulic binder treatment is a widely used technique. In the short term, lime (CaO) reacts with the free water to produce hydrated lime, known as portlandite Ca(OH)2. This first reaction leads to a consumption of large amount of water content and a significant heat release. The followed dissociation of the portlandite provides sufficient Ca 2+ and HO -ions. Then, the increase in pH and calcium concentration leads to soil flocculation/agglomeration [START_REF] Eades | Reaction of hydrated lime with pure clay minerals in soil stabilization[END_REF][START_REF] Little | Handbook for stabilization of pavement subgrades and base courses with lime[END_REF], which results in significant decrease of the soil plasticity and changes of the soil engineering properties [START_REF] Sherwood | Soil stabilization with cement and lime[END_REF]. In the long term, pozzolanic reactions result in the production of cementitious gel, such as calcium silicate hydrates (C-S-H), calcium aluminate hydrates (C-A-H) and calcium alumino silicate hydrates (C-A-S-H), which play the major role in improving soil mechanical behaviour in terms of compressive strength, cohesion and friction angle and compressibility [START_REF] Bell | Lime stabilization of clay minerals and soils[END_REF][START_REF] Brandl | Alteration of soil parameters by stabilization with lime[END_REF][START_REF] Croft | The structures of soils stabilized with cementous agents[END_REF][START_REF] Eades | Reaction of hydrated lime with pure clay minerals in soil stabilization[END_REF][START_REF] Rajasekaran | Compressibility behaviour of lime-treated marine clay[END_REF][START_REF] Robin | Chemo-mechanical modelling of lime treated soils[END_REF].

The selected lime contained more than 94% of quicklime (CaO) on a dry-weight basis. The used hydraulic binder (CEM II/B-M (LL-V) 32.5 R CE) contained 65 % of clinker, 35 % of calcareous material and fly ash. Two types of treatment were considered in this study: lime treatment of 2%, and combined lime-hydraulic binder treatment, with the addition of 1% of lime and 4% of hydraulic binder. These contents were selected with references to current practices in soil treatment in France. Preliminary tests showed that they are sufficient to get satisfactory improvement of soil mechanical properties. The untreated soil was also tested as a reference to evaluate the changes in the thermal and mechanical properties arising from the treatment.

Samples preparation

The compaction characteristic curves were determined for each type and percentage of treatment according to the standard ASTM-D 698. The soil was left in an airtight container for at least two days to reach moisture equilibrium. The soil and the treatment product were then mixed up in a mechanical mixer for five minutes approximately. After the lime treatment, the mixture was left for 1 hour in an airtight container before compaction. When the cement treatment was used, compaction was carried out within a few minutes (maximum of 30 min) after treatment to account for the setting time of the cement. Figure 2 shows the influence of the different treatments on the compaction characteristics of the tested soils. As expected, the data show that the addition of treatment induced an increase of the optimum water content, and a decrease of the maximum dry density (Table 2), in line with other works on soil stabilization [START_REF] Little | Handbook for stabilization of pavement subgrades and base courses with lime[END_REF][START_REF] Lcpc-Setra | Traitement des sols à la chaux et/ou aux liants hydrauliques -Application à la réalisation des remblais et des couches de forme[END_REF].

The soil samples, untreated and treated, were statically compacted by static axial compression in a cylindrical mould to the target dry density [START_REF]Methods for the manufacture of test specimens of hydraulically bound mixtures using axial compression[END_REF]. Once the soil was air-dried and sieved with dmax = 2.5 mm, its water content was adjusted up to the optimal Proctor water content (determined form the Standard Proctor Test). This mixture was left in an airtight container for one hour prior to compaction to allow the development of immediate reactions. Cylindrical specimens of 50 mm in diameter and 100 mm in height were then prepared for thermal conductivity tests. The samples employed for the thermal measurements were larger to comply with the dimension of the testing device employed (see section 2.4). The specimens for the unconfined compression tests were 35 mm in diameter and 70 mm in height. Immediately after compaction, the specimens were wrapped with plastic-aluminium foil to prevent any exchange with the atmosphere, and stored at 20°C until testing time.

Suction control and measurement

The initial total suctions were determined by the chilled-mirror dew-point technique using the WP4C dew point potentiometer device (Decagon). More details on the water potential measurements can be found in [START_REF] Boukelia | Effect of temperature and initial state on variation of thermal parameters of fine compacted soils[END_REF].

To impose different suctions to the soil samples, two suction control techniques were employed.

(1): Pressure plate device was used to impose suction values below 1 MPa, while vapour equilibrium method was employed for suction values higher than 3.5 MPa. The pressure plate device principle is based on the axis translation method, imposing a positive air pressure inside the sample and controlling the water pressure [START_REF] Fredlund | Soil Mechanics for Unsaturated Soils[END_REF]. (2): The vapour equilibrium technique which consists in placing the specimens (cylinder of 50 mm in diameter and 75 mm in height) into desiccators containing saturated saline solutions was employed [START_REF] Cuisinier | Testing the hydromechanical behavior of a compacted swelling soil[END_REF][START_REF] Cuisinier | Influence of the hydric solicitations and mechanical complexes on the behaviour compacted expansive soil[END_REF]. The lowest suction imposed with a saturated saline solution (3.5 MPa) was obtained by using CuSO4. The highest suction (150 MPa) was imposed with a saturated saline solution of MgCl2. Samples were then left in the desiccators until reaching mass stabilization, checked by periodic weighing. Once this stabilization obtained, the imposed suction was controlled with Decagon WP4®. The moisture content was then determined by oven drying. The dimensions of samples were also measured at each step.

Thermal conductivity measurements

The thermal conductivity was measured using a handled apparatus named KD2 Pro Thermal Properties Analyser (Decagon Devices Inc.). This device complies with the requirements of ASTM Standards [START_REF]Standard Test Method for Determination of Thermal Conductivity of Soil and Soft Rock by Thermal Needle Probe Procedure[END_REF]. A dual needle (1.3 mm in diameter and 30 mm in length) was used to measure the thermal conductivity of the compacted silty soil through the principle of hot-wire transient method. Its accuracy is ±10% in the range of 0.2-2 W/(m•K) and ±0.01% for 0.02-0.2 W/(m•K). Penetration of needles is not possible in hardened soils. Thus, two holes of 1.3 mm in diameter and 30 mm in length were drilled in the central part of the upper section of each tested sample to ease the insertion of the dual needle sensor. A thin layer of a thermal conductive paste was applied on the surface of the sensors to ensure good contact with the soil. The dual needle was then placed inside the specimen and left for about 5 minutes to reach the temperature equilibrium between the soil and sensors. Then, the test started, 2 minutes were needed for one measurement. The samples remained wrapped in the plastic foil during the measurement to minimize any possible loss in moisture content. The mass of the sample was checked before and after thermal conductivity measurements to control water content variations.

Unconfined compressive strength (UCS)

Unconfined compressive strength (UCS) was determined with a displacement rate of 1.04 mm.min -1 . For each combination of parameters, three samples were tested and the results provided are the mean of these three values.

Test program

A first series of experiments was performed to investigate the relationship between the soil water retention curves, and the thermal properties for untreated silt (US), lime treated silt (LS) and lime-hydraulic binder treated silt (LHS). To do so, thermal conductivity and volumetric thermal capacity measurements were made by using the KD2 Pro device at initial state and along the drying path from the optimum water content once the suction equilibrium was reached.

A second series of samples was used to evaluate the change of thermal conductivity, water content and unconfined compressive strength (UCS) during curing. Thermal conductivity and UCS tests were performed at 0, 7, 28, 45 and 90 days of curing. Two specimens were tested to check repeatability. The specimens used for the UCS tests were then cut into small pieces to measure their water content by oven drying at each given curing time.

Finally, the effects of drying/wetting cycles on the thermal conductivity and the unconfined compressive strength (mechanical performance) of compacted silty soil were also addressed.

To do this, samples at 45 days of curing time were placed in a climatic chamber to simultaneous control of temperature and relative humidity. Thermal properties measurements were carried out at initial state and after 3, 6, 9 and 12 drying/ wetting cycles between 50% and 98% of relative humidity. The UCS tests were performed after the end of a wetting stage under a relative humidity of 98% for 3, 6 and 12 drying/wetting cycles. by some authors [START_REF] Wang | Changes in thermal conductivity, suction and microstructure of a compacted lime-treated silty soil during curing[END_REF][START_REF] Russo | Water retention curves of lime stabilised soil[END_REF][START_REF] Zhang | A study of the water retention curve of limetreated London Clay[END_REF]. This can be connected to the impact of these treatments on the soil micro-structure [START_REF] Cuisinier | Microstructure and hydraulic conductivity of a compacted lime-treated soil[END_REF][START_REF] Tang | Effects of the maximum soil aggregates size and cyclic wetting-drying on the stiffness of a lime-treated clayey soil[END_REF][START_REF] Le Runigo | Impact of initial state on the fabric and permeability of a lime-treated silt under long-term leaching[END_REF][START_REF] Stoltz | Multi-scale analysis of the swelling and shrinkage of a lime-treated expansive clayey soil[END_REF].

Experimental results

Water retention curvethermal properties

The thermal parameters determined for each suction upon the drying path were the thermal conductivity () and the volumetric thermal capacity (C). Results are presented in terms of changes of thermal conductivity versus suction and water content (Figure 4a,b) and in terms of changes in volumetric thermal capacity versus suction and water content (Figure 4c,d). At initial state, the thermal conductivity of the untreated silt is higher than that obtained with the treated silts ( =  and  W/m•K for untreated and treated silt, respectively). The data also showed that drying from the initial state resulted in a limited change of the thermal conductivity up to a suction of about 3.5 MPa. It decreased by 5.4 % for the untreated silt and by around 15.0 % for both treated silts. Increasing suctions above 3.5MPa resulted in a more significant reduction of the thermal conductivity. Similar conclusions can be drawn from Figure 4b where the thermal conductivity is plotted with respect to water content changes, with little change in thermal conductivity at water contents between 23.2 and 15% (initial state and 3.5MPa, respectively). The lime treated silt and lime-hydraulic binder treated silt had similar impact on the thermal conductivity, with values below the values obtained on the untreated silt, and almost the same difference at each suction along the drying path (Figure 4a andb).

Figure 4c and d present the changes in volumetric thermal capacity of each specimen. The increase in suction from the initial state to 3.5 MPa induced significant changes of the volumetric thermal capacity (76% for US and 86% for LS and LHS). Above 3.5 MPa, the rate of the change in volumetric thermal capacity is less important, unlike what was observed in thermal conductivity change (Figure 4a andb). At initial state, it can be also observed that the volumetric thermal capacity of the LHS was higher than that obtained for US and LS. However, at high suctions the difference between the three states became negligible.

Impact of curing time

Figure 5 shows the changes in thermal conductivity, water content of untreated, lime treated and lime-hydraulic binder treated silt versus curing time. It can be observed that, at t = 0 day (initial state), the untreated silt has a significantly higher thermal conductivity than the treated samples. This can be connected to the data observed in the thermal conductivity/suction curve (Figure 4a) along the drying path from the initial state to 152.5 MPa of suction. For the untreated and the treated silts, the curing time seems to have no effect on the thermal conductivity, the values remaining around 1.32 and 1.14 W/m•K for untreated and treated silts, respectively (Figure 5a). Observation of water content versus curing time in Figure 5c indicates that water content slightly decreased. For instance, the water content of the US was about 23.4% at t = 0 day and 22.4% at t = 90 days. The effects of this variation of water content on thermal conductivity changes seems to be negligible.

The UCS of the samples was also determined as an indicator of the development of the setting reactions within the samples. The UCS of the untreated soil was equal to 112 kPa. The treatments improved the mechanical performance of the soil (Figure 5c). For LS, the UCS was about 195 kPa at t = 0 day; then it gradually increased to 243 kPa at t = 90 day. For LHS, the increasing of UCS was much higher. It increased from 167 kPa at t = 0 day to 670 kPa at t = 90 days.

Effect of drying/wetting cycles

As previously described in Section 2.3, the drying/wetting cycles were applied after a curing period of 45 days to allow a significant improvement of the mechanical characteristics of the treated samples.

The changes in thermal conductivity of the US, LS and LHS versus the controlled relative humidity (50 and 98 %) are plotted in Figure 6 after 3, 6, 9 and 12 cycles. As expected, the data of the US is located above the data obtained on LS and LHS. Interestingly, with an increasing number of cycles, no effect on the thermal conductivity at 50% of relative humidity was observed (Figure 6). A slight reduction in the thermal conductivity after 3 cycles has been observed, while this difference is actually in the range of the dispersion observed when testing silt specimens. At 98% of relative humidity, it seems also that increasing the number of hydric cycles has a limited effect in the thermal conductivity. For the US and LS, after 3 cycles, we observed a decrease in the thermal conductivity followed by an increase up to a value close to that obtained at 3 cycles for 9 and 12 cycles. For the LHS, no significant change was neither observed in the thermal conductivity up to 6 cycles. Afterwards, the soil thermal conductivity obtained at 9 and 12 cycles is higher than that obtained after only 3 cycles, showing some irreversibility in the thermal properties at higher relative humidity. This set of data will be further commented in the discussion section.

The impact of the wetting/drying cycles on UCS is presented in Table 3. The results are presented as a function of elapsed time since the preparation of the samples. The detrimental effect of the cycles can be quantified by comparing the UCS together with the data of UCS changes with curing time, and the samples that were cured up to 270 days without being exposed to any wetting/ drying cycle.

The suction of the samples should be considered when doing the comparison. Indeed, suction of the samples after their preparation can be estimated from the retention curve, between 200 and 300 kPa (Figure 3). However, the wetting phases were conducted by applying a relative humidity of 98 %, corresponding to a suction of about 3 MPa. Therefore, the experiments were completed by determining the performance of the soils after a curing under a relative humidity of 98 %. It can be seen that the performance of those samples was significantly higher than the ones kept at constant moisture content. This difference can be explained by the higher suction of the samples cured under a relative humidity of 98 %, as showed for treated soils by De Bel et al. [START_REF] Bel | Influence of curing time, percolation and temperature on the compressive strength of a loam treated with lime[END_REF]. These results showed that the application of the first three cycles did not altered the performance of the samples, for both treatments. However, subsequent cycles resulted in a significant decrease after 6 and 12 cycles. In both cases, the performance after 12 cycles was significantly lower than the UCS of the samples cured under constant water content. The alteration of the lime-treated samples was much more important than those of the samples treated with the hydraulic binder.

Discussion

Impact of treatments on thermal conductivity

Thermal conductivity and volumetric thermal capacity were measured along the drying path from the initial state for US, LS and LHS. As described in section 1, the thermal conductivity is primarily controlled by the soil texture and structure, defined by soil nature, density, porosity, water content and aggregate size distribution. According to some authors, the maximum thermal conductivity is reached at the optimum moisture content [START_REF] Ekwue | Thermal Conductivity of Some Compacted Trinidadian Soils as affected by Peat Content[END_REF][START_REF] Eslami | Impact of temperature variation on penetration test parameters in compacted soils[END_REF] and depends on soil microstructure [START_REF] Zhou | Mesoscopic prediction on the effective thermal conductivity of unsaturated clayey soils with double porosity system[END_REF]. The thermal conductivity is therefore significantly impacted by the initial compaction level. As shown in Figure 4, the initial thermal conductivity of US is higher than those of LS and LHS. This could be probably due to the higher dry density obtained in the untreated case (Figure 2). However, Figure 4 shows that US and LHS have different thermal conductivities upon the drying path, despite their similar initial dry densities (Figure 2). Indeed, as reported by various authors, the thermal conductivity of silty soils is around 2.0 W/m•K. This is significantly higher than those of the cementitious compounds (C-S-H; C-A-H) produced during pozzolanic reactions when using lime and/or hydraulic binder treatment. The thermal conductivity of such compounds is comprised between about 0.2 and 1 W/m and is a function of their hydration density and packing density [START_REF] Do | Microstructure and Thermal Conductivity of Hydrated Calcium Silicate Board Materials[END_REF][START_REF] Abdolhosseini Qomi | Physical Origins of Thermal Properties of Cement Paste[END_REF][START_REF] Kim | An experimental study on thermal conductivity of concrete[END_REF]. As a result, the cementitious compounds in the soil may contribute to lower the overall soil thermal conductivity. Moreover, some authors showed that during the mixing process, the treatment product (lime or cement) is mainly located around soil aggregates, the inner part of the aggregates containing almost no treatment product [START_REF] Cabane | Sols traites à la chaux et aux liants hydrauliques : contribution à l'identification et à l'analyse des éléments perturbateurs de la stabilisation[END_REF][START_REF] Lemaire | Effects of lime and cement treatment on the physicochemical, microstructural and mechanical characteristics of a plastic silt[END_REF]. These authors showed that the cementitious compounds are formed at the contact points between the particles, with a slow diffusion towards the inner part of the aggregates when the curing time is increased. As a result, the conduction process can be significantly altered by the presence of the cementitious compounds at the contact point between the aggregates.

Impact of suction variation

Figure 4a shows that the changes in terms of thermal conductivity with suction increase were firstly characterized by a limited change between initial state and 3.5 MPa of suction for the three soils. Afterward, the thermal conductivity started decreasing significantly with suction increase. It is well known that the thermal conductivity is largely controlled by the water content, and also by the solid contacts between aggregates (soil density) [START_REF] Zhou | Mesoscopic prediction on the effective thermal conductivity of unsaturated clayey soils with double porosity system[END_REF][START_REF] Zhou | A new thermo-mechanical model for structured soil[END_REF]. Because of the soil shrinkage behaviour due to drying, the effect of the water content decrease on the thermal conductivity is certainly combined by the effect of dry density increase at the beginning of drying. Moreover, drying from the initial state (optimum proctor) up to 3.5MPa seems to occur at higher degree of saturation. Consequently, the liquid phase in pores remains continuous and the change in the overall thermal conductivity of soil becomes negligible. Beyond 3.5 MPa, a stabilization of volumetric shrinkage was observed. This means that the dry density could be considered constant, and the significant thermal conductivity change is only governed by the water content decrease.

Upon the drying path from the initial state, the volumetric thermal capacity was also measured.

The values are plotted versus suction and water content in Figure 4c andd, respectively. The 15/31 results showed that the volumetric thermal capacity seems to be slightly affected by the use of treatment along the drying path. This is in agreement with the data of Eslami et al. [START_REF] Eslami | Impact of temperature variation on penetration test parameters in compacted soils[END_REF] who found that the difference between the changes in volumetric thermal capacity versus water content of different soils is not significant. Note that, some differences were observed on the three specimens at the initial state, with a higher volumetric thermal capacity for LHS. For a given soil, it can be assumed that the higher the dry density and the water content, the higher the volumetric thermal capacity. This could explain the higher initial volumetric thermal capacity obtained for the LHS because of its higher dry density (d =1.52 Mg/m 3 ) and water content (w = 25%,).

Unlike what was observed in the thermal conductivity change, with a limited change before 3.5 MPa followed by a significant decrease, the volumetric thermal capacity decreases with suction and the decrease rate seems to be more important before 3.5 MPa (Figure 4c). This trend is also in agreement with the results of Eslami et al. [START_REF] Eslami | Impact of temperature variation on penetration test parameters in compacted soils[END_REF] who observed that the rate of volumetric thermal capacity increases with water content. Another conclusion that can hence be drawn is that the volumetric thermal capacity is mainly governed by water content, whereas in the range between the initial state and 3.5MPa the drying has occurred at high degree of saturation and consequently with the presence of continuous liquid phase in pores.

Impact of curing time

An important question is the change of the thermal conductivity with respect to curing time.

The results obtained here on samples compacted at the optimum showed no significant change in the thermal conductivity with curing time (Figure 5). This is in agreement with the study of Wang et al. [START_REF] Wang | Changes in thermal conductivity, suction and microstructure of a compacted lime-treated silty soil during curing[END_REF], who investigated the change in thermal conductivity, suction and water content of a lime treated silt. They observed that the thermal conductivity of samples compacted on the dry side decreases slightly with curing time, while for the samples compacted wet of optimum; the change in thermal conductivity is not significant. Indeed, it is well established that compaction at different water content results in different micro-structure of the soil. At the optimum water content and on the wet side, the samples present the same microstructure with only one pore population (intra-aggregates) and continuous liquid phase in the pores [START_REF] Delage | Mechanical behaviour of unsaturated soils: understanding the behaviour of unsaturated soils requires reliable conceptual models[END_REF]. It is hence expected to have a similar response in terms of thermal conductivity change with respect to curing time.

As showed by the results in Table 3 the positive effects of lime and/or hydraulic binder treatment on strength are altered by successive wetting/ drying cycles. However, the thermal properties of the tested soils remained almost constant after 12 cycles of wetting /drying process. The mechanical alteration can be explained by the alteration of bonds during the cycles as it has been evidenced by others authors [START_REF] Tang | Effects of the maximum soil aggregates size and cyclic wetting-drying on the stiffness of a lime-treated clayey soil[END_REF][START_REF] Consoli | Impact of Severe Climate Conditions on Loss of Mass, Strength, and Stiffness of Compacted Fine-Grained Soils-Portland Cement Blends[END_REF]. The stability of the thermal conductivity however indicates that the micro-structure of the different material was not dramatically altered by the wetting/drying cycles. The thermal conductivity is primarily controlled by the water content of the samples.

Conclusions

This objective of the study was to analyze the impact of two soil treatment products on the thermal performances of a compacted silt, in the short term and the durability of the performances after the imposition of several wetting/drying cycles. The following conclusions can be drawn from the study:

• Lime and hydraulic binder treatments could induce a significant decrease of the thermal conductivity of compacted silty soils. This modification is related to the impact of the treatments on the density of the compacted soil, but it is also a consequence of the microstructural changes induced by the treatments.

• Moisture content variation, i.e. suction variation, have a major effect on the thermal conductivity of the soil. A drying down to the residual water content can reduce by a factor of two the thermal conductivity of the material.

• The imposition of wetting/drying cycles alter significantly the mechanical performances of lime and hydraulic binder treated soils. However, the thermal characteristics remain constant. The primary effect of the wetting/drying cycles is to alter the bonds, and thus the mechanical characteristics. Such degradation should be taken into account in the design of the road structure in which the cable could be installed.

Acknowledgment

Figure 3

 3 Figure3shows the SWRC of the silt, with and without treatments. The drying path of untreated

  Published in Transportation Geotechnics https://doi.org/10.1016/j.trgeo.2021.100515 13/31

  This work was partly funded by the French Environment & Energy Management Agency ADEME in the framework of the project Valo-CQFD: « Valorisation des déblais de tranchées sur Chantier pour une Qualité Fiable et Durable ».

Figure 1 .

 1 Figure 1. Aggregate size distribution of soil with Dmax = 2.5mm (dry sieving and hydrometer

Figure 2 .

 2 Figure 2. Proctor curves of untreated, lime treated and lime-hydraulic binder treated silt.

  binders treated S r = 100% S r = 80% S r = 90% Published in Transportation Geotechnics https://doi.org/10.1016/j.trgeo.2021.100515 28/31

Figure 3 .

 3 Figure 3. Water retention curves of untreated and both treated soils obtained by suction

Figure 4 .

 4 Figure 4. Thermal conductivity and thermal capacity changes with respect to (i) suction

Figure 5 .

 5 Figure 5. Changes in thermal conductivity, water content and UCS during curing (a, b and c).

Figure 6 .

 6 Figure 6. Impact of successive drying-wetting cycles on the thermal conductivity of


Jean-Nicolas Dumez

Perspectives on hyperpolarised solution-state magnetic resonance in chemistry

This perspective article reviews some of the recent developments in the field of hyperpolarisation, with a focus on solution-state NMR spectroscopy of small molecules.

Two techniques are considered in more detail, dissolution dynamic nuclear polarisation (D-DNP) and signal amplification by reversible exchange (SABRE). Some of the opportunities and challenges for applications of hyperpolarised solution-state magnetic resonance in chemistry are discussed.

Graphical table of contents

This perspective article reviews some of the recent developments in the field of hyperpolarisation, with a focus on solution-state NMR spectroscopy of small molecules, and the methods of dissolution dynamic nuclear polarisation (D-DNP) and signal amplification by reversible exchange (SABRE).

Introduction

Nuclear magnetic resonance spectroscopy (NMR) is a very powerful and versatile analytical tool, with applications in fields as diverse as energy materials and medicine. In chemical science, solution-state NMR is essential for structure determination as well as the detection, identification and quantification of molecules in mixtures, for both static and time-evolving samples. NMR relies on properties of the nuclear spins as probes of their environment, through a vast array of experiments that provide unparalleled levels of structural information. NMR measurements are non-destructive and provide access to quantitative information on concentrations. For small molecules, these features are valid for near-arbitrary chemical structures, and the technique is often referred to as a "universal detector".

The main limitation of NMR is arguably low sensitivity, which arises from the small population difference between nuclear spin energy levels in usual experimental conditions. This population difference may be quantified as the polarisation P, which ranges from 0 (no population difference) to 100 % (fully polarised spins). As an example, at a magnetic field of 11.7 T and a temperature of 298 K, P is only 0.004 % for protons. Compared to other spectroscopy and spectrometry techniques, the collection of NMR data requires large sample quantities, with detection limits in the micromolar range for classic 1 H 1D NMR experiments. As a result, mass-limited chemicals may be difficult to characterise, transient processes may be unobservable and dilute components in mixtures may go undetected. The scope of applications of NMR increases dramatically with every step towards unit polarisation of the nuclear spins.

The sensitivity limitations of NMR may be addressed with "hyperpolarisation" methods, which increase nuclear spin polarisation and in turn NMR signals well beyond their thermal equilibrium values, with polarisation approaching unity in some cases.

Hyperpolarisation methods differ in the source of spin order on which they rely. In dynamic nuclear polarisation, the high polarisation of electron spins is transferred to surrounding nuclear spins. [START_REF] Ardenkjaer-Larsen | Proc. Natl. Acad. Sci[END_REF][START_REF] Ni | [END_REF] In optical pumping, the unit polarisation of photons is transferred in part to noble gases nuclei through spin exchange interactions. [3] In parahydrogen-based methods, the singlet order of parahydrogen is released by a chemical addition. [4,5] A variety of experimental schemes have been developed to harness these sources of polarisation. Polarisation levels may either be reported directly, or through the signal enhancement, which is calculated as the ratio of a given signal in the hyperpolarised experiments to the same signal after thermal equilibration.

With great polarisation comes great applicability. The recent surge in hyperpolarisation research, driven by a series of breakthroughs in concepts and instrumentation, has led to a wealth of applications that encompass in vivo metabolic imaging, [6] bioprobes with exquisite sensitivity [3] or the characterisation of large biomolecules and advanced materials in the solid state. [START_REF] Ni | [END_REF] In comparison, fewer investigations have been reported for some of the classic applications of solution-state NMR of small molecules, such as structure elucidation, the monitoring of chemical reactions or quantification in mixtures. Enhanced sensitivity also has obvious benefits in these areas as illustrated by several pioneering studies. [7,8] In this perspective article, a selection of current developments in hyperpolarised magnetic resonance is reviewed, and several challenges and perspectives in the field are discussed, with a focus on high-resolution, solution-state NMR of small molecules. Two hyperpolarisation methods are considered in more detail -dissolution dynamic nuclear polarisation (D-DNP) [START_REF] Ardenkjaer-Larsen | Proc. Natl. Acad. Sci[END_REF] and signal amplification by reversible exchange (SABRE), [5] since they have already led to applications in that area. This perspective article is written from the point of view of the end-user, for whom the ideal hyperpolarisation method would enhance polarisation levels by several orders of magnitude and preserve all the existing advantages of NMR spectroscopy; the method would work for arbitrary molecules and chemical moieties, and be compatible with the entire range of existing NMR pulse sequences, in particular multi-scan, multidimensional experiments. From this naive angle, current hyperpolarisation methods present both great opportunities for applications and significant challenges.

Dissolution dynamic nuclear polarisation

Concept

In dynamic nuclear polarisation (DNP), nuclear spins are hyperpolarised by microwave irradiation of a sample doped with radicals, in a magnetic field. DNP relies on the high polarisation of electron spins compared to nuclear spins. The dissolution-DNP (D-DNP) approach yields enhanced signals in solution through a two-step process. [START_REF] Ardenkjaer-Larsen | Proc. Natl. Acad. Sci[END_REF] First, the sample is polarised by DNP in the solid state, usually at temperatures of 1 to 4 K and magnetic fields of 3 to 7 T. Second, the hyperpolarised sample is rapidly dissolved with a superheated solvent, and transferred to the observation system. For applications in high-resolution solution-state NMR, the sample is injected in a conventional highresolution setup. The combined effect of solid-state DNP and the temperature jump from ~1 K to ambient temperature yields polarisation enhancements of up to 50 000. [START_REF] Ardenkjaer-Larsen | Proc. Natl. Acad. Sci[END_REF] D-DNP requires a complex and expensive apparatus. A commercial, fully automated system is available, which is suitably scaled for applications in chemistry and pre-clinical research, while a more recent system is designed for clinical applications. [6] Many recent hardware developments, however, are only available on custom-built systems. [9,10] Figure 1 shows the example of the custom-built system of Ernst and coworkers. [9] The main strength of the D-DNP approach is that it yields very high polarisation levels (of 50 % or more) and in turn signal enhancements, for a broad range of nuclei and chemical structures. Because the dissolution step of the D-DNP method is not easily reversible, however, the entire process is only carried out once for a given experiment; D-DNP is implemented as a single-shot technique. (Footnote: here single-(resp. multi-) shot refers to the fact that the sample can be polarised only once (resp. repeatedly), while multi-scan refer to the possibility to collect multiple free induction decays)

Features

Samples

The DNP process in the solid state can hyperpolarise a large range of substrates.

A majority of applications of D-DNP deal with highly concentrated, 13 C-labelled samples, and rely on a direct polarisation of the carbon-13 spins. For the analysis of molecules at natural abundance, however, especially at low concentration, the direct-polarisation approach may be unsuccessful. [11,12] This is in part because 13 C spin diffusion process, through which polarisation spreads from the paramagnetic centres to the bulk of the sample, is too slow at low concentrations in 13 C spins. The use of partially 13 C-labelled solvents to prepare the DNP matrix was proposed to facilitate the spin diffusion process. [11] Alternatively, dilute 13 C spins may be polarised by repeated cross polarisation (CP) steps from DNP-hyperpolarised 1 H spins, [13] as illustrated in Fig. 2. This CP-based approach provides polarisation levels of up to 40 % with a short build-up time of ~10 min. The efficient 1 H spin diffusion process makes it possible to polarise a broad range of samples, including mixtures of small molecules at natural abundance. [12] Efficient polarisation in the solid state is not a sufficient criterion to obtain hyperpolarised signals in solution. Nuclear spin relaxation during the transfer process can return spin populations to near equilibrium before any observation has occurred. In typical D-DNP implementation, transfer times of 5 to 10 s are used. This is suitable for many heteronuclear spins, such as non-protonated 13 C spins, which have relaxation rates of several 10's of seconds. Such transfer times, however, are not compatible with the direct DNP enhancement of 1 H signals -although cross-relaxation processes form slow-relaxing nuclei may still yield significant 1 H enhancements. [14] Using fast transfer and injection devices hyperpolarised 1 H experiments can be carried out, and a broader range of signals are observed for heteronuclei. [15] The harsh conditions of the dissolution and transfer step make the analysis of biomacromolecules by D-DNP challenging, as they may not recover their conformation of interest post dissolution. For small molecules, however, this is rarely a limitation and a broad range of substrates has been successfully polarised.

NMR experiments

D-DNP in its current form is a single-shot experiment. After dissolution, the enhanced polarisation decays irreversibly, through nuclear spin relaxation processes and upon excitation by radiofrequency pulses. As a result, D-DNP is not generally compatible with NMR experiments that require multiple consecutive scans, and in particular 2D experiments.

In many applications of D-DNP, time series of one-dimensional spectra are obtained with small-flip-angle pulse acquire experiments. For applications in metabolic imaging, a vast array of fast acquisition schemes has been developed, which combine one spectral dimension with several spatial dimensions. [6] For spectroscopy, twodimensional spectra may be collected using pulse sequences that can preserve part of the polarisation through consecutive scans. [16,17] Single-scan, "ultrafast" NMR pulse sequences are also particularly well suited to collect 2D spectra from DNP hyperpolarised samples. [12,18] In parallel to fast 2D methods, several pulse sequences have been developed, to obtain correlation information from 1D spectra. For example, J-couplings can be identified with off-resonance decoupling. [19] For the monitoring of chemical reactions, the use of selective inversion pulses provides a method to track nuclear spins during chemical transformations. [20]

Other properties

The ideal hyperpolarisation method would be non-destructive and compatible with quantitative measurements, like non-hyperpolarised NMR. In the most common protocol for D-DNP, the sample of interest is dissolved in a mixture of solvent, glassing agent and radical-bearing molecule. Samples are usually not recovered after dissolution for further analyses. Several strategies have been introduced to separate the radicals from the sample of interest during the dissolution process, and obtain a neat hyperpolarised sample. For example, a mixture of two solvents can be used for dissolution, chosen so that the sample of interest dissolves in the aqueous phase, while the radicals are mostly in the organic phase. [21] This approach has the additional advantage of reducing the dilution of the sample during dissolution. An alternative strategy consists of grafting radicals on the surface of a porous material, which is impregnated with an aqueous solution of the substrate. In this "HYPSO" method, the radical-containing polarising solid is retained upon dissolution by simple filtration, and the glassing agent is unnecessary. [START_REF] Gajan | Proc. Natl. Acad. Sci[END_REF] Hyperpolarisation methods rarely share the powerful feature of 1 H NMR of having a unique proportionality factor between concentration and peak volume for virtually any resonance in the spectrum. Still, quantitative results may still be obtained, using calibration methods, provided that the measurement is repeatable. The D-DNP process involves many sources of variability, for both the solid-state polarisation and the dissolution and transfer steps. A recent analysis of hyperpolarised 13 C spectra of metabolomics samples shows, however, that a repeatability of better than 5 % can be achieved with D-DNP. This suggests that quantitative results may be obtained with D-DNP in the near future. [START_REF] Bornet | [END_REF]

Areas of application

The main driving force for the development of D-DNP is the in vivo, real-time monitoring of metabolism, with notably examples of cancer studies in humans [24] . Kinetic and mechanistic studies of biochemical reactions, as well as ligand binding studies, are also active areas of applications. There are many fewer studies in analytical and organic chemistry. The two main types of applications reported so far concern the monitoring of chemical reactions and the detection of dilute components of mixtures of small molecules for, e.g., metabolomics applications. D-DNP makes it possible to record 13 C 1D spectra for substrates at natural isotopic abundance, thanks to enhancement of the order of 10 000, as well as 1 H 1D spectra that are enhanced by > 1000. Hilty and co-workers have exploited these enhanced signals to analyse several chemical reactions. They showed, with the example of a classic Diels-Alder reaction, that chemical kinetics may be measured efficiently with D-DNP. [25] More recently, they studied polymerisation reactions, using D-DNP to identify intermediates and gain insight into the mechanism of living anionic polymerisation, with hyperpolarised 13 C 1D NMR, as illustrated in Fig. 3. [7] Such analyses of chemical kinetics are carried out on timescales governed by the irreversible decay of the hyperpolarised signal, which typically range from a few seconds to a few tens of seconds.

The use of D-DNP to detect a larger range of molecules in the analysis of mixtures has been proposed several years ago. [17] Only few examples have been reported, however, of solution-state spectra of mixtures hyperpolarised with DNP. This is due in part to the difficulty to polarise dilute mixtures of molecules at natural abundance, and in part to the challenge of identifying signals in unusual experimental conditions, for which no reference data are available. Recent development in CP-based DNP and fast 2D NMR may help to address these limitations. [12] Virtually no examples have been reported of using D-DNP for the classic NMR application of determining the structure of an unknown chemical, either freshly synthesised or purified from natural sources.

Signal amplification by reversible exchange

Concept

Hydrogen gas can be enriched in its para form, the spin state of which consists of pure, long-lived singlet order. Parahydrogen (pH2) is a reservoir of spin order, a fraction of which may be transferred to other molecules for NMR observation. In the original parahydrogen-induced polarisation (PHIP) experiments, the chemical addition of pH2 onto the substrate releases its spin order, in the form of population differences across observable transitions that are significantly enhanced compared to their thermal equilibrium value. [4] This PHIP approach, however, involves an irreversible chemical modification of the substrate.

Signal amplification by reversible exchange (SABRE) relies on transient spin interactions, in a metal complex, between the nuclear spins of a substrate and those of hydride protons that originate from the addition of parahydrogen to the metal centre (Figure 4). [5] With SABRE, in contrast to earlier PHIP methods, substrates can be hyperpolarised with no chemical modification. In addition, the polarisation process can be repeated multiple times. For 1 H spins at high field, enhancements of the polarisation of over 1000 have been reported. [26] In their simplest implementation, SABRE experiments consists of mixing the substrate, a suitably chosen metal complex and parahydrogen in a gas-tight NMR tube, and manually shaking the sample in the stray field of the NMR magnet. The sample is then quickly inserted into the NMR magnet for detection. More advanced implementations include the use of automated parahydrogen bubbling [27] as well as sample shuttling. [28] The compatibility with multi-shot and/or continuous polarisation together with a relatively straightforward implementation make the SABRE process a very promising hyperpolarisation method.

Features

Samples

The SABRE concept was first demonstrated with the enhancement of the 1 H NMR signals of pyridine, and pyridine-like molecules remains the substrate for which the highest enhancements have been reported. A broad range of heterocycle-bearing molecules have been polarised with SABRE. [8,26,29,30] The magnetic field dependence for a variety of substrates was found to display common features, which may be explained with models based on either a density-matrix description of the spin dynamics, [31] or the analysis of level anti-crossings. [32,33] The SABRE process has also been demonstrated for nuclei other than 1 H, and in particular 13 C and 15 N and 31 P. [5,34,35] Using polarisation field in the microTesla range, nitrogen-15 can be polarised, in the so-called SABRE-SHEATH approach. [34] Recent studies have shown that the SABRE process is applicable "beyond heterocycles", notably with the example of Schiff bases, [36] as well as acetonitrile. [37] Current implementations of parahydrogen-based hyperpolarisation are not broadband, in the sense that only specific chemical motifs are polarised. This feature that may be turned into an advantage, however, to develop selective detection experiments. [8] The SABRE effect may yield enhanced signals for which the intensity does not scale linearly with concentration. When 2 mM Ir(IMes)(COD)Cl is used as a catalyst, with pyridine as a substrate, in methanol as a solvent, the enhancements decrease when the pyridine concentration decrease to 1 mM or less. [38] This observation may be explained by the role of the solvent, which competes with the substrate as a ligand. The use of a suitably chosen "co-substrate" restores the SABRE enhancement, for concentrations in the low micromolar range. [38]

NMR experiments

The SABRE method has the major advantage of being compatible with multiple consecutive repetitions; in contrast to D-DNP, it is not necessarily a single-shot method.

The simplest implementation of SABRE, which involves manually shaking the sample before insertion in the detection magnet, is not generally compatible with multi-scan experiments; the entire process may be repeated multiple times, but not with sufficient stability. Multidimensional spectra may still be collected with this approach, using, e.g. single-scan 2D acquisition techniques. [29,39] Several experimental setups have been described, which make it possible to carry out multi-scan SABRE experiments, to either record multidimensional spectra or enhance sensitivity further through signal averaging. A first possibility is to shuttle automatically the sample between a low-field region, for polarisation, and the bore of the NMR magnet, for detection. Figure 5 shows a scheme of the flow device and a 2D spectrum acquired with this setup; [28] the acquisition of multidimensional spectra with several classic pulse sequences has been described with this implementation. [29] Alternatively, the entire experiment can be carried out in the NMR magnet, using Jcoupling driven correlation experiments between the hydride and substrate protons to detect the bound substrates. [27] The matching conditions for spontaneous SABRE are found at magnetic fields in the mT range for 1 H and the µT range for heteronuclei (e.g., 15 N). Several methods derived from SABRE operate at several Teslas and thus do not require a sample shuttling step. In RF SABRE, a strong spin-lock field is applied to obtain, in a doubly titled rotating frame, matching conditions that are analogous to those employed for classic SABRE in low fields. [40] In LIGHT-SABRE, a very weak and selective pulse drives the conversion between the singlet order of the hydride pair and magnetisation of 15 N spins. [41] These schemes could also be combined with multi-scan, multi-dimensional acquisitions. The polarisation levels reported so far, however, are lower than for the low-field approach.

Other properties SABRE in its original form requires several dissolved compounds in addition to the substrate of interest: the metal complex, optionally a co-substrate and of course para-hydrogen. Even if no chemical modification occurs, subsequent separation of the analyte is not straightforward. The use of SABRE catalysts tethered to a solid in principle makes it possible to recover the sample of interest. Examples of heterogeneous SABRE have been reported, with enhancements of about 5. [42] One of the main current challenges for SABRE is development of catalysts that are active in solvents other than methanol and ethanol. A majority of studies focus on water, for biomedical applications. [43] Recently, adaptable catalysts have been described, which provide good enhancements in several different solvents. [44] Several applications of SABRE for quantitative measurements demonstrate the high repeatability of the methods. Surprisingly perhaps, the original "shaking" protocol was found to be appropriate for quantitation. [30] The entirely automated and high-field process of Tessari and co-workers provides a sufficient repeatability; [27] so does the shuttling apparatus of Duckett and co-workers. [29] In addition, when the total concentration of substrate (including an optional co-substrate) is sufficient, the SABREenhanced signals of dilute analytes varies linearly with to their concentration, which makes it possible to use a standard-addition approach for quantitation. [38]

Areas of application

The majority of applications of SABRE reported so far concern magnetic resonance imaging and the production of hyperpolarised MRI agents. SABRE is explored as a way to produce hyperpolarised MRI agents in a continuous and scalable way, as opposed to the batch mode in which D-DNP operates.

As it provides high enhancements for selected chemical motifs, SABRE is also assessed as an analytical tool for the detection of classes of analytes in mixtures. Several examples of trace detection in model samples have been reported. [29,45] More recently, Tessari and co-workers described the chemoselective detection of pyridine and pyrazine derivatives in coffee extracts, as illustrated in Fig. 6. [8] Another promising area of application for SABRE in chemistry is the monitoring of organic reactions. Strong synergies exist between SABRE, as a cost-effective and straightforward hyperpolarisation method, and compact NMR instruments, which can be operated under the fume hood. [46]

Discussion

The field of hyperpolarised magnetic resonance is currently very active, with many ongoing developments, for a variety of applications. For solution-state NMR of small molecules, two hyperpolarisation methods, D-DNP and SABRE, are particularly popular. Both have led to experiments that would not be possible without hyperpolarisation, such as the mechanistic studies of polymerisation with in-situ, realtime monitoring or the detection of dilute analytes in complex mixtures.

The benefits of hyperpolarisation, however, come at a cost; hyperpolarised experiments typically sacrifice some of the features of their thermal equilibrium counterparts. D-DNP provides incredible signal enhancements, but only once. The single-shot nature of the experiment limits the timescales that can be probed, as well as the range of experiments that can be recorded. SABRE can be implemented in multi-shot mode, so that conventional multidimensional experiments become possible. The range of substrate that may be polarised, however, is limited by the need to bind a metal centre, on a suitable time scale. Both methods, in their current implementation, also sacrifice the non-destructive nature of non-hyperpolarised NMR experiments, as they require the use of additive such as radicals or metal complexes.

A range of solutions is being developed to address these limitations. For D-DNP, fast acquisition methods yield multidimensional information from a single experiments. [12,16,19] For SABRE, the scope of substrates keeps on expanding. [36,37] For both methods, there are prospects of polarisation schemes that would yield hyperpolarised samples free of impurities. [START_REF] Gajan | Proc. Natl. Acad. Sci[END_REF]42] These developments push the limits of what can be achieved with hyperpolarisation. Still, several applications remain difficult to conceive with these methods, such as elucidating the structure of a mass limited natural product. This would require a hyperpolarisation scheme that is both broadband and compatible with a multi-shot implementation.

Current developments in dynamic nuclear polarisation offer the perspective of a multi-shot, broadband hyperpolarisation method for solution-state NMR. DNP in the liquid state through the Overhauser effect is very challenging water at high magnetic field. [47] However, rapid sample shuttling between a low-field polarisation region and a high field detection region, or the use of supercritical CO2 as a solvent, make solutionstate DNP conceivable. [47,48] An alternative approach, rapid-melt DNP (Figure 7), [49] shares the solid-state DNP step of D-DNP. In contrast to D-DNP, which involves an irreversible dissolution step, rapid-melt DNP relies on rapid sample melting, which is reversible. Rapid-melt DNP is thus compatible with multidimensional experiments. These methods offer promising perspectives; even if the enhancements were eventually lower than in D-DNP, e.g., because of a smaller temperature jumps, for many applications signal enhancements of several 100's in a multi-shot way would be more useful than single-shot enhancements in the 10 000's. Challenges for these multi-shot approaches include the design of instrumentation that yield high-resolution data, as well as the effect of polarising agents at relatively high concentration.

An analogy can be made between rapid-melt or Overhauser DNP and dynamic nuclear polarisation in solid-state magic-angle spinning NMR, which is also a multi-shot, broadband method. [START_REF] Ni | [END_REF] In MAS DNP, many classic NMR experiments can be carried out, with DNP enhancements in the 10's or 100's. The price to pay, however, is that experiments are typically carried out at 100 K, with radicals and at moderate spinning frequencies and magnetic fields, which may result in a lower resolution than for thermal-equilibrium experiments. [START_REF] Ni | [END_REF] Each hyperpolarisation method retains clear advantages, and the choice of method depends largely on the targeted applications. D-DNP is particularly well suited to analyse the kinetics of chemical reactions. [6] Real-time monitoring indeed benefits from the highest possible polarisation and is not compatible anyway with long acquisition times. In contrast, multi-shot DNP would be particularly useful for the analysis of unknown, mass limited compounds, for which D-DNP offers too narrow a range of NMR spectra. For the detection and quantification of "known unknowns" in mixtures, each method has distinct advantages, e.g., chemoselectivity and repeatability for SABRE, and future studies will reveal their suitability for "real-world" applications.

Hyperpolarisation methods are typically characterised by the signal enhancement (noted e) that they provide,. While this enhancement is very informative to understand the properties of the hyperpolarisation methods, it does not entirely capture the actual sensitivity enhancement for a given application. [50] For example, the current implementation of D-DNP comes with several sensitivity penalties, which are not accounted for in the raw signal enhancement e. Because of sample dilution upon dissolution, only a fraction of the initial sample is injected for detection. Also, experiments are typically carried out with sub-optimal shims. While 13 C detection provides a much higher resolution than 1 H, it also comes with a sensitivity penalty at natural abundance. For rapid-melt DNP, the presence of radicals will a priori degrade resolution and relaxation rates. For these and other reasons, the enhancement obtained with a given hyperpolarisation method is not obvious to characterise and is highly application dependent (is the sample-mass limited or not? does it evolve in time? etc).

All of these aspects provide further avenues to improve hyperpolarisation methods and obtain higher sensitivity enhancements.

In summary, the developments in hyperpolarisation that have occurred over the last 10 years have opened a vast array of applications in solution-state NMR of small molecules. Continuous developments in these areas keep on pushing the limits of realtime monitoring and trace detection. Other applications, including the classic use of NMR for structure determination of unknown compounds, will benefit from emerging approaches that provide a steady and broadband enhancement. Helium is dragged into the sample space by evacuating the cryostat with two vacuum pumps (3) connected in series. The DNP probe ( 4) is mounted and sealed to the cryostat within the bore of the magnet. A microwave source ( 5) is connected to the waveguide leading to the sample space. The dissolution system ( 6) is attached to the tubing of the dissolution stick (7) for dissolution and shuttling to the nearby NMR/MRI spectrometer.

An NMR console (8) is used to monitor the nuclear polarization while the entire system is controlled by computer software (9). Dotted lines indicate data communication pathways. Reproduced with permission from Ref. [9] © 2012 Elsevier Inc. with permission from Ref. [13] © 2012 American Chemical Society. 13 C NMR spectra recorded from a single sample of hyperpolarised styrene mixed with NaC10H8. Reproduced with permission from Ref. [7] © 2013 American Chemical Society. with permission from Ref. [5] © 2009 AAAS Fig. 5 SABRE with an NMR flow system. (a) Schematic of the Polariser, the hyperpolarisation process and its subsequent NMR analysis. (b) 1 H 2D OPSY-COSY NMR spectrum of hyperpolarised quinoline in methanol-d4 achieved using 1 and p-H2 with an applied polarisation transfer field of 0 G. Reproduced with permission from Refs [28] © 2014 The Authors and [29] © 2012 American Chemical Society. showing the major components within the magnet bore: the cooling region where microwave irradiation occurs, the melt region, where heated nitrogen gas is directed onto the frozen sample, and finally, the stripline NMR detection region. Both NMR and DNP sections are located within the homogeneous region of the magnet, as indicated by the distance z, relative to the center of the magnet. A linear actuator is used to move the capillary through the system, thereby moving the sample between system components. 95 GHz Microwaves are introduced from the bottom of the probe, as are cryogens and heated nitrogen gas. (b) A Thermal polarised room temperature NMR signal for 99% d8toluene, with 50 mM BDPA radical doping, averaged for 1024 scans (normalised by a factor 1024 and displaced vertically for clarity). B Rapid-melt DNP enhanced spectrum (single scan) at a power of 16.8 W for 10 s. The small peak near 3.4 ppm is due to 20 mM caffeine that was added to the toluene solvent. Note that the presence of caffeine cannot be determined from the thermal spectrum, even after 1024 scans. C Rapid-melt DNP enhanced spectrum after 300 consecutive scans with a cycle delay, including freezing, DNP and melting, of 6 s per scan. The total measurement time is 30 min. Reproduced with permission from Ref. [49] © 2015 Elsevier

FiguresFig. 1

 1 Figures

Fig. 2 D

 2 Fig. 2 D-DNP with cross-polarisation. (a) Signals of 13 C NMR of 50 μL of a 3 M frozen solution of 1-13 C-enriched sodium acetate in a deuterated water/ethanol mixture (67:33 v/v) doped with 50 mM TEMPO measured without CP (blue) at thermal equilibrium (T = 4.2 K and B0 = 6.7 T, scaled by a factor 100) and with CP-DNP (red) (Pμw = 120 mW at fμw = 188.3 GHz). (b) 13 C DNP buildup with (red) and without (gray) CP measured every 30 s with β = 5° pulses. CP was performed every 240 s with B1 = 15 kHz and a contact time of 1 ms. (c) The dissolution and transfer process requires tdiss = 10.7 s. (d) Relaxation of 13 C in solution at ∼T = 300 K after transfer to a magnetic field B0 = 7.05 T, measured with β = 5° pulses at 5 s intervals. (e) Signals of 1-13 C sodium acetate immediately after dissolution (red) and at thermal equilibrium (blue, scaled by a factor 2048). Reproduced

Fig. 3

 3 Fig. 3 Hyperpolarised NMR of polymerisation reactions. (a) Living anionic polymerisation of styrene. (b) Series of 13 C NMR spectra recorded from a single sample

Fig. 4

 4 Fig. 4 Signal amplification by reversible exchange. (a) Schematic representation of the magnetisation transfer process in SABRE. (b) Single scan NMR spectra of samples containing a templating medium, the indicated substrate, and para-H2 at 295 K in d4methanol where the polarization transfer step was achieved in a 2 × 10 -2 T field. The 1 H control trace (top) of 6 nmol of pyridine with 128-fold vertical expansion relative to the bottom 1 H trace that was recorded immediately after polarization transfer. Reproduced

Fig. 6 Fig. 7

 67 Fig. 6 p-H2 based chemosensing in natural extracts. (a) High-field p-H2 enhanced 2D correlation spectrum between hydrides and substrate aromatic protons in the receptor complexes (1), acquired on a coffee extract in methanol-d4 sample in 20 min. The sample contains 1.2 mM metal complex, 18 mM mtz, and 5 bar 51% enriched p-H2. Assignment of the most concentrated species is indicated. The 1D trace is shown to illustrate the signal-to-noise ratio at the dotted line in the spectrum. (b) Standard-addition curves for ortho proton resonances of pyridine, 2-ethylpyrazine, pyrazine, and 2,6dimethylpyrazine. Concentrations are estimated from the abscissa intercept (circled) of the standard-addition curves (gray lines). Experimental uncertainties were derived byerror propagation. Reproduced with permission from Ref.[8] © 2016 American Chemical Society

Acknowledgments

The author thanks many colleagues and collaborators for inspiring discussions on hyperpolarisation.