# Practical dissolution dynamic nuclear polarization

Stuart Elliott, Quentin Stern, Morgan Ceillier, Théo El Daraï, Samuel Cousin, Olivier Cala, Sami Jannin

► To cite this version:

Stuart Elliott, Quentin Stern, Morgan Ceillier, Théo El Daraï, Samuel Cousin, et al. Practical dissolution dynamic nuclear polarization. Progress in Nuclear Magnetic Resonance Spectroscopy, 2021, 126-127, pp.59-100. 10.1016/j.pnmrs.2021.04.002. hal-03954523

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Submitted on 24 Jan 2023

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Practical Dissolution Dynamic Nuclear Polarization

Stuart J. Elliottª, Quentin Sternª, Morgan Ceillierª, Théo El Daraïª, Samuel F. Cousinª, Olivier Calaª and Sami Janninª†

Edited by Geoffrey Bodenhausen and Dominique Massiot

ª Centre de Résonance Magnétique Nucléaire à Très Hauts Champs - FRE 2034 Université de Lyon / CNRS / Université Claude Bernard Lyon 1 / ENS de Lyon, 5 Rue de la Doua, 69100 Villeurbanne, France

† sami.jannin@univ-lyon1.fr

**Glossary**

NMR nuclear magnetic resonance

MRI magnetic resonance imaging

MAS magic angle spinning

OE Overhauser effect

CIDNP chemically induced dynamic nuclear polarization

dDNP dissolution dynamic nuclear polarization

bDNP bullet dynamic nuclear polarization

EPR electron paramagnetic resonance

ESR electron spin resonance

LODESR longitudinally detected electron spin resonance

FID free induction decay

SNR signal-to-noise ratio

CP cross-polarization

RF radiofrequency

AHP adiabatic half-passage

VNA vector network analyzer

P2P peak-to-peak

PA polarizing agent

BG background

TE thermal equilibrium

PTFE polytetrafluoroethylene

PEEK polyether ether ketone

HYPSO hybrid polarizing solids

HYPOP hyperpolarizing polymers

FLAP filterable labelled agents for polarization

CSA chemical shift anisotropy

SR2K scalar relaxation of the second kind

SPY spin polarimetry

ZULF zero- to ultra-low field

LAC level anti-crossing

UF ultrafast

HSQC heteronuclear single quantum coherence

HMQC heteronuclear multiple quantum coherence

HMBC heteronuclear multiple bond correlation

DOSY diffusion order spectroscopy

COSY correlation spectroscopy

SO-FAST-HMQC selective optimized flip-angle short-transient heteronuclear multiple quantum coherence

**Abstract**

This review article intends to provide insightful advice for dissolution-dynamic nuclear polarization in the form of a practical handbook. The goal is to aid research groups to effectively perform such experiments in their own laboratories. Previous review articles on this subject have covered a large number of useful topics including instrumentation, experimentation, theory, etc. The topics to be addressed here will include tips for sample preparation and for checking sample health; a checklist to correctly diagnose system faults and perform general maintenance; the necessary mechanical requirements regarding sample dissolution; and aids for accurate, fast and reliable polarization quantification. Herein, the challenges and limitations of each stage of a typical dissolution-dynamic nuclear polarization experiment are presented, with the focus being on how to quickly and simply overcome some of the limitations often encountered in the laboratory.

Keywords: NMR, Hyperpolarization, DNP, dDNP, CP, Sample Preparation, Systems Maintenance, Transport Dynamics, Polarization Quantification, SPY-NMR
# 1. Introduction

Ordinary signals in conventional nuclear magnetic resonance (NMR) and imaging (MRI) experiments are intrinsically weak. For a state-of-the-art radiofrequency (rf) NMR probe, the signal-to-noise ratios (SNRs) achievable are subject to factors such as rf-coil and preamplifier design, choice of pulse sequence, probe circuit, sample temperature and static magnetic field strength [1]. This is due to the relatively small Zeeman splitting between nuclear spin states (~2.7 mJ.T⁻¹ for a ¹H spin), even if the sample of interest is placed within the highest fields of today's superconducting NMR magnets, compared with the thermal energy available at room temperature (~2.4 kJ.mol⁻¹). This leads to a relatively flat Boltzmann distribution of nuclear spin populations, and consequently to a very low nuclear spin polarization. The polarization Pᵢ of a nuclear spin-½ ensemble is defined as follows:

$$P_i = \tanh\left(\frac{\hbar\gamma_i B_0}{2\kappa T}\right) (1)$$

where γᵢ is the magnetogyric ratio of spin i, B₀ is the static magnetic field and T is the spin temperature that is normally determined by the sample temperature. A typical polarization for a ¹H nucleus at 298 K and 6.7 T is on the order of ~5.6·10⁻⁵. This amounts to ~100'001 ¹H spins aligned with B₀ for every ~100'000 ¹H spins aligned against B₀. The inherent insensitivity is worse for NMR active nuclei with lower magnetogyric ratios. For many potential applications [2], nuclear spin polarizations close to unity are desirable.

From examining Equation 1, there are two key factors which control the level of nuclear polarization: (i) the magnetic field B₀; and (ii) the spin temperature T. Unfortunately, there are no commercial NMR magnets currently available with a sufficiently high magnetic field that would naturally hyperpolarize a nuclear spin ensemble. So-called “brute force” hyperpolarization techniques are available to significantly reduce the temperature of a sample inside an NMR magnet to the milliKelvin range by using a dilution refrigerator [3]–[6]. However, the method has many drawbacks: (i) cooling power limitations place constraints on usable sample volumes (≤40 µL); (ii) the timescales of sample cooling are typically long (hours or days); and (iii) relaxation of nuclear spins at millikelvin temperatures is inherently slow due to a lack of molecular motions and, as a result, samples for brute force experiments typically require doping with paramagnetic agents to drastically shorten nuclear relaxation times. Consequently, other methods are required to bring the polarization of a nuclear spin ensemble closer to unity.

Dynamic nuclear polarization (DNP) is a hyperpolarization technique which has been around since the early 1950s [7] and aims to substantially boost the polarization level of nuclear spins. Since its conception the approach has seen dramatic developments and now the method is widely employed in both solid-state experiments, either under magic angle spinning (MAS) conditions at ca. 100 K [8] or static conditions at ca. ≤4.2 K [9].

The dissolution variant of the approach has also gained significant traction within the last two decades. J.-H. Ardenkjær-Larsen and co-workers first presented their results on dissolution-dynamic nuclear polarization (dDNP) in 2003

[9], and since then there has been vibrant activity within the community. dDNP methods often lead to liquid-state NMR signal enhancements approaching 10⁴ [10], [11], with the increased sensitivity resulting in experiment times reduced by large factors. Further details regarding DNP mechanisms [7], [12]–[18] and applications of dDNP [19]–[32] are available. A two-magnet dDNP approach [33] and bullet-DNP (bDNP) [34] have additionally been shown to generate impressive NMR signal enhancements but will not be discussed herein.

A number of key requirements are generally necessary in order to perform dDNP measurements:

(i) A homogeneous freezing of the sample of interest in a glassy DNP matrix [35];

(ii) An optimal concentration of paramagnetic radical species uniformly distributed throughout the sample [36];

(iii) Low temperatures -- often provided by a cryogenic reservoir of liquid helium with 1.2 K < T < 4.2 K;

(iv) A magnetic field -- the majority of dDNP experiments are conducted in the range 3.35 T < B₀ < 10.0 T [37]–[39];

(v) A source of microwaves with capabilities for frequency adjustment or modulation [40];

(vi) Dissolution and transfer to facilitate liquid-state NMR or MRI applications.

The sample of interest is typically dissolved in a mixture of protonated and deuterated aqueous solvents, commonly H₂O or D₂O combined with glycerol or DMSO, homogeneously mixed with paramagnetic radical agents, e.g., TEMPOL, trityl etc. The sample is transferred to a holder and inserted into a polarizer at sufficiently high field, the sample space of which is flooded with liquid helium ensuring that the sample solution forms a glass upon freezing. The microwaves irradiate the sample at a specific frequency close to the electron spin resonance. This process transfers the near unity electron polarization directly to the nuclei of interest or indirectly via nearby nuclei of differing isotopic type. After sufficient nuclear spin polarization has been obtained, e.g. P(¹³C)>30%, the frozen media is flushed out of the sample space using a jet of hot solvent, e.g., D₂O, and transferred to separate NMR magnet for detection.

The field of dDNP has made a number of advances due to improved sample formulation [41]. The need for a glassy DNP solvent matrix comes from the desire to homogenously freeze the sample medium in the superfluid helium bath. However, the presence of electron-bearing species can also significantly attenuate the lifetime of nuclear polarization in the solid-state. To avoid this effect, a range of silica and polymer materials have been developed to ensure a distance between the paramagnetic centres and the nuclei to be polarized [41]–[44]. Such materials are compatible with a wide range of compounds [45], and allow for the removal of glass-forming materials within the sample.

The performance of NMR experiments conducted under dDNP conditions relies on the precise implementation of each of the key components listed above. An important question to answer is: What experimental conditions are required? dDNP experiments are typically performed between 3.35-7.05 T and 1.2-4.2 K. The reasons for this choice are motivated by the high polarization of electron spins at liquid helium temperatures.

Paramagnetic sources, i.e., unpaired electrons, are fundamentally required for DNP [46]. The electrons form dipolar coupled spin systems with the nuclei of interest. At low temperature, the electron species are highly polarized, i.e., Pₑ = 99.93% at 1.2 K and 7.05 T, whilst the nuclear spins lack a
significant degree of polarization. This is due to the large magnetogyric ratio $\gamma_e$ of the electron compared with those of nuclei, e.g., $\gamma_e/\gamma_H \approx 660$ where $\gamma_H$ is the proton magnetogyric ratio. The application of microwave irradiation at a frequency which is slightly off-resonance with respect to the electron transition frequency leads to a transfer of polarization to the nuclear spins via mutual flip-flop interactions.

At this point the spin system is no longer in equilibrium, and relaxation processes drive the population distribution back towards its initial state. This process mainly occurs via electron relaxation, which is a significantly faster phenomenon at low temperature than nuclear spin relaxation. The electron relaxation time $T_{1e}$ is on the order of ~30-100 ms at liquid helium temperature for radical species such as TEMPOL [23], [47] but can be significantly longer in other cases, e.g., for trityl radicals.[36] It is therefore important to saturate the electron spin transitions, the extent of which is controlled by whether the EPR line is homogeneously or heterogeneously broadened, spectral diffusion and radical concentration, to force the electron spins to find new dipolar coupling partners that can again participate in the DNP process. For dDNP systems, microwave powers on the order of 30-120 mW are required [48]. The ability to modulate both the frequency and bandwidth of the microwave source can significantly boost polarizations and build-up times whilst reducing the concentration of free radicals required [40].

The rate of the different DNP processes, i.e., the build-up of the DNP signal, the electron relaxation, etc., are dependent on the concentration of electron centers embedded within the glassy matrix. A compromise of 10-50 mM radical concentration is often used in experiments. This quantity of radical sources ensures that DNP build-up times $\tau_{DNP}$ are reasonable, on the order of minutes, and that a satisfactory level of nuclear spin polarization can be achieved, e.g., $P(^1H) \approx 30\%$ at 3.8 K. in the case of nitroxide radicals. Moreover, after dissolution, the radical concentration can have a major influence on the nuclear $T_1$ in regions of low magnetic fields [49]–[51].

Dissolving frozen samples at liquid helium temperatures provides the greatest possible signal enhancements for solution-state NMR experiments. At these temperatures, it is possible to rapidly dissolve the frozen samples by directing a blast of superheated solvent into the sample space [2], [9]. Furthermore, the time taken to dissolve the sample of interest is typically much shorter than the longitudinal nuclear relaxation time $T_1$. More details regarding the energy transfer and the thermodynamics of sample dissolution can be found elsewhere. [2]

The capabilities of *polarizers* to perform more traditional NMR experiments under dDNP conditions has been drastically improved by the implementation of cross-polarization (CP) [52], [53]–[56]. This method has allowed significant levels of $^{13}$C (60%) and $^{15}$N (25%) polarization to be achieved in a few tens of minutes [57]. The high levels of nuclear polarization allow for additional applications to be developed, such as structural elucidation at natural abundance [58].

Figure 1 depicts a flow diagram of a typical dDNP experiment. The flow diagram consists of three loops. These loops are related to the following experimental steps: (i) sample preparation and verification of sample properties; (ii) preparing the components of the dDNP system and performing standard experiments; and (iii) enacting a dissolution experiment with subsequent analysis of the NMR data. Each step should be successfully completed before moving onto the next, e.g., the

fact that without a glassy environment, the sample of interest will not polarize sufficiently for subsequent experiments clearly demonstrates this principle (see Section 2.3 for details). Furthermore, if unexpected levels of polarization are achieved later on in the experiment, this could be attributed to the fact that the sample properties, e.g., its radical concentration, were not verified beforehand using EPR. The flow diagram is therefore designed to ensure that the experiment is completed to a high standard.

In this review, we aim to share our knowledge regarding how to best combat partial shortcomings of a complete dDNP experiment. We have targeted the following key subjects: sample preparation and health; dDNP and CP procedures; mechanical aspects and spin dynamics of sample dissolution and transfer; and quantification of the $^{1}$H and $^{13}$C polarization. The various aspects of this review are broken down further in Table 1. Herein, we present hands-on information with a focus on experimental formulas, recipes and hardware innovations that will help other dDNP groups around the world better perform their own experiments. We also present potential limitations of dDNP experiments and common reasons for failure. Photographs will be given in order to shine more light on the tips and tricks necessary to effectively perform optimal dDNP experiments. Theoretical underpinnings will also be provided where necessary.

<figure><img src="image_1.png" /><figcaption>Figure 1: Complete flow diagram to be used during a typical dDNP experiment in our laboratory. “Validate by EPR” and “Cross-Polarization” are optional steps.</figcaption></figure>

<caption>Table 1: Summary of topics discussed in this work.</caption>
<table><thead><tr><td>Section</td><td>Topic</td><td>Sub-Topics</td></tr></thead><tbody><tr><td>2.</td><td>Sample preparation</td><td>Concentration of PAs<br>Glass formation<br>Preparing a standard<br>dDNP sample<br>Alternative samples</td></tr><tr><td>3.</td><td>Sample health</td><td>PA choice<br>Chemical conservation<br>Nitroxide stability<br>Nitroxide degradation<br>EPR quantification</td></tr><tr><td>4.</td><td>Systems health</td><td>RF-probe construction<br>Sensitivity estimates<br>Tuning and matching<br>Nutation curves<br>Directional coupler usage<br>Oscilloscope protection<br>RF-probe arcing<br>RF-pulse reflection<br>RF-coil maintenance</td></tr><tr><td>5.</td><td>dDNP experiments</td><td>DNP build-up experiments<br>Microwave optimization<br>Effect of PA concentration<br>Effect of temperature<br>Effect of magnetic field<br><sup>13</sup>C Optimization<br>Multiple-CP<br>Thermal equilibrium</td></tr><tr><td>6.</td><td>Dissolution mechanics</td><td>Dissolution strategy<br>Dissolution preparation<br>Shimming procedure<br>Dissolution stick<br>Fluid path<br>Energy required for dissolution<br>Optimizing dissolution efficiency<br>Transfer and injection<br>Gas-driven systems<br>Liquid-driven systems<br>Bubble contamination<br>Sample contamination<br>Avoiding low-field</td></tr><tr><td>7.</td><td>Dissolution physics</td><td>Relaxation theory generalities<br>Solid-state relaxation<br>Liquid-state relaxation<br>Coherent polarization loss</td></tr><tr><td>8.</td><td>Hyperpolarized liquid-state NMR</td><td>Detection parameters<br>Polarization quantification</td></tr></tbody></table>
## 2. Sample preparation for dDNP

### 2.1. Introduction

<figure><img src="image_2.png" /><figcaption>Figure 2: Picture of 10 uL drops of a sample frozen in liquid nitrogen, forming a homogeneous transparent glassy bead with 60% glycerol - 40% H₂O (right) or a milky microcrystalline bead with 40% glycerol – 60% H₂O (left).</figcaption></figure>

The motivation for this section is to give the basic requirements and suitable protocols for conventional sample preparation in dDNP experiments. We will explain the main requirements for dDNP samples to be optimally polarizable and give a step-by-step procedure to properly prepare, store and freeze the samples.

The main desired goal of dDNP sample preparation is to allow maximum polarizability of the molecule(s) of interest. The two most important features that enable a good sample polarizability are: (i) an adequate polarizing agent concentration (typically 10-50 mM); and (ii) an intimate mixing of the molecules of interest and the polarizing agents. This intimate mixing needs to be established at the sample preparation stage and should remain upon freezing, i.e., one should favour glassy state and avoid aggregates or microcrystals (see Figure 2). For this reason, in addition to water, co-solvents are often used which improve the probability of freezing the sample into a glassy state. The sample preparation protocol needs to be reproducible across laboratories, and we therefore provide a protocol that has proven to be reproducible in our laboratory. Finally, sample storage requires special attention as the paramagnetism of the polarizing agent may decrease with time.

### 2.2. Polarizing agents at the right concentration

Doping the dDNP sample with an adequate radical concentration is of utmost importance. However, very few studies report a thorough optimization of this parameter. The concentration usually lies between 10 and 50 mM, and the data available in the literature suggest that DNP performance is rather flat and robust within a certain range. For example, the radical 4-hydroxy-2,2,6,6-tetramethylpiperidin-1-oxyl, also known as TEMPOL, can be used for DNP at 9.4 T and 1.5 K, as presented in Figure 2.2 [59]. The DNP enhancements were measured for concentrations ranging from 25 to 100 mM. In all cases, the same mixture of H₂O/D₂O/glycerol-ds (1/3/6 v/v/v) was used. The optimal TEMPOL concentration is around 80 mM, somehow higher than the optima usually found at 6.7 T (50 mM) and 3.35 T (30 mM). Other concentration optimization studies are reported at other magnetic fields and in other sample formulations [42] [60].

<figure><img src="image_3.png" /><figcaption>Figure 3: a) Proton polarization P(H) and b) DNP build-up rates 1/τDNP as a function of TEMPOL concentration in H₂O/D₂O/glycerol-ds (1/3/6 v/v/v) at 9.4T and 4.2 K (open circles) or 1.5 K (filled circles). Adapted with permission from [59].</figcaption></figure>

### 2.3. The requirement to form a glass

The second criteria is that a glass should be formed upon freezing [35], [61]–[67]. Vitrification is necessary for a homogeneous distribution of radicals and substrates which enables efficient DNP and nuclear spin diffusion resulting in a spatially uniform nuclear spin polarization across the sample.

For frozen solutions, two solid forms can be found: glassy and crystalline (and also mixtures thereof) [68]. Crystal formation will introduce heterogeneity into the system by rejecting other molecules (radicals) at the crystal interface [69]. Such heterogeneity often leads to low DNP performance with some areas saturated with radicals and other areas free from radicals. This leads to stretched exponential build-up curves, rather that mono-exponential build-up curves, that have longer build-up time constants τDNP and with lower levels of final polarization (see Figure 4).
<figure><img src="image_4.png" /><figcaption>Figure 4: Example of ¹H DNP build-up curves measured at 7.05 T and 1.2 K for a glassy (black) and non-glassy (grey) sample.</figcaption></figure>

To avoid water crystallization, glass-forming agents are usually employed, such as glycerol (50-60%w) or DMSO (<77%w) [35]. Transitions from glassy states to crystalline states can occur even below the freezing temperature of the solution, by a mechanism called “cold crystallization” [70]. It is therefore important to store samples at sufficiently low temperatures before using them in order to avoid unexpected phenomena such as radical quenching or sample degradation. It was recently observed that spontaneous nanoscopic phase separation can occur in water/glycerol solutions although they appear macroscopically homogeneous [71], leading to reductions in polarization efficiency by up to 20%.

In order to check the sample health visually, 10 µl droplets of the solution can be dropped into liquid nitrogen. The resulting frozen beads should remain translucent, which is evidence of their glassy state, while partial crystallization leads to opaque beads (see Figure 2). The sample can then be transferred as is to the DNP polarizer at 4.2 K. During this process, if the water/glycerol ratio is not well respected, or if other glass-forming agents are used, the beads can become opaque. Figure 2 presents two frozen beads with the transparent one (right) considered as glassy and a milky opaque one (left) as micro-crystalline. Transparency in its own is not a strict warranty of non-crystallisation but rather an indication that the maximum size of the crystallites or domains are small compared to wavelength of visible light.

## 2.4. Preparation of a standard dDNP sample

### 2.4.1. General information

Here we describe the procedure for preparing a “standard” sample for DNP. Having a standard DNP sample is important in the context of dDNP in order to make sure that the DNP polarizer is performing well before switching to new sample formulations. We consider the example of a sample composed of 3 M [1-¹³C] sodium acetate dissolved in H₂O/D₂O/glycerol-d₈ (1/3/6 v/v/v) containing 50 mM TEMPOL. This is used by several groups as a reference sample. The storage of each compound and the preparation of the sample is important to get the best and most reproducible DNP performance. For example, when radicals are stored at room temperature, the concentration of the paramagnetic radical species can decrease over time; or if the glass-forming agent, glycerol in our case, is not meticulously mixed, the process of vitrification does not take place as expected, reducing overall DNP performances. Taking

that into account, we now present two ways of preparing a standard sample for dDNP. The first one allows one to prepare 10 aliquots of 100 µL to be then frozen and stored at -80°C for later or immediate use. The second for preparing each compound separately in advance and storing at -80°C to be in a position to rapidly prepare fresh new samples when required.

### 2.4.2. Preparation of a standard sample for frozen storage

Preparation of a 1 mL sample aliquoted into 100 µL batches and frozen. In a **graduated glass cylinder** weight precisely 249 mg of [1-¹³C] sodium acetate, for a 3 M final concentration. Note that after adding 1 mL of solvent, the total volume occupied by the solvent and the 249 mg of [1-¹³C] sodium acetate is approximately 1.2 mL. This has to be taken into account for calculating the final concentrations. Separately, weight in a microtube (**microtube A**) 8.6 mg of TEMPOL, to have a 50 mM final concentration. In a second microtube (**microtube B**), mix H₂O/D₂O/glycerol-d₈ (1/3/6 v/v/w), 100 µL of milli-Q water, 300 µL of D₂O (99.9%) and 822.6 mg of glycerol-d₈ (density: 1.371 g/mL). Dissolve the TEMPOL of **microtube A** with 6 µL of D₂O (the limit of the solubility in D₂O is 1670 g/L). Add 800 µL of **tube A** to the **graduated glass cylinder**. Sufficiently vortex and then sonicate for ~10 mins in a sonicator bath at 30°C. Repeat the last step until all is dissolved. Add the content of **microtube A** to the graduated glass cylinder. Adjust the volume with **microtube B** to 1 mL. Split the sample into 100 µl aliquots in separately labelled tubes. Store in a freezer at -80°C.

### 2.4.3. Preparation of the constituents of the standard sample for later rapid preparation

In 10 microtubes, weigh 25 mg of sodium acetate. Prepare 100 µL of 400 mM TEMPOL in D₂O (68.8 mg) and split into 8 microtubes (12.5 µL volume). Prepare 10 tubes with 68 mg glycerol-d₈ (~54 µL). Freeze all the microtubes (with clear labels!) in a -80°C freezer. To prepare a fresh sample: take 1 microtube of sodium acetate (a), 1 tube of TEMPOL (b), 1 microtube of glycerol-d₈ (c) and let them melt at room temperature. Mix (a) and (b) with 10 µL of milli-Q water, 12 µL D₂O and (c). Sufficiently vortex and then sonicate for ~10 mins in a sonicator bath at 30°C. Once the sample is ready to analyze, pipette 100 µL into a home-built sample holder and centrifuge for 4 seconds at 1000 rev/min on a benchtop centrifuge. Insert the sample carefully into the polarizer to avoid the formation of bubbles.

## 2.5. Alternative samples

Samples of interest can be loaded directly in porous DNP matrices with free radicals located on the surface of the pores or in the bulk of the matrix. In this case, there is a balance between advantages: no glass-forming agent is necessary, samples can be extracted from matrices reducing paramagnetic relaxation and molecules of interest can thus be separated from free radicals which could generally interact together in a conventional sample formulation [31]. There are also disadvantages: chemical synthesis could alter radicals, an optimal filtration system is needed, and overall performances are intimately related to the material properties: pore size, radical distribution and concentration. Some examples of such polarizing matrices are reported in the literature and are based on polymers or silica materials [42], [44], [72]–[77]. Nitroxides
can also be covalently attached to sepharose beads or on thermoresponsive gels. The porous thermoresponsive thermoplastic hydrogel, which can be dispersed as a powder in the sample, precipitates during the dissolution process [41], [43]. In these cases, the sample under investigation is dissolved in the appropriate solvent without cryo-protectant and the matrix powder is impregnated directly before loading into the polarizer. These polarizing media can be synthetized through published protocols, or provided upon reasonable request by our group concerning HYPSO or HYPOP materials.

As mentioned above, the choice of solvent and freezing technique is crucial in order to form a glass and have a homogeneous distribution of radicals and substrates to enable efficient spin diffusion and homogeneous polarization throughout the sample. However, it is sometimes difficult to freeze an aqueous solution quickly enough to form a glass using liquid nitrogen. An alternative method of sample preparation which removes the need for glass-forming agent is possible by increasing the freezing speed. It is well known that liquid alkanes have appreciably better heat transfer efficiencies than liquid nitrogen [78]–[80]. For instance, liquid ethane, propane and 2-methyl butane (isopentane) are all superior freezing agents for the vitrification of aqueous solutions.
### 3. dDNP sample health

<figure><img src="image_5.png" /><figcaption>Figure 5: Different derivatives of nitroxide derivatives that may co-exist in a DNP sample.</figcaption></figure>

#### 3.1. Introduction

The motivation for this section is to draw attention to important issues related to *d*DNP sample health that can be encountered, and to detail clear procedures to allow the user to assess the health of a *d*DNP sample.

Evaluating the *d*DNP sample health before performing dissolution experiments is highly desired in order to avoid unnecessary loss of time and resources working on unhealthy samples that may not give rise to expected DNP performances. Poor sample health systematically leads to slower polarization build-up times and lower overall polarizations. The two most common health issues for a *d*DNP sample are: (i) a PA concentration below its expected value; and (ii) an inadequate PA distribution (see Figure 4). Problems concerning these two sample requirements can arise even though great care has been given to the sample preparation. The next sections regarding the *d*DNP sample health will discuss the following important aspects in detail:

**PA stability.** The stability of the PA is a critical parameter, which depends on its chemical state and environment. The first goal of this section is not to review the stability properties of all PAs used in *d*DNP, but only for the nitroxide class of radicals. Their stability depends on different environments that are typically encountered. Indeed, the PA is usually provided in the form of a pure powder, and then dissolved in water, possibly together with a glass-forming agent such as glycerol, and finally together with the molecules of interest. The second goal of this section is to provide guidelines for PA and *d*DNP sample storage that guarantees the best PA stability and therefore most efficient and reproducible *d*DNP experiments.

**PA concentration and relaxation.** Poor handling of PAs often leads to a lower electron spin concentration in the final *d*DNP sample, which ultimately leads to reduced DNP performances (for short build-up times). Given the relatively long build-up times of typical DNP-compatible sample formulations, it is of interest to assess the sample health before polarizing the sample. This can in principle be done in a qualitative manner by simply measuring the nuclear spin-lattice relaxation towards thermal equilibrium right after insertion into the *polarizer*, i.e., without microwave irradiation and therefore without DNP, at 4.2 K (even before cooling the cryostat to its

lowest temperature). As shown in Figure 3, a lower active PA concentration tends to slow down the nuclear spin-lattice relaxation. Estimating this relaxation rate in about 5 minutes provides a way of qualitatively estimating the active PA concentration.

**Radical quantification.** Several methods exist to quantify radicals: gas and liquid chromatography [81][82], potentiometric analyses [83] and electron paramagnetic resonance (EPR) [84]. This last technique has the advantage, in our field, of also providing information about the EPR line, which can have a tremendous impact on DNP performance, mechanisms, etc. We will describe here a basic protocol for PA quantification in both liquid- and solid-state at room temperature using a benchtop X-band continuous wave EPR spectrometer. We will describe the calibration and data analysis in order to avoid as much as possible the classical pitfalls of quantitative EPR.

#### 3.2. PA choice

Several different radicals have been used in *d*DNP, such as trityl [79] and BDPA [80], which are both aromatic radicals, nitroxides [85] and Galvinoxyl [86]. The choice of the radical depends on the target nuclear spin and the polarization strategy. For instance, trityl and BDPA have sharp EPR lines and achieve good performances for direct ¹³C polarization while nitroxides have much broader EPR spectra and have better performances for proton and fluorine polarization. For our *d*DNP experiments, we use mainly nitroxide-based samples, and we therefore describe here how to avoid their degradation and how to handle them properly.

#### 3.3. Conservation of chemicals

As mentioned previously, standard samples are made of four classes of molecules: (i) radicals (polarizing agents); (ii) H₂O (or D₂O); (iii) glass-forming agents (glycerol, DMSO); and (iv) a target molecule (often ¹³C enriched) [9], [87], [88]. To perfectly control the composition of the sample which will be used in DNP experiments, good sample component storage is often the first requirement. D₂O, glycerol, nitroxides and ¹³C enriched target molecules should be stored at low temperature (~5°C) but should be carefully warmed up before use in order to avoid moisture which may contaminate these samples. The storage conditions can be more or less strict depending on the molecule: pyruvic acid which can degrade easily over time should be stored at -20°C whereas acetate can be stored at ~5°C for instance. However, under such conditions, it is perfectly possible to observe a decrease in the radical purity over a few months, which can be a major threat in the case that one does not have a means to quantify it. Both DNP performance and reproducibility may be greatly impacted.

#### 3.4. Nitroxide stability

"Stable" radicals are subjected to various threats depending on their chemistry (see Figure 5). For example, dimerization may be a non-negligible quenching mechanism of triarylmethyl (trityl) radicals while alpha-saturated nitroxides are not impacted by this mechanism under normal conditions [89], [90]. We will focus, in our case, on nitroxide stability by highlighting decomposition mechanisms that should be avoided. Based on a previous review of the subject [91], we show the Pourbaix
diagram of the most common nitroxides, e.g., TEMPO, including the redox equation of oxygen/water (see Figure 6).

<figure><img src="image_6.png" /><figcaption>**Figure 6:** Pourbaix diagram of TEMPO. Adapted with permission from [91].</figcaption></figure>

The greatest threat of nitroxide stability, under standard conditions of temperature and pressure, are acids (see Figure 7). Indeed, nitroxides are always in equilibrium with the associated nitrosonium ion (RN⁺O) and the hydroxylamine (RNOH or RN⁺OH²).

<figure><img src="image_7.png" /><figcaption>**Figure 7:** Disproportionation and comproportionation of TEMPO.</figcaption></figure>

This equilibrium between the radical and two other compounds is mainly ruled by the ability of the media to provide Brønsted acidity. A major advantage of this radical is its stability under basic conditions, which can also be a method to regenerate the radical. A simple way to see this clearly consists of plotting the Frost diagram of TEMPO (see Figure 8) as a function of pH. This diagram shows the free energy of each molecule as a function of their degree of oxidation, and as such lower free energies correspond to more stable states. At pH 10 and higher, nitroxide redox potentials are below those of the other two compounds. Such patterns indicate that the comproportionation mechanism is the leading reaction and the disproportionation can be considered as inactive.

<figure><img src="image_8.png" /><figcaption>**Figure 8:** Frost diagram of TEMPO. Hydroxylamine is considered as the reference with a neutral degree of oxidation.</figcaption></figure>

Furthermore, we can anticipate the opposite phenomenon for pH < 3, where the potential of nitroxides should become sufficiently high so that comproportionation need not be considered further. But in the pH interval ~3-11 both mechanisms co-exist and we need to consider kinetics to estimate the equilibrium of the system [91].

Another aspect that can be mentioned is the role of oxygen. It is a potential oxidant of radicals and may react differently depending on the type of radical. In our case, we will consider its role on the redox equilibrium of TEMPO. In Figure 9a, we plotted the apparent voltage potential of each reducer/oxidizer couple in two pH intervals (between 8.2 and 14 as well as between 4 and 8.1). We also consider the main reactions that should occur (see Figure 9b and 9c). For pH > 8.2, we can see that oxygen has a protective role as a weak oxidizer and so can only react with the RNOH form, which is favorable to the formation of nitroxides, already in good shape due to the comproportionation. However, for pH < 8.1, oxygen starts being the strongest oxidizer and can start reacting with TEMPO to form nitrosonium ions. Still, these reactions are not a major threat as long as pH > 8 but needs to be considered for lower pH.
<figure><img src="image_9.png" /><figcaption>Figure 9: Redox half-equations involved in the degradation of TEMPOL, including oxygen. a) Evolution of apparent voltage potentials for pH ∈ [8.2 14] and pH ∈ [4 8.1]. b) Main reactions involved for 8.2 < pH < 14. c) Main reactions involved for 4 < pH < 8.1.</figcaption></figure>

### 3.5. Degradation of nitroxides during storage

As discussed previously, nitroxide stability can be impacted by two major mechanisms during storage. Disproportionation generates both nitrosonium ion and hydroxylamine in the same amount. This phenomenon is mainly impacted by water, moisture or more generally the presence of protic solvents. Temperature and pH impact the thermodynamic equilibrium. Oxygen oxidation can also occur in solution, mainly by avoiding the formation of the hydroxylamine at high pH but can also impact nitroxides at pH < 8. Unlike the disproportionation, this reaction is asymmetric. Note that ascorbic acid, if used as a reducing agent, will have an effect opposite to oxygen. To illustrate the main phenomena involved we performed several tests on a 1.5-year-old batch of TEMPOL stored in our fridge (4°C). We weighted 3 samples for different purposes (see Figure 10a):

- The first sample (17.4 mg) was dissolved in 1 mL of THF, and then 100 µL of the mixture was analyzed by quantitative EPR to determine the concentration of radicals, and ultimately the “survival rate” of TEMPOL in the powder.

- The second sample (22.2 mg) was dissolved in 500 µL of a 10:1~THF/water solution. The mixture was diluted by a factor 5 in THF before EPR quantification on a 100 µL volume of the final solution. A nano-drop UV-vis analysis was performed on a droplet of this solution.

- The third sample (22.6 mg) was dissolved in 500 µL of a 10:1~THF/water solution previously saturated with NaOH. The mixture was diluted by a factor 5 in THF before EPR quantification on a 100 µL volume of the final solution. A

nano-drop UV-vis analysis was performed on a droplet of this solution.

EPR experiments were performed on a continuous-wave X band EMXnano apparatus from Bruker Biospin using 3 mm outer (OD) diameter quartz tubes provided by Wilmad. Data processing, including baseline corrections, were performed with the software of the spectrometer (Xenon). For experimental details, see next section. UV visible experiments were performed on a NanoDrop 1000 from Thermoscientific.

<figure><img src="image_10.png" /><figcaption>Figure 10: a) Sample preparation procedure. b) Percentage or “survival fraction” of TEMPOL radical used for each sample. Results from the original certificate of analysis are indicated as horizontal lines.</figcaption></figure>

EPR spectra show a significant degradation of this batch of TEMPOL (see Figure 6.b). However, we can observe a fast restoration of the TEMPOL radical in basic media. Such a fast mechanism, without bubbling oxygen, suggests that disproportionation occurred during the storage, meaning that the disproportionation can occur quickly under basic conditions without any stoichiometric issue. Such degradation could be explained by the presence of moisture due to the hygroscopicity of TEMPOL, which can be further increased by a bad handling, e.g., the product may still have been cold when opened. This degradation over time can become very important depending on how often the batch is handled and how. We already observed in our laboratory some TEMPOL survival fractions dropping below 70% over a few months, which can lead to significant detrimental effects on DNP performances.

To avoid such issues several simple rules can be applied:
- Buy small batches.

- Warm up carefully before each use.

- The hygroscopy of nitroxides being quite different (TEMPO < TEMPOL < amino TEMPO), use preferentially the less hygroscopic one.

- In solution, keep the media as basic as possible to be safe (pH > 10 being a very safe zone).

- Quantify radical purity by EPR if possible.

### 3.6. EPR quantification

Quantitative CW-EPR provides a way (not necessarily the easiest) to quantify radical concentrations [84]. For example, GC and iodometric titration are preferred by TCI to determine the purity of TEMPOL, whereas Sigma Aldrich uses infrared coupled to elementary analysis for TEMPOL or Thin layer chromatography for amino TEMPO. Furthermore, EPR spectrometers less frequently available compared to chromatography devices for example. EPR quantification is difficult and suffers from high uncertainties (ca. 5%). Despite this, EPR is a unique method which focuses on electronic spins and can provide a lot of relevant information in addition to the concentration of the radicals (EPR lineshape, radical dispersion, and presence of paramagnetic impurities, to name a few). Radical powders, e.g. TEMPO, are bought from Sigma Aldrich and used immediately when a calibration is required in our laboratory.

**Liquid calibration.** Standard solutions are prepared by mixing known amounts of TEMPO powder in a given volume of THF. Analyses can be performed in a 3 mm OD quartz tube from Wilmad with a 100 µL sample volume of the described solutions (2 cm sample height in each tube).

**Solid calibration.** Standards are prepared by mixing known amounts of TEMPO powder with KBr. Analyses are performed in a 4 mm OD quartz tube from Wilmad (2 cm sample height in each tube).

The EPR spectra are integrated before a baseline correction is performed (see Figure 11). Baseline corrections are performed using polynomials. EPR spectra are then integrated a second time. The resulting integrals are normalized using the following formula [84]:

$$I_{corrected} = \frac{\int_{325}^{355} S(B_0)dB_0}{Q_{factor} \times B \times \sqrt{P} \times NS \times 10^{RG} \times T_c} \quad (2)$$

with:

- $Q_{factor}$ Quality factor of the cavity used under our experimental conditions;

- $B_0$ Magnetic field (mT);

- $B$ Field modulation (Gauss);

- $P$ Microwave power (mW);

- $T_c$ Conversion time (ms);

- $NS$ Number of scans;

- $RG$ Receiver gain (dB).

$NS$ and $RG$ are both taken directly into account by the software. All spectra were obtained at room temperature.

$I_{corrected}$ values can be plotted as a function of the radical concentration within the sample to obtain a calibration curve. However, such a calibration curve obtained with a benchtop X-band EPR spectrometer Bruker EMX nano (see Figure 11) will

only be reliable if the samples are analyzed at the same temperature and with identical sample volumes.

<figure><img src="image_11.png" /><figcaption>Figure 11: a) Raw CW-EPR spectrum. b) Integrated EPR spectrum. c) Baseline corrected EPR spectrum. d) Solid-state calibration curve. e) Residuals of the solid-state calibration. f) Liquid-state calibration curve. g) Residuals of the liquid-state calibration.</figcaption></figure>
# 4. Characterization of microwave and radiofrequency systems

## 4.1. Introduction

<figure><img src="image_12.png" /><figcaption>Figure 12: Schematic overview of a *d*DNP *rf*-probe in the bore of a *polarizer*, including connections to essential apparatus: dissolution box (1e), microwave source (2a), oscilloscope (3d) and various *rf*-elements (3a-h). The sleeve of the *rf*-probe (1a) can accommodate the dissolution stick (1b), the microwave waveguide (2b) and co-axial cables (3a). The cavity contains the sample cup (1c), *rf*-resonator structure (1d) and coupling loops (3b).</figcaption></figure>

The motivation for this section is to describe the major components of a *d*DNP *rf*-probe and its accessories. We will explain the main characteristics of each element and provide a step-by-step procedure to correctly configure a *d*DNP *rf*-probe for optimal usage. These checks ensure that the *d*DNP *rf*-probe is in good condition before, during and after experiments.

The main function of a *d*DNP *rf*-probe is to provide an optimal environment to polarize a *d*DNP-compatible sample via a beam of microwave irradiation. The ability to measure NMR signals during the course of a *d*DNP experiment, with the objective of assessing the rate at which the polarization of the sample builds up, is greatly desired. Such a detection is possible with the *HyperSense* or *SPINLab polarizers* [92]. However, to be able to accurately quantify nuclear spin polarization and observe thermal equilibrium NMR signals without DNP in a sensitive, stable and quantitative manner requires more sophisticated instrumentation, such as the polarizer developed by Bruker Biospin. In a more advanced version presented here, the *d*DNP *rf*-probe can additionally feature cross-polarization (CP) capabilities, typically from sensitive ¹H spins to rare ¹³C spins, to boost both ¹³C polarization levels and build-up rates [23]. After sufficient levels of nuclear polarization have been achieved, the *d*DNP *rf*-probe must also provide a pathway to rapidly eject the sample from a frozen state with a jet of superheated solvent. The *d*DNP *rf*-probe also houses other elements essential to the successful usage of *d*DNP instrumentation (see Figure 12).

The next sections regarding the *d*DNP *rf*-probe will discuss the following important aspects in detail (Figure 12 components given in brackets):

**Probe construction.** The components of the *rf*-probehead are housed inside a non-magnetic sleeve (1a) usually made of brass or copper to ensure good thermal contact with the liquid helium cryogen. The *rf*-probe positions the *rf*-coil structure inside the bore of the *polarizer* at the magnetic sweet spot.

Through the centre of the *rf*-probe is a tube which acts as a guide for an insertion stick (1b) to position the sample cup (1c) at the location of the *rf*-resonator (1d). The geometry of the sample cup has to be optimized to maximize the *rf*-coil filling factor. The sample cavity needs to be used as a fluid path when the hyperpolarized sample is rapidly melted with a high temperature solvent and flushed out of the *polarizer* using pressurized helium gas. A dissolution stick (1b) and box (1e) are generally used for this process [9]. The brass material of the *rf*-probe framework, including cavity and microwave mirrors (2c), is suitable for use in cryogenic fluids, since it has good thermal conductivity, an extremely low thermal coefficient of expansion and is non-magnetic even upon machining [8], [93]. Stainless steel is used for parts that connect low and high temperature environments, since this material does not transport heat efficiently. The design permits a good flow of liquid helium towards the sample for efficient cooling, ultimately allowing an improved *d*DNP performance. Rubber o-rings are additionally used to make sure the *rf*-probe is secured tightly to both the bore of the polarizer and the sample insertion stick, which prevents the suction of air into the *rf*-probe and the consequential build-up of ice inside the cryostat when the *d*DNP system is being pumped.

**Microwave source.** A stringent requirement of all *d*DNP mechanisms is that the microwaves (2a) must irradiate the sample off-resonance, i.e., there must be a slight mismatch between the frequency of the microwave field and the electron transition frequencies. Coherent microwave irradiation is not strictly necessary, and as such oversized waveguides (2b) can be employed to minimize power losses during microwave delivery. Furthermore, the microwave waveguide material, commonly stainless steel, should possess suitable thermal properties to reduce heat losses from the superfluid liquid helium bath. The microwave waveguide will also typically contain a set of carefully positioned mirrors (2c), which directs the microwave beam down the *rf*-probe and allows it to shine onto the sample. If the microwave source can deliver a power in the order of a few tens of milliwatts by the time the beam reaches the sample, then a portion of the EPR line will become sufficiently saturated. For the best possible experimental results, it is imperative that the following steps are ensured: (i) the microwaves can be activated/deactivated/gated; and (ii) the positive and negative microwave irradiation frequencies, including associated frequency and bandwidth modulations, can be optimized.

**NMR system.** The *rf*-probe is comprised of a stainless-steel frame which securely holds co-axial cables (3a) in place, allowing *rf*-waves to travel to and from a number of coupling loops (3b) via a preamplifier (3c) to the NMR console (3d). The choice of a poor thermally conductive stainless-steel material limits heat transfer from the room temperature *rf*-connections to the cryogenically cooled *rf*-probehead. Most *d*DNP *rf*-probes are only capable of single *rf*-channel irradiation, and as such the *rf*-probe is usually implemented to monitor only the build-up of ¹³C polarization as a function of the microwave irradiation time [94]–[97]. The *rf*-probe requires tuning to the correct *rf*-frequencies and signal matching can be improved by sensible coupling coil design; particularly in the case of low-γ nuclei. Tuning the *rf*-channel frequency can be performed when the *rf*-probe is inside (using external tuning and matching devices (3e)) or outside (replacing circuit capacitors) of the *polarizer* [98], [99]. The *rf*-coil must produce a suitably homogeneous and stable B₁-field at high *rf*-pulse powers. Materials such as copper, silver and gold exhibit good cryogenic properties under
dDNP conditions [100] and are used in the coupling loops (3b) of the dDNP rf-probe. The favourable electrical conductivity is required to produce a strong B₁-field to excite nuclear spins, and subsequently amplify and detect the signal response with sufficient SNR. This further improves the tuning and matching capabilities of the rf-coil insert.

More functional dDNP rf-probes may contain 2 (or more) rf-channels, which allow for ¹H→¹³C/¹⁵N nuclear polarization transfer rf-pulse schemes, such as CP. The quality and filling factors of the rf-probe will substantially impact the ability to perform 90° rf-pulses at desired powers, which can be characterized by nutation experiments. Implementation of the CP approach requires excitation of the entire NMR lineshape for each rf-frequency (which can be challenging for high frequency spins) and the application of high-power double rf-irradiation. At high rf-powers, arcing can be frequently engendered in the superfluid helium bath which is deleterious to the transfer of nuclear polarization. Furthermore, cross-talk between rf-channels and rf-pulse reflections are also common in home-built dDNP rf-probes. It is possible to use a directional coupler (3f) to syphon a small quantity of power away from the transmitted and reflected rf-waves and send these signals to an oscilloscope (3h) protected by a 50 Ω resistance (3g). With such an architecture in place the above topics can be experimentally investigated, identified and characterized in the context of the rf-probe.

In the following sections, we will discuss the main points that ensure microwave source and rf-probe condition.

## 4.2. Probe construction

<figure><img src="image_13.png" /><figcaption>Figure 13: Photograph of the perpendicular coupling coils used for inductive detection attached to co-axial transmission cables. The ¹H channel uses a single loop, whilst the ¹³C channel employs three tightly wound loops of smaller diameter. This structure is housed within a brass “cap” whilst in liquid helium. The choice of a cylindrical rf-coil support is necessary to accommodate the sample dissolution stick and to fit into the bore of the polarizer. The two rf-coil loops are elliptical loops of 12×16 mm in diameter.</figcaption></figure>

The design of a dDNP probehead has to fulfil a number of constraints: (i) present a suitable space in which to perform adequate dDNP on a sample of interest; (ii) allow a beam of microwave irradiation to shine upon the sample; and (iii) monitor NMR signals throughout a dDNP experiment. Such requirements are met by the design shown in Figure 13, which shows a common arrangement of the microwave delivery conduit and the coupling loops used for inductive detection (Figure 12, 3b). Several geometries have been proposed for CP-

dDNP [9], [101] and herein we describe a probe setup with two geometrically decoupled channels [52].

The coupling loops are required to induce and detect the response of the nuclear spins within a dDNP sample. The design of the radiofrequency field coils depends on the information sought by the user. The design additionally allows detection of thermal equilibrium NMR signals without hyperpolarization, i.e., in the case where the SNR is low, and as a result; accurately quantify levels of nuclear spin polarization in a repeatable manner.

When constructing the coupling loops, as a rule of thumb, more sensitive nuclei require fewer turns, and the diameter of the loop can be larger. The converse is true for less sensitive nuclei. This will ensure a capacity for improved matching of the low-γ nucleus. The two coupling loops are made from silver-coated copper wire (95% Ag/5% Cu, OD = 1 mm) and should be perpendicular to each other. The coupling loops are connected to co-axial cables (Figure 12, 3a), which are soldered to the (electrical) ground-plate of the probe for structural rigidity. The co-axial cables are chosen to have the following special properties: (i) A stainless-steel outside to ensure a low thermal conductivity; and (ii) A copper beryllium central wire to ensure good electrical conductivity with a low thermal conductivity. The co-axial cables provide a way of shielding rf-irradiation during its journey to and from the NMR console (Figure 12, 3d) via a circuit containing preamplifiers (Figure 12, 3c).

<figure><img src="image_14.png" /><figcaption>Figure 14: Photograph of an rf-coil structure used for dDNP experiments, including: a plastic (KelF) support, copper coils and spacings for ceramic capacitors (not shown).</figcaption></figure>

A typical rf-coil assembly is depicted in Figure 14. There are two parallel rf-coils on the opposing faces of the rf-coil insert (¹H and ¹³C in the case of Figure 14). The rf-coil insert has been designed such that: (i) the dDNP sample cup (Figure 12, 1c) can fit into the resonator structure (Figure 12, 1d) with a maximized filling factor; and (ii) a brass cap can fit onto the rf-probehead without disturbing the central components. One downside of such an insert is the use of plastic (KelF) material, which although chosen to minimize the background ¹H NMR signal, nevertheless contains a non-negligible quantity of ¹H spins. This can be avoided by using a “background-free” rf-coil structure [102].

The majority of commercial dDNP rf-probes are configured for single rf-channel irradiation, and the nucleus of study is often chosen to be ¹³C. In this case, the rf-probe is designed to monitor the ¹³C polarization build-up curve before dissolution.
The beneficial choice of a design with two coupling loops is the detection of NMR signals from different isotopes. Polarization transfer methodologies such CP allow low-γ nuclei to be polarized and detected in significantly shorter time periods by transferring polarization from sensitive nuclear spins, e.g., ¹H. The freedom granted by this design allows for a number of opportunities for method development [103].

### 4.3. Sensitivity estimates

As discussed above, dDNP experiments are routinely conducted at temperatures of 1.2 K < *T* < 4.2 K and static magnetic field strengths in the range of 3.35 T < *B*₀ < 10.0 T. Under such conditions, we need to be able to provide an order of magnitude calculation regarding the sensitivity of a dDNP rf-probe per millimole. For a ¹H NMR spectrum acquired with 16 transients and a 0.1° rf-pulse angle, a typical proton SNR for a 100 µL sample of 3 M [¹-¹³C] sodium acetate in DNP juice™ at thermal equilibrium at 3.8 K and 7.05 T is ~155 (see Figure 15).

<figure><img src="image_15.png" /><figcaption>Figure 15: Relevant portion of the experimental ¹H NMR spectrum of a 100 µL sample volume of 3 M [¹-¹³C] sodium acetate dissolved in H₂O/D₂O/glycerol-ds (1/3/6 v/v/v) and doped with 50 mM TEMPOL without hyperpolarization at a temperature of 3.8 K. The spectrum was acquired at 7.05 T (¹H nuclear Larmor frequency = 300.13 MHz) and 3.8 K with 16 transients (rf-pulse angle = 0.1°).</figcaption></figure>

The concentration of polarizing agents is neglected in subsequent calculations for the sake of simplicity. Corrections are required in order to appropriately normalize the SNR for the number of transients and rf-pulse angle implemented to acquire the desired NMR spectrum. The correction factor is ~143 for the number of scans and rf-pulse angle given above (compared with a single transient and a 90° rf-pulse angle). A dDNP sample of this type will have a ~18.6 M ¹H sample concentration, and consequently the sensitivity per millimole is ~1.2·10⁴ mmol⁻¹. A similar calculation for ¹³C nuclei yields a sensitivity per millimole of ~1.1·10² mmol⁻¹. The low temperature of the superfluid liquid helium bath is largely responsible for the relatively good sensitivity of a typical dDNP rf-probe, since this aspect alone increases the thermal polarization by a factor of ~78.5, and likely outweighs the influence of the poor rf-coil filling factor, the excitation bandwidth and other deleterious aspects. Other reasons for the increase in sensitivity at liquid helium temperatures are: (i) a reduction in thermal noise; and (ii) an increase in Q-factor. It is worth noting that good performances are obtained despite ¹H

and ¹³C linewidths on the order of ca. 10-30 kHz for typical dDNP-compatible sample formations.

### 15. NMR system

#### 4.4.1. Tuning and matching

In order for the rf-coil structure (Figure 12, 1d) to resonate at the desired nuclear transition frequencies for the chosen nuclei and magnetic field, the rf-probe requires tuning to the correct frequency. This will maximize the NMR signal obtainable from an experiment. This is typically done by inserting capacitors into the circuitry. The value of the capacitances used for each rf-coil determines the frequency at which the rf-coils can absorb and re-emit rf-irradiation. The value of the capacitances should obey the laws of basic circuit theory:

$$ \omega_0 = \frac{1}{\sqrt{LC}} \quad (3) $$

where $ω_0$ is the resonant frequency of the rf-coil, *L* is the inductance of the circuitry and *C* is the total capacitance of the rf-coil.

The rf-coil frequencies are measured by placing the ¹H-¹³C rf-coil into the probehead of the dedicated dDNP probe. It is of paramount importance that the rf-coil structure is correctly aligned with the intended coupling loops, since the orientation of the rf-coils with respect to the coupling loops will alter the tuning and matching properties of the rf-probe. Alignment aids are suggested to help the reader to achieve this. Tuning the rf-coil to the correct coil frequency is an iterative process, which is impacted by the temperature of the rf-coil and of external tuning and matching devices (Figure 12, 3e), as shown in Table 2.

<table><caption>Table 2: Typical rf-coil frequencies and quality (Q) factors (at -3 dB) as a function of the rf-coil surrounding temperature and use of external tuning and matching devices. *ℓN₂* = liquid nitrogen, *ℓHe* = liquid helium. T&M = external tuning and matching device used. * = Desired tuning frequency at *B*₀ = 7.05 T.</caption><thead><tr><th rowspan="2">Conditions</th><th colspan="2">¹H</th><th colspan="2">¹³C</th></tr><tr><th>ω₀ / MHz</th><th>Q-Factor at -3 dB</th><th>ω₀ / MHz</th><th>Q-Factor at -3 dB</th></tr></thead><tbody><tr><td>No Cap</td><td>289.84</td><td>59</td><td>70.81</td><td>42</td></tr><tr><td>Cap</td><td>295.07</td><td>62</td><td>72.86</td><td>40</td></tr><tr><td>Cap + ℓN₂</td><td>298.21</td><td>155</td><td>73.69</td><td>73</td></tr><tr><td>Cap + ℓHe</td><td>299.20</td><td>201</td><td>73.90</td><td>97</td></tr><tr><td>Cap + ℓHe + T&M</td><td>300.14*</td><td>251</td><td>75.47*</td><td>113</td></tr></tbody></table>

It can clearly be seen, when stepwise adding the brass cap, cooling the rf-coils and using external tuning and matching devices (Figure 12, 3e), that the correct rf-probe frequency can be obtained for both rf-channels. It is worth noting, at least in the case of the ¹H rf-channel, that the initial rf-coil frequency is >10 MHz lower in frequency than the target rf-channel frequency. The case is less extreme for the ¹³C rf-channel. This demonstrates the strong influence of temperature etc. on the rf-probe frequencies. Depending on the available capacitors, it may be the case that the value of each capacitor has a certain tolerance. This suggests that rf-probe tuning is in fact an art which cannot be predicted. It is therefore best practice to target the desired nuclear transition frequency once inside the superfluid liquid helium bath of the polarizer, i.e., aim for the closest initial resonant frequencies in the absence of external
tuning and matching equipment, and subsequently use the external tuning and matching devices to finely optimize the desired frequency thereafter (Figure 12, 3e). Finally, the Q-factors for each rf-channel are not as high as for a typical liquid-state NMR probe. However, the lower Q-factors are sometimes useful for suppressing the effects of radiation damping [104], especially for protons.

<figure><img src="image_16.png" /><figcaption>Figure 16: Vector network analyser (VNA) attenuation traces of reflectance (dark blue curves) and transmittance (dark red curves) in units of dB acquired for the a) ¹H and b) ¹³C rf-channels of a dDNP rf-coil insert as a function of input frequency in units of MHz. The horizontal dashed lined marks -20 dB, and the vertical dashed line indicates the nuclear Larmor frequency for the nucleus of interest at cryogenic temperatures (~1.2 K) and 7.05 T (¹H nuclear Larmor frequency = 300.13 MHz, ¹³C nuclear Larmor frequency = 75.47 MHz).</figcaption></figure>

The use of external tuning and matching devices (Figure 12, 3e) at room temperature achieves both of the desired resonant frequencies, with good matching, as shown by the ¹H and ¹³C vector network analyser (VNA) attenuation traces in Figures 16a and 16b, respectively. The dark blue curves show the reflectance of each rf-coil, whilst the dark red curves show the transmittance of the rf-coils. Greater signal matching can also be achieved by improved coupling coil design, which is particularly useful in the case of low-γ nuclei.

The rf-coil has its own self-resonance, as stated above. The addition of co-axial rf-cables to the rf-probe does not change the self-resonance of the rf-coil. However, these co-axial cables, which are used to connect the rf-probe to the preamplifier of the spectrometer, and also incorporate external tuning and matching devices into the rf-circuit, induce spurious self-resonances involving a combination of the co-axial rf-cable, rf-coupling loop and the external tuning and matching devices. These resonances contribute an insignificant B₁-field at the position of the sample. The lengths of the co-axial rf-cables must be chosen as to set the spurious cable resonances as far away as possible (in frequency) from the self-resonance of the rf-coil. However, moving the rf-cable resonances slightly closer to the rf-coil self-resonance can be used to shift the frequency of the true rf-coil resonance, which is coupled to the rf-coil loop, co-axial rf-cables and tuning and matching system.

An ideal rf-coil would have a transmittance, i.e., the transmitted power from one rf-channel to the other, lower than

-20 dB. In the case of the ¹H rf-channel, the transmittance is clearly above -20 dB, indicating that there is likely cross-talk from the ¹³C rf-channel to the ¹H rf-channel, see Section 4.4.6. However, the fact that the transmittance is well below -20 dB for the ¹³C VNA trace indicates that the ¹H rf-channel does not interact strongly with the ¹³C rf-channel. Clearly, there are no visible effects of cable resonances in the vicinity of the desired rf-coil frequency.

### 4.4.2. Nutation frequency curves

<figure><img src="image_17.png" /><figcaption>Figure 17: Nutation frequency curves for the a) ¹³C and b) ¹H rf-channels of a rf-coil insert using a sample of 3 M [1-¹³C] sodium acetate dissolved in H₂O/D₂O/glycerol-d₈ (1/3/6 v/v/v) and doped with 50 mM TEMPOL acquired at liquid helium temperatures (~1.2 K) and 7.05 T (¹H nuclear Larmor frequency = 300.13 MHz, ¹³C nuclear Larmor frequency = 75.47 MHz).</figcaption></figure>

The choice of materials such as copper, silver and gold for the coupling loops (Figure 12, 3f) of the dDNP rf-probe allows the production of a strong, stable and homogeneous B₁-field to maximize the SNR of a dDNP experiment. Furthermore, the filling- and Q-factors of the rf-probe significantly influence the 90° rf-pulse characteristics, e.g., their duration for a given power. Such effects are investigated by nutation frequency curve experiments.

Figure 17a shows a ¹³C nutation frequency curve for a sample of 3 M [1-¹³C] sodium acetate dissolved in H₂O/D₂O/glycerol-d₈ (1/3/6 v/v/v) and doped with 50 mM TEMPOL acquired using the ¹³C rf-channel of a rf-coil insert (Figure 12, 1d). The duration of the ¹³C 90° rf-pulse was determined to be $τ_{90}^C = 10.9 µs$ at 150 W ¹³C rf-pulse power and a liquid helium temperature of ~1.2 K, which implies a ¹³C rf-pulse bandwidth of 22.94 kHz under the same conditions. This gives an rf-probe efficiency of $B_1/√W ≈ 1.87 kHzW⁻¹/²$, where $B_1$ is the rf-field amplitude and W is the power of the rf-pulse. This is sufficient to cover the frequency range of the ¹³C NMR lineshape for this sample under dDNP conditions (ca. ~30 kHz linewidth at FWHM). The effects of auto-refocussing are clearly observable at 270°, the NMR signal being more intense than for 90°. The ratio of the NMR signal intensities at the 90°
and 810° data points is ~0.71, which indicates a good rf-homogeneity of the ¹³C rf-channel of the rf-coil insert.

Implementation of CP methods requires sufficient excitation of the whole NMR line for both rf-frequencies. This is often difficult for high frequency spins, since high-power rf-irradiation is typically required, which can engender deleterious rf-probe arcing in the superfluid helium bath, see Section 4.4.5.

Figure 17b shows a ¹H nutation frequency curve for a sample of I acquired using the ¹H rf-channel of a rf-coil insert. The duration of the ¹H 90° rf-pulse was determined to be $τ_{90}^H = 5.6~μs$ at 60 W ¹H rf-pulse power and a temperature of ~1.2 K, which implies a ¹H rf-pulse bandwidth of 44.64 kHz under the same conditions. This gives an rf-probe efficiency of $B_1/√W ≈ 5.76$. This may be insufficient to cover the very broad ¹H NMR resonance in the case of high proton concentrations (ca. ~100 kHz linewidth at FWHM), in which case more sophisticated techniques can be employed [105]. Given the profile of the ¹H nutation frequency curve in Figure 17b, measured on a frozen dDNP sample, it may be the case that the bandwidth of the ¹H rf-pulse is insufficient to homogeneously excite the entire ¹H NMR resonance for long rf-pulse durations (>10 µs), when this phenomenon becomes more prominent. The ¹H nutation frequency curve would likely look much better in a liquid-state NMR sample. The inhomogeneity of the rf-pulses produced may contribute to the signal decay shown in Figure 17b. The effects of auto-refocussing are again observable at 270°. In this case, however, the ratio of the NMR signal intensities at the 90° and 810° data points could not be obtained.

### 4.4.3. Directional coupler usage

<figure><img src="image_18.png" /><figcaption>**Figure 18:** Directional couplers used to investigate rf transmission and reflection. Blue = connection to monitor ¹H rf-pulse reflection. Red = connection to monitor ¹H rf-pulse transmission.</figcaption></figure>

Figure 18 shows a photograph of a commonly used directional coupler (Figure 12, 3f) attached to the ¹H rf-channel of the preamplifier in our laboratory (Figure 12, 3c). Underneath, a second directional coupler can be seen connected to the ¹³C rf-channel of our preamplifier. The directional couplers are used to investigate the rf transmission and rf-pulse reflection. In the current configuration (blue shading), the directional coupler takes only a small fraction (-35.2 dB) of the rf-power and directs it to an oscilloscope (Figure 12, 3h). In this way, the reflection from both rf-channels can be observed. If the alternative configuration is used (red shading), the transmission of the rf-pulses of both rf-channels of the preamplifier can be investigated.

### 4.4.4. Oscilloscope protection

<figure><img src="image_19.png" /><figcaption>**Figure 19:** Photograph of 50 Ω resistors (grey shading) used to protect the oscilloscope whilst performing rf-coil cross-talk characterizations.</figcaption></figure>

To avoid damage to the oscilloscope (Figure 12, 3h) whilst investigating rf-coil reflections and arcing, protection of the oscilloscope is required (Figure 12, 3g). 50 Ω resistors must be attached to the rf-channels of the oscilloscope at all times, as indicated by the grey shading in Figure 19. The additional resistance due to these connections must be corrected for in the calculations, see Section 3.5. The 50 Ω resistor allows the oscilloscope to handle a ~5 W maximum power. Furthermore, the impedance of the oscilloscope is set to 1 MΩ and the 50 Ω resistor is in parallel so that the rf-power is absorbed by the resistor rather than by the oscilloscope. Such a preventive measure substantially reduces the chance of potential damage to the oscilloscope in cases where the rf-power exceeds the oscilloscope specifications. In reality, what is actually measured is the voltage generated across the resistor.

### 4.4.5. RF-probe arcing

Figure 20a shows an oscilloscope plot of ¹H (blue curve) and ¹³C (red curve) spin-locking rf-pulses implemented for a typical cross-polarization (CP) contact, see Section 5.6, using a ¹H-¹³C rf-coil insert (Figure 12, 1d) displayed in units of V (voltage) as a function of the CP contact duration (ms). Throughout the entire 7 ms CP contact time, the amplitude of the rf-pulses remains stable. This provides a good indication that there is no rf-probe arcing during the rf-pulses.
<figure><img src="image_20.png" /><figcaption>Figure 20: Oscilloscope voltage traces of square rf-pulses emitted by a rf-coil insert for a) 7 ms and b) 30 ms for ¹H (dark blue curve) and ¹³C (dark red curve) cross-polarization (CP) contact after 3 s of ¹H DNP acquired at ~1.2 K and 7.05 T (¹H nuclear Larmor frequency = 300.13 MHz, ¹³C nuclear Larmor frequency = 75.47 MHz). For details of the CP rf-pulse sequence, see Section 5.6.</figcaption></figure>

The oscilloscope plot displayed in Figure 20b provides an example of rf-probe arcing during the simultaneously applied ¹H and ¹³C rf-fields during the CP contact. The arcing limit was reached at ~1.2 K using rf-pulse powers of 120 W (¹H) and 300 W (¹³C), and a CP contact duration of 30 ms. The arcing event commences ~8 ms into the CP contact, at which point there is a significant jump in the ¹H rf-pulse voltage (blue trace). The ¹³C rf-pulse power (red trace) decreases slightly at the beginning of the arcing event. Arcing subsequently continues through the remaining duration of the CP contact rf-pulses. After arcing it is important to replenish liquid helium into the rf-probe space, since this will prevent further arcing in following experiments.

### 4.4.6. RF-coil reflection

Below we provide an example of how to quantify rf-pulse reflection between the rf-channels of the dDNP probe: Consider an rf-pulse of power $P_{trans}$, which is transmitted through a directional coupler (see Figure 12, 3f) with a given attenuation. The transmitted rf-pulse generates a reflection with a peak-to-peak (p2p) voltage of $V_{ref}^{p2p}$. The reflected p2p voltage can be readout directly using an oscilloscope (Figure 12, 3h). The power of the reflected rf-pulse $P_{ref}$ is determined by employing the following equation:

$$P_{ref} = \left( \frac{V_{ref}^{p2p}}{2\sqrt{2}} \right)^2 \cdot \frac{1}{R} (4)$$

where R is the circuit resistance. The attenuation factor $A_{dB}$, which is a result of transmitting the rf-pulse through a directional coupler, is given by the logarithm of the ratio of the square of the reflected $V_{ref}$ and transmitted $V_{trans}$ voltages, proportional to the power levels of the rf-pulses by the circuit current, according to the following equation:

$$A_{dB} = 10 \log \left\{ \left( \frac{V_{ref}}{V_{trans}} \right)^2 \right\} (5)$$

By using Equation 4, and often assuming a resistance $R = 50 \Omega$, see Section 4.4.4, we can estimate the power of the reflected rf-pulse $P_{ref}$. Typical rf-pulse reflections have powers which are on the order of ~5-10% of the value of $P_{trans}$. The same protocol can be used for any rf-pulse. Ideally, the best way to effectively tune and match an rf-probe would be to directly minimize the reflected power of the rf-pulses.

### 4.4.7. RF-probe maintenance

If a probe breaks, a sudden shift in the NMR tuning frequency for one of the rf-coil channels will be observed. This can also be detected by observing large rf-pulse reflections when pulsing. This usually implies one of three issues (listed in increasing order of severity):

(i) There has been a shear in the soldering. This is difficult to find, but will only require resoldering;

(ii) The metal contact of one of the capacitors has become detached from the central ceramic material. These are even more difficult to find, and can result in having to change all of the capacitors one by one in order to find the broken item;

(iii) A capacitor has “blown”. Sometimes this is relatively easy to spot, since the capacitor will be covered by black marks.

Such rf-coil repairs are necessary since using an external tuning and matching architecture to overcompensate for a mis-tuned rf-circuit would jeopardize the performance of the rf-probe, and the user should rather take precautions and change the damaged capacitor(s).
# 5. dDNP experiments

## 5.1. Introduction

The main goal of this section is to give a detailed description of the experimental protocol for setting up and optimizing direct ¹H (or other nuclear spin) DNP and ¹H→X cross-polarization (CP) DNP, and for quantifying the achieved solid-state polarizations and potential errors at any time of the DNP process. The main function of the DNP experiments that are carried out in the context of dDNP is to provide the user with maximal polarization levels, often for low-gamma nuclear spins X such as ¹³C, in a robust, repeatable, and quantified manner, and in a minimum amount of time.

The DNP experiments involve the measurement of the DNP build-up in a way that is precise, and free of all distortions or artefacts that can be present in a highly polarized and low temperature environment. Microwave irradiation needs to be carefully optimized in order to ensure the fastest and/or optimal DNP. Optionally, ¹H→X CP can be implemented along with a careful optimization of numerous parameters in order to further boost the polarization, here illustrated with ¹³C. Finally, the DNP signal may sometimes be compared with the thermal equilibrium signal, that is considerably lower in intensity, in order to properly quantify the nuclear polarization attained. This requires special care to ensure that the nuclear spin system has reached thermal equilibrium and is minimally perturbed in a controlled and quantifiable manner by the NMR pulses used to measure it. Although not often performed in practice, this thermal equilibrium measurement allows one to know the actual polarization levels prior to dissolution, and therefore to quantify the polarization losses that are brought about by the dissolution and transfer steps.

## 5.2. DNP build-up measurements

Measuring the direct DNP build-up of any particular nuclear spin, often ¹H or ¹³C, generally consists in the following steps:

(i) **Saturating** the initial polarization, either the thermal polarization or the polarization remaining from previous experiments, typically with a train of 90° pulses;

(ii) **Acquiring** NMR signals during the polarization build-up, with small angle pulses, at regular intervals;

(iii) **Estimating** the measured absolute polarization by comparing the polarized signal with a thermal equilibrium signal (measured without DNP, see Section 5.7), and;

(iv) **Analyzing** and possibly correcting for potential artefacts that may affect the estimation of the polarization, such as: (i) heteronuclear polarization transfer; (ii) polarization depletion, (iii) saturation of the receiver; (iv) lineshape effects; and (v) radiation damping.

**Saturating** the initial polarization sufficiently may appear trivial at first (with a simple 90° rf-pulse for example) but often turns out to be very challenging. Unfamiliar nuclear spin polarization transfer effects can come into play under dDNP conditions and interfere with efficient saturation. More precisely, the nuclear spin polarization of invisible spins (the so-called “hidden reservoir”) that are physically located near the electron spins (within the so-called “spin diffusion barrier”) and therefore strongly coupled to it, may have NMR frequencies far from the carrier frequency and therefore not be affected by the saturating rf-pulses [106]. This “hidden” polarization can replenish the polarization of the observed visible spins very

rapidly (on a millisecond timescale) during the saturation process, ultimately making the saturation appear incomplete. For that reason, proper saturation sometimes requires a series of 90° rf-pulses recycled a number of times with suitable delays so as to entirely deplete the polarization of the “hidden reservoir” (typically 10-30 pulses at 1 ms intervals, repeated 5-10 times at 100 ms intervals).

**Acquiring** the NMR signal during DNP (after switching on the microwaves) at regular intervals has to be done in a careful manner, but without significantly eroding the polarization nor saturating the receiver (low receiver gains are usually to be preferred especially for high nuclear spin polarizations). This is therefore usually carried out with small mutation angle rf-pulses (for example with 0.1 to 5° mutation angles applied every 1 to 5 seconds). The signal, and therefore the polarization, observed with an rf-pulse of mutation angle θ are proportional to $S ∝ P_0 sin θ$, while the remaining polarization after the pulse is $P = P_0 cos θ$, where $P_0$ is the initial nuclear spin polarization before pulsing. Often, the NMR signal can be acquired by an averaged series of n pulse-acquire blocks on a short timescale with respect to the DNP build-up time constant (typically 1 to 64 pulse-acquire events lasting less than a millisecond each, while DNP build-up times are on the order of several minutes). This strategy provides a way to combine high sensitivity without saturation of the receiver and minimal depletion of the building-up polarization. Under such circumstances, the measured summed signal is:

$$S_n ∝ P_0 sin θ ∑_{i=0}^{n-1} cos^i θ \quad (6)$$

While the SNR is:

$$SNR_n ∝ n^{-1/2} P_0 sin θ ∑_{i=0}^{n-1} cos^i θ \quad (7)$$

On the other hand, the remaining polarization at the end of the train of pulse-acquire events is simply:

$$P_n ∝ P_0 cos^n θ \quad (8)$$

As an example, if one measures the DNP signal with a single 5° rf-pulse, the observed signal amounts to ~8.7% of the one measured with a 90° pulse-acquire scheme while preserving as much as ~99.64% of the polarization (only ~0.4% is taken away). Typical values used for ¹H and ¹³C at different temperatures are given in Table 3. Figure 21 shows the NMR rf-pulse sequence used for pre-saturating and measuring a thermal or DNP build-up curve.

<figure><img src="image_21.png" /><figcaption>Figure 21: Sequence of rf-pulses used for pre-saturating and measuring a thermal equilibrium or DNP build-up curve. Experiments typically use the following parameters: n = 50; tDNP = 5 s; βΦ₁ = 0.1°; L = 128. RF-pulse and</figcaption></figure>
receiver phases: {$\Phi_1, \Phi_d$} = {x, x}. The resonance offset is placed at the centre of the ¹H NMR peak.

<table><caption>**Table 3:** Typical parameters used for measuring NMR signals under DNP conditions for ¹H and ¹³C nuclei in a 7.05 T Bruker Biospin prototype polarizer.</caption><thead><tr><th>Property</th><th colspan="2">¹H</th><th colspan="2">¹³C</th></tr></thead><tbody><tr><td>Temperature</td><td>3.8 K</td><td>1.2 K</td><td>3.8 K</td><td>1.2 K</td></tr><tr><td>τ<sub>DNP</sub></td><td>1-2 mins</td><td>3-5 mins</td><td>20-40 mins</td><td>1-2 hrs.</td></tr><tr><td>d<sub>1</sub></td><td colspan="4">20-30 s</td></tr><tr><td>RG</td><td colspan="4">1-8</td></tr><tr><td>θ</td><td colspan="4">1-5°</td></tr><tr><td>n</td><td colspan="4">1-8</td></tr></tbody></table>

Estimating the absolute polarization is usually performed by comparing the polarized signal with a thermal equilibrium signal acquired ideally on the same sample, but sometimes on another reference sample (such as line shape polarimetry), see Section 5.8. The measured polarization is:

$$P = P^{TE} \frac{S^{DNP}}{S^{TE}} \epsilon^{RG} \epsilon^{n,\theta} \quad (9)$$

where $P^{TE}$ is the thermal equilibrium polarization, and $S^{DNP}$ and $S^{TE}$ are the DNP and TE signal integrals, respectively. The correction factor for the receiver gain is:

$$\epsilon^{RG} = \frac{RG^{TE}}{RG^{DNP}} \quad (10)$$

with a small receiver gain $RG^{DNP}$ (with an assumed linear scale) often used for polarized signals (so as to prevent receiver saturation) while a higher receiver gain $RG^{TE}$ (typically > 4) is used for the thermal equilibrium signal so as to maximise the SNR (often plateauing for gains larger than 8 depending on spectrometer specifications). The correction ratio for the pulse angles used is:

$$\epsilon^{n,\theta} = \frac{\sin \theta^{TE}}{\sin \theta^{DNP}} \frac{\sum_{l=1}^{n^{TE}} \cos^{l-1} \theta^{TE}}{\sum_{l=1}^{n^{DNP}} \cos^{l-1} \theta^{DNP}} \quad (11)$$

With $\theta^{TE}$, $n^{TE}$, $\theta^{DNP}$ and $n^{DNP}$ being the rf-pulse nutation angles and numbers of scans used for thermal and polarized signals measurements, respectively. This correction ratio greatly simplifies when the nutation angles used for DNP and thermal equilibrium are the same $\theta^{DNP} = \theta^{TE} = \theta$:

$$\epsilon^{n,\theta} = \frac{(\cos \theta)^{n^{TE}-1}}{(\cos \theta)^{n^{DNP}-1}} \quad (12)$$

For a detailed explanation on the choice of these parameters for the thermal equilibrium signal measurement, see Section 5.8.

Analyzing and possibly correcting for potential artefacts is fundamental for properly estimating the polarization build-up rates or final polarization attained, or at least for being aware of existing sources of error. Here is a list of possible artefacts that might arise in the course of these measurements:

i) **Heteronuclear polarization transfers.** The nuclear spin polarization of other nuclear spins may be relatively high at the very start of build-up measurements, especially if not saturated. Therefore, depending on the DNP history of the sample, high polarizations of other nuclear spins may get

transferred to the measured nuclear spins either by direct nuclear→nuclear cross-relaxation (for example from abundant ²H spins in the case of partially deuterated DNP samples) or by more complex electron spin mediated polarization transfers such as the four-spin cross-effect [15] or thermal mixing [107]–[109][108]. Such effects may significantly affect the build-up curves, but in principle not the final polarized steady state (if one waits long enough). Such heteronuclear polarization transfer effects become more intense and problematic when measuring signals with weak DNP enhancements, especially when other nuclear spin species are highly polarized.

ii) **Polarization depletion.** Measuring the NMR signal necessarily implies eroding the nuclear spin polarization. An acquisition performed with a series of n pulses of nutation angle $\theta$ will result in an attenuation of the resulting averaged signal measured by a factor $\frac{1}{n} \sum_{l=1}^{n} \cos^{l-1} \theta$ accounting for the nuclear spin polarization remaining for each successive scan. In many cases, for example when the polarized signal needs to be compared with the thermal equilibrium signal for evaluation of the nuclear spin polarization, this needs to be carefully evaluated. This is far from being trivial as it requires a very precise knowledge of the nutation angle used. An error of a few percent on $\theta$ can have tremendous impact on the estimation of the polarization, further worsened when using large numbers of pulses n. The following experiment allows one to very precisely evaluate $\theta$ directly on the DNP sample during the course of the experiment. We call it the *angle-tune* experiment.

<figure><img src="image_22.png" /><figcaption>**Figure 22:** Angle-tune approach, where *k* trains of *N* pulse-acquire experiments are performed on a timescale which is very short compared to nuclear-spin lattice relaxation. Each of the *N* pulse-acquire signals is Fourier transformed, integrated and plotted here as a function of the number *k* of *N* pulse-acquire events. The decay of the acquired signals, solely due to the depletion of polarization by the applied pulses, can be fitted with equation $S_k = S_0 \cos^{kN} \theta$ to precisely determine the nutation angle.</figcaption></figure>

It simply consists of repeating the series of *n* pulse-acquire segments a small number of times with a short delay, compared to the build-up time constant, and then evaluating precisely the
polarization losses induced by this series of n pulses. One can fit the decay of signal intensities from successive experiments, and determine θ with very high precision, with the following function:

$$S_k = S_0 \cos^{kN} \theta \quad (13)$$

where S₀ is the signal integral after the application of the first rf-pulse, N is the number of scans per acquisition block and k is the number the pulse-acquire blocks.

iii) **Saturation of the receiver.** Measuring highly polarized signals often requires the use of a small receiver gain and small mutation angle rf-pulses so as to avoid saturating the receiver. Saturation of the receiver is a recurrent issue in dDNP and usually implies noticeable anomalies in the free induction decay and Fourier transformed signals.

iv) **Lineshape evolution.** During the course of a DNP experiment, the nuclear spin polarization of one or several nuclear spin species often dramatically increases, violating the high spin temperature approximation, even sometimes approaching values very close to unity. This can lead to changes in NMR lineshapes as observed and reported in some studies [110]–[120]. Such changes in lineshapes are theoretically not a problem for polarization estimation. Indeed, the NMR signal integrals are by nature proportional to the polarization. However, this is only true when the signal is being measured without any dead time after the application of an infinitely short rf-pulse. In practice, NMR rf-pulses and spectrometer dead times (between pulse and acquisition) are typically on the order of a few (typically 5) microseconds each. On the other hand, under dDNP conditions, nuclear spin T₂* can be as short as tens of microseconds. Changes in NMR lineshape can result in significant changes in T₂* decay happening during the pulse and dead time. As a result, NMR integrals can no longer be considered proportional to the polarization, and polarization estimation can become inaccurate.

v) **Radiation damping.** The large magnetization brought about by DNP can lead, under some circumstances, to massive radiation damping effects [121], [122]. Radiation damping can greatly change the NMR lineshape as shown in Figure 23, which can lead to dramatic inaccuracies in polarization estimations. Such radiation damping can lead to the observation of unusual NMR masers under dDNP conditions as reported recently [122]–[124]. Radiation damping can sometimes be avoided either by reducing the sample volume, and/or detuning or lowering the quality factor of the NMR circuit, or by implementing more sophisticated suppression methods [121].

<figure><img src="image_23.png" /><figcaption>Figure 23: Typical ¹H NMR signal measured at 1.2 K on a DNP sample with narrowing by radiation damping of the NMR linewidth for</figcaption></figure>

negative polarization (blue) or broadening of the NMR linewidth for positive polarization (orange).

### 5.3. Microwave optimization

Very few studies report careful optimization of microwave parameters. However, this is key for efficient DNP and sometimes performances can be further boosted by applying a frequency-modulated microwave irradiation rather than a monochromatic one. Microwave irradiation parameters to be optimized are:

(i) Frequency $f_{μw}$;

(ii) Modulation type (usually simply triangular);

(iii) Modulation breadth $\Delta f_{μw}$;

(iv) Modulation rate $f_{mod}$; and

(v) Power $P_{μw}$.

The optima of these parameters can depend on many factors such as:

(i) Static magnetic field strength;

(ii) Sample temperature;

(iii) Polarizing agent (PA) type;

(iv) Concentration of PAs;

(v) Space distribution of PAs.

In principle, after changing one of these microwave parameters, a DNP build-up needs to be measured over a sufficiently long timescale to attain full DNP equilibrium. In practice, DNP studies often report parameter optimization with short DNP times (therefore without reaching DNP equilibrium). The microwave frequency modulation and power optimization has been described in detail [125]. Further experiments on frequency modulation have been reported and interpreted using numerical simulations [126].
<figure><img src="image_24.png" /><figcaption>**Figure 24:** (a) ESR lineshape of TEMPOL measured by longitudinally detected ESR (LODESR) in a DNP polarizer at *T* = 1.2 K and *B*₀ = 6.7 T. (b) Proton polarization *P*⁽¹H⁾ with and without frequency modulation (Δ*f*<sub>μW</sub> = 100 MHz) in a H₂O/D₂O/glycerol-*d*₈ (1/4/5 v/v/v) mixture with 25 mM TEMPOL, as a function of microwave frequency and (c) as a function of microwave power. Lines are drawn to guide the eye. Adapted with permission from [125].</figcaption></figure>

Figure 24a shows the electron spin resonance (ESR) signal of TEMPOL measured under dDNP conditions by longitudinally detected ESR (LODESR) [47]. Each point of Figure 24b shows the ¹H polarization *P*(*H*) attained for different microwave frequencies *f*<sub>μW</sub> with and without microwave frequency modulation. Such curves displaying polarization versus microwave frequency are usually called *DNP spectra* or *DNP profiles*. The figure shows that frequency modulation and central irradiation frequency are interdependent parameters, and that using microwave frequency modulation significantly increases the optimal polarization that can be reached by DNP (in this particular example). Figure 24c shows how by using microwave frequency modulation, one can afford better DNP performances with less microwave power *P*<sub>μW</sub>. In this example the polarization was measured for steady-state DNP, which is not often the case for other studies. One should be aware that measuring DNP optima at short times (compared to the DNP build-up time) can result in great distortions of the so-called DNP spectrum and can therefore lead to a suboptimal choice of microwave parameters. This distortion in DNP spectra arises as soon as DNP build-up rates vary as a function of microwave parameters. Figure 25 illustrates clearly how much polarization build-up rates (or times) can vary across the DNP spectrum, by as much as an order of magnitude.

<figure><img src="image_25.png" /><figcaption>**Figure 25:** Polarization time constants τ<sub>pol</sub> measured across the DNP spectrum with 50 mM TEMPOL at 5.0 T. Adapted with permission from [127].</figcaption></figure>

The microwave modulation rate *f*<sub>mod</sub> and breadth Δ*f*<sub>μW</sub> similarly need to be optimized (see Figure 26). The modulation seeks to provide a way of saturating electron spins over a broader band of the ESR spectrum. It therefore needs to be performed at a rate higher than that the electron spin lattice relaxation rate 1/*T*<sub>1e</sub>. This is experimentally observed by the fact that DNP reaches an optimum at sub-kHz modulation frequencies (see Figure 26a). The modulation amplitude also needs to be carefully optimized so as to saturate an appropriate portion of the ESR line that gives rise to constructive DNP. The optimum of the modulation amplitude is usually reached at a fraction of the total ESR width, and DNP tends to deteriorate when modulation is further increased (see Figure 26b).

<figure><img src="image_26.png" /><figcaption>**Figure 26:** Proton polarization *P*⁽¹H⁾ in a H₂O/D₂O/glycerol-*d*₈ (1/4/5 v/v/v) mixture with 25 mM TEMPOL at 1.2 K and 6.7 T (a) as a function of the frequency of the modulation *f*<sub>mod</sub> (with a fixed amplitude Δ*f*<sub>μW</sub> = 100 MHz and power *P*<sub>μW</sub> = 87.5 mW) and (b) as a function of the modulation amplitude Δ*f*<sub>μW</sub> (with a fixed modulation frequency *f*<sub>mod</sub> = 10 kHz and power *P*<sub>μW</sub> = 87.5 mW). Adapted with permission from [125].</figcaption></figure>

### 5.4. *Effect of radical concentration*

The PA concentration is an important parameter that needs to be optimized as it has a great impact on DNP performance. Figure 27 shows DNP spectra and DNP build-up times (without
microwave modulation) measured for different TEMPOL concentrations ranging from 20 to 65 mM. Changing the PA concentration not only greatly affects the DNP spectrum and therefore the DNP optimum, but also significantly affects the DNP build-up times (here measured at T = 4.2 K).

<figure><img src="image_27.png" /><figcaption>Figure 27: a) Proton polarizations $P(^{1}\text{H})$ and b) DNP build-up times for TEMPOL at different concentrations in the range 20–65 mM, for different microwave frequencies 187.5 < $f_{\text{muW}}$ < 188.5 GHz, at $B_{0}$ = 6.7 T and T = 4.2 K. Adapted with permission from [60].</figcaption></figure>

Once the optimal PA concentration is found, together with its optimal microwave irradiation parameters (see Section 5.3), any significant change in DNP, or simply $T_{1}$, time constants, or DNP performances over time is characteristic of either an experimental imperfection (damaged microwave source or attenuated microwave beam), or a sample formulation issue (inadequate radical concentration or scavenged radicals [51]). Therefore, when no ESR apparatus is at hand, simply measuring the $T_{1}$ relaxation at 4.2 K (usually on the order of a minute for $^{1}\text{H}$) can be a simple tool to assess the sample condition, and more precisely the PA concentration and/or distribution, see Section 3.5.

### 5.5. Effect of temperature and field

DNP is usually performed at temperatures down to ~1.0 K in helium bath cryostats pumped down to the millibar range (temperatures lower than ~0.9 K are more challenging and not practical for dDNP). Going to low temperatures has the advantage of maximizing the electron polarization and therefore the DNP efficiency, however, at the price of longer DNP build-up time constants. Another means of further increasing the electron spin polarization consists of increasing the magnetic field. During the last decade, thanks to the development of high frequency microwave sources that can deliver sufficient power (usually >10 mW needed), DNP has been performed at increasingly higher magnetic fields [59], [127]–[130], ultimately providing electron polarization levels close to unity. Figure 28 shows how temperature and magnetic field affect polarization values and build-up times.

a)

<figure><img src="image_28.png" /><figcaption>Figure 28: (a) $^{1}\text{H}$ polarizations $P(^{1}\text{H})$ and (b) DNP build-up time constants $\tau_{\text{DNP}}$ in 3 M [1-$^{13}\text{C}$] sodium acetate in D$_{2}$O/ethanol (2/1) at different temperatures with 30 mM and 50 mM TEMPOL at $B_{0}$ = 3.35 T (black) and 6.7 T (grey), respectively. Data adapted with permission from [32].</figcaption></figure>

### 5.6. $^{13}\text{C}$ CP optimization and multiple-CP

DNP is usually performed on low-gamma nuclear spins such as $^{13}\text{C}$ because of their long $T_{1}$ in the liquid-state after dissolution. The most straightforward way to polarize $^{13}\text{C}$ spins consists of directly transferring the electron polarization from adequate PAs such as TEMPO(L) [131], trityl [132], BDPA [133], Galvinoxyl [86], DPPH [37] or other radicals. Amongst these PAs, some have the property of polarizing $^{1}\text{H}$ spins as well (in particular when their ESR spectra are wider than the $^{1}\text{H}$ NMR frequency). In that case, not only $^{1}\text{H}$ spins become polarized, but they become polarized faster and to higher levels (presumably due to the higher gyromagnetic ratio leading to higher DNP transition probabilities, and also presumably faster spin diffusion). It is therefore of interest to combine DNP with cross-polarization (CP) [54] methods in order to take advantage of the highly and rapidly building-up $^{1}\text{H}$ polarization, and transfer it to the less polarized $^{13}\text{C}$ spins [52], [98], [129], [134], [135]. CP under dDNP conditions is very challenging since NMR lines are very broad (typically 10-100 kHz in linewidth) and therefore requires the application of intense rf-fields, during extended periods (typically 1-10 ms) in superfluid helium. This can easily result in probe arcing, see Section 4.5.5, and result in the failure of CP experiments. However, suitable rf-probe design (see Section 4.2 for an example of an rf-coil design suitable for low temperature CP), combined with suitable CP rf-pulse sequences have enabled the preparation of very high $^{13}\text{C}$ polarizations with CP in very short timescales. CP provides a way of consistently polarizing a broad range of molecules in standardized DNP solutions, usually containing around 10 M of $^{1}\text{H}$ spins to ensure proper $^{1}\text{H}$ spin diffusion and high proximity to the $^{13}\text{C}$ spins, which facilitates the CP transfer.
Demonstrations have been made showing that CP can work equally well with very low ¹³C abundance (for example in natural samples [136], [137]) or even with deuterated molecules, where CP operates solely from the ¹H's of the solvent [138]. One major challenge of such an approach is related to the scaling-up of the sample size (for example for clinical studies) which inevitably requires more rf-power and exacerbates arcing issues. Alternatives to conventional CP requiring less rf-power are currently being developed and implemented in the context of dDNP [139], [98]. The CP strategy that we describe here is the one currently used in the context of dDNP that has proven to yield best performances until now.

<figure><img src="image_29.png" /><figcaption>Figure 29: Pulse sequences used for a step-by-step optimization of the cross-polarization rf-pulse sequence.</figcaption></figure>

The CP rf-pulse sequence used, and its optimization steps, are shown in Figure 29:

(a) **Initializing the polarization.** Saturation of the ¹H and ¹³C polarization by a train of 90° rf-pulses, followed by a polarization time (typically 5 s) so as to build-up a repeatable ¹H polarization, and finally a microwave gating time (typically 0.5 s) [23] so as to let the electron spins relax to a highly polarized state. Microwave gating results in a dramatic reduction of paramagnetic relaxation during CP and therefore significantly increases the overall performance [23].

(b) **Inspecting the initial ¹H polarization level.** Measurement of the ¹H NMR signal with a small angle pulse (typically 1°).

(c) **Checking that the adiabatic rf-pulses preserve ¹H polarization.** An adiabatic half passage (AHP) rf-pulse sweep from -100 kHz to the center of the line in 175 ms (with a sweep rate of 0.57 kHzms⁻¹) brings the ¹H magnetization in the transverse plane (with a pulse strength of typically γB₁(¹H)/(2π) = 10-20 kHz), followed by a similar AHP rf-pulses sweep from the center of the line to -100 kHz to restore the ¹H magnetization along z, followed by the measurement of the ¹H NMR signal with the same small angle pulse as in step b (typically 1°). The measured signal is compared with the one measured in step b, and typically ~90% is preserved.

(d) **Checking that the spin-lock preserves ¹H polarization.** A rectangular pulse with the same phase as the adiabatic rf-pulses is placed in between the two adiabatic rf-

pulses (with an rf-pulse strength of typically γB₁(¹H)/(2π) = 10-20 kHz, and a length incremented from typically 100 µs-5 ms). The measured signal should not show any significant decay during the spin-locking period if the microwaves have been gated off (see Figure 30). At this point, one is reassured that the CP sequence does not wipe out the ¹H polarization, and one can therefore implement the full sequence.

<figure><img src="image_30.png" /><figcaption>Figure 30: ¹H polarization measure after a spin-locking period with the rf-pulse sequence described in Figure 30d with and without microwave irradiation. Adapted with permission from [23].</figcaption></figure>

(e) **Transferring the ¹H polarization to ¹³C.** A replica of the ¹H pulse sequence is applied on the ¹³C nuclear spins simultaneously, with identical adiabatic and spin-locking rf-pulses, and the ¹³C signal is measured with a small angle rf-pulse (typically 5°). The rf-pulse power on the ¹³C (or ¹H) rf-channel is optimized in order to match the so-called Hartmann-Hahn condition [53] so as to yield the best transfer of polarization. The length of the ¹³C and ¹H spin lock pulse is optimized separately (typically 1 to 10 ms length) (see Figure 31a for typical optimization curves of the CP contact time). Optionally, one of the square locking pulses can be replaced by a ramp (typically a 50→100% or 80→100% amplitude ramp) to compensate for potential rf-coil B₁-field inhomogeneities.

**Repeating the CP transfer at optimal time intervals.** The maximum ¹³C polarization is rarely attained with a single CP transfer step, but rather after a series of CP steps performed with optimal time intervals between them. This time interval needs to be experimentally optimized and usually lies between once and twice the ¹H DNP build-up time. This can be understood by the fact that one needs to wait after a CP step, for the ¹H polarization to build up close to its maximum, before performing another CP step. Figure 31b shows a typical multiple-CP build-up with and without microwave gating. More details regarding the behaviour of the ¹H polarization during the multiple-CP experiment can be found in [23]. A detailed study of the optimization of the inter CP delay can also be found in [140].

<figure><img src="image_31.png" /></figure>
<figure><img src="image_32.png" /><figcaption>**Figure 31:** a) <sup>13</sup>C signal amplitudes after a single CP transfer from <sup>1</sup>H to <sup>13</sup>C as a function of the CP contact time τ<sub>CP</sub>. b) Build-up of <sup>13</sup>C polarization P(<sup>13</sup>C) during a multiple-CP experiment with a CP step applied every 2.5 minutes. All data measured with continuous (●) or gated (○) microwave irradiation with P<sub>μW</sub> = 87.5 mW, f<sub>μW</sub> = 188.3 GHz, Δf<sub>μW</sub> = 50 MHz and f<sub>mod</sub> = 10 kHz in a 3 M sodium [1<sup>-</sup><sup>13</sup>C]acetate solution doped with 40 mM TEMPOL at 1.2 K and 6.7 T. Adapted with permission from [23].</figcaption></figure>

## 5.7. Thermal equilibrium

Measuring the thermal equilibrium signal of a given sample at a given temperature is in principle the best practice for enabling an accurate quantification of its absolute polarization at any time of a DNP experiment.

**When should one measure it?** Thermal equilibrium is best measured before any DNP is performed, after the insertion of the sample in the polarizer, so as to prevent heteronuclear polarization transfers from other polarized spins, see Section 5.2. The thermal equilibrium signal must, however, be measured after a sufficiently long time to allow the nuclear spins to reach their thermal equilibrium population distribution.

**At what temperature should one measure it?** The sample temperature at which the thermal equilibrium should in principle be measured is ideally the same temperature at which the DNP experiment is carried out, so as to make sure that the *rf* properties of the NMR circuit do not change (in particular the *Q*-factor of the probe, and therefore the sensitivity and *rf*-pulse angle for a given power and *rf*-pulse length). Therefore, one would theoretically prefer to measure the thermal equilibrium signal around 1 K. This is however rarely done in practice because *T*₁ relaxation times tend to become excessively long at such temperatures (typically several hours for <sup>13</sup>C [141]). In order to measure the thermal equilibrium signal in reasonable time, one should better measure it at around 4.2 K (or even better at a fixed pressure slightly below atmospheric pressure, resulting in a precise fixed temperature close to 4 K, typically 3.8 K in our studies). Under such conditions, nuclear spin-lattice relaxation times in the presence of free radicals are generally around a few minutes for <sup>1</sup>H and less than 1 hour for <sup>13</sup>C, depending on the spin system under investigation and the sample radical concentration. However, one has to make sure that the *rf* properties are unchanged, for example, by monitoring the *Q*-factor of the probe with a network analyzer (as explained in Section 4.4.1). At a given magnetic field and temperature, the fully relaxed thermal equilibrium polarization of a spin ½ ensemble can be calculated with Equation 1.

**How should one measure it?** A procedure routinely used to measure the thermal equilibrium is the following:

(i) **Saturating** the initial polarization (thermal polarization or polarization remaining from previous experiments), typically with a train of 90° *rf*-pulses;

(ii) **Acquiring** NMR signals at regular intervals during the polarization build-up, with small θ<sup>TE</sup> and n<sup>TE</sup> so as not to deplete the polarization that is building up, however, with sufficient RG<sup>TE</sup> so as to maximise sensitivity, see Section 5.2;

(iii) **Estimating** the relaxation time and ensuring that a steady-state thermal equilibrium is attained (see Figure 32);

(iv) **Acquiring** an NMR signal S<sup>TE</sup> possibly with enhanced sensitivity for better estimation of the polarization (see Figure 33), i.e., with larger θ<sup>TE</sup> and number n<sup>TE</sup> of pulse-acquire events, see Section 5.2;

(v) **Subtracting the background signal**, arising from the sample cup and the *rf*-probe itself, measured without DNP sample, with the same procedure (i→iv).

<figure><img src="image_33.png" /><figcaption>**Figure 32:** a) <sup>1</sup>H build-up of the background (BG) signal and thermal equilibrium signal with background (TE+BG), and after subtraction of the background (TE). b) Corresponding NMR spectra. Experiments were performed at 3.8 K and 7.05 T on a 100 mT sample of 3 M [1<sup>-</sup><sup>13</sup>C] sodium acetate solubilized in H₂O/D₂O/glycerol-d₈ (1/3/6 v/v/v) containing 50 mM TEMPOL. Parameters for signal acquisition were: θ<sup>TE</sup> = θ<sup>DNP</sup> = 0.1°, n<sup>TE</sup> = n<sup>DNP</sup> = 64, RG<sup>TE</sup> = 16 and RG<sup>DNP</sup> = 0.25.</figcaption></figure>

Often, for <sup>1</sup>H spins, a more sensitive acquisition is not always required, as relatively high SNRs are attained with very small nutation angle *rf*-pulses (typically 64 *rf*-pulses of 0.1°) leading to an insignificant depletion of only 0.001% of the initial polarization. For <sup>13</sup>C, the build-up of the thermal equilibrium signal is typically acquired with 5° *rf*-pulses (a small number, typically 1 to 4, for minimal saturation but sufficient sensitivity) applied every 5 to 20 minutes, followed by a train of up to 64 *rf*-pulses of 5° so as to maximize sensitivity. Figure 33 shows how remaining polarization and resulting sensitivity are affected by the number n<sup>TE</sup> of 5° pulse-acquire events used for measuring the NMR signal. As an example, a train of n<sup>TE</sup> =
16 pulse-acquire units with a nutation angle of 5° results in an NMR sensitivity corresponding to 33.4% of the maximal theoretical SNR (of a single 90° pulse-acquire event), while depleting the polarization by only 6%.

<figure><img src="image_34.png" /><figcaption>**Figure 33:** Polarization fraction remaining as a function of the number of 5° rf-pulses applied (blue) and corresponding SNR obtained (red, normalised with respect to a single 90° pulse-acquire experiment).</figcaption></figure>

A substantial depletion of the ¹³C polarization is necessarily induced by such an approach, but this does not matter in principle since the DNP sample is meant to be subsequently re-polarized. The depletion can be estimated by directly repeating the same acquisition as described in Section 5.2 and Figure 22 (using the so-called angle-tune experiment). Such a procedure provides a way to both measure a thermal equilibrium signal with good sensitivity and estimate the nutation angle precisely which is important to quantify precisely the absolute polarization brought by DNP.

**What if it cannot be measured?** Sometimes the thermal equilibrium signal cannot realistically be measured because of the low number of spins in the sample (for example, in the case of low concentrations of molecules at ¹³C natural abundance), or because nuclear spin-lattice relaxation times turn out to be too long (for example, with low concentrations of PAs below 10 mM). In such cases, provided that the number of nuclear spins in the sample is known, one can estimate the polarization by cross-calibrating with a reference sample with a higher known number of nuclear spins (ideally fast relaxing). One example of such a reference sample cited earlier that has sometimes been used in our laboratory is a 3 M [1-¹³C] sodium acetate solubilized in H₂O/D₂O/glycerol-d₈ (1/3/6 v/v/v) containing 50 mM TEMPOL. This method, although it is routinely described in the literature, and automatically implemented in commercial polarizers, ought to be avoided if possible, for several reasons that makes it hardly quantitative: (i) the presence of PAs bleaches part of the NMR signal [142][143], possibly in a different way in the DNP and reference samples, and (ii) the NMR lineshape can differ in both samples which affects the signal attenuation during the spectrometer dead time [144], see Section 5.2.
## 6. Mechanics of sample dissolution and transfer

<figure><img src="image_35.png" /><figcaption>**Figure 34:** 3D overview of the dissolution, transfer and injection system based on a liquid-driven system, including a sample cup (left) for dissolution, a set of two 10-way valves (middle), a loop (orange capillary) and an optical sensor (black, top left) for the sample bolus selection, a liquid pump (not shown), a magnetic tunnel (top right) for transferring the selected sample, and an injector (right) for injection.</figcaption></figure>

### 6.1. Introduction

The objective of this section is to describe the hardware and the protocols for dissolution, transfer and injection in *d*DNP experiments. Dissolution takes place after the frozen sample has been polarized to a satisfactory level. This is followed by the transfer and injection of the sample in a separate NMR spectrometer. These steps will be described, as well as the main challenges of the approach, and the pros and cons of the existing solutions. A particular focus will be placed on the hardware of such dissolution systems.

The main purpose of the dissolution process in *d*DNP experiments is to melt the frozen hyperpolarized sample while retaining the high nuclear spin polarization that is brought about by DNP, and to transfer it to an associated NMR or MRI machine. This process can be split in three parts: (i) the dissolution aims to warm up the frozen sample (initially at *ca.* *T* = 1.2 K) as fast as possible, to minimize polarization losses, and to melt the sample completely to make it available for liquid-state analysis; (ii) transferring the liquid hyperpolarized sample to an NMR machine for analysis requires special attention in terms of speed and magnetic field along the transfer pathway to minimize relaxation in the liquid-state. Typically, ¹³C spins may relax towards thermal equilibrium in tens of seconds, while other nuclear spins such as ¹H may relax in a matter of a few seconds. This highlights the need for a fast transfer to keep the highest polarization possible and enable hyperpolarization and subsequent dissolution of faster relaxing nuclear spins. Having a reproducible means to transfer a precise and controlled sample volume is also of great interest so as to enable reproducible injections; and (iii) injecting the hyperpolarized sample into a dedicated receiver while minimizing fluid motions, gas bubbles and degassing processes in the NMR detection coil is desirable in order to prevent inhomogeneous line broadening. Reproducibility in terms of timing, volume and analyte concentration, in order to ensure reproducible *d*DNP-enhanced NMR spectra, is also greatly desired. Finally, the NMR system needs to be prepared in an adequate state including pre-shimming on a similar solution before dissolution to ensure the acquisition of high-resolution spectra.

The following sections will detail the different steps of the dissolution process:

**Dissolution system.** To achieve fast dissolution, a large amount of heat needs to be rapidly transferred to the sample. This includes the energy needed to warm up and melt the frozen sample of *ca.* 50-200 µL at ~1 K, as well as the losses due to heat exchange with the system along the solvent path, including the capillary walls and sample cup. While many strategies can be designed, one commonly uses hot pressurized solvents such as *D*₂O for this purpose. The chosen solvent is pushed using helium gas onto the sample through capillaries, dissolves the sample, and is then pushed and transferred out of the polarizer. Two strategies exist to couple the capillaries to the sample cup for the dissolution: (i) either by coupling a warm dissolution stick to the cold sample cup; or (ii) using a built-in fluid path already attached to the cold sample cup. Great attention has to be given in both cases to the temperature of the dissolution solvent, the helium gas pressure, and the capillary diameters to ensure complete melting of the DNP sample and to prevent freezing along the fluid path. Melting of the sample can under some circumstances be improved by modifying the geometry of the inlet capillary to the DNP sample with a so-called “nozzle” (freezing the DNP sample into small pellets, rather than a block may also help). In addition, the dead volume of the sample cup must also be carefully considered to minimize mixing-induced bubbles which may affect the reproducibility of the transfer.

**Transfer system.** The hyperpolarized sample is usually transferred over a few metres of capillary with a driving fluid which is either a gas or a liquid. Gas-driven transfer has the advantage of being simple as the dissolved sample is directly pushed from the sample cup into a receiving container situated within the bore of the NMR spectrometer. One problem that can arise with this strategy is that the hyperpolarized sample, which initially presents itself as a single liquid bolus in the capillary, may be “contaminated” by the pushing gas during transfer. This may be due to turbulences, high speed, and slow transfer, which can lead to the fragmentation of the bolus of the dissolved sample. Transferring a mix of liquid and bubbles will lead to a poor transfer and injection reproducibility. It is possible to limit this problem by adjusting the capillary’s diameter and the driving pressure of the gas, usually at the expense of speed. Liquid-driven transfers do not suffer from such problems and can achieve fast and high precision injections, especially over long distances using high performance liquid pumps. This method involves the use of dedicated valves that first select a bolus of the hyperpolarized sample just after the dissolution, and then transfer this bolus using a dedicated pump (see Figure 34 for a schematic representation of such a system). In this case, turbulences may induce mixing between the driving liquid and the dissolved sample along the transfer. Such mixing can contaminate the front of the dissolved hyperpolarized sample bolus which is ultimately injected. The capillary diameter, the driving flow as well as the driving liquid properties must be carefully chosen to prevent such contaminations. Another important concern with the transfer of the hyperpolarized sample is the loss of polarization due to zero to low field regions. The mechanisms responsible for this loss are discussed in Section 7. Several approaches exist to produce a field high enough to limit polarization losses, generally using permanent magnets or electromagnets.

**Injection.** The injection of the dissolved sample requires a dedicated device that holds the NMR tube, here called the injector. We will limit ourselves to the case of 5 mm NMR tubes, as those are more frequently used. Since many applications require reproducibility, precise control of the injected volume and sample concentration is important. Having
a fully automated system that selects a desired volume can be
an answer, since it can improve reproducibility. Another way
consists of transferring the whole bolus to a reservoir prior to
injection, which is time consuming and ultimately less
reproducible [52]. Finally, avoiding broadening of the NMR
linewidth is essential to reaching the standard of high-resolution
NMR. Compared to direct classical acquisition, dDNP involves
fluid motion due to the transfer and injection, and micro-
bubbles potentially caused by degassing. Both will lead to line
broadening. Among the ways of dealing with those issues, using
liquid-driven transfers can help reduce fluid motion, applying a
back-pressure can limit degassing and treating the NMR tube
walls with dedicated solutions can prevent bubble blockage
during injection.

## 6.2. Dissolution strategy

### 6.2.1. System preparation for dissolution

After achieving a satisfactory level of polarization, the
dissolution step is conducted, which consists of sending a hot
liquid solvent into a cryostat filled with liquid helium. A few
points must be taken into consideration before starting the
dissolution step.

First, the hot solvent must be warmed prior to dissolution.
The solvent, usually D₂O, is placed in a reservoir surrounded by
resistive wires. A simple power supply can then warm up the
solvent to the desired temperature. Pressure is often chosen to
monitor the solvent temperature, since it can be more difficult
to precisely know the temperature inside the heater. To reach
higher temperatures, the solvent is first pre-pressurized with
helium gas at room temperature, and then warmed up until the
pressure of the heater reaches a target value. In our laboratory,
we usually pre-pressurized the solvent up to 6 bar, and then
warm up to 9 bar. The heating step takes ~10 mins and should
be started before the end of the polarization step to synchronize
with the time when the build-up of the polarization is optimal.

A key point for numerous successful dissolutions is to
decrease thermal contact between the sample cup and the liquid
helium bath. While having liquid helium surrounding the
sample cup during dissolution will lead to a big heat load in the
bath, thus wasting liquid helium, it will also lead to increase the
risk of freezing the dissolution solvent. The sample cup must
therefore be lifted above the liquid helium bath, usually using
dynamic o-rings or standard compressed o-rings. Liquid helium
level sensors can prove useful to determine the height of the lift.

Considering the long T₁ of commonly studied nuclei such
as ¹H and ¹³C at liquid helium temperatures, rf-pulses and
microwaves should be stopped prior to the dissolution process.
Though dependent on the nuclear species, relaxation will be
negligible in most cases during the time span required to start a
dissolution. See Section 7 for more details regarding relaxation
during this step.

When sending the hot solvent onto the sample, input and
output capillaries must be connected and coupled to the sample
cup to avoid spraying solvent into the cryostat. Two main
approaches exist: (i) the capillaries are connected to the sample
cup during the entire polarizing step using a so-called “fluid-
path”; or (ii) the capillaries must be manually connected just
prior to the dissolution. Both approaches will be discussed in
more detail in the following subsections. However, the latter
usually necessitates opening the cryostat to insert a tube, here
called a “dissolution stick”, containing the input and output
capillaries. To avoid cryo-pumping during this operation, an

overpressure of helium gas is applied, usually a few tens of
millibar above atmospheric pressure. The increase in pressure
in the cryostat will induce an increase in the sample
temperature, since the helium bath temperature will rise to
~4.2 K. A fluid-path associated with dynamic o-rings allows
dissolution in a pumped cryostat, with a ~1 K helium bath
temperature.

### 6.2.2. Shimming procedure

While increasing the NMR signal amplitude (integral) of
the sample is the main goal of *dDNP*, having high resolution
spectra is also of great importance. The relaxation of the
hyperpolarized species in the liquid-state prevents the user from
shimming after the injection. Instead, proper shimming
parameters must be known before performing the dissolution. A
possible method used in our laboratory is to perform a “fake”
dissolution in liquid nitrogen outside the polarizer on a similar,
ideally identical, sample using the same solvent, pressure and
temperature as in the actual dissolution. Indeed, there is no need
for hyperpolarization here. Shimming can then be optimized on
the sample injected through the injector. The same shimming
parameters are then used for the actual dissolution experiments,
resulting (in our case) in ¹³C linewidths of <1 Hz on [1-¹³C]
sodium acetate dissolved in D₂O solvent at 700 MHz.

After preparing the system, including the shimming
procedure, one is now ready to perform a dissolution by
coupling input and output capillaries to the sample cup. The
design details of two approaches will be presented in the next
section.

### 6.2.3. Dissolution stick and fluid path

When considering the dissolution process, one has to
consider how to connect the cooking pot to the sample cup. Two
predominant methods are used: (i) manually coupling a
dissolution stick; or (ii) using a fluid path.

The first approach consists of a tube housing two
capillaries, one for injecting the hot solvent and one for ejecting
the hyperpolarized solution. Both capillaries are attached at the
bottom of the tube to a so-called “dissolution interface”. This
part, usually machined in polytetrafluoroethylene (PTFE) or in
polyether ether ketone (PEEK), has a specific geometry used to
couple it to the sample cup. The system is made leak-tight by
manually pressing the dissolution stick to the sample cup. The
coupling must be done just before sending the hot solvent, to
reduce heat transfer from the warm dissolution stick to the cold
sample, which would decrease the nuclear spin polarization in
the solid-state. Thus, using a dissolution stick requires trained
operators.

Figure 35 shows the design of our dissolution stick. The
sample cup is screwed to a washer and soldered to an outer
stainless-steel tube. During the dissolution step, the dissolution
stick is inserted inside the outer tube, and is coupled to the
sample cup. A small stainless-steel tube is used to reduce the
inner diameter of the input capillary to improve the dissolution
efficiency. This will be discussed in more detail in a following
subsection.
<figure><img src="image_36.png" /><figcaption>F : a) 3D model and b) photograph of the dissolution stick and sample cup, comprised of: (1) PEEK sample cup; (2) 1/16" OD stainless-steel tube; (3) washer with screwing hole; (4) 16 mm OD stainless-steel tube; (5) PEEK dissolution interface; (6) two 1/8" OD and 1/16" inner diameter (ID) PEEK tubes; and (7) 13.37 mm OD stainless-steel tube.
*Shows the area that must be made leak tight at the time of the coupling.</figcaption></figure>

Another approach consists of keeping the input and output capillaries attached during the whole polarization step. Such a method has important advantages: (i) it becomes possible to perform a dissolution without opening the cryostat to couple the capillaries, thus allowing a dissolution at ~1 K; (ii) no trained operators are needed for the dissolution step, since no manual coupling is required; and (iii) by using dynamic o-rings it becomes possible to automate the whole dissolution process, including the lifting of the sample cup prior to sending the hot solvent. Such automated processes are a crucial step towards making *d*DNP accessible for all and improving reliability and reproducibility.

The main problem when dealing with a fluid path is to
make the sample/capillaries leak tight with respect to superfluid
liquid helium. Indeed, if the liquid helium of the bath enters this
system, it will fill the capillaries, creating a column of liquid
helium that will most likely freeze the hot solvent during the
dissolution. Ardenkjær-Larsen et al. showed the first fluid path
[92], [145], originally designed for the commercial *SPINLab*. It
features concentric capillaries, with the hot solvent coming
through the inner one, and coming out through the annular space
between the concentric tubes. A UV-cured epoxy (*Dymax Corp*,
CT, USA) is used between the outer tube and the sample cup to
obtain a leak tight system. Due to the sterility requirements of
the *SPINlab*, this fluid path can only be used once. The same
group has developed two other non-sterile versions [146], [147].
The concentric capillaries are glued onto an intermediate part,
which is screwed to the sample cup with a disposable PTFE o-
ring (see Figure 36). This reusable fluid path makes it easier to
access the sample cup.

<figure><img src="image_37.png" /><figcaption>**Figure 36:** Alternative version of the fluid path developed by Capozzi et al. [146]. The sample cup (e) is screwed to the intermediate part (c), and is made leak tight using a PTFE o-ring (d). The concentric capillaries (a) are glued using an UV-cured epoxy onto the intermediate part. Homebuilt wrenches (b) and (f) are used to tighten the o-ring. Adapted with permission from [146].</figcaption></figure>

Krajewski et al. proposed a method that combines the two discussed above, with a dissolution stick present in the cryostat during the polarization step, but not coupled to the sample cup [148]. A motor is triggered just prior to the dissolution to lift the sample cup above the liquid helium bath and couple it to the dissolution stick without pressurizing the cryostat. This automated dissolution system allows up to four samples to be polarized simultaneously in the cryostat.

To complete the idea of performing the dissolution in a ~1 K liquid helium bath, a gate valve system has also been proposed to insert the sample cup without pressurizing the cryostat [92], [130], [148], [149]. The sample is first inserted into a closed chamber from which the air is pumped. A lower gate valve is then opened to the cold cryostat and the sample cup is inserted using a dynamic o-ring. This system prevents the cryostat from warming up due an overpressure, thus reducing the loss of helium. However, it requires a more expensive and complex instrumentation.

Once the sample cup is lifted and coupled to the input and
output capillaries, hot solvent can be sent onto the sample to
dissolve it. One must consider the amount of energy needed to
melt the sample for this step.

6.2.4. *Energy required for dissolution*

During the dissolution process, a certain amount of heat
must be transferred to the sample to make sure it will melt, as
well as to make sure that the solvent will not freeze. This heat
is directly linked to the solvent volume and temperature. To
determine the volume and temperature, one could start by looking at the energy needed to melt the sample. However, as Bowen and Ardenkjær-Larsen showed [150], when a mass of solvent ~10 times higher than the mass of the sample is warmed up to 170 °C, ~5% of the heat available is needed to melt the sample and bring it to room temperature. At this point, it is reasonable to assume that too much solvent was used. However, as presented in their article, the frozen sample is not always recovered in the liquid-state after the dissolution (see Figure 37). The sample recovery gets worse when lowering the solvent temperature. The reason is that a large part of the heat is transferred to the system components, such as the capillaries or the valves. The efficiency of the heat transfer to the sample is also important, but this will be discussed further in the next subsection.

<figure><img src="image_38.png" /><figcaption>**Figure 37:** Recovery of acetate samples (sodium acetate/glycerol/H₂O (4.7/2.1/3.2 g/w/g) with 0.5 mM of bromocresol green) depending on the solvent temperature, pre-pressurization and sample size. (a) 4 mL of solvent (water) was used. (b) 10 mL of solvent (water) was used for larger sample sizes. Adapted with permission from from Bowen and Ardenkjær-Larsen [150].</figcaption></figure>

Freezing, which can happen if the dissolution stick or fluid path are poorly cleaned and dried prior to dissolution, can also occur if the solvent temperature is not high enough. The dissolution efficiency can be optimized through different parameters and is presented in the next subsection.

### 6.2.5. Optimizing the dissolution efficiency

With either a dissolution stick or fluid path, a few key parameters must be considered when dealing with the dissolution: (i) the volume and temperature of the solvent; (ii) the pressure at which the solvent is pushed; (iii) the diameters and length of the capillaries; and (iv) the dead volume of the sample cup.

Solvent volume and temperature, as discussed above, must be chosen so that enough energy will be available to melt the sample and avoid freezing. Freezing is also linked to the

diameter of the capillaries in the polarizer, since smaller capillaries will increase the contact surface of the solvent to the cold capillary walls. Longer capillaries also increase the contact time and thus the risk of freezing, but this parameter is usually set by the polarizer design.

One study by Ardenkjær-Larsen et al. [151] investigated the dissolution efficiency depending on the solvent velocity and temperature, and showed that the jet impingement of the solvent onto the frozen sample plays an important role in speeding up the sample dissolution. Higher solvent mass flow rates, due to higher pushing pressure of the solvent and smaller capillaries, increases the impingement. However, it will decrease the contact time between the solvent and the sample, which decreases the efficiency of the heat transfer by diffusion. The study also showed that the solvent tends to vaporize when entering the sample cup, which lowers the heat transfer capability. To prevent this, the capillary diameters must be carefully chosen, and the solvent temperature should not be too high. Furthermore, adding a step diameter, a nozzle, can significantly improve the melting efficiency [150], [152]. Indeed, a nozzle will increase the flow rate, and thus the impingement, and decrease vaporization. By carefully choosing its dimensions, Ardenkjær-Larsen et al. showed that a pyruvic acid sample could be entirely dissolved in 4 s using a nozzle, whereas a part of the sample still remains solid when no nozzle is used, even after all the solvent went through the sample cup (10 s later, same solvent parameters in both cases).

Finally, the dead volume of the sample is also important, since it will affect the efficiency of the following transfer. Indeed, the sample cup volume is a place where the initial helium gas can mix with the solvent due to high turbulences. This mixing induces bubbles and makes precise and repeatable transfers complicated. To reduce this effect, we lengthened the dissolution interface of our dissolution stick with a cylinder that enters the sample and fills a part of the dead volume (see Figure 6.2).

The dissolution process can be complex from a thermodynamic point of view and finding the optimal parameters can be challenging. After melting the sample, one has to transfer it as fast and as possible for analysis.

## 6.3. Transfer and injection for a gas-driven system

### 6.3.1. Direct gas-driven transfer

Originally, the dissolved sample leaving the polarizer was gathered in a reservoir, and injected manually into a 5 mm NMR tube [9]. Although simple, this method is relatively slow and the transfer to the NMR tube happens in low field, potentially inducing additional polarization losses, see Section 7. Furthermore, the timing is hardly repeatable, which affects the reproducibility of the signal amplitude ultimately measured.

Although this method still exists, especially for MRI applications [148], [153], efforts have been made towards automated injection of the hyperpolarized sample. Jannin et al. have reported an automated system that first gathers the liquid sample in a reservoir to mix it homogeneously with the solvent, and then injects a controlled volume into the NMR tube. Overall timings of ~7-10 s were obtained [52], [129], [154], [155]. By injecting directly into the NMR tube and carefully controlling the driving gas pressure and internal capillary diameters, Granwehr et al. [156] obtained a transfer time of ~2.5 s. Pinon et al. [147] decreased the transfer time down to ~2 s, though their approach injected the sample in a 10 mm NMR tube,
which allows higher driving pressure without risking a blockage
due to bubbles during the injection. Frydman at al. showed
transfer times as fast as ~1.2 s [157] using non-miscible
solvents. Pushing forward the idea of faster transfer, more
sophisticated and exotic approaches have been proposed, as
presented in the next subsection.

6.3.2. Dedicated transfer system

Instead of pushing a liquid hyperpolarized sample, Meier et al [34] transferred the sample in the solid-state, in a pellet of PTFE. The dissolution and injection take place inside the NMR spectrometer. A transfer time of ~70 ms, with ~ 800 ms for the dissolution and injection, was reported. Another way of reducing transfer time is to shorten the distance between the polarizing and acquisition areas. Two different groups have proposed to integrate both areas in the same device. The time between the dissolution and analysis has been reported to be 700 ms [33] and 300 ms [158]. Although extremely fast, such methods require dedicated, complex and expensive infrastructures.

To improve the transfer speed in a more classical way, Hilty
et al. developed a transfer and injection device comprised of a
8-way valve and a two different driving gas pressures [159].
After dissolution, a portion of the hyperpolarized sample is first
selected in a capillary called a loop, whereupon the 8-way valve
is switched, connecting the loop to the second driving gas
pressure for the transfer to the NMR tube. An overall timing
from dissolution to analysis was reported to be ~1.2 s. This
transfer system has also been implemented in other laboratories
[160], [161]. One should note at this point that the sample
selection in the loop must be done carefully if good
reproducibility is desired. Indeed, the sample concentration
profile is not constant across the bolus of solvent, as shown by
Bowen and Ardenkjær-Larsen [150] (see Figure 38). After
switching the 8-way valve, the highest concentration of the
profile should be at the front of the bolus, increasing the
sensitivity and decreasing concentration variations.

<figure><img src="image_39.png" /><figcaption>Figure 38: Absorbance, proportional to the sample concentration, along the solvent bolus after dissolution, depending on the sample size (50-600 mg aliquots). The sample, sodium acetate/glycerol/H₂O (4.7/2.1/3.2 w/w/w) with 0.5 mM of bromocresol green, was dissolved in H₂O. Adapted with permission from from Bowen and Ardenkjær-Larsen [150].</figcaption></figure>

When pushing a liquid over long distances with pressurized
gas, contamination by bubbles will occur and can ultimately
degrade injection.

6.3.3. Bubble contamination

When a liquid is pushed in a tube using gas as the driving
fluid, mixing will occur due to turbulences [156], [162],
creating bubbles along the liquid bolus of liquid. Increasing the
gas pressure, and thus the transfer speed, will increase the
turbulences and therefore the extent of the resulting mixing.
Furthermore, the liquid will leave a trail along the tube walls,
decreasing the liquid bolus length [163]–[166]. This trail
becomes thicker when increasing the gas pressure and thus the
transfer speed. Transfer over longer distances will also imply a
shorter liquid bolus at the time of injection. Such a loss of liquid
bolus will decrease the reproducibility of the injection.

6.3.4. *Injections with gas-driven transfer*

Injecting a gas-driven liquid sample can be difficult. Especially when injecting in a 5 mm NMR tube, since gas bubbles might be present in the coil detection area. Furthermore, after ending the injection, the driving pressure is released, inducing degassing within the sample [156], [159], [160]. The resulting microbubbles will broaden the signal. Hilty et al. proposed a system with an applied back-pressure at the end of the injection step to prevent degassing [159]. Fluid motion after injection has been reported [156], [160], [167], which also leads to line broadening.

For most injections, a custom-built injector has to be
developed. Such injectors must hold the NMR tube, include the
input capillary through which the liquid is injected, as well as
an exhaust for the gas. It also has to fit within the NMR
spectrometer bore. If a back-pressure is applied, the injector
must remain leak tight and resistant to pressure, usually in the
order of 10 bar. Our homebuilt injector is presented Figure 39.
It includes a 5 mm medium-wall NMR tube that handle up to
10 bar of pressure, an input 1/16" OD capillary for injection
and an 1/8" OD capillary for exhaust and back-pressure gases.
A custom 3D printed spinner, made leak tight with o-rings, links
the capillaries and the NMR tube.

Very few studies have investigated the reproducibility of the
obtained liquid-state polarization level with a gas-driven
transfer. Indeed, the compressibility of the gas used might prove
to be an obstacle in reaching an acceptable level of
reproducibility. Krajewski et al. [148] have reported a
polarization level of 18.7 ± 2.3% over 24 experiments, using
four different dissolution sticks. This study, however, was for
*in vivo* studies in rats, using a small animal MRI system. Bornet
et al. showed, over 8 dissolutions with a 500 MHz spectrometer,
a coefficient of variation of ~3.6% [154]. Even though this work
requires trained operators for the dissolution process, such
repeatable results such repeatable results have paved the way
towards applications requiring high repeatability, such as
hyperpolarized metabolomics studies [136].

Gas-driven transfers are the most widely used method in
dNPD. However, the approach has challenging fluidic issues
that could be overcome by using a different driving fluid, as
presented in the next section.
<figure><img src="image_40.png" /><figcaption>Figure 39: a) 3D model and b) photograph of an injector, comprised of: (1) 5 mm NMR tube with 3.4 mm ID; (2) 1/16" OD PEEK tube; three o-rings with 1 mm cross section and 5 mm ID (3), 5.5 mm ID (6) and 1/16" ID (9); (4) tube head in PEEK; (5) custom-made PEEK nut; (7) 3D-printed custom spinner; (8) o-ring with 1/16" cross-section and 1/8" ID; (10) 3D-printed plug; two 1/8" OD PEEK tubes with 2.2 mm ID (11) and 1/16" ID (12).</figcaption></figure>

## 6.4. Transfer and injection for a liquid-driven system

### 6.4.1. Liquid-driven transfer

Considering the challenges brought by gas-driven injection, one might consider pushing the sample with a different fluid. Hilty et al. developed a liquid-driven transfer based on their previously described fast gas-driven transfer [167], [168]. The selection of a part of the sample in a loop capillary using a 10-way valve remains the same, but a powerful liquid pump is triggered to transfer the loop segment instead of pressurized gas. Such systems can achieve fast transfer times, with ~0.7 s reported (~1.6 s for the overall dissolution to injection time).

Although this system was used with a flow cell, it is possible to adapt it to a classical 5 mm NMR tube. The advantages of such liquid-driven transfers become especially important when dealing with long distance transfers. Indeed, as explained in the previous section, a gas-driven high-speed transfer will decrease the liquid bolus length. Over longer distances, a liquid bolus rupture can occur, leading to a poor injection consisting of droplets. A liquid-driven injection avoids this problem. Figure 40 shows our transfer and injection system. The dissolution step using a dissolution stick and the injector have been presented in the previous sections. The transfer system, based on the work of Hilty et al., uses the first 10-way fast switching valve and an optical sensor to select a part of the dissolved sample in the loop capillary. A micro-annular gear pump is used to transfer the sample in the injector through a magnetic tunnel [50]. A second 10-way fast switching valve is triggered at the end of the injection to apply a backpressure to prevent degassing. A transfer time of ~2 s can be obtained over 9.5 m of capillary.

Long distance transfer can be useful in laboratories where the spectrometer configurations cannot be changed.

<figure><img src="image_41.png" /><figcaption>Figure 40: Schematic overview of the dissolution, transfer and injection system based on a liquid-driven system, including a dissolution box and sample cup for the dissolution step, a set of two 10-way valves, a loop and an optical sensor for the selection of the sample bolus, a liquid pump and a magnetic tunnel for transferring the selected sample bolus, and an injector with a back-pressure of helium gas for the injection.</figcaption></figure>

### 6.4.2. Sample contamination

Liquid-driven transfers avoid any rupture with the liquid sample bolus. However, turbulences and axial diffusion can still create a mixing between the driving liquid and the dissolved hyperpolarized sample [169]–[172]. The mixing length depends on several factors, among which are the capillary dimensions, the fluid properties and the driving liquid speed. To avoid contamination and further dilution of the injected sample, one must carefully choose the parameters used for the transfer. Fortunately, as described in the literature [171], [172], when the turbulences becomes high enough, the axial dispersion decreases as well as the mixing length. Such observations have been made in our group, with no contamination observed for the faster transfer.

### 6.4.3. Injections with liquid-driven transfer

Injection using liquid-driven transfer can prove to be efficient, as reported by Hilty et al. [167]. Linewidths of ~1.8-4.0 Hz have been shown. Furthermore, a comparison between gas-driven injections in a 5 mm NMR tube and liquid-driven injections in a flow-cell, shown in Figure 41, indicates that liquid-driven injections have a faster stabilization time. As indicated above, liquid-driven injections into a 5 mm NMR tube should be associated with a back-pressure to avoid degassing.

<figure><img src="image_42.png" /><figcaption>Figure 41: Diffusion coefficients of hyperpolarized samples transferred and injected using gas (white circles) or liquid (black squares) showing a faster stabilization with liquid transfer. Image adapted with permission from the work of Chen and Hilty [167].</figcaption></figure>
6.5. Avoiding low-field regions during the transfer

When transferring a hyperpolarized sample from the
polarizer to the acquisition device, whether an NMR
spectrometer or an MRI, it is of primal importance to avoid low-
field regions. Such regions will destroy the polarization, see
Section 7. To maintain a magnetic field high enough to limit
polarization losses, usually greater than a few milliTesla, two
main approaches are used. The first is based on permanent
magnets. Milani et al. [50] proposed a magnetic tunnel where
the hyperpolarized solution travels through an array of
permanent magnets placed in a Halbach configuration. This
system can produce a field >0.9 T (see Figure 42). Other studies
proposed transportable systems, used for MRI, with magnetic
fields of ~0.2 T [173], [174].

Another similar approach consists in using electromagnets for transporting the hyperpolarized solution. This method can be safer especially when approaching an NMR or MRI instrument, since the electromagnet can be turned off. Shang et al. [175] proposed a handheld device producing over 5 milliTesla over the dissolution sample container. In our laboratory, when a rigid permanent structure such as a magnetic tunnel cannot be used for practical reasons, we wind a single-layer coil around the capillaries to create a 4 mT field using a 2 A power source. The single layer configuration keeps the capillary flexible, which can be useful especially while performing a manual coupling of the dissolution stick.

<figure><img src="image_43.png" /><figcaption>Figure 42: The magnetic field strength in the course of the transfer of the hyperpolarized fluid from an unshielded DNP polarizer to an unshielded 300 MHz NMR spectrometer through a magnetic tunnel (black line) or without tunnel (red line). The stars and crosses indicate the polarizer-tunnel and tunnel-spectrometer junctions. Adapted with permission from Milani et al. [50].</figcaption></figure>
# 7. Physics of sample dissolution

## 7.1. Introduction

This section aims to present the mechanisms through which nuclear spin polarization might decay during the processes of dissolution and transfer from the polarizer to the liquid-state NMR or MRI magnet. We will discuss the key relaxation mechanisms as well as the strategies that allow for prevention of some of these polarization losses.

of the polarization to thermal equilibrium through relaxation, that is, longitudinal or spin-lattice relaxation. During steps A and B, the sample is in the solid-state and relaxes mainly through paramagnetic relaxation, which is described in Section 7.2. During steps D-G, the sample is in the liquid-state and may relax through a number of mechanisms. Section 7.3 presents the most usual liquid-state relaxation mechanisms for dDNP, namely, through dipole-dipole couplings, chemical shift anisotropy (CSA) and paramagnetic interactions. Some relaxation mechanisms are stronger at lower magnetic fields

<table><caption>Table 4: Steps of the dissolution and transfer process, and the corresponding sources of polarization losses. *Strongly dependent on the experimental setup.</caption><thead><tr><th></th><th>Step</th><th>Phase</th><th>Temperature</th><th>Field</th><th>Incoherent mechanisms</th><th>Coherent mechanisms</th></tr></thead><tbody><tr><td>A</td><td>End of the DNP build-up</td><td rowspan="2">Solid</td><td rowspan="2">~1.2-4.2 K</td><td>High (3.35-7 T)</td><td rowspan="2">Solid-state paramagnetic relaxation</td><td rowspan="2">If the solid is exposed to lower fields, nuclear thermal mixing may occur</td></tr><tr><td>B</td><td>Before dissolution</td><td>Moderate (1-7 T)</td></tr><tr><td>C</td><td>During dissolution</td><td>Solid to liquid</td><td>Increasing (4.2→350 K)</td><td></td><td></td><td></td></tr><tr><td>D</td><td>Exiting the polarizer</td><td rowspan="4">Liquid</td><td rowspan="4">High (300-350 K)</td><td>Decreasing (T→mT/μT)</td><td rowspan="3">Liquid-state relaxation at low to moderate fields</td><td>Non-adiabatic field decrease may create coherences</td></tr><tr><td>E</td><td>Transfer between the magnets</td><td>Low to moderate* (&lt;mT)</td><td>Rotation of the field creating coherences</td></tr><tr><td>F</td><td>Entering the spectrometer</td><td>Increasing</td><td>Non-adiabatic field increase the creation of coherences</td></tr><tr><td>G</td><td>After injection</td><td>High field</td><td>High field liquid-state relaxation</td><td></td></tr></tbody></table>

**Main functions.** During the processes of dissolution and transfer, the sample goes from a solid to liquid phase. Furthermore, the spins experience a varying magnetic field, temperature, pressure and in some cases pH. Table 4 decomposes the entire process into steps from A to G and relates each step to the sources of polarization losses. The steps are illustrated on Figure 43.

A. At the end of the DNP build-up, the sample is at low temperature and high field;

B. Prior to dissolution, the sample is usually lifted by a few centimetres above the helium bath in a cold helium gas atmosphere to improve the thermodynamics of the dissolution process;

C. Upon injection of hot solvent, the temperature of the sample increases and the sample melts, in principle remaining at high field;

D. The sample is expelled from the polarizer (discussed in the previous sections), and as a result; the spins experience a rapid decrease in magnetic field. At the same time, the temperature increases;

E. The sample is transferred to the liquid-state at a temperature that is difficult to estimate and is highly dependent upon the experimental setup. The magnetic field during the transfer also depends on the experimental setup since it is a sum of contributions from the surrounding magnets and the earth. In some cases, guiding fields may be added;

F. The sample enters the liquid-state NMR magnet, and the spins experience an increase in magnetic field;

G. The sample is in the liquid-state NMR magnet at high field and is generally close to room temperature.

During each of these steps, a variety of relaxation mechanisms may cause losses of polarization [50], [176], [177]. The interactions are separated into two types: incoherent and coherent. What we call incoherent polarization loss is the return

(although the difference is not always significant) and as such may be mitigated by the use of a guiding field during the sample transfer (stage E). Section 7.3 aims to account for the field dependence of the relaxation mechanisms to understand in which cases the magnetic field may have to be actively increased to preserve the nuclear spin polarization during the transfer. This is usually enacted by setting up a magnetic tunnel around the capillary through which the solution travels.

The loss of polarization through coherent mechanisms is the result of non-adiabatic field variations, either rotations or changes in intensity, which induce coherences between nuclear spin states. The latter may be avoided by using a guiding field as well as by adjusting the flow rate of the solution during sample transfer.

<figure><img src="image_44.png" /></figure>
## 7.2. Generalities of relaxation theory

Relaxation theory is a large and complex topic and so the following sections only aim to cover aspects which are necessary to understand how to perform a dissolution experiment with minimal polarization losses. Hyperpolarized nuclear spins return to Boltzmann equilibrium because they are subject to random fluctuations of their Hamiltonian. These fluctuations are stochastic and depend on the physical parameters related to the experimental setup (temperature, magnetic field profile, etc.), the sample formulation, dissolution solvent (presence of radicals, dissolved oxygen, protonation level, etc.) and the properties of the hyperpolarized molecule (dipolar couplings, CSA, *J*-couplings, chemical exchange, etc). By definition, these fluctuations average to zero if we consider a single spin on a sufficiently long timescale or a sufficiently large number of spins. Intuitively, one can say that a nuclear spin may relax to thermal equilibrium whenever it experiences a magnetic field which oscillates near or at its Larmor frequency. For example, a pair of neighbouring ¹H spins in a molecule exert a magnetic field on each other. The intensity of this interaction depends on the orientation of the molecule. Due to the rapid reorientation of the molecule in solution, this interaction averages to zero and does not influence the Larmor frequency of the spins, i.e., it does not shift the resonance peak associated with these spins. Now, imagine that the molecule is rotating in space at a frequency near the Larmor frequency: the intensity of the interaction will vary in time at the Larmor frequency, which will give the opportunity for spins to relax.

It is impossible, or at least challenging, to describe this sort of interaction completely or in a deterministic manner. The common strategy is to describe them with probabilities. A key parameter is then the correlation time of the fluctuating interaction, which usually takes the symbol $\tau_c$. Many definitions may be found for this quantity. To give a qualitative and intuitive account, we may often refer to $\tau_c$ as the average time during which the interaction causing relaxation keeps a given value. For example, in the case of solid-state paramagnetic relaxation, $\tau_c$ corresponds to the average time during which an unpaired electron remains in the $\alpha$ or $\beta$ state (often in the microsecond to millisecond range). In the case of liquid-state intramolecular dipole-dipole relaxation, the correlation time corresponds to average time during which a molecule rotates through an angle of 1 radian (typically in the picosecond to nanosecond range). It is important to notice that relaxation theory is usually more concerned by the order of magnitude of the correlation time than by its precise value. As we go through the relaxation mechanisms that are important to *d*DNP in the following sections, we will mention the interactions on which each mechanism relies and the timescales on which such interactions oscillate [178]–[183].

## 7.3. Solid-state relaxation

Under *d*DNP conditions, the main source of solid-state polarization losses is paramagnetic relaxation, which we intend to briefly summarize. The unpaired electron of a paramagnetic agent and the nuclear spins in the sample interact through dipolar interactions (also referred to as a hyperfine or super hyperfine interactions). Since the spin state of the electron fluctuates, the nearby nuclear spins experience a randomly

varying magnetic field which causes them to relax. The relaxation of these nuclear spins is then spread throughout the sample via nuclear flip-flops (nucleus-nucleus dipolar interactions). Macroscopically, this process is referred to as “spin diffusion”. The paramagnetic centers and their surrounding nuclear spins thus act as relaxation sinks which affect nuclear spins even if the nuclear spins themselves do not interact directly with an electron spin. This two-step mechanism was first proposed by Bloembergen in 1949 [184] and was followed by a vast literature in the 60s and 70s. Ramanathan’s review on spin diffusion in 2008 [185] provides an overview of the field. Relevant treatments of relaxation mechanisms can be found in Section 8.7 and 8.9 of a review on paramagnetic NMR [186], or in the recent literature on low temperature static DNP [16], [187]–[189]. Two key parameters dictate the efficiency of this relaxation mechanism:

1) The temperature influences the correlation time of the electronic spin state and hence the intensity of direct paramagnetic relaxation. The higher the temperature, the shorter the correlation time. In the limit where the correlation time is small with respect to the nuclear Larmor period, the nuclear spin relaxation rate constant becomes proportional to the correlation time.

2) The rate at which polarization may diffuse depends on the strength of the dipolar interactions between nuclear spins [190]. We will not go into the details of this dependence here, but we note that lower-gamma nuclear spins experience weaker spin diffusion and are less susceptible to indirect paramagnetic relaxation. In addition, more dilute nuclear spins have larger average internuclear distances and thus weaker dipolar interactions, and hence also weaker spin diffusion. As a consequence, diminishing the concentration of the nuclear spins of interest also diminishes the effect of paramagnetic relaxation. It should be noted that minimizing spin diffusion, if mitigating paramagnetic relaxation, can also result in hindering the efficiency of DNP.

We now move to the practical implications of paramagnetic relaxation for the dissolution experiment itself. Once the sample is hyperpolarized and ready for the dissolution and transfer steps, most experimental *d*DNP setups require the sample space to be pressurized above atmospheric pressure and the sample to be lifted outside of the liquid helium bath to prevent the dissolution solvent from freezing upon arrival at the sample cup. During this time, the sample is no longer being irradiated by the microwave source and is thus subjected to relaxation without being repolarized by DNP. In the case of ¹³C DNP, the nuclear longitudinal relaxation time constant $T_1$ in standard DNP juice remains on the order of hours, provided the temperature does not increase significantly above that of liquid helium temperature (ca. 4.2 K) and the magnetic field does not significantly drop below (ca. 1.0 T). In the case of ¹H DNP, the relaxation time constant is in the order of minutes so the rapidity at which the dissolution is performed starts to play an important role in preserving the previously accrued nuclear polarization. The different behaviour of ¹³C and ¹H nuclear spins is an illustration of the principles presented previously. Indeed, the larger gyromagnetic ratio typically engenders shorter relaxation time constants. In addition, ¹H not only has a high gyromagnetic ratio but is usually present at concentrations higher than those of ¹³C spins, which engenders faster nuclear spin diffusion and ultimately faster paramagnetic relaxation. Another important parameter is the paramagnetic agent concentration. At higher concentrations, the correlation time of the electron decreases due to stronger electron-electron dipolar couplings and the
average distance between the paramagnetic agents and nuclear
spins also decreases. Both factors account for stronger nuclear
spin-lattice relaxation.

A critical moment of the dissolution process occurs when the dissolution stick comes into contact with the sample. At this point, the room temperature dissolution stick brings a significant heat load causing the temperature of the sample to raise rapidly, which dramatically shortens the electron correlation time and hence the nuclear longitudinal relaxation time constant. To avoid detrimental polarization losses, the sample should be dissolved as rapidly as possible. This implies that the dissolution solvent should be injected immediately after coupling the dissolution stick to the sample. This point is as critical as the rapidity of the dissolution process itself. Furthermore, the dissolution solvent heats the sample before it can melt and be dissolved into solution. During this time, the sample is warming up towards the melting point but is still solid, and therefore not yet diluted and with a high polarizing agent concentration. Therefore, paramagnetic relaxation can become very efficient, especially for high-gamma nuclear spins. This is therefore important for the dissolution process which much be carefully optimized. See Section 6 for more information. Although there are no detailed studies on this question, one can expect that a lower radical concentration in the DNP sample will cause lower polarization losses through the mechanism described above.

In addition to paramagnetic relaxation, nuclear thermal mixing in regions of low magnetic field should be avoided to prevent polarization losses. At low magnetic field (typically in the mT field range), the difference in Zeeman energies between heteronuclear spins might be compensated by the dipolar interaction allowing for the direct transfer of polarization [5], for example between ¹H and ¹³C nuclear spins. All nuclear spins connected via thermal mixing relax together, and thus act as relaxation sinks for each other. This effect is only present in the solid-state, where the dipolar interaction is not averaged. This relaxation mechanism is avoided by performing the dissolution step in a region of sufficiently high magnetic field. However, in the case where the sample would escape the sample space as a suspension of partially melted particles, nuclear thermal mixing can be expected to cause significant polarization losses. Therefore, one has to set up dissolution parameters so as to ensure that the sample leaves the high magnetic field once entirely melted and dissolved.

7.4. *Liquid-state relaxation*

In this section, we will list the main relaxation mechanisms which operate in the liquid-state (during steps D-G of the *d*DNP experiment, see Table 4), with a particular attention to the magnetic field dependence of each interaction. Understanding the magnetic field dependence allows the experimentalist to choose an appropriate strategy for the sample transfer step. It will be shown that, in some cases, adding a magnetic tunnel between the polarizer and liquid-state NMR spectrometer so that the solution experiences a non-vanishing field during the transfer can help to sustain polarization. Section 6.4 reviews some practical solutions.

Providing a full description of each relaxation mechanism is
beyond the scope of this review but the reader will be referred
to the appropriate literature. Table 5 summarizes the physical
parameters which govern the relaxation dynamics of each
mechanism, in particular their field dependence; an overview of
the relaxation rates of ¹³C spins in bio-relevant molecules is

given elsewhere [28]. The theory underlying liquid-state
relaxation is available can be found in several texts [178]–[181],
[191], [192].

**Dipole-dipole couplings.** Nuclear spins interact through space via an interaction known as the dipole-dipole (DD) coupling. In the solid-state, this interaction leads to distinctive spectral patterns [193]. In the liquid-state, this interaction does not lead to any observable spectral features since it is averaged to zero (apart from line broadening through relaxation). Nonetheless, the random motion of molecules in solution (orientational tumbling) causes rapid variations of this interaction and engenders nuclear relaxation. In the case of intramolecular DD relaxation, two (or more) nearby nuclear spins experience a fluctuating magnetic field due to the rotation of the molecule in solution, and hence the variation of the DD interaction with respect to the static magnetic field. The time constant which governs this interaction is the rotational correlation time of the molecule which is on the order of tens or hundreds of picoseconds for small molecules in water at room temperature [194]. DD relaxation rates are proportional to the square of the dipole interaction between nuclei, which is proportional to the inverse cube of the distance between the spins. DD relaxation rates are thus proportional to the inverse sixth power of the distance between spins and so it is most effective for very close nuclei. For example, DD relaxation is efficient for geminal ¹H spins in amino acids or peptides [195] or ¹³C spins with adjacent ¹H nuclear spins, such as in a ¹³C-formate anion HCOO⁻. In the case of non-rigid molecules, extra degrees of freedom add to the effects of rotational diffusion. Methyl groups are a common example of this process. The rapid rotation of the three ¹H spins in ¹³C-methyl groups shortens the relaxation time of the ¹³C spin via the intramolecular DD interactions, although rotation of the methyl group itself attenuates those couplings.

Most *d*DNP experiments aim at polarizing small molecules which have sub-nanosecond rotational correlation times that are short compared to the Larmor period of nuclear spins even at high magnetic fields. This limit, known as extreme narrowing, implies that the DD relaxation rate is magnetic field-independent and proportional to the overall correlation time of the molecule in solution. As a consequence, if the principal source of signal attenuation during the sample transfer step is DD relaxation, adding a magnetic tunnel to sustain a higher magnetic field, see Section 6.5, is not expected to bring any improvement. On the contrary, increasing the temperature ensures longer relaxation times since it decreases the rotational correlation time, except in unusual circumstances.

DD relaxation may also occur between molecules, *i.e.*, intermolecular DD relaxation. In this case, translational diffusion of molecules leads to nuclear relaxation. For example, the rapid diffusion of ¹H nuclear spins in water may relax spins on nearby molecules. This is the reason why deuterated solvents are preferred as solvents for dissolution. For the case of water hyperpolarized by *d*DNP, this mechanism is the main source of polarization losses, apart from those caused by traces of paramagnetic species remaining in solution. In this case, raising the temperature of the solution during the transfer step was shown to greatly increase the hyperpolarization lifetime of water during the transfer [196].

**Chemical shift anisotropy.** The induced magnetic field in the electron cloud around the nucleus shifts the nuclear Larmor frequency in a predictable manner. The isotropic part of this shift, which corresponds to the average of the shift over time or molecular orientation, leads to the isotropic chemical shift that
is observed in liquid-state NMR experiments. The anisotropic part of the chemical shift tensor, named chemical shift anisotropy (CSA), leads to distinctive patterns in solid-state NMR spectra. As a molecule tumbles in solution, the CSA tensors reorient, leading to a time dependent variation of the chemical shift. Although this variation averages to zero, it may still cause relaxation, as in the case of the DD relaxation mechanism. Since CSA depends on the tumbling of the molecule, it also depends on a reorientational correlation time, in a fashion similar to DD relaxation. The strengths of both the symmetric and antisymmetric CSA interactions are proportional to the strength of the static magnetic field $B_0$. It follows that the CSA relaxation rate is proportional to the square of the static magnetic field, in contrast to DD relaxation. Since CSA relaxation results from the shielding of a nuclear spin by the electron cloud, it does not require the participation of a second nuclear spin.

In the case of ¹H spins, the CSA is often weak and thus rarely provides an efficient relaxation pathway. On the contrary, ¹³C spins may experience large CSAs, especially for the case of carbonyl groups [197]. This example is important for dDNP as many experiments are performed on [1-¹³C]-pyruvic acid, [1-¹³C]-acetic acid and other molecular derivatives which are labelled at the carbonyl position. At high magnetic fields, CSA might therefore provide an efficient relaxation pathway for these molecules. As the intensity of the interaction increases with the magnetic field, using a magnetic tunnel during the sample transfer step is of no help in mitigating this source of nuclear relaxation. Nonetheless, the typical field strength of magnetic tunnels constructed using a Halbach array of permanent magnets is at best about ~1 T [50] where CSA relaxation is weak for most molecules. Consequently, the use of a magnetic tunnel might diminish some polarization losses but is not expected to significantly increase relaxation from CSA.

**Liquid-state paramagnetic interactions.** The strong magnetic moment of unpaired electrons of paramagnetic agents provides an efficient relaxation source in the liquid-state. This relaxation mechanism is important for dDNP as all polarizing agents are paramagnetic. Furthermore, solutions naturally contain dissolved dioxygen which is also paramagnetic.

As solutes diffuse in solution, their distance from paramagnetic agents fluctuates, which modulates the magnetic field experienced by the nuclei of the solutes, causing nuclear relaxation which occurs when the random field variation matches the Larmor frequency of the nuclear spins (or other frequencies corresponding to zero and double quantum transitions of the electron-nucleus spins system). It follows that the rate at which the solute diffuses near the paramagnetic centre determines the efficiency of the relaxation mechanism. Hence, the diffusion coefficient of the solute usually governs the paramagnetic relaxation rate [198].

There is an intricate dependence of the paramagnetic relaxation rate constant on the diffusion coefficient and the magnetic field. As a rule of thumb, increasing the temperature (diminishing the viscosity) decreases the paramagnetic relaxation rate [198]. In common cases, for a given temperature and solvent viscosity, the relaxation rate increases at lower magnetic field and plateaus below a certain value, as shown on Figure 44 [49], [177], [198]. The magnetic field strength below which paramagnetic relaxation usually becomes efficient is on the order of 0.1 to 1.0 T [49], [177]. In other words, paramagnetic relaxation is usually efficient, i.e., detrimental, in the mT regime while it is weak, i.e. safe, in the Tesla regime. In a common laboratory, as the solution travels between the

polarizer and the liquid-state spectrometer, it experiences magnetic fields of a few mT and sometimes lower, especially if the NMR magnets are shielded or far apart. This means that paramagnetic relaxation might be detrimental during the transfer of the hyperpolarized solution. A magnetic tunnel may therefore be employed to sustain the magnetic field during the transfer. Magnetic tunnels using Halbach arrays of four permanent magnets can readily produce guiding fields up to ~1 T and have proved to greatly improve the final liquid-state polarization in certain cases [50]. Indeed, it can increase the relaxation time of certain molecules by factors up to 3 or 4 [49], [50], [177].

<table><caption>Table 5: Summary of the main relaxation sources for small molecules in solution. The symbols $\tau_c$, $T$, $\eta$ and $B_0$ stand for the rotational correlation time, temperature, viscosity of the liquid and magnetic field, respectively. The symbols $\gamma_l$, $\gamma_s$, and $r_{ls}$ stand for the gyromagnetic ratios of spins I and S and the distance between them, respectively, which governs the size of the dipole-dipole coupling constant $D_{00}$. $\delta^{aniso}$ is the chemical shift anisotropy parameter. In the context of intermolecular DD relaxation, C is the concentration of a spin bearing molecule causing a species to relax. In the context of paramagnetic (“para”) relaxation, $C_{radical}$ is the radical concentration. Finally, $J(\omega, \tau_c) = \tau_c/(1+\tau_c^2\omega^2)$ is the spectral density function.</caption><thead><tr><th></th><th>Relevant parameters</th><th colspan="2">Field dependence</th></tr></thead><tbody><tr><td rowspan="3">DD</td><td>$\tau_c(T, \eta)$</td><td>General:</td><td>$J((\gamma_l-\gamma_s)B_0, \tau_c)$</td></tr><tr><td>$B_0$</td><td></td><td>$J((\gamma_l+\gamma_s)B_0, \tau_c)$</td></tr><tr><td>$D_{00} \propto (\gamma_l^2, \gamma_s^2, r_{ls}^{-3})$</td><td></td><td>$J(\gamma_l B_0, \tau_c)$</td></tr><tr><td></td><td>C (intermolecular DD)</td><td>Extreme narrowing:</td><td>$J \approx \tau_c$, no field dependence</td></tr><tr><td rowspan="2">CSA</td><td>$\tau_c(T, \eta)$</td><td>General:</td><td>$B_0^2 J(\gamma_l B_0, \tau_c)$</td></tr><tr><td>$B_0^2$</td><td>Extreme narrowing:</td><td>$\tau_c B_0^2$</td></tr><tr><td>Para</td><td>$\eta$</td><td colspan="2">$C_{radical}$</td></tr><tr><td></td><td>$C_{radical}$</td><td colspan="2">Usually higher at lower fields</td></tr></tbody></table>

Adding a magnetic tunnel mitigates the losses due to paramagnetic relaxation but does not completely suppress them. Complementary strategies consist in reducing the radical concentration in solution. The first obvious way is to use lower radical concentrations in DNP samples. For ¹H DNP, TEMPOL is an efficient polarizing agent for typical concentrations up to 50 mM. The dissolution process dilutes the sample by a typical factor 50, so that the TEMPOL concentration drops to ~1 mM in the liquid-state. A concentration of 25 mM TEMPOL in the DNP sample reaches nearly the same DNP performance as 50 mM TEMPOL [40] but will lead to a concentration of only ~0.5 mM in the liquid-state. The liquid-state paramagnetic relaxation rate constant is proportional to the radical concentration [199]. Diminishing the radical concentration in the liquid-state by a known factor reduces paramagnetic relaxation by the same amount. It is therefore often preferable to use a TEMPOL concentration of 25 mM when performing dDNP experiments. The concentration of TEMPOL in solution can be further reduced by quenching the radicals at the moment of dissolution with sodium ascorbate (vitamin C). [51] Sodium ascorbate may either be added to the dissolution solvent at a concentration of typically >10 mM or in pellets mixed with the sample in the sample holder in higher concentration, typically >1 M. In either case, sodium ascorbate must be in large excess with respect to TEMPOL immediately after dissolution so that the reaction is fast and consumes most of the TEMPOL.
<figure><img src="image_45.png" /><figcaption>**Figure 44:** a) ¹H relaxometry measurements for several molecules in D₂O without and with 0.5 mT TEMPOL in liquid-state at room temperature in a field of 1 mT to 10 T. b) Relaxation rates as a function of the magnetic field. CTC stands for 3-chlorothiphene-2-carboxylate. Adapted with permission from [177].</figcaption></figure>

More sophisticated strategies consist of covalently attaching radical molecules to materials that are filtered out after the dissolution step, producing a radical-free solution, without relying on any chemical reaction [41], [42], [44], [200]. In the case of hybrid polarizing solids (HYPSOs), the radical molecules are grafted onto the surface of a porous silica matrix and the solution of interest is impregnated in the pores of the material [42], [44], [200]. Similarly, hyperpolarizing porous polymers (HYPOPs) are epoxide-based porous polymers where the radical is incorporated within the polymer walls [77]. In the case of filterable labelled agents for polarization (FLAP), the radical molecules are attached to an organic polymer which precipitates at high ionic strength. [41] The solution of interest is impregnated in the polymer powder. The dissolution is performed with a sodium chloride solution which ensures that the polymer precipitates and can be filtered out before the transfer. Alternatively, non-persistent radicals such as UV-induced radicals are another promising strategy [147]. These *in situ*-generated radicals efficiently polarize the ¹H spins but recombine at ~100 K, therefore producing radical-free hyperpolarized solutions.

The strategies above were developed for ¹H using radicals with broad EPR lines to produce hyperpolarized ¹H or ¹³C using cross polarization. In the case of direct hyperpolarization of ¹³C using narrow line radicals such as trityls, the radical can also be filtered out after precipitation by an acidic dissolution solvent [150].

**Other relaxation mechanisms.** The liquid-state relaxation mechanisms listed above are those which are most effective and common during the sample transfer stage of a typical *d*DNP experiment. The relevant parameters for each of the aforementioned relaxation mechanisms can be found in Table 5. Yet, there are a number of other mechanisms that may be encountered and cause further relaxation losses in *d*DNP experiments. Such mechanisms are not detailed in this review, but references are given in some cases:

(i) **Chemical exchange** may cause relaxation when the exchange induces a change in chemical shift and occurs on the timescale of the nuclear Larmor frequency of the spins of interest. In some cases, chemical exchange depends on pH and therefore the relaxation rate constant itself also depends on pH [201].

(ii) **Scalar relaxation of the second kind** (SR2K) is a mechanism whereby a nuclear spin relaxes on a timescale that matches the nuclear Larmor frequency of a *J*-coupled neighbour, therefore causing it to relax. At high field, nuclei

causing SR2K often have very short values of nuclear $T_1$. Common cases often involve quadrupolar nuclei [202]. At low fields, nuclei such as ¹⁴N can also cause relaxation by SR2K [173] [191].

(iii) **Spin rotation** is a mechanism whereby nuclear spin states couple to rotational states engendering relaxation [203], [204]. A common case where such as relaxation mechanism occurs is in rapidly rotating methyl groups [205]–[207].

### 7.5. Coherent losses of polarization

During a *d*DNP experiment, the hyperpolarized solution travels from one magnet, the polarizer, to another, the liquid-state spectrometer. As the solution leaves the polarizer, it experiences a stray field with decreasing intensity. Conversely, as the sample enters the liquid-state spectrometer, it experiences its increasing stray field. How do the spins react to this field decrease and increase? Furthermore, what happens in the middle where the field might go to very low values or possibly vanish completely. This section aims at answering these two questions. In some cases, a rapid variation of the intensity or of direction of the field experienced by the nuclear spins during the transfer can excite coherence between NMR transitions. The portion of hyperpolarization that is turned into coherence rapidly dephases and is lost. We refer to these sorts of losses as “coherent” because they are the result of a deterministic process. No stochastic or random interactions are involved.

The ideal scenario for *d*DNP experiments is that the polarizer and the liquid-state spectrometer have non-shielded magnets with opposite polarity [50]. Indeed, non-shielded magnets have strong stray fields and, when the polarity of the magnets is opposite, their stray fields add up in the space between them. Such a situation typically ensures a minimal magnetic field on the order of mT along the transfer, with the direction of the field experienced by the spins changing smoothly from the polarizer to the liquid-state spectrometer. On the contrary, shielded magnets have rapidly decaying stray fields, which will cause fast variations of the field experienced by the nuclei during transfer. Furthermore, when the polarity of the two magnets is the same, their stray fields may cancel out at some point along the transfer pathway. In such cases, the use of a magnetic tunnel might be essential to preserve the polarization during the transfer.

**Creation of coherences by rotation of the magnetic field.**
Let us consider a single spin subject to a magnetic field. Let us now assume that this magnetic field has a fixed intensity but is rotating in space around an axis. We assume that, at time $t = 0$, the spin is aligned with the magnetic field. If the rotation of the field is infinitely slow, the spin always remains aligned with the magnetic field. Such a transformation is said to be “adiabatic”. In the opposite limit, if the direction of the field jumps infinitely fast by an angle, say $\pi/2$, the spin effectively experiences a sudden change of its Hamiltonian. This kind of transformation is said to be “non-adiabatic” or sudden [208]. Its state is now the superposition of two eigenstates in the basis of the new Hamiltonian. In other words, the spin is no longer in a stationary state: the instantaneous rotation has turned the population difference into a coherence. Whether the rotation may be considered as slow or fast is determined by the Larmor frequency of the spin. If the field rotates at a frequency that is slow with respect to the Larmor frequency, the spin is able to adapt and remains in an eigenstate of the Hamiltonian.

For example, during a *d*DNP experiment, a ¹³C spin travels at 5 ms⁻¹ from a polarizer to a liquid-state spectrometer with
opposite polarities separated by 5 m (transfer in 1 s). The field experienced by the spin goes from $-z$ to $+z$ (or conversely) which corresponds to a $\pi$ rotation. We assume for simplicity that the rotation has a constant frequency. The field thus rotates at a frequency of 0.5 Hz. The gyromagnetic ratio of $^{13}$C is 10.7 MHzT$^{-1}$. If the minimal field experienced by the spin is 1 mT during the transfer, its minimal Larmor frequency will be of 10.7 kHz. This is far above the frequency of the field rotation so the transfer will surely be adiabatic and will not cause any loss of polarization. If the magnetic field goes as low at 1 $\mu$T, however, the Larmor frequency of the $^{13}$C spin will be 10.7 Hz. This is still factor 20 higher than the frequency of the magnetic field rotation but is not as safe.

This simple reasoning allows one to develop an intuition for situations where the magnetic field rotation may not be adiabatic, and therefore induce the creation of coherences and consequent polarization losses. The risk of polarization losses may be assessed quantitatively, provided the precise field profile experienced by the spins during the transfer is known. Derived from Bloch's equations, the considerations above can be formalized by defining an adiabaticity parameter based on the comparison of the field rotation frequency with the Larmor frequency [50], [176], [208]:

$$ \frac{1}{B^2} |\vec{B} \times \frac{d\vec{B}}{dt}| \ll \gamma B \quad (14) $$

where $B$ and $\gamma$ are the magnetic field and the gyromagnetic ratio of the spins, respectively. The adiabaticity parameter may then be defined as:

$$ A = |\vec{B} \times \frac{d\vec{B}}{dt}| \frac{1}{\gamma B^3} \quad (15) $$

The transfer is adiabatic when $A$ is small compared to 1.

Such calculations might be important when shielded spectrometers are used. When the solution enters the stray field of the magnet, the direction of the field varies rapidly. In the case of a shielded magnet, this occurs at a lower magnetic field than for a non-shielded magnet. Equation 15 also shows that although going through a region of zero field or worse, going through a field inversion may cause polarization losses. Indeed, when the magnetic field becomes vanishingly small, the denominator of the adiabaticity parameter goes to zero causing the parameter $A$ to become infinite. In this situation, any variation of the field direction may induce coherences. The use of a magnetic tunnel is then crucial to maintain the polarization during the transfer [50]. Equations 14 and 15 are derived from Bloch's equations [208], and so only apply for an isolated single spin. Coupled spins may behave similarly in many cases but in special circumstances, one might have to take more effects into account by using a quantum mechanical description of the transfer. Such cases are illustrated in the next section.

Section 6.4 reviews some practical solutions to increase the magnetic field between the polarizer and the liquid-state spectrometer. Such strategies may prevent coherent polarization losses.

**Creation of coherences by a variation of intensity of the magnetic field.** For a single isolated spin, a change in the magnetic field intensity affects the Larmor frequency of the spin but does not mix its eigenstates. As a consequence, no matter how fast the variation of the magnetic field intensity is, it cannot induce coherences. On the other hand, pairs of $J$-coupled spins have different eigenstates depending on the magnetic field

strength. There is a critical magnetic field where the difference in Zeeman energies matches the $J$-coupling. When the magnetic field is far above this critical value, the spins can be considered to be in the Zeeman basis. When it is far below, the spins can be considered to be in the singlet-triplet basis [209]. The effect of transport through low fields on the lineshape of NMR spectra in the liquid-state has already been documented for the case where the spins enter the strong coupling regime adiabatically, i.e., when the field decreases slowly enough to preserve populations without creating any coherences [177]. If the field drops or increases rapidly near the critical field value, it may induce coherences and therefore cause polarization losses. The critical field value at which the transition between the two regimes occurs strongly depends on the spin system. For heteronuclear spin systems, this may occur in the $\mu$T regime, which is well known and exploited in the field of zero- to ultra-low field NMR (ZULF). [210] For homonuclear spin pairs, the critical point can occur at a magnetic field that depends on the strength of the $J$-coupling and the chemical shift difference between the two spins of interest [177]. Although this has not been reported yet, one may expect that the spin dynamics at low field may induce polarization losses by creating coherences in certain spin systems. This may occur at any point where the field intensity varies strongly. This could be when the solution leaves the polarizer, when it enters or leaves a magnetic tunnel, when it enters the liquid-state spectrometer or when it travels through an undesired field inversion. The phenomena that we foresee here as pitfalls for maintaining polarization are in fact deliberately encountered by those using parahydrogen hyperpolarization [211] and level anti-crossings (LACs) to transfer polarization [212], [213].
## 8. Hyperpolarized liquid-state NMR

One of the challenges of dDNP is that the detection in the liquid-state is an experiment in which the hyperpolarization is only possible once, after a long preparation in the solid-state. This section aims at guiding the operator through the choice of parameters for the liquid-state detection. We will then present two methods for the quantification of the liquid-state polarization which is a key result of all dDNP experiments.

### 8.1. Parameters for liquid-state detection

Virtually all conventional NMR experiments can be applied to samples hyperpolarized by dDNP. However, since the polarization and signal decay with time, one has to adapt the rf-pulse sequences and experimental schemes. As an example, 2D experiments may be performed on a dDNP hyperpolarized sample, provided one uses ultrafast (UF) versions of the rf-pulse sequences. In this section, we will detail how to set the parameters for a series of 1D acquisitions with small nutation angle rf-pulses and separated by a constant delay. This type of state detection, referred to as pseudo-2D, is the simplest and most common in dDNP and is illustrated in Figure 8a. Since each acquisition only costs a fraction of the magnetization, the evolution of the hyperpolarized spins can be monitored as a function of time. As simple as this detection scheme can be, it may give access to information on the longitudinal relaxation of the hyperpolarized spins, chemical exchange, chemical reaction and the stability of the injection process.

Due to the transient nature of hyperpolarized magnetization, one cannot shim the magnet, tune the probe and choose the acquisition parameters after the injection of the hyperpolarized sample in the liquid-state spectrometer. By the time these procedures would be finished, the polarization would have largely decayed. Therefore, one must prepare the liquid-state spectrometer for the acquisition on a different sample. An efficient strategy consists in performing a “blank” dissolution experiment, that is, to perform the dissolution and injection procedure on a sample that was not hyperpolarized but with the same experimental parameters and sample as the actual dDNP experiment, in order to obtain a sample in the liquid-state with the same composition and physical properties as the one that will result of the true dDNP experiment. This blank sample may be used to shim the magnet and tune the rf-probe. The final concentration of solutes in the liquid-state is usually on the order of 10 mM or less. Performing a nutation experiment with such low concentrations might not always be straightforward for low-gamma nuclei. In this case, one might have to increase the concentration of the solute so as to be able to perform nutation experiments. One must make sure that the change in concentration does not change the nutation parameters, especially if the solute is a salt.

The magnetic field used for liquid-state detection plays an important role here: higher magnetic fields of course imply improved sensitivity which is useful both for reference experiments at thermal equilibrium and to gain extra sensitivity in the actual dDNP experiment. On the other hand, the higher the magnetic field, the more shimming is required, and the rf-probe tuning is sensitive to subtle changes in the sample composition, filling of the NMR tube and physical parameters such as susceptibility and temperature. Such parameters may not be perfectly repeatable from one dDNP experiment to the next, which may affect the magnet shimming and rf-probe tuning at higher fields.

Since the intensity of NMR signals obtained by dDNP is large, care must be taken not to saturate the receiver. Furthermore, one usually does not want to use the entire polarization of the sample in a single acquisition. A natural choice is then to detect the hyperpolarized signal using a series of small angle rf-pulses separated by a delay. Ideally, one would first estimate the expected signal intensity so as to set the detection parameters rationally. Using the blank sample described above, one can determine the signal integral per mol.L⁻¹ of solute for a single scan with a gain of 1:

$$S_{n,m} = \frac{S}{NS \cdot RG \cdot C} \quad (16)$$

where S$_{n,m}$, NS, RG and C are the normalized molar signal, the number of scans, the receiver gain and the concentration of the solute, respectively. Based on the expected DNP enhancement and expected final concentration, one can estimate the signal integral that will be measured when performing the hyperpolarized experiment:

$$S^{\text{DNP}} \approx \epsilon \cdot S_{n,m} \cdot C^{\text{DNP}} \cdot RG^{\text{DNP}} \cdot \sin \theta^{\text{DNP}} \quad (17)$$

where S$^{DNP}$, ε, C$^{DNP}$, RG$^{DNP}$ and θ$^{DNP}$ are the estimated signal integral, the expected DNP enhancement, the expected solute concentration, the receiver gain and the pulse angle, respectively. With this in mind, one can set the gain and the rf-pulse angle so that the resulting signal remains below the saturation limit of the receiver. A common choice is to use 5° rf-pulses with a gain between 4 and 16, provided the signal does not saturate the receiver.

One also ought to choose the delay between acquisitions. Three considerations dictate this choice: the rf-pulse angle, the T$_2^*$ of the hyperpolarized solutes and the timescale of the process being studied. If P$_0^{\text{DNP}}$ is the polarization of the solute just after injection, the remaining polarization after the i$^{th}$ signal acquisition is given by (in analogy with Equation 8):

$$P_{i+1} = P_0^{\text{DNP}} (\cos \theta^{\text{DNP}})^i \quad (18)$$

The larger the rf-pulse angle, the more polarization each acquisition takes from the hyperpolarized solute. For example, applying 100 rf-pulses with an angle of 5° leaves 68% of the initial polarization. If the operator wishes to observe the decay of hyperpolarization during 100 s and chooses to separate each acquisition by 1 s, at the end of the detection a non-negligible portion of the signal decay (~32%) will be due to the application of the rf-pulses. Whether this is acceptable or not all depends on the aim of the experiment. How to account for the effect of the pulses in the data analysis is discussed in the next section. The time between each acquisition also limits the acquisition time, i.e., the time during which the free induction decay (FID) may be recorded. If the acquisition time is longer than 5 times the T$_2^*$ of each hyperpolarized solute the FID will be truncated, and the Fourier transformed signals will be distorted. Finally, whether the aim of the dDNP experiment is to monitor chemical reactions or to study relaxation, among other applications, the time between acquisitions will be crucial to appropriately capture the dynamics under scrutiny. Figure 45b-c shows an example of hyperpolarized decay recorded using a pseudo-2D experiment.