Marie Juramy

Giulia Mollica

Recent Progress in Nuclear Magnetic Resonance Strategies for Time-Resolved Atomic-Level Investigation of Crystallization from Solution

Recent progress in nuclear magnetic resonance strategies for time-resolved atomic-level investigation of crystallization from solution

Marie Juramy, Giulia

Introduction

Crystallization is a ubiquitous phenomenon and one of the most important physicochemical processes, underpinning numerous natural and synthetic fundamental processes in our everyday life, from biomineralization, weathering, or ice formation, to industrially and technologically relevant processes, such as the production of nanomaterials, ceramics or pharmaceuticals.

In materials science, crystallinity is highly valued. Indeed, the ordered spatial arrangement of the repeating structural motifs of a crystalline solid (e.g. atoms, ions, molecules) can lead to materials with very specific and well-controlled properties, and hence functionalities. Therefore, crystallinity can offer a handle over structure-property relations, helping the development of new functional materials with tailored properties.

Interestingly, organic molecular solids are often polymorphic, i.e. can form multiple crystalline structures. Polymorphism can constitute a true opportunity for materials science because, although chemically identical, the different polymorphs of a molecular compound can display radically distinct physico-chemical properties, which makes them, de facto, different materials in terms of their end-use.

As a consequence, when dealing with polymorphic solids, it is crucial to be able to direct crystallization towards the selective production of a specific polymorph if we want to control the material properties. This aspect is particularly important in pharmaceutical applications, where different polymorphs of an active pharmaceutical ingredient (API) can induce significant variations in solubility and bioavailability of the drug formulation, eventually determining the action of the drug. However, achieving polymorph selection requires the ability to control the outcome of crystallization, which in turn necessitates to understand the mechanisms governing crystallization. This remains today a major challenge that many techniques try to address.

Over the years we have observed the development of numerous experimental approaches directed at monitoring crystallization processes in real time over different time and space scales. Ideally, this requires to be able to monitor the sequence of events leading to the formation of the crystal from the solvated species, at the molecular, or even atomic, level.

Reaching the required atomic-scale details and ~s time resolution for both liquid and solid phases present in a crystallizing medium has been difficult so far because of limitations of existing analytical approaches. Indeed, from an analytical point of view, crystallizing solutions are complex chemical and physical mixtures. At any given crystallization time, multiple species with different physical state (liquid, solid), size (nm to μm scale), order (amorphous, crystalline), lifetime (sub-seconds to years), concentration (pM to M), can be simultaneously present. This complexity, together with difficulties in controlling sample preparation, contributes to the experimental challenge of reaching atomic-level structural details of key crystallization events. Among the most popular methods for time-resolved investigation of crystallization from solution, microscopy and diffraction have provided interesting insights. Spectacular advances in cryo Electron Microscopy (cryo-EM) brought a true revolution in structural biology by providing angstrom-scale structural resolution of proteins with no need of crystallinity.

Importantly, cryo-EM also helped prove the existence of non-classical mechanisms of crystallization in proteins and calcium carbonate. [START_REF] Pouget Emilie | The Initial Stages of Template-Controlled CaCO3 Formation Revealed by Cryo-TEM[END_REF][START_REF] Smeets | Calcium carbonate nucleation driven by ion binding in a biomimetic matrix revealed by in situ electron microscopy[END_REF] This technique is unique for imaging liquid and solid particles morphology (also distinguishing crystalline from amorphous species) and to identify the size of aggregates formed in crystallizing solutions over the nm-μm scales.

However, cryo-EM also shows several drawbacks that are critical for investigating crystallizing systems: i) it lacks chemical specificity; ii) sample preparation can be delicate; iii) while singleparticle cryo-EM provides Å-resolution images of proteins, the maximum resolution currently achievable on molecular compounds is ~nm. Diffraction, on the other hand, remains unique in providing Å-resolution structures of crystalline species, but cannot investigate amorphous solids, often present as intermediates of crystallization, with this level of resolution. Both techniques have been successfully employed for studying the evolution of crystallization from solution. Notably, in-situ diffraction approaches have been developed, in which crystallization occurs inside the diffractometer, enabling crystallization to be monitored as a function of time.

On the other hand, cryo-EM has also been employed for collecting nm-scale images of crystallizing solutions frozen at different crystallization times. The temporal resolution of these techniques is often system-and technique-dependent. [START_REF] Pienack | In-Situ Monitoring of the Formation of Crystalline Solids[END_REF] Alternatively, NMR appears as a viable technique because it can provide atomic/molecularlevel structural information on liquid or solid (amorphous or crystalline) matter with chemical specificity. [START_REF] Abragam | The principles of nuclear magnetism[END_REF] Therefore, NMR can potentially provide structural details on all the crystallization species with an atom-(or even isotope-) specific response, and without requiring long-range order. Recent studies clearly showed that in situ magic-angle spinning (MAS) solidstate NMR is a powerful approach to investigate crystallizing solutions (see figure 1B), although, as it will discussed later, it remains limited by the inherently low sensitivity of NMR. [START_REF] Hughes | A technique for in situ monitoring of crystallization from solution by solid-state 13C CPMAS NMR spectroscopy[END_REF][START_REF] Hughes | Direct observation of a transient polymorph during crystallization[END_REF][START_REF] Hughes | Exploiting In Situ Solid-State NMR for the Discovery of New Polymorphs during Crystallization Processes[END_REF][START_REF] Hughes | CLASSIC NMR": an in-situ NMR strategy for mapping the time-evolution of crystallization processes by combined liquid-state and solidstate measurements[END_REF] The aim of this review is to present a concise overview of recent strategies and applications of time-resolved NMR investigation of crystallization from solution, covering the last four years (see figure 1A). The manuscript is organized as follows. After introducing, in Section 2, the current challenges in the investigation of crystallization from solution for polymorphic organic solids, Section 3 focusses on the role of NMR in addressing these challenges. First, the essential tools of NMR required for the discussion are introduced. Then, the state-of-the-art of in-situ solid-state NMR methods for monitoring crystallization from solution appeared in the course of the last decade is briefly summarized, before discussing the limitations of this approach. The core of the review is covered in Sections 4 and 5, which present in more detail recent experimental developments to address the current challenges in monitoring crystallization processes using NMR and hyperpolarization (see figure 1D). Specifically, new in-situ and exsitu NMR strategies (see figure 1B,C) for investigating crystallization are introduced and discussed. These strategies rely on the use of cryogenic conditions (Section 4) and/or hyperpolarized NMR (Section 5). After a brief introduction on the basic principles and instrumentation of dynamic nuclear polarization (DNP) in the solid state (magic-angle spinning DNP, or MAS DNP) and by dissolution (dDNP) in Section 5.1, Section 5.2 presents the results obtained using MAS DNP through the so called "snapshot DNP" approach for ex-situ timeresolved study of crystallization from bulk and confined solutions. It is shown how the increased sensitivity of DNP, combined with the cryogenic operational conditions of MAS DNP, allow to significantly extend the temporal and structural resolution of more traditional in-situ solid-state NMR approaches, even enabling the acquisition of 2D NMR correlation experiments precious for detailed structural characterization of the observed species. It is also discussed how this approach enables the detection of transient and dilutes species, such as those forming at early-stages of crystallization, which had escaped observation using more traditional in-situ NMR approaches. Section 5.3 is dedicated to the sole application to date of dDNP to study in situ the early stages of crystallization in minerals. The review closes with an overview on future challenges in the field (Section 6). ] glycine in water/methanol solution, at 20°C. [START_REF] Hughes | Direct observation of a transient polymorph during crystallization[END_REF](Reused with permission from RSC: https://doi.org/10.1039/C0CC01007C). The method can also be applied on frozen solutions at cryogenic temperature to increase the time resolution. C) Ex-situ monitoring of bulk or confined crystallization by the "snapshot" approach. The evolution of crystallization is monitored by flash cooling, at specific points in time, a crystallizing solution that evolves at room temperature, hence capturing "snapshots" of the evolving system. The figure shows 13 C CPMAS NMR spectra of [1-13 C] glycine crystallizing in pure water recorded at 100 K at increasing crystallization times [START_REF] Vioglio | A Strategy for Probing the Evolution of Crystallization Processes by Low-Temperature Solid-State NMR and Dynamic Nuclear Polarization[END_REF]. D) Monitoring crystallization in-situ and exsitu using hyperpolarization techniques. The previous methods can be combined with hyperpolarization approaches to increase the sensitivity of NMR, enabling the detection and characterization of early stage of crystallization in bulk and confined media. The figure shows 13 C CPMAS (orange) and 13 C T1r-filtered CPMAS (green) DNP NMR spectra recorded at 100 K on [1-13 C] glycine confined in the pores of a mesoporous material at increasing crystallization times [START_REF] Juramy | Monitoring Crystallization Processes in Confined Porous Materials by Dynamic Nuclear Polarization Solid-State Nuclear Magnetic Resonance[END_REF].

Crystallization of polymorphic solids: current challenges

Since Kepler's interest in the symmetry of snowflakes, the origin of crystals has intrigued scientists for centuries. Over the years, theories of crystal nucleation and growth have been formulated, in which crystallization processes were interpreted as the result of layer-by-layer growth of monomeric chemical constituents such as atoms, ions or molecules. Description of crystallization has relied on such classical models for many years. In the last two decades, experimental observation of the presence of amorphous, transient species, preceding the non-classical crystallization (NCC) pathways. [START_REF] Gebauer | Prenucleation clusters and non-classical nucleation[END_REF] NCC relies on the aggregation of building blocks of higher complexity than monomers, such as droplets, nanoparticles, clusters or oligomers. Differently from classical views, NCC pathways can be multistep, and include the i) initial formation and ii) stabilization of the building blocks and the iii) subsequent formation of crystalline (or mesostructured) architectures. [START_REF] De Yoreo | Crystallization by particle attachment in synthetic, biogenic, and geologic environments[END_REF] These theories are not always easy to be validated by experimental data. This is particularly true for small organic molecules in solution, for which little experimental evidence of mechanisms of crystallization is available today. To make this picture even more complex is the fact that crystallization is (often rightfully) considered by many as an "art", as strategies for controlling the outcome of crystallization (i.e. which polymorph is eventually obtained) mostly rely on empirical approaches. Although the number of parameters that we can actively control is limited (e.g. solvent, temperature, rate of evaporation or cooling, concentration/supersaturation, etc), it can still be challenging to obtain completely reproducible results under the same experimental conditions. (In)famous cases of disappearing polymorphs, or unexpected polymorph conversions occurring after the -supposed -completion of crystallization can also happen, with potentially disastrous consequences in terms of the material's properties, affecting its end-use. For instance, patents of solid drug formulations must clearly state the crystal form in which the active pharmaceutical ingredient -API, often an organic molecular crystal -is present, because crystal form affects the solubility (and hence the bioavailability) of the API, eventually determining the drug action. Therefore, every unexpected polymorph change incurred during or after manufacturing the drug solid dosage form can result in serious health and economic damages.

In view of controlling the outcome of crystallization, it is necessary to clarify the molecular and atomic-level mechanisms leading to the formation of a specific polymorph, which requires to address the following three challenges:

1) Follow the sequence of events of crystallization at the atomic/molecular scale -To clarify the mechanisms underlying crystallization and achieve control of crystallization outcome, it is crucial to access to the sequence of events leading to the formation of a given polymorph from solution, detecting and identifying all the transient species formed along the crystallization pathway, with the appropriate time resolution and atomic/molecular spatial resolution.

2) Capture key events of crystallization: metastable forms, prenucleation, nucleation -Among the transient species that are worth investigating, recent studies show that pre-nucleation and nucleation events, happening early-on during crystallization from solution, are pivotal in determining the final crystal structure. However, at these stages the aggregates are generally nanometric, their concentration is very low, they move very fast in solution and might be extremely short-lived (ms to minutes, depending on the experimental conditions).

Consequently, detecting, characterizing, and following the evolution of these transient species into the crystallization medium, is a true experimental challenge -but vital to control the properties of the final product. More generally, capturing transient forms along the crystallization pathway is relevant for polymorph discovery.

3) Understand polymorph selection -In the case of polymorphic solids reviewed here, controlling the outcome of crystallization corresponds to directing the crystallization process so that one specific polymorph is exclusively formed. Such polymorph does not necessarily coincide with the thermodynamically stable form. Therefore, achieving polymorph selection requires for the most part to find experimental conditions that stabilize metastable (i.e. transient) polymorphs. One efficient strategy to achieve stabilization of metastable forms is to let crystallization occur in confined spaces, i.e. in crystallization chambers with typical size of the order of nm to μm [START_REF] Jiang | Crystallization under nanoscale confinement[END_REF][START_REF] Meldrum | Crystallization in Confinement[END_REF]. Under these conditions, common to many real-world crystallization processes, the average chamber size can approach the typical nucleus size of the crystallizing compound (~nm), inducing significant deviations from the outcome of bulk crystallization, although effects are seen at length scales far exceeding those of a critical nucleus (~μm). Interestingly, organic compounds possess strong pore-size and pore-geometry dependence on the polymorph formed: pores with a diameter below a certain critical size tend to stabilize amorphous forms, which can be used in drug formulations to increase the solubility of poorly soluble drugs.

Addressing these challenges is vital in view of improving our control over crystal formation.

In the next section, we discuss the tools that NMR can deploy to tackle these challenges.

NMR for the investigation of crystallization

Experimental aspects

The first reason that justifies the use of NMR for investigating crystallization of polymorphic solids is the simple fact that high-resolution solid-state NMR allows straightforward identification of the different solid forms (amorphous or crystalline polymorphs) of a solid. For instance, in the case of organic (molecular) solids, the high resolution 1D carbon-13 ( 13 C) NMR spectrum acquired under magic-angle spinning (MAS) conditions shows in principle a separate peak for each crystallographically distinguishable carbon atom -although fortuitous overlap can occur [16,[START_REF] Apperley | Solid-state NMR: basic principles and practice[END_REF]. For a given carbon atom, the position of the corresponding 13 C isotropic peak depends on the atom environment. Differently from the case of liquid-state NMR, peak positions in MAS NMR spectra of solid samples are not only sensitive to the intra-molecular structure (i.e. conformation), but also depend on the supra-molecular structure (i.e. crystal packing). Therefore, i) conformational changes occurring between different crystal forms of the same molecular compound, or ii) different supramolecular arrangements, or both, can all lead to differences among the isotropic 13 C chemical shifts of a given carbon site across different polymorphs. As a result, the 13 C isotropic NMR spectrum of a crystalline solid becomes a "fingerprint" of the polymorph, and can be used for its identification. In the last two decades, this unique sensitivity of the chemical shift to the atom environment in the crystal has led to the development of a new branch of crystallography, termed "NMR crystallography", [16][START_REF] Apperley | Solid-state NMR: basic principles and practice[END_REF][START_REF] Ashbrook | Combining solid-state NMR spectroscopy with first-principles calculations -a guide to NMR crystallography[END_REF][START_REF] Baias | De Novo Determination of the Crystal Structure of a Large Drug Molecule by Crystal Structure Prediction-Based Powder NMR Crystallography[END_REF][START_REF] Bryce | NMR crystallography: structure and properties of materials from solid-state nuclear magnetic resonance observables[END_REF][START_REF] Szell | A curious case of dynamic disorder in pyrrolidine rings elucidated by NMR crystallography[END_REF] in which experimental NMR parameters (isotropic or anisotropic chemical shifts, but also dipolar and quadrupolar interactions -for nuclei with spin I>1/2) are combined with the same parameters computed on a series of candidate structures predicted through crystal structure prediction (CSP) methods, with the aim of reaching complete structure determination of powdered crystalline samples that can hardly be characterized by other experimental methods [START_REF] Ashbrook | Combining solid-state NMR spectroscopy with first-principles calculations -a guide to NMR crystallography[END_REF][START_REF] Bonhomme | First-Principles Calculation of NMR Parameters Using the Gauge Including Projector Augmented Wave Method: A Chemist's Point of View[END_REF].

Beyond straightforward polymorph identification, NMR also provides chemical specificity through its nuclear isotope selectivity, providing the atomic-level speciation required to interpret crystallization events. In organic solids, in spite of its low natural abundance (~1%), 13 C nuclei are extremely popular because of their otherwise favorable NMR properties (gyromagnetic ratio, I=1/2), making it an "easy" identification probe. Other NMR-active nuclei omnipresent in organic compounds, such as 1 H, 15 N, 17 O, can also be exploited with similar purposes, to obtain even more detailed structural information through the acquisition of 1D and 2D correlation experiments. Unfortunately, the low natural isotopic abundance of 15 N and 17 O nuclei is a strong limitation to their routine use for structure analysis, unless isotopic enrichment or hyperpolarization techniques are used [START_REF] Métro | Unleashing the potential of 17O NMR spectroscopy using mechanochemistry[END_REF][START_REF] Blanc | Dynamic Nuclear Polarization Enhanced Natural Abundance 17O Spectroscopy[END_REF].

Another major advantage of solid-state NMR for the study of crystallization from solution is its ability to investigate both crystalline and amorphous solids. Typically, the simple observation of the NMR lineshape already provides an indication on the crystalline or amorphous nature of the identified solid phase: amorphous (rigid) phases are characterized by large peaks (typically several hundred up to thousands of Hz for 13 C signals in MAS spectra), while crystalline forms show correspondingly narrower peaks (50-100 Hz). Of course, dynamics can affect the linewidth and should be taken into account, also providing a further source of information on its own. [START_REF] Szell | Taming the dynamics in a pharmaceutical by cocrystallization: investigating the impact of the coformer by solid-state NMR[END_REF] Finally, it is worth mentioning that the singularity of NMR comes from the possibility of employing an almost infinite set of 1D and 2D correlation experiments sensitive to the presence of specific interactions among the nuclear spins and able to reveal the presence of structural motifs such as hydrogen bonds, but also to provide quantitative structural information such as internuclear distances (through the measurement of dipolar interactions) or domain dimensions (through the analysis of the spin diffusion phenomenon), across the Angstrom-μm scales.

Although these aspects mainly concern the advantages of using NMR to investigate solid phases, it should not be forgotten that NMR can also analyze liquid phases, making it an extremely versatile tool for the study of the liquid components of crystallizing solutions. As it will be discussed later, the sensitivity of solid-state NMR to the dynamic properties of the species present can be exploited to selectively observe liquid or solid species based on their mobility.

From this discussion it is clear that NMR can provide the atomic-level details required for clarifying the mechanisms of crystallization. In the following sections: first, we will present how NMR has been successfully used in the last decade for investigating crystallization in situ (i.e. inside the spectrometer) and mention the limitations of this approach (Sections 3.2 and 3.3); second, we will discuss recent efforts in overcoming such limitations through the development of new in-situ (Section 4) and ex-situ approaches combined with hyperpolarization techniques (Section 5).

State of the art of in-situ NMR for crystallization

In mid 2000's, K.D.M. Harris and coworkers introduced for the first time the idea of using solid-state NMR for in-situ (i.e. inside the spectrometer) monitoring of crystallization from solution. The concept is to let crystallization occur directly into the NMR sample holder -a ceramic cylinder (NMR rotor) -and acquire multiple high resolution 1D MAS spectra of the crystallizing solution as a function of the crystallization time. [START_REF] Harris | NMR Crystallization': insitu NMR techniques for time-resolved monitoring of crystallization processes[END_REF] In the most popular version of this approach, a supersaturated solution of the solute to crystallize is first prepared at room temperature and transferred to the NMR rotor. Then, while spinning, the rotor containing the solution is warmed up using the temperature control of the spectrometer until complete dissolution of the solid particles, which can be verified by NMR. Then, the temperature is set to a lower temperature to induce supersaturation and hence crystallization inside the rotor, which is monitored using 1D solid-state NMR techniques.

The numerous studies appeared in the last decade using this approach have demonstrated that NMR is an efficient tool to monitor the structural variations occurring during crystallization as a function of time. The first reported applications exploited the ability of solid-state NMR to selectively monitor the solid phase of heterogenous liquid-solid systems typical of crystallizing solutions through the choice of NMR pulse sequences able to select the sole solid phase, such as cross-polarization (CP), hence eliminating the contribution of solvated species dominating the NMR spectrum. [START_REF] Hughes | A Technique for In Situ Monitoring of Crystallization from Solution by Solid-State 13 C CPMAS NMR Spectroscopy[END_REF] This enabled the possibility of detecting the formation of the first solid particles from solution as well as their identification. Moreover, this approach could be exploited to follow the subsequent structural evolution of these solid particles. [START_REF] Hughes | Direct observation of a transient polymorph during crystallization[END_REF] As previously discussed, this aspect is particularly relevant for polymorphic solids, as it can shed light on the pathway of crystallization. The method was first applied to follow the crystallization of 13 Cisotopically enriched glycine from different solvents. [START_REF] Hughes | A Technique for In Situ Monitoring of Crystallization from Solution by Solid-State 13 C CPMAS NMR Spectroscopy[END_REF] Later this approach was extended to the observation of both the solid and liquid phases by measuring (almost simultaneously) the solid-and liquid-state NMR spectra of the crystallizing solution using techniques able to select either rigid or mobile phases, respectively. This approach, termed "CLASSIC NMR", could yield information on structural changes occurring in the solid and liquid phases as a function of time. [START_REF] Hughes | CLASSIC NMR": an in-situ NMR strategy for mapping the time-evolution of crystallization processes by combined liquid-state and solidstate measurements[END_REF] Through the detection of changes in the 1D 13 C spectra of either 13 C-enriched or natural isotopic abundance samples, it was possible to reveal the time window in which each transient solid form was present, and even discover the existence of new polymorphs.

[7]

Glycine/water: a model system for the crystallization of polymorphic solids

Most of these developments were tested on polymorphic model systems with known crystallization behavior to evaluate the impact of the experimental protocol on the crystallization itself. Among these systems, solutions of glycine in water are considered as an archetypal system for investigating crystallization of polymorphic organic solids. Glycine has three known polymorphs under ambient conditions, denoted as α, β and γ. [START_REF] Boldyreva | Polymorphism of Glycine, Part I[END_REF][START_REF] Boldyreva | Polymorphism of glycine, Part II[END_REF] The least stable form is β-glycine, which tends to transform more or less rapidly into α-glycine depending on humidity. The α polymorph of glycine eventually transforms into γ-glycine, the thermodynamically stable polymorph of glycine. In the literature, it is reported that α-glycine tends to form from pure water at neutral pH, while the use of deuterated water increases the probability of producing the γ form. Glycine is a very convenient model system not only for its rich polymorphism and well-known crystallization properties, but also for its NMR properties.

In fact, the 13 C isotropic chemical shift of the carbonyl carbon of glycine differs significantly (ca. 1 ppm) among these three polymorphs, providing their easy identification by solid-state NMR. Specifically, at room temperature, the 13 C chemical shifts of α, β and γ forms are, respectively: 176.5 ppm, 175.5 ppm and 174.5 ppm. [START_REF] Taylor | 13 C CP/MAS: Application to Glycine[END_REF] These chemical shifts vary slightly at cryogenic temperature, as indicated in Figure 2C.

Glycine was adopted as a model system also for in-situ NMR. For instance, this approach was used to investigate the effect of deuteration on the formation of γ-glycine, [START_REF] Hughes | A Multi-technique Approach for Probing the Evolution of Structural Properties during Crystallization of Organic Materials from Solution[END_REF][START_REF] Hughes | The eEfect of Deuteration on Polymorphic Outcome in the Crystallization of Glycine from Aqueous Solution[END_REF] and of the addition of methanol to the formation and transformation of β-glycine. [START_REF] Hughes | Direct observation of a transient polymorph during crystallization[END_REF] Since these initial applications, the approach has then been extended to the study of the formation of complex polymorphic systems, including urea/α,ω-dihydroxyalkanes cocrystals [START_REF] Hughes | Exploiting In Situ Solid-State NMR for the Discovery of New Polymorphs during Crystallization Processes[END_REF], m-ABA [START_REF] Williams | Discovery of a New System Exhibiting Abundant Polymorphism: m-Aminobenzoic Acid[END_REF] and more recently, MOFs [START_REF] Jones | Exploiting in situ NMR to monitor the formation of a metal-organic framework[END_REF] or cements [START_REF] Hughes | Exploiting in-situ solid-state NMR spectroscopy to probe the early stages of hydration of calcium aluminate cement[END_REF].

Limitations of in-situ NMR

Although in-situ NMR provides a unique opportunity to investigate liquid and solid phases of a crystallizing solution with atomic-level sensitivity, this approach presents several limitations.

As discussed by Harris [START_REF] Hughes | A Multi-technique Approach for Probing the Evolution of Structural Properties during Crystallization of Organic Materials from Solution[END_REF], crystallization reactors used for in-situ MAS NMR are relatively inaccessible, mm-sized, closed ceramic cylinders ("NMR rotors"). Under these conditions, crystallization can be triggered by inducing supersaturation in the crystallizing solution via a temperature drop. However, other approaches, such as solvent evaporation, reactant mixing, or addition of an antisolvent, are impractical. Moreover, the NMR spectra of the crystallizing solution are acquired while the rotor is spinning at thousands of revolutions per second under strong magnetic fields: both rotor spinning and the presence of a magnetic field might affect the crystallization outcome. The other main drawback of in-situ NMR approaches arises from the low sensitivity of NMR. Indeed, when detecting rare nuclei on natural isotopic abundance samples, the effective time resolution of in-situ NMR is determined by the time required to obtain a good S/N, ranging from minutes to hours, depending on the system investigated. Such time resolution might be too long to detect short-lived transient phases such as nucleation and prenucleation species, or metastable polymorphs, which could have evolved by the end of the experiment. At the same time, it might be too short to apply more elaborate, 2D NMR correlation experiments involving rare nuclei on samples analyzed at natural isotopic abundance. As a result, the reported in-situ NMR studies only relied on isotropic chemical shifts (i.e. 1D MAS NMR spectra) as the sole exploitable structural information on the species present in the crystallization medium. Moreover, the low sensitivity of NMR prevented the detection of nucleation and pre-nucleation species, which are both diluted and transient.

In the last four years, new experimental NMR strategies have been developed in our group and others to try to overcome these limitations. These developments, reviewed in the following sections, essentially rely on the use of i) cryogenic conditions (Section 4) and/or ii) hyperpolarized NMR (Section 5).

In-situ NMR investigation of crystallization from frozen solutions

We recently showed that playing with temperature can provide a partial solution to limitations of in-situ NMR for investigating crystallization. By reducing the temperature below the solvent freezing point, viscosity increases significantly, inducing slower diffusivity of the solute species and longer correlation times for molecular tumbling. Overall, these conditions can help trapping transient forms of crystallization, hence strategies were explored in our group to see whether this might be an efficient way of increasing the time resolution of the analysis.

As a first attempt, we explored the possibility of adapting the in-situ NMR approach to monitor crystallization of glycine from frozen aqueous solutions [START_REF] Vioglio | Insights into the Crystallization and Structural Evolution of Glycine Dihydrate by In Situ Solid-State NMR Spectroscopy[END_REF]. After flash cooling the solution to 160 K, a broad signal was obtained, centered at 173.9 ppm, which did not coincide with any of the known glycine polymorphs at this temperature. This signal, identified as a glassy (i.e. amorphous) phase of solvated glycine molecules, was a clear indication that the flash cooling occurs rapidly enough to avoid glycine crystallization.

However, warming the solution up to 209 K led to the progressive disappearance of the broad peak and corresponding appearance of a sharp peak at 173.5 ppm, compatible with an amorphous => crystalline phase transformation. Interestingly, this new peak did not coincide with any known crystalline form of glycine at the same temperature (see Figure 2C), indicating the presence of a polymorph never observed before in NMR. Further warming of the sample induced transformation of this new phase into β-glycine. Hence, this simple 1D 13 C CPMAS experiment enabled i) the observation of the formation and transformation of a crystalline phase from a frozen solution using NMR, ii) the detection of a new crystalline phase for glycine, and iii) the first in-situ NMR observation of the formation of β-glycine from pure water. A very important point of this approach is that, by controlling the temperature, the (time) evolution of crystallization could also be controlled (slowed down, or even stopped, depending on the temperature). Therefore, the temperature-dependent study of frozen solutions also enabled the acquisition of 2D experiments in the framework of in-situ NMR for the first time. In particular, by repeating the crystallization procedure up to 212 K, 1 H-13 C HETCOR 2D experiments could be acquired on the new polymorph. The 1 H- 13 C HETCOR spectrum acquired in these conditions, shown in Figure 2D, revealed the presence of a correlation between the carbonyl carbon of the new polymorph and the protons belonging to water molecules, suggesting the presence of a hydrated polymorph of glycine. Interestingly, this correlation could not be observed for the β-polymorph, simultaneously present in the sample following partial transformation. A dihydrate polymorph of glycine (glycine dihydrate, GDH) had recently been reported by PXRD in similar cryogenic conditions but had never been observed before by NMR [START_REF] Xu | The Structure of Glycine Dihydrate: Implications for the Crystallization of Glycine from Solution and Its Structure in Outer Space[END_REF]. Interestingly, the crystal structure reported for this polymorph has one molecule of glycine in the unit cell. The observed 13 C CPMAS spectra were consistent with this assignment, since the number of distinct carbon signals in the 13 C spectrum coincides with the number of carbon atoms in the glycine molecule. To confirm that the new polymorph was indeed GDH, 13 C-13 C dipolar recoupling experiments were carried out, which could provide quantitative structural information in terms of carbon-carbon distances. Specifically, 13 C-13 C dipolar buildup curves were acquired as a function of the recoupling time τDQ on 13 C1-glycine aqueous solution showing the narrow 173.5 ppm signal. These curves only depend on the intermolecular 13 C××× 13 C distances between the carboxylate groups of glycine underlying the signal selected for the analysis, and can be used to estimate the effective distance between the corresponding carbon atoms in the observed solid phase. As shown in Figure 2E, these build-up curves showed a very good agreement with the theoretical curves expected for the GDH crystal structure, hence confirming the new polymorph as being GDH.

These results clearly showed the added value of investigating crystallization from frozen solutions using in-situ NMR. The main outcome of this investigation was the proof that cryogenic conditions improve the stability of metastable phases over time. As a consequence, these phases can be trapped and then characterized successfully at the atomic level using solidstate NMR techniques, overcoming the time resolution limitation of traditional in-situ NMR approaches and enabling the acquisition of structurally informative 2D NMR experiments with no or minimal evolution of the crystallizing system during the acquisition. Moreover, because the solution is frozen, the effect of magic angle spinning on crystallization is reduced.

Nonetheless, the method still presents some of the limitations previously discussed. First, since crystallization still occurs inside the spectrometer, possible effects of magnetic field on the crystallization process are not eliminated. Moreover, although this approach was successful for glycine, the use of cryogenic crystallization conditions might not be ideal for other crystallizing systems. On the bright side, however, cryogenic conditions increase the time resolution of the analysis, which in turn helps sensitivity by enabling longer signal acquisitions. Similarly, using cryogenic temperatures also increases sensitivity through the Boltzmann law. Notwithstanding these improvements with respect to in-situ NMR analysis at room temperature, sensitivity still remains the main limitation to the detection of diluted species such as prenucleation and nucleation species. In the next sections, recent attempts at overcoming sensitivity issues while providing more flexible crystallization conditions are discussed.

5 Overcoming sensitivity limitations in the NMR analysis of crystallization: ex-situ and in-situ hyperpolarized NMR approaches

Dynamic nuclear polarization: general principles and instrumentation

Hyperpolarization methods are a valid approach enabling the sensitivity of NMR to be increased by several orders of magnitude, depending on the specific approach employed.

Among the existing hyperpolarization methods, in recent years, the development of high-field Dynamic Nuclear Polarization (DNP) reshaped the field of magnetic resonance by alleviating the issue of low sensitivity. [START_REF] Michaelis | Handbook of high field dynamic nuclear polarization[END_REF][START_REF] Griffin | High field dynamic nuclear polarization-the renaissance[END_REF] In DNP NMR, the sample is doped with paramagnetic compounds containing unpaired electrons, referred to as polarizing agents (PA). Electron polarization (i.e. signal) is transferred to the nuclei of the sample upon microwave (MW)

irradiation (usually at cryogenic temperatures), yielding maximum NMR signal enhancements equal to the ratio between the gyromagnetic ratios of the electron and the observed nucleus.

Thanks to the pioneering work of R. Griffin and coworkers, [START_REF] Griffin | High field dynamic nuclear polarization-the renaissance[END_REF] DNP could be combined with magic-angle spinning (MAS) solid-state NMR techniques at high magnetic fields for investigating complex solid materials including proteins, battery materials, catalysts, nanoparticles, active pharmaceutical ingredients (APIs), pharmaceutical formulations, organic nanotubes, polymers and many others, helping address important scientific questions. [START_REF] Rankin | Recent developments in MAS DNP-NMR of materials[END_REF][START_REF] Rossini | Materials Characterization by Dynamic Nuclear Polarization-Enhanced Solid-State NMR Spectroscopy[END_REF] Sensitivity enhancement obtained by MAS DNP, of about 1-2 orders of magnitude at typical operational temperatures of ~100 K, enabled NMR detection of dilute sample moieties, such as surfaces, [START_REF] Berruyer | DNP in Materials Science: Touching the Surface[END_REF] and could even provide quantitative structural details such as internuclear distances between rare nuclei on natural isotopic abundance samples. [START_REF] Mollica | Quantitative Structural Constraints for Organic Powders at Natural Isotopic Abundance Using Dynamic Nuclear Polarization Solid-State NMR Spectroscopy[END_REF] Figure 3 In parallel to the development of MAS DNP, dissolution DNP methods were also developed, pioneered by Ardenkjaer-Larsen and coworkers [START_REF] Ardenkjaer-Larsen | Increase in signal-to-noise ratio of > 10,000 times in liquidstate NMR[END_REF], which enabled the NMR analysis of hyperpolarized samples in the liquid state. Although the DNP principle is the same (electron spin=>nuclear spin polarization transfer under microwave irradiation at low temperature), the instrumentation for dDNP has its own specificities, which are briefly summarized below.

Because in dDNP the sample is polarized at T < 4 K, much larger signal enhancements, of 3 to 4 orders of magnitudes, are commonly achieved in dDNP. A dDNP instrument, depicted in Figure 3B, is essentially composed of an NMR magnet adapted for the study of liquid-state sample under static conditions, a polarizer, and a transfer line allowing to inject the hyperpolarized sample from the polarizer to the NMR magnet.

Under the typical operational conditions of dDNP, the sample of interest is dissolved in a mixture of protonated and deuterated solvent (usually H2O and D2O) in the presence of a glass forming agent as glycerol or DMSO, as well as the PA. In dDNP, the formation of a good glass is essential to the success of the analysis, so significant amounts of glycerol (~60 %) are typically added to the initial solution. The solution is then inserted inside the polarizer, where the sample space is flooded with liquid helium, turning the liquid sample into a glass. At a temperature between 1 and 2 K, the sample is irradiated with microwaves at a frequency near the electron spin resonance of the PA, allowing to transfer the electron spin polarization to the nearby nuclei. Once polarized, the sample is rapidly melted using a high-pressure flush of hot liquid. The hyperpolarized liquid is then propelled out of the polarizer and rapidly (~ms to s) transferred through a magnetic transfer line to the NMR magnet for detection at room temperature. Since, in the absence of microwave irradiation, the polarization only survives for a few seconds before the system returns to equilibrium, current applications of dDNP only allow acquisition of single scan spectra. Moreover, following the addition of the hot liquid, the sample is diluted and polluted.

DNP under MAS conditions: ex-situ approaches

As discussed in Section 5.1, to maximize the sensitivity enhancement produced by dynamic nuclear polarization, dedicated spectrometers must currently operate at cryogenic temperature.

Specifically, the optimal operational temperature in commercial MAS DNP spectrometers is 100 K. In the application discussed in Section 4, a MAS DNP spectrometer was employed by modifying the operational conditions so that the temperature could be increased up to ~200 K, hence enabling in-situ NMR investigation of crystallization from frozen solutions as a function of temperature. However, when using bis-nitroxide radicals as polarizing agents, the DNP sensitivity enhancements sensibly decrease with increasing the temperature [START_REF] Rankin | Recent developments in MAS DNP-NMR of materials[END_REF]. As a consequence, no DNP effect could be exploited for investigating crystallization from frozen solution using in-situ NMR approaches. However, by fixing the temperature to 100 K to satisfy DNP requirements, in-situ NMR analysis of crystallizing systems becomes impractical. The problem hence seemed unsolvable.

Inspired by the work of R. Tycko [START_REF] Hu | Detection of a transient intermediate in a rapid protein folding process by solid-state nuclear magnetic resonance[END_REF], an alternative strategy to in-situ NMR was developed in our group to overcome this limitation and take advantage of DNP sensitivity enhancement for the study of crystallization. This approach, depicted in Figure 4A, relies on ex-situ analysis of crystallizing solutions using MAS DNP. The crystallizing system is studied at specific time points during crystallization (that takes place at ambient temperature) by quenching the system rapidly to low temperature. Rapid freezing of the solution stops the crystallization process and the frozen solution can then be investigated in detail using a vast range of NMR techniques.

Because the solution remains frozen while inside the spectrometer, more elaborated NMR experiments can be applied to reveal detailed structural insights. Moreover, the operational conditions are compatible with DNP.

In Section 5.2.1 we discuss how this ex-situ NMR strategy can be used to study crystallization processes occurring in the bulk. Then, Section 5.2.2 presents a modification of this strategy also recently reported by our group, which enables solid-state NMR and DNP study of crystallization under confinement. The experimental procedure developed to study crystallization from bulk solutions using exsitu NMR is depicted in Figure 4A. An under-saturated solution of the solute to crystallize is prepared at high temperature, and then is separated into several identical NMR rotors. Because the rotors are conserved at room temperature, the solution contained in each rotor is slowly cooled down, reaching supersaturation and triggering crystallization. Then, crystallization takes place in parallel in each rotor under identical conditions, at constant temperature. At specific points in time during crystallization, one of the rotors is inserted into the DNP spectrometer at 100 K, and the solution contained in it is frozen rapidly (to ca. 100 K in less than 1 min). Then, NMR (and DNP) experiments are carried out on the frozen solution to characterize the solid phase(s) present, hence providing a "snapshot" of the crystallization solution at a specific point in time.

Ex-situ investigation of crystallization from bulk solutions

The method was demonstrated on the crystallization of glycine [START_REF] Vioglio | A Strategy for Probing the Evolution of Crystallization Processes by Low-Temperature Solid-State NMR and Dynamic Nuclear Polarization[END_REF]. The first aspect that had to be assessed was whether the rapid quench of the crystallization system could trigger crystallization, hence compromising the interpretation of the data. To verify this aspect, glycine was used as a model system. Indeed, by rapidly freezing a glycine/water solution that is undersaturated at room temperature, no crystallization should be observed, unless it is induced by the experimental protocol itself. The NMR results acquired on rapidly frozen undersaturated aqueous solutions of glycine only revealed a large signal centered at 173.9 ppm for the carbonyl carbon. This signal (coincident with the one detected in the 13 demonstrated that the strategy adopted had no significant impact on the crystallization process, and that it was an efficient way to trap metastable forms in the NMR spectrometer. The main drawback was the low DNP enhancement obtained, comprised between 1 and 2 for all the signals detected. Indeed, unless freezing occurs very rapidly (at least 10 5 °/s), the use of pure H2O is not recommended for DNP as it tends to form microcrystalline domains, causing PA segregation and hence decreasing the efficiency of the DNP polarization transfer. To overcome this limitation, a common practice is to add a glass-forming agent -such a glycerol -to water so as to favor a more homogeneous distribution of the PA within the analyzed sample (here, the crystallizing solution), helping the formation of a vitreous phase. To guarantee optimal glass formation, typical solvent formulations for DNP, such as the "DNP juice", often contain large amounts of glassy agents (up to 60%). However, this solution is incompatible with most applications for the investigation of crystallization, because the solubility of the crystallizing species (but also the crystallization pathway in case of polymorphic solutes) is strongly affected by the choice of solvent.

To make the snapshot strategy compatible with good DNP sensitivity enhancements while minimizing the risk that the amount of glycerol added to the solution might affect the crystallization process, a minimum amount of glycerol (5% in volume) was added to the solution. The results showed in Figure 4C 3.09 Å and 3.34 Å for these two polymorphs, respectively. However, the presence of an autocorrelation peak between solvated molecules of glycine in the glassy phase (peak at 173.9 ppm) was unexpected under the concentration conditions used. Indeed, this peak revealed the existence of short intermolecular distances in this phase that were interpreted as possible pre-nucleation or nucleation clusters present in the supersaturated crystallization solution prior to quenching.

Finally, the method was also tested by repeating the same analysis on a sample prepared using D2O instead of H2O, all the other experimental parameter being unchanged. The expected glycine polymorphic transformation β => α => γ was observed within 24 h from the beginning of crystallization, exactly as reported form the literature.

Overall, the "snapshot DNP" approach significantly expanded the possibilities offered by NMR for studying crystallization solutions, giving the opportunity to acquire more sophisticated 2D NMR spectra for quenched samples of the crystallization system preserved at the quench temperature and significantly increasing the sensitivity of NMR by DNP. Moreover, the results obtained on glycine confirmed that the experimental procedure used, including the rapid quench of crystallization and the presence of the PA in the crystallization medium, does not affect the expected crystallization outcome or the sequence of solid forms present during the crystallization process pathway. These results suggest that the snapshot approach is a promising way to achieve molecular-level characterization of crystallization from solution, hence enhancing our fundamental understanding of crystallization mechanisms in the case of polymorphic solids.

Importantly, in the snapshot approach, the PA is added directly into the crystallizing solution at millimolar concentration. In the case of glycine presented here, no effect due to the presence of the PA in the crystallization medium could be discerned. However, this might not be the case for all the systems and generalization is impossible. Therefore, other sample preparation methods compatible with the investigation of crystallization under DNP conditions were highly sought-after. Recent efforts by our group to solve this issue are presented and discussed in Section 5.2.2.

DNP approaches for the study of crystallization in confinement

As discussed in Section 5.2.1, the snapshot approach enabled sensitivity-enhanced ex situ NMR investigation of crystallization from bulk solutions using DNP. However, in this approach the PA is in direct contact with the crystallizing solution and could potentially influence the crystallization process. Recently, we reported a new strategy to investigate crystallization from solution using DNP that eliminates the possible interference between the PA and the crystallizing species [START_REF] Juramy | Monitoring Crystallization Processes in Confined Porous Materials by Dynamic Nuclear Polarization Solid-State Nuclear Magnetic Resonance[END_REF]. This strategy relied on the use of a new class of polarizing agents for DNP developed in our laboratory, consisting of mesoporous SBA-15 silica material (pore diameter ~7-8 nm) in which the DNP polarizing agents (TEMPO nitroxide radicals) are embedded in the pore walls (see Figure 5A) [START_REF] Besson | Silica materials with wall-embedded nitroxides provide efficient polarization matrices for dynamic nuclear polarization NMR[END_REF]. These materials have several advantages: i) being incorporated into the walls of the material, the PA is hidden (physically separated) from a solution filling the mesopores, eliminating the risk of interference; ii) the PA is uniformly distributed within the pore walls, hence eliminating the need of a glass-forming agent to improve radical dispersion, and thus enabling DNP in pure water; iii) crystallization occurs under nanoconfinement. The latter point comes as an extra benefit when investigating the mechanisms of crystallization in polymorphic solids. In fact, it is well known that, when crystallization occurs in chambers with typical size of the order of the critical nucleus of the crystal, the outcome of crystallization is strongly affected, generally leading to stabilization of forms that are highly unstable (hence usually short-lived) under bulk conditions [START_REF] Jiang | Crystallization under nanoscale confinement[END_REF][START_REF] Meldrum | Crystallization in Confinement[END_REF]. Therefore, the use of mesoporous radical species can be an efficient way not only to explore crystallization using DNP, but also to select specific polymorphs.

The DNP NMR strategy adopted to monitor the evolution of crystallization from solution under confinement is depicted in Figure 5B. An undersaturated solution of 13 C1-glycine in H2O is used to impregnate the pore volume of the mesoporous silica material. Then, the impregnated material (a "dry" powder) is left open in a desiccator at fixed humidity at room temperature, allowing crystallization to occur under nanoconfinement, by solvent evaporation. The "snapshot DNP" approach is then applied to the impregnated material. At a specific time point after the impregnation (which corresponds to t=0), an aliquot of the material is extracted from the vial and transferred to the DNP rotor. Then, the rotor is inserted into the DNP solid-state NMR spectrometer at ~100 K, quenching the crystallization process. As previously described in the case of the snapshot DNP approach applied to the study of bulk solutions, no further evolution of the crystallization process occurs while the sample is conserved (under magic angle spinning) inside the DNP NMR spectrometer, and the sample represents the crystallizing solution frozen at the time of quenching. The sample can then be analyzed using DNP NMR.

This procedure is repeated at subsequent time points: for each time point, a new aliquot is extracted from the same crystallization system, so that individual snapshots of the crystallization system can be investigated using NMR to identify the different phases present as a function of time.

Figure 5C shows the results obtained by monitoring the evolution of the crystallization of glycine in pure water using this approach. In this case, three snapshots of glycine crystallization were analyzed, collected 15 min, ~2 days, and ~3 days after the impregnation of the material, respectively. On each snapshot, different 13 C CPMAS experiments were performed, and, similarly to previous studies where glycine was used as a model system, the 13 C spectral region corresponding to the carboxylate group was explored. Interestingly, the simple comparison between the 13 C CPMAS spectra acquired on the first snapshot in the presence and in the absence of microwaves (i.e. with and without DNP sensitivity enhancement) provided a sensitivity enhancement of about 25, showing a significant improvement with respect to the case of snapshot DNP of bulk solutions after the addition of glassy agent, previously discussed.

However, all the 13 C CPMAS spectra collected under microwave irradiation on the snapshots between 15 min and 3 days after impregnation could only reveal the presence of solvated glycine molecules in the glassy phase (like in the orange spectrum in Figure 5C). By acquiring T1ρ relaxation-filtered CPMAS experiments, it was possible to remove the signal from the glassy phase to detect the possible presence of low-intensity signals corresponding to more rigid phases (crystalline and amorphous) that could be hidden underneath. Interestingly, this experiment, acquired under DNP conditions, could reveal the presence of a large signal centered at 173.5 ppm that differed from the spectrum of the glycine/water amorphous frozen solution as well as from the other polymorphs of glycine, including glycine dihydrate (whose signal is centered at the same chemical shift). This signal (Figure 5C, "15 min", green spectrum) persisted for more than a day after the beginning of crystallization. However, the T1ρ-filtered experiment acquired on the snapshot collected 2 days after the beginning of crystallization revealed the presence of a sharp peak at 175.9 ppm (Figure 5C, "48 h", green spectrum), identified as the β-polymorph of glycine. Interestingly, the large peak previously observed was no longer visible on the spectrum. This observation suggested that this large peak could correspond to an intermediate phase on the pathway between the amorphous glycine/water solution and the beta polymorph, possibly a pre-nucleation phase in which the glycine molecules are present in solution at higher local concentration.

This observation was confirmed by the analysis of a snapshot of the crystallization acquired 3 days after impregnation. Interestingly, although the peak corresponding to β-glycine was clearly visible in the (6h long) T1ρ-filtered experiment (Figure 5C, "72 h", green spectrum), this signal was still not visible in the standard 13 C CPMAS spectrum acquired under DNP conditions (Figure 5C, "72 h", orange spectrum). This observation is a clear indication of the unique value of DNP in the investigation of early stages of crystallization. In fact, investigating crystallization under nanoconfinement allowed more detailed insights as the transformation between different solid forms are significantly slowed down under these conditions. For instance, the transformation of β into the α polymorph of glycine typically occurs in a few minutes in the bulk, but it took three full days under confinement, extending the time for NMR investigation of the first stages of crystallization. Importantly, the detection of the precursor signal using T1ρ-filtered experiments required ~6h of acquisition time under DNP conditions:

reaching the same sensitivity in standard solid-state NMR would have been totally impractical, requiring more than 50 days of experimental time.

Overall, using PA embedded into the mesopores of silica materials, the snapshot DNP method introduced a new opportunity to detect the initial stages of crystallization through the combination of i) confinement and ii) the unique sensitivity enhancement provided by DNP.

This method opens the way towards a full structural characterization of prenucleation and nucleation clusters, which could help unravel the molecular-level mechanisms of crystallization processes and polymorph selection.

As an alternative to MAS DNP, in the next section we discuss a recently reported dDNP approach to detect the early stages of precipitation of calcium phosphates, relevant for mineral systems.

Probing early stages of bulk crystallization in-situ using dDNP

Unveiling the mechanisms of crystal nucleation today remains a true experimental challenge because of difficulties in accessing these processes on sufficiently short timescales and with atomic-level detail. This aspect is particularly important for biomineralization processes involving the formation of calcium phosphates and carbonates, whose precipitation typically occurs on timescales of seconds to minutes, and for which the MAS DNP approaches previously discussed might present limitations. Recently, Kurzbach and Azaïs reported an experimental approach based on the use of dDNP that enabled the onset of calcium phosphate nucleation to be assessed in situ, in real time [START_REF] Weber | Assessing the onset of calcium phosphate nucleation by hyperpolarized real-time NMR[END_REF]. Following the same notation used by the authors, "CaP" will be used here to generally indicate calcium phosphate species, with no reference to a specific chemical formula. The authors exploited the peculiar instrumental setting of dDNP to trigger the precipitation of CaP and monitor the first seconds of the reaction leading to the formation of the solid species. The experimental approach is depicted in Figure 6A. As discussed in Section 5.1, dDNP requires first to rapidly freeze the solution to be analyzed using liquid He. Once the solution -containing the PA and a glass forming agent like glycerol -is frozen, it is first polarized into the polarizer. Then, a hot liquid is injected at high pressure into the frozen solution to rapidly melt it. Finally, the liquid is propelled into the NMR spectrometer through a magnetic tunnel in less than 5 s. In this specific case, after freezing a hyperpolarized phosphate (Pi) aqueous solution, the frozen solution was melted and then mixed in the NMR spectrometer with a buffered aqueous solution containing CaCl2 at various (mMol level) concentrations contained in an NMR tube within the probe, at 298 K. Detection of 31 P spectra every 0.5 s enabled time-resolved monitoring of CaP precipitation process through NMR. Interestingly, the observed behavior varied by varying the calcium concentration of the solution between 8 and 13 mMol.

Specifically, two different signals could be observed in the conditions explored, shown in Figure 6B: i) a narrow peak ascribed to free Pi species, and ii) a broader signal, ascribed to bound phosphate species. Interestingly, both chemical shifts increased with increasing the [Ca],

although to a different extent. From the lineshape analysis of the observed 31 P signals, information about the rotational diffusion could be obtained, which led to estimation of the hydrodynamic radius of the particles corresponding to phosphate in bound forms, ascribed to stable prenucleation species (PNS). Notably, the results were in agreement with PNS radius values reported by previous studies. The authors also used the NMR data to estimate the upper bound of dynamic exchange rates of Pi between bound and free forms. Finally, the acquisition of 31 P data every 0.5 s enabled real-time analysis of the kinetics of PNS formation. In this case, the study of 31 P signal of a Cafree solution was used as a reference to evaluate the decay time of 31 P signal due to NMR relaxation phenomena. It was observed that the Pi decay rates are largely independent of the B)

A)

Ca-ions concentration [Ca 2+ ], indicating that the T1 relaxation is not strongly impacted by varying the ionic strength. Similarly, the build-up of the PNS formation appears to be independent of [Ca 2+ ]. Contrastingly, its decay seems to be affected by the fate of the PNS, that probably undergo dynamic processes involving post-nucleation aggregation, but also relaxation processes. These observations were corroborated by cryo-EM images and turbidimetry measurements enabling the macroscopic observation of CaP precipitation.

Conclusions and future directions

We reviewed the main advances in the investigation of crystallization from solution using NMR covering the last four years. First, we introduced the main challenges associated with the study of crystallization processes. Focusing on polymorphic crystals, we discussed the importance of accessing the atomic/molecular-level details of crystallization as a function of time to understand the mechanisms of crystallization leading to the formation of the first solid particles, as well as crystal polymorph formation and transformation. This information is crucial in view of achieving crystal polymorph selection, enabling the control of materials properties and opening the way towards new applications in fields such as pharmacy, electronics, and many others.

We introduced the capabilities of NMR to investigate crystal polymorphism and structure in general, before summarizing the main developments realized in the last decade by K.D.M. These developments open new possibilities towards the study of crystallization phenomena and have the potential to disclose atomic-level details of these processes that have remained elusive until present. However, further developments remain necessary to extend these capabilities so that detailed mechanistic aspects of crystallization can be efficiently retrieved from DNP NMR experiments.

The first important development required concerns sensitivity. Considerable sensitivity gains can be obtained using the dDNP and MAS DNP protocols previously discussed. These gains enable the acquisition of experiments that would -timewise -simply be impractical using standard solid-state NMR. However, full structural characterization of the species present in the crystallization medium at the smallest concentration levels requires to maximize the sensitivity of the experiment, so that more elaborated 2D experiments can be carried out efficiently. Although the DNP sensitivity enhancements obtained so far are significant, they remain comparatively low (in ex-situ experiments, about one order of magnitude) with respect to state-of-the-art values, which can prevent detection of dilute species. However, the results obtained so far are encouraging and suggest that the development of new DNP polarizing agents, united to improved sample preparation methods, could provide the required level of sensitivity. Specifically, the sensitivity of snapshot DNP experiments could be significantly improved by controlling the sample freezing conditions. In the current snapshot approach, freezing occurs in the magnet, and precise estimation of the time required to freeze the solution contained in the rotor remains difficult. Indeed, the fact that low DNP enhancements are obtained for crystallization processes occurring in pure water indirectly suggests that freezing does not occur rapidly enough to avoid the formation of microcrystalline water domains, leading to radical segregation and hence less efficient DNP polarization transfer. Moreover, although this aspect can be verified using NMR, slow freezing might induce crystallization.

Therefore, reaching rapid freezing of crystallizing solutions is paramount for creating the correct operational conditions and sensitivity enhancements to investigate crystallization using MAS DNP. Some promising results have been reported by R. Tycko [START_REF] Jeon | Millisecond time-resolved solid-state NMR reveals a twostage molecular mechanism for formation of complexes between calmodulin and a target peptide from myosin light chain kinase[END_REF][START_REF] Jeon | Application of millisecond time-resolved solid state NMR to the kinetics and mechanism of melittin self-assembly[END_REF] and J. Long [START_REF] Lama | Expeditious dissolution dynamic nuclear polarization without glassing agents[END_REF],

showing that rapid freezing (i.e. occurring in less than < 1 s) might indeed lead to a significant reduction of the amount of glycerol required to get good sensitivity enhancements in the bulk, or even to its elimination. Efforts are currently underway in our lab, too, to develop freezing stations adapted to the specific manipulation of crystallizing solutions.

Another important point that has to be improved is time resolution. Currently, the time resolution of ex-situ MAS DNP applications is of the order of a few minutes. Specifically, ~5 min are required to the experimenter for transferring the solution into the DNP sample holder, seal it, and insert it into the MAS DNP spectrometer before the first snapshot can be acquired. This time resolution hampers the detection of short-lived metastable forms and limits the shortest observable crystallization time (thereby potentially preventing the observation of early stages of crystallization). Several approaches should be explored to improve the time resolution of the analysis. One of them is the automatization of sample preparation procedure, which can significantly shorten the sample preparation time. Although for a different application, a successful example of this approach was recently reported by R. Tycko in view of studying the ms-timescale dynamics of biological systems using MAS DNP [START_REF] Jeon | Millisecond time-resolved solid-state NMR reveals a twostage molecular mechanism for formation of complexes between calmodulin and a target peptide from myosin light chain kinase[END_REF]. The study of crystallization reactions shares the same general idea, i.e. to be able to manipulate μlvolumes of liquids with the help of controlled-flow devices adapted to the study of rapid reaction kinetics, and to couple them to suitable freezing stations to efficiently quench the crystallization processes on the ms to s timescale. Of course, the rapid freezing mentioned above could also serve to improve the time resolution of the analysis by reaching ~ms snapshots of crystallizing systems, so as to access rapid precipitation processes and/or detect prenucleation and nucleation events. Importantly, as already mentioned in the Introduction, crystallization processes are characterized by a certain inherent variability, so reproducibility of the results should always be carefully checked to ensure their reliable interpretation. Indeed, the development of automated sample preparation methods would also help improve the reproducibility of the DNP analysis.

An important future direction that will be explored further concerns the development of porous polarizing matrices adapted to the study of confined crystallization. Modification of the material matrix, pore size, as well as surface postprocessing are some of the developments that will help expand the range of accessible -confined -crystallization systems, while helping increase the sensitivity of DNP and the time resolution (by efficiently trapping transient amorphous and crystalline forms).

Of course, efforts must also be realized in identifying the best NMR protocols for analysing these complex physical systems, where multiple species with very similar chemical identity (but structurally different) can be simultaneously present. In this respect, the unique versatility of MAS DNP can provide a large number of tools, including, among others, the use of relaxation filters, the development of indirect acquisition methods in MAS DNP [START_REF] Wang | Combining fast magic angle spinning dynamic nuclear polarization with indirect detection to further enhance the sensitivity of solid-state NMR spectroscopy[END_REF] (increasing both sensitivity and spectral resolution of the analysis) and the analysis of spin diffusion [START_REF] Pinon | Measuring Nano-to Microstructures from Relayed Dynamic Nuclear Polarization NMR[END_REF][START_REF] Walder | Measurement of Proton Spin Diffusivity in Hydrated Cementitious Solids[END_REF].

As previously mentioned, glycine is used as an archetypal system for the development of methodologies to study crystallisation and polymorphism and therefore most of this review focuses on glycine/water systems. In parallel to the development of new NMR methodologies for investigating crystallization, it is also crucial to evaluate the applicability to other systems.

In this respect, MAS DNP applications on frozen solutions are expected to be particularly promising because, by trapping transient states "indefinitely" inside the spectrometer, they open the possibility of fully exploiting the extremely rich panoply of available NMR experiments (especially the multidimensional ones) without worrying about the evolution/disappearance of the detected species in the course of crystallization. For this reason, although the NMR response will somehow remain system-dependent, we do not expect any particular limitation in the study of alternative molecular materials, even when the structural complexity increases. In our group, some of these methods are currently being applied to other organic and inorganic polymorphic systems with promising results, which will be reported in future publications.

Concerning dDNP, it is clear that the main limitation today is related to the short lifetime of polarization once the sample is inside the NMR spectrometer. This essentially restrains current applications of dDNP to the sole acquisition of single-scan spectra. Several groups are currently working on creating more flexible environments for dDNP analysis that could enable longer NMR acquisitions. Nonetheless, although with a much larger sensitivity, dDNP shares similar limitations as traditional in-situ solid-state NMR approaches in terms of time resolution: because the analysis takes place at room temperature, short-lived species might disappear during the NMR experiment, limiting the acquisition of time-consuming 2D/3D correlation experiments that are essential for structural elucidation (although single-scan approaches remain viable).

Overall, the studies reviewed here show the great potential of hyperpolarized NMR in the investigation of complex evolving systems such as crystallizing solutions. We anticipate that discoveries in this field should bring fundamental new knowledge on crystallization mechanisms that could lead to major advances in many applications where polymorphic materials play a key role, such as pharmaceutics and electronics. Eventually, this might open the way towards targeted polymorphism, with a deep impact in materials science and related fields of application.

Figure 1 :

 1 Figure 1: Illustration of the different NMR approaches for time-resolved monitoring of crystallization reviewed here. A) Schematic representation of the crystallization evolution and timescale, illustrating the crystallization events that can be accessed using the different approaches shown in B), C) and D). B) In-situ NMR monitoring of crystallization. This approach enables detection of the formation of the solid species and identification of the time window of the existence of a given polymorph, as well as observation of polymorph transformation. The figure shows 13 C CPMAS NMR spectra recorded in situ as function of time to follow the crystallization of [1-13 C] glycine in water/methanol solution, at 20°C. [9](Reused with permission from RSC: https://doi.org/10.1039/C0CC01007C). The method can also be applied on frozen solutions at cryogenic temperature to increase the time resolution. C) Ex-situ monitoring of bulk or confined crystallization by the "snapshot" approach. The evolution of crystallization is monitored by flash cooling, at specific points in time, a crystallizing solution that evolves at room temperature, hence capturing "snapshots" of the evolving system. The figure shows13 C CPMAS NMR spectra of [1-13 C] glycine crystallizing in pure water recorded at 100 K at increasing crystallization times[START_REF] Vioglio | A Strategy for Probing the Evolution of Crystallization Processes by Low-Temperature Solid-State NMR and Dynamic Nuclear Polarization[END_REF]. D) Monitoring crystallization in-situ and exsitu using hyperpolarization techniques. The previous methods can be combined with hyperpolarization approaches to increase the sensitivity of NMR, enabling the detection and characterization of early stage of crystallization in bulk and confined media. The figure shows13 C CPMAS (orange) and 13 C T1r-filtered CPMAS (green) DNP NMR spectra recorded at 100 K on [1-13 C] glycine confined in the pores of a mesoporous material at increasing crystallization times[START_REF] Juramy | Monitoring Crystallization Processes in Confined Porous Materials by Dynamic Nuclear Polarization Solid-State Nuclear Magnetic Resonance[END_REF].

  crystal nucleus have challenged classical theories, suggesting the existence of

Figure 2 :

 2 Figure 2:In-situ monitoring of glycine crystallization at low temperature. A) Schematic representation of the methodology used to detect the formation of GDH and its transformation in the b polymorph of glycine. B)13 C CPMAS NMR spectra recorded on an aqueous solution of [1-13 C] glycine after flash cooling the solution at 160 K followed by a slow temperature increase up to 222 K. C)13 C CPMAS NMR spectra of the carbonyl carbon of glycine for each polymorph (GDH, g, b and a) at 100 K. D) 1 H-13 C HETCOR spectrum recorded on an aqueous solution of glycine after flash cooling it to 160 K and then increasing the temperature up to 212 K. E)13 C-13 C double quantum filtered/zero quantum filtered (DQF/ZQF) dipolar build-up curves plotted against the recoupling time tDQ for GDH (gray diamonds) and a polymorph (black circles) recorded on [1-13 C] glycine. Theoretical DQF/ZQF dipolar build-up curves calculated for the crystal structures of GDH (gray dashed line) and a polymorph (black line) are also shown.

  Figure 3 schematically shows the typical instrumentation employed for MAS DNP and

Figure 3 :

 3 Figure 3: Schematical illustration of typical MAS DNP (A) and dDNP (B) spectrometers. (A) A MAS DNP spectrometer is composed of a standard NMR magnet (right) linked to a microwave source (left) by a wave guide. The NMR magnet is equipped with a Low Temperature MAS (LTMAS) probe enabling continuous microwave irradiation of the sample. MAS DNP experiments are typically performed at 100 K on solid samples and allow multiscan acquisition. B) dDNP spectrometer composed of a standard NMR magnet (right) linked to a polarizer (left) through a transfer (magnetic) line. The sample is polarized inside the polarizer at a temperature < 4 K before it is melted and then injected into the NMR magnet through a transfer line. dDNP experiments are performed at room temperature on a liquid sample and only allow single scan acquisition.

Figure 4 :

 4 Figure4: Ex-situ monitoring of bulk crystallization using low temperature. A) Schematic representation of the snapshot methodology used to monitor glycine crystallization. B)13 C CPMAS NMR spectra recorded with (orange) and without (blue) microwave irradiation at 100 K on a crystallizing solution of [1-13 C] glycine and AMUPol in H2O. Spectra were recorded after flash cooling the solution at 10 min, 70 min and 23 h after the beginning of crystallization. C)13 C CPMAS NMR spectra recorded with (orange) and without (blue) microwave irradiation, 100 K on a crystallizing solution of [1-13 C] glycine and AMUPol in H2O/glycerol (95:5) (v:v). Spectra were recorded after flash cooling the solution at 5 min, 95 min and 24 h after the beginning of crystallization. D)13 C-13 C double quantum/single quantum (DQ/SQ) dipolar correlation spectrum recorded under microwave irradiation at 100 K, on a crystallizing solution of [1-13 C] glycine and AMUPol in H2O/glycerol (95:5) (v:v) after 5 min of crystallization. Experiment was recorded using a recoupling time (τDQ) of 2 ms.

  C CPMAS spectrum of Figure 2B, at 160 K) corresponds to an amorphous (vitreous) phase of solvated glycine molecules. No sharp signals characteristics of crystalline phases were detected, indicating that no detectable amount of crystallization was induced by the rapid freezing procedure.The protocol shown in Figure4Awas then applied to investigate the crystallization of aqueous bulk solutions of glycine supersaturated (6 M) at room temperature, to collect multiple snapshots of crystallization at specific points in time. To increase sensitivity, a DNP polarizing agent soluble in aqueous solutions (AMUPol[START_REF] Sauvée | Highly Efficient, Water-Soluble Polarizing Agents for Dynamic Nuclear Polarization at High Frequency[END_REF], 0.02 M) was added to the supersaturated solution, which was then warmed up to 80°C to completely dissolve glycine. Crystallization was triggered by recovering the supersaturation conditions after cooling down the solution into the DNP rotors. Figure4Bshows the 1 H-13 C CPMAS spectra obtained by freezing a solution of glycine/AMUPol (6M/0.02M) in pure H2O 10 min, 70 min and 23 h after the beginning of crystallization. The results clearly indicated that, 10 min after the beginning of the crystallization, solvated glycine molecules, as well as β and α forms of glycine were simultaneously present in solution. The β-polymorph was detected at early stages of crystallization, and evolved into the α-polymorph with time (the transformation was complete 23 h from the beginning of crystallization), in agreement with previous studies realized under similar experimental conditions. Also, the signal corresponding to solvated glycine molecules disappeared after 23 h. Interestingly, this strategy could reveal the presence of the β-polymorph of glycine in pure H2O, which had remained elusive by NMR until then. Overall, the results

  Figure 4B (pure H2O), only the kinetics being slightly affected.

Figure 5 :

 5 Figure 5: Monitoring confined crystallization ex-situ with MAS DNP. A) Schematic representation of the protocol used to monitor the crystallization of [1-13 C] glycine in the pores of a mesoporous silica material containing wallembedded TEMPO radicals. B) Schematic representation of the ex-situ MAS DNP snapshot methodology used to monitor the confined crystallization of glycine. C)13 C CPMAS (blue and orange) and T1r-filtered13 C CPMAS (green) NMR spectra recorded with (orange and green) and without (blue) microwave irradiation, at 100 K, on a mesoporous silica material with wall-embedded TEMPO radicals impregnated with an aqueous solution of [1-13 C] glycine. Spectra were recorded after flash cooling the sample at 15 min, 48 h and 72 h after the beginning of crystallization. The window on the right shows the superposition of 13 C CPMAS and T1r-filtered13 C CPMAS spectra recorded at 15 min of crystallization with intensities scaled to correspond to the same absolute intensity.

Figure 6 :

 6 Figure 6: A) Schematic representation of the experimental approach used to trigger the precipitation of calcium phosphate (generally referred to as "CaP") with dDNP and monitor the early stage of CaP PNS formation. After being hyperpolarized in the polarizer, 31 P phosphates (Pi) (blue circles) are mixed in situ to a solution containing Ca 2+ ions (red circles), leading to the formation of CaP PNS. B) Detection of PNS in supersaturated solutions prepared with 3 different concentration of CaP (0 mM, 8 mM and 13 mM of Ca 2+ ): the 31 P NMR spectra on the left indicate the presence of free (Pi, red signal) and bound (PPNS, blue signal) phosphate species for each preparation. The red/blue dots in the center/right panels show the evolution of 31 P signal intensity of free/bound species over time after mixing Pi with the different Ca 2+ solutions. Figures reused with permission from ACS[51]: https://doi.org/10.1021/acs.analchem.0c00516. Further permissions related to the material excerpted should be directed to the ACS.

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  Harris and coworkers on the investigation of crystallization from solution using in-situ NMR approaches: experimental protocols in which crystallization occurs directly inside the solidstate NMR sample holder, so that NMR can be used to characterize the species forming into the solution as a function of time. The review then focuses on experimental developments reported recently by our group and other groups, in which the current limitations in timeresolution and sensitivity of traditional in-situ approaches have been -at least partially -overcome. First, we discussed the use of in-situ solid-state NMR approaches applied to frozen solutions. This approach allows transient forms of crystallization to be trapped inside the spectrometer, enabling the acquisition of 2D experiments and detecting the formation and transformation of metastable forms. We then reviewed recently developed alternative, ex-situ solid-state NMR methods, which enable time-resolved investigation of crystallization from bulk and confined solutions. In these approaches crystallization occurs ex-situ, at room temperature, and the MAS DNP spectrometer is used to capture snapshots of the crystallizing solution by flash freezing the solution inside the DNP spectrometer at cryogenic temperature, which quenches crystallization. Also due to the development of tailored PA, these approaches are compatible with MAS DNP, and can significantly increase the sensitivity of in-situ

approaches, making prenucleation or nucleation species detectable using solid-state NMR. We conclude presenting a recent work in which dissolution DNP is used to detect the first seconds of the precipitation of CaP, allowing the detection of the formation and transformation of prenucleation species in real time.

Acknowledgments

This project received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (Grant Agreement No. 758498) and A*MIDEX project (ANR-11-IDEX-0001-02) funded by the "Investissements d'Avenir" French Government program and managed by the French National Research Agency (ANR).

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Highlights

-NMR is an efficient tool for atomic-scale time resolved monitoring of crystallization processes -Recent developments improved time-resolution and sensitivity of traditional in-situ NMR -In-situ NMR can be carried out at cryogenic conditions to increase time resolution -Ex-situ MAS DNP approaches increase both sensitivity and time resolution -Early stages of crystallization can be investigated in the bulk and under confinement with DNP