# Development of fast and flow-compatible NMR diffusion methods for online reaction monitoring

Achille Marchand

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Achille Marchand. Development of fast and flow-compatible NMR diffusion methods for online reaction monitoring. Analytical chemistry. Nantes Université, 2022. English. NNT: 2022NANU4087. tel-04106183

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## THESE DE DOCTORAT DE

NANTES UNIVERSITE

ECOLE DOCTORALE N° 596

Matière, Molécules, Matériaux

Spécialité : Chimie analytique et radiochimie

Par

Achille MARCHAND

Development of fast and flow-compatible NMR diffusion methods for online reaction monitoring.

Thèse présentée et soutenue à Nantes, le 14 décembre 2022

Unité de recherche : Laboratoire CEISAM (UMR 6230)

### Rapporteurs avant soutenance :

Ulrich HINTERMAIR Associate professor at University of Bath (UK)

Patrick BERTHAULT Directeur de recherche au CEA Paris-Saclay Gif-sur-Yvette

### Composition du Jury :

Président : Fabien FERRAGE

Examinateurs : Véronique GILARD

Dir. de thèse : Jean-Nicolas DUMEZ

Directeur de recherche à L'ENS Paris

Professeur des universités à l'Université Paul Sabatier Toulouse

Directeur de recherche à l'Université de Nantes
Remerciement / Acknowledgments

This work was done on the laboratory CEISAM using the NMR instrument of the CEISAM's platform. I want to thank J.-M. Bouler, director of the CEISAM, as well as P. Giraudeau, director of the MIMM team.

I also want to acknowledge the member of my jury especially the rapporteurs P. Berthault and U. Hintermair as well as V. Gilard and F. Ferrage.

I cannot give enough thanks to Mr J.-N. Dumez for being my supervisor for his legendary patience and the sum of what I have learned at this contact. I will try my best to carry this to my future professional life. Now that the thesis writing is finished I admit we did not have the time for a historical part.

I want to thank my colleague Rituraj Mishra that helped me so much understanding the math and NMR theory. His kindness and pedagogy were highly valued, I keep with me a better lifestyle with less meat-eating and I hope that a portion of his great organization skills have diffused to my nearby desk.

Warmest thanks to Arnab Dei for all the interesting discussion and NMR related meme. He managed to convince me to do some sport which is no easy task. Thanks for all the invitation, all the food shared etc.

a general thanks to all my Indian colleague at the CEISAM Assad, Shrikant, Aravind for being supportive helping me improve my English and all the laughs and tea time together. I would have never seen Mt St Michel without them. Somehow, I'm now better at filling tax.

Je voudrais remercier l'ensemble de la plateforme RMN du CEISAM, en particulier :

Virginie Silvestre pour toutes les discussions passionnantes autour de l'analyse structurale et du traitement de spectre. Merci pour le soutien.

Merci à Aurélie B. pour l'aide avec les gradients la DOSY et la bonne humeur, dans les bons et moins bons moments.

Merci à Mathilde Grand sans laquelle je n'aurais pas trouvé le moindre produit chimique dans le laboratoire, ni réussi la moindre commande correctement.

Merci à Benoît Charrier, son expérience et ses conseils, sa bonne humeur ; son expertise sur les pompes et les solutions pratiques est inégalable.

Merci à mes collègues francophones :

Margherita pour toute l'aide et les bons conseils, merci d'avoir répondu à tant de questions.

Merci à Marine pour le soutien et pour avoir écouté certaines de mes angoisses. Bon courage avec le petit.

Merci à Corentin J. qui m'a quasiment appris la RMN pratique, sa pédagogie a fait de moi un meilleur scientifique, et on partait de loin.
Merci à Jonathan Farjon pour le soutien moral, les blagues et les discussions, l'aide pour trouver un post-doc. Merci pour toutes les discussions scientifiques, du premier au dernier jour de la thèse.

Merci à Clément pour son calme, mais aussi pour les discussions jeux vidéo et pop culture.

Merci à Celia d'avoir toujours gardé son calme, même lorsque je posais pour la nième fois la même question sur l'organisation d'un événement d'équipe ou l'administration.

Merci à Sophie, si elle n'avait pas passé du temps à me réexpliquer inlassablement les consignes de la soutenance, je n'aurais même pas pu soumettre un brouillon de manuscrit.

Merci à Maelys d'avoir gardé un bon sens de l'humour, et ce malgré l'utilisation d'HPLC et de mass spectrométrie (vade retro)

Merci à Thomas, entre autres, de ne pas m'avoir tenu rigueur pour une tentative d'assassinat peu délicate.

Merci à Benjamin pour les discussions pop culture, sur le streaming et d'autres, sur la science et les gradients à l'occasion.

La liste étant déjà si longue, désolé a ceux que j'oublie, merci à Aurore, Ilya, Estelle, Nour, Joris, Tania...

Merci à mes amis, à ma famille qui m'ont soutenu durant cette thèse, sans eux je ne serais rien, déjà qu'avec eux on ne va pas bien loin.

Pour citer le poète « je me sens si fort quand y'a ces gens qui m'portent »

Merci Kevin Vongprachahn pour la relecture du français et les discussions scientifiques, sans lui cette thèse ne serait pas ce qu'elle est. Courage pour les études, force à toi ; MAIS la chimie c'est mieux que la physique, je mourrai sur cette colline qui n'a pas de sens.

Merci à Guilhem Besson, pour être un exemple de rigueur et de travail. Tu nous as toujours soutenu, courage au meilleur sondier ici-bas. Les meilleures discussions sur la musique, demain mon prof de solfège (non). Pas merci pour m'avoir montré Elder Ring et ainsi menacé mon projet de thèse.

Merci à David pour tous les échanges depuis Lyon, les discussions électroniques et sur le taff... Un soutien de qualité. Bientôt un projet commun (c'est faux).

Merci à Alisson pour son enthousiasme continu et immarcescible, même lorsque ta maison brûle tu es moins stressée que lorsque je dois envoyer ma thèse.

Merci à Chloé, Reine de l'Albion endormi, Reine par la volonté de Titania, gouvernante d'Alfeim, etc.

Merci à Raphaël, courage pour les Beaux-Arts, les séances de Magic me manquent. J'espère que vous allez bien à Tours.

Merci à Sacha le grand thaumaturgiste, te parler me donne toujours plus de forces ; les 90-1 en versus fighting me manquent.

Merci à Richard qui m'a soutenu depuis mon stage de M2, force a lui, le vagabondage c'est dur mais les histoires qui en résultent ont un parfum de paradis.
Merci à Théo, le meilleur illustrateur pour le meilleur fond d'écran du monde, des fois je le regarde et je rêve. Merci pour Magic, sans toi à Nantes ça n'aurait pas été pareil je t'en dois une.

Merci à Thomas alias Blaise et à l'ARD, j'ai beaucoup trop ri et mon avocat me conseille de me dissocier de vos propos. Dédicace au doomer.

Merci à Charline pour les discussions scientifiques (de sociologie...) et la mauvaise humeur qui fait plaisir. Les partie d'Endless Space c'était incroyable et très cool.

Merci à Aradana, ta gentillesse et ta persévérance m'impressionnent toujours autant, merci d'être là depuis si longtemps.

Pour Heng désolé de ne pas avoir été là lorsqu'il aurait fallu, j'espère que tu as trouvé ce que tu cherchais par-delà le rêve.

Merci à Dylan du Master de Paris Descartes, ça me fait plaisir que l'on garde le contact, force à toi. Pour moi la chimie organique c'est beau quand je ne la manipule pas.

Merci à tous les autres, mais j'ai promis de pas faire plus de deux pages : Zoé, Jude, Yagaré, Maxime, Armelle, Antoine, Nas, Sarrasin, Killroy...

Merci à ma famille
Ma sœur Zoé
Mon frère Joseph
Mon père et ma mère François et Carole
Romain, Marion, Hélène, Yvette, Annie, Jean...

Ça n'a pas toujours été facile mais je crois qu'on reste plus forts que ça. Merci à eux de me supporter depuis le plus longtemps, je ne sais pas comment ils font...

Un dernier merci à tous ces gens qui m'ont laissé une chance en dépit du bon sens.
Jean-Nicolas Dumez de m'avoir pris en thèse, je ne serai jamais assez reconnaissant.
Nicolas Giraud pour m'avoir pris en stage et m'avoir introduit à la RMN.

Guillaume Prestat et Mélanie Ethève-Quelquejeu pour m'avoir pris en Master après une année semi-blanche et un dossier plutôt mauvais, merci d'avoir cru en moi alors que moi-même je n'étais pas si optimiste.

L'équipe pédagogique de chimie du CNAM de Paris notamment Marc Port et Zacharias Amara pour m'avoir aidé a trouvé un Master et me remettre sur les rails de la science.

Je pourrais continuer plus loin mais voici déjà des remerciements bien longs.
Résumé en français

La spectroscopie RMN est une technique d'analyse particulièrement utilisée dans le domaine de la chimie. Elle est couramment utilisée pour la caractérisation de molécules organiques pour différentes raisons. Parmi les plus importantes figurent notamment l'innocuité de cette technique d'analyse, mais encore sa grande capacité à résoudre les énigmes structurelles et à donner des spectres riches en informations sur la structure des molécules étudiées. Notons enfin que les noyaux sensibles à la RMN, et en particulier le proton, sont extrêmement courant. Compte tenu de ces faits, cet outil se révèle utile pour le suivi de réactions chimiques.

En l'occurrence pour ce dernier usage, la RMN a aussi ces limites. En effet, l'utilisation du contenant habituel de la RMN, un tube fin de 5 mm de diamètre généralement, ainsi que l'inaccessibilité du milieu réactionnel une fois dans le spectromètre, constituent un exemple de ces limites. Une manière alternative de prélever le milieu réactionnel de façon avantageuse est le flux. De la même manière, les expériences analytiques les plus riches sont souvent plus longues, notamment en ce qui concerne la RMN 2D, ce qui peut être contraignant dans le cadre de l'analyse d'un milieu qui évolue et impose donc ses propres contraintes de temps.

Nous nous proposons de nous concentrer sur un type d'expérience RMN, appelée DOSY, et d'en faire un outil de suivi réactionnel. Cette expérience s'intéresse au phénomène de diffusion au sein d'un liquide, que nous pourrions résumer en un ensemble de mouvements subtils des molécules et particules qui le constituent. Nous ajoutons à cela la possibilité d'étudier le milieu en flux afin de travailler avec une méthode qui nous rapproche des conditions de paillasse.

Durant ce travail, nous avons étudié les moyens permettant d'arriver à faire de la DOSY en flux. Notre méthode, basée sur l'utilisation de plusieurs axes de gradient de champ magnétique, a été développée pour l'observation du mouvement subtil de la diffusion, le milieu étant lui-même entrepris du mouvement de flux, moins subtil. Nous verrons aussi comment nous avons accéléré les expériences DOSY à l'aide de champs magnétiques pulsés, utilisés à des fins de sélection de cohérence.

Bibliographie

Tout d'abord, nous nous proposons d'expliquer le nécessaire sur la diffusion en solution et de la définir. Il s'agit d'un mouvement aléatoire des particules constituantes d'un liquide résultant de leur mouvement brownien dû à leur agitation thermique. Dans ce contexte, ce que nous appellerions intuitivement « vitesse des particules », nous l'appelons « coefficient de diffusion », dont la valeur dépend de la taille des molécules analysées et de la température ambiante.

Afin d'expliquer notre choix, pas forcément évident, d'étudier la DOSY à des fins de suivi réactionnel, nous avons développé un premier chapitre sur les utilisations diverses de la DOSY dans la
littérature. Nous y détaillons tout d'abord les méthodes de RMN diffusionnelle que nous utilisons, notamment la méthode STE. Pour la décrire brièvement, l'utilisation de gradients de champ magnétique permet d'encoder la diffusion. Le gradient permet d'organiser les spins de l'échantillon en fonction de leur position dans l'espace, et cette organisation prend la forme d'une hélice qui devrait être refocalisée par le gradient final de décodage de la diffusion. Du fait de la diffusion durant le temps qui sépare ces deux gradients, un mouvement moléculaire va avoir lieu, déformant l'hélice et rendant incomplète sa refocalisation. La perte de signal liée à l'imparfaite refocalisation est comparée au modèle théorique de la diffusion décrit par l'équation de Stejskal-Tanner, dont l'adéquation permet de retrouver le coefficient de diffusion.

Nous nous proposons également un état de l'art par l'étude de plusieurs exemples. Nous ne nous concentrerons pas tant sur les méthodes d'acquisition de la diffusion, mais plutôt sur l'intérêt de l'information de diffusion. En effet, en fonction de la diffusion des molécules, il est possible de remonter à des informations de taille, de longueur de chaîne voire de masse moléculaire. D'autres informations, concernant notamment les interactions entre les molécules ou des molécules avec le solvant, peuvent également être récupérées. La taille de des molécules considérées est appelée plus rigoureusement dans notre cas le « rayon hydrodynamique ».

On trouvera également une utilisation, non pas basée sur l'intérêt du coefficient de diffusion en soi, mais davantage sur sa capacité à différencier des molécules dans un mélange. Permettant ainsi une séparation par la taille des molécules au sein du mélange. Cette séparation virtuelle au sein du spectre est à rapprocher des méthodes de séparation physique, souvent fondées sur la taille des objets à séparer. C'est cette dernière utilisation couplée aux autres qui nous motive le plus à étudier la DOSY, afin d'avoir des méthodes de caractérisation, mais aussi de séparation au sein d'un mélange complexe, ceci sans interférer avec ledit mélange.

Nous étudions également la littérature afin de motiver notre choix du suivi en flux, notamment dans une méthode dite en ligne (online) de suivis réactionnels. Pour ce faire, nous discutons d'exemples d'intérêt et des limitations de plusieurs méthodes répandues qui permettent l'échantillonnage du milieu réactionnel.

Enfin, dans le cadre du projet qui vise à une méthode de suivi en ligne de milieux réactionnels par RMN diffusionnelle, nous étudions les possibilités présentes dans la littérature autour de l'accélération et d'alternatives aux méthodes de type STE.

## Évaluer et accélérer l'expérience RMN

Après cet état de l'art, nous nous intéressons au cœur de ce travail, à savoir la DOSY. Les méthodes DOSY, bien que très utilisées dans divers domaines, ne sont pas les plus standardisées dans le monde de la RMN. Nous présentons donc rapidement le graphe représentant la DOSY et ses particularités.
Nous nous intéressons plus particulièrement à l'intérêt en termes de séparation virtuelle qu'offre ce
graphe.

En effet, le graphe DOSY donne une séparation par l'attribution à des pics de leurs coefficients
de diffusion respectifs. Ceci permet de savoir quels pics appartiennent à quelles molécules au sein du
mélange et communique de premières informations sur la taille relative des molécules dans le
mélange. À cette fin, le graphe DOSY donne des points de corrélation à chaque pic choisi par
l'utilisateur. En abscisses sont donnés les déplacements chimiques, l'unité classique de la RMN ; en
ordonnées sont représentés les coefficients de diffusion. Ainsi, les pics appartenant à la même
molécule sont alignés ensemble, ce qui nous permet de commencer à parler de séparation. La diffusion
étant issue de rapports d'adéquation entre une équation modèle et le signal détecté, deux
informations sont présentes au niveau du point de corrélation : la coordonnée qui donne le
déplacement chimique et la diffusion, et la largeur verticale de la tâche qui en donne l'erreur
d'adéquation, ou incertitude, entre le modèle et les points expérimentaux. Néanmoins, pour
réellement parler de séparation, il y a la nécessité d'une concordance. Ainsi, les points d'une même
molécule doivent être fins et alignés, donc être le plus précis possible, et avoir des coefficients de
diffusion proches, si ce n'est identique.

Nous montrons un système fait pour l'occasion qui utilise l'écart-type entre les valeurs de
diffusion de coefficient des pics d'une même molécule afin d'évaluer l'alignement, puis nous utilisons
la moyenne quadratique des écarts-types liée à l'incertitude, ceci afin d'avoir une idée de la précision.
Nous nous retrouvons avec un système de coordonnées bidimensionnel où les points les plus proches
de l'origine témoignent d'une qualité de séparation, et il y a perte en qualité à mesure que l'on
s'éloigne de l'origine.

Avec ce système, nous procédons au test de plusieurs méthodes d'accélération de la DOSY en
utilisant des gradients afin d'avoir une sélection de cohérences alternatives. En effet, classiquement,
la sélection de cohérence se fait par le cyclage de phase qui rallonge l'analyse en imposant un nombre
minimum de scans. L'utilisation de gradients orthogonaux ou parallèles permettrait de réduire ce
minimum et d'accélérer significativement l'expérience. Il s'avère que la méthode utilisant des
gradients orthogonaux marche significativement mieux et a été adoptée comme méthode
d'accélération.

RMN diffusionnelle en flux

Afin d'atteindre le suivi de réaction en ligne comme nous le souhaitons, nous devons être doté d'un
appareil capable de fonctionner en flux. Nous avons choisi le package insightMR par Bruker, parfois
appelé flowtube. Il est constitué en trois parties, d'abord, une partie régulation de température à l'aide
d'une pompe, d'un liquide thermique et une enveloppe ne rentrant jamais en contact direct avec le
spectromètre et/ou le milieu étudié. Un liquide thermique et une enveloppe qui ne rentre jamais en contact direct avec le spectromètre et/ou le milieu étudié. Ensuite, nous avons la partie qui transporte le milieu. Comprenant un tube en verre, similaire à un tube classiquement utilisé en RMN, des capillaires prélevant la solution à analyser puis l'amènent dans ledit tube qui se remplit, et un autre capillaire renvoie le trop-plein dans la solution mère, créant ainsi une boucle continue sans perte. Enfin, nous avons la pompe servant à donner le flux et conditionnant sa vitesse : c'est un appareil clef qui peut être changé selon les besoins.

Nous avons utilisé deux pompes : la pompe par défaut recommandée par le constructeur du flowtube, ainsi qu'une pompe HPLC Azura à bi-piston. Cette dernière, bien que performante en théorie, n'a pas donné pleine satisfaction. En effet, il semble qu'elle n'est pas faite pour pomper des liquides complexes, amenant à de nombreux problèmes et blocages.

Nous avons également utilisé la pompe Vapourtec à mouvement péristaltique. Un mouvement de ce type est, semble-t-il, bien plus adapté pour pomper des liquides divers, pouvant même pomper des gaz ou des solides en cas de problème. L'utilisation de cette pompe a permis de rendre plus simple l'étude en flux, elle a ainsi été choisie pour devenir la nouvelle pompe par défaut.

Toujours dans le but de pouvoir suivre une réaction à l'aide de RMN diffusionelle en flux, et donc d'en chercher les méthodes en amont, nous avons trouvé qu'il existe un type de séquence DSTE faite pour « compenser les effets de vitesse constants ». Bien que conçue à l'origine pour compenser les effets de convection, autre mouvement lié à la différence de température, les caractéristiques et propriétés de cette séquence RMN semblent toutes indiquées pour compenser l'effet d'un flux laminaire.

Nous comparons ainsi l'effet du flux à plusieurs vitesses de 1 à 3 mL/min sur les DOSY de type DSTE et constatons une augmentation des coefficients de diffusion avec la vitesse du flux. Cette augmentation s'accompagne de problèmes tels que l'augmentation de l'incertitude (la largeur des taches), rendant les spectres finalement peu exploitables pour un quelconque usage. L'utilisation de la DSTE dans des conditions un peu particulières, où l'utilisation des gradients d'encodage de la diffusion ne se fait non pas parallèlement mais perpendiculairement à la direction du flux, donne des résultats significativement meilleurs. Nous arrivons finalement à une erreur maximum de ~4% entre la référence (hors flux) et l'expérience en flux, ce qui est correct. En particulier et surtout, ni la valeur du coefficient de diffusion, ni l'incertitude associée ne semblent être liées à la vitesse du flux.

## Le suivi d'une réaction

Armés de ces outils que sont l'accélération de séquence, l'appareillage permettant le suivi en ligne, et des séquences de RMN diffusionnelle compatible avec le flux, nous décidons d'effectuer des essais. La réaction que nous étudions est la double imitation du p-phenylènediamine par l'acétaldéhyde dans
l'acétonitrile. Une réaction simple et bien connue, mais intéressante en cela que les produits sont structurellement proches et suffisamment fragiles pour ne pas permettre une isolation ou séparation par des moyens physiques.

Le suivi de la réaction dure environ 5h durant lesquelles nous pouvons faire une expérience par minute, ce qui garantit un nombre de points conséquent. Nous discutons des limites de cette méthode de suivi qui se manifestent notamment autour de l'impossibilité d'utiliser le « lock », un système permettant de corriger de nombreuses perturbations grâce au deutérium habituellement présent dans les échantillons RMN. Du fait de son coût et de l'augmentation de volume, il n'est pas souhaitable d'utiliser des solvants deutérés. La perte ou dégradation de l'homogénéité du champ, le décalage des spectres lié à un changement de température ainsi que la dérive du champ magnétique de l'aimant sont les problèmes les plus importants que nous avons rencontré. Malgré ces préoccupations, ceux-ci restent mineurs et n'empêchent pas de mener à bien l'expérience.

Le suivi à proprement parler montre de bons résultats, notamment en ce qui concerne la stabilité dans le temps des coefficients de diffusion, qui ne semblent pas ou peu impactés par l'effet du flux. Relevons également l'effet du changement de concentration, compensé par une méthode appelée « permutation aléatoire de gradient » (p-DOSY). L'une des difficultés est la sensibilité : nous estimons qu'un minimum de ~200 en signal sur bruit est nécessaire afin que la diffusion puisse être estimée correctement. Enfin, la DOSY permet de récupérer l'information de concentration relative similairement à des méthodes classiques de RMN 1D, ce qui est appréciable.

## Conclusion résumée

Pour résumer, nous avons essayé d'expliquer les fondations de la RMN diffusionelle ou DOSY, de montrer son intérêt dans le suivi réactionnel en ligne, notamment grâce à ses capacités de séparation virtuelle. Nous avons montré comment évaluer la DOSY selon ces critères, et essayé d'accélérer celle-ci par des méthodes faisant usage des gradients orthogonaux à l'encodage de la diffusion. Finalement, nous avons développé une approche permettant de compenser l'effet du flux, en combinant l'utilisation d'une séquence DSTE avec l'encodage de la diffusion selon un axe orthogonal au flux. Avec ceci, nous avons pu suivre une réaction en ligne de manière satisfaisante.

Nous espérons qu'arrivera un jour où notre méthode permettra d'aller plus loin dans le suivi de réaction et qu'elle sera accessible à des chimistes de tous bords, en dehors des spécialistes de la RMN. Nous pensons que cela constituerait un outil intéressant et efficace. Pour cette raison, nous travaillons sur de nouvelles améliorations telles que l'utilisation d'analyses multivariées qui rendent l'analyse spectrale plus simple.
Table of content

<table><tr><td>Remerciement / Acknowledgments</td><td>1</td></tr><tr><td>Résumé en français</td><td>4</td></tr><tr><td>Bibliographie</td><td>4</td></tr><tr><td>Évaluer et accélérer l'expérience RMN</td><td>5</td></tr><tr><td>RMN diffusionnelle en flux</td><td>6</td></tr><tr><td>Le suivi d'une réaction</td><td>7</td></tr><tr><td>Conclusion résumée</td><td>8</td></tr><tr><td>Notation et abbreviation</td><td>13</td></tr><tr><td>Introduction</td><td>14</td></tr><tr><td>Part A bibliographic and theory work</td><td>16</td></tr><tr><td>1. Diffusion in NMR</td><td>16</td></tr><tr><td>1.1. Diffusion by NMR</td><td>16</td></tr><tr><td>1.1.1. What are diffusion, self-diffusion and restricted diffusion</td><td>16</td></tr><tr><td>1.1.2. Measuring diffusion by NMR</td><td>21</td></tr><tr><td>1.1.3. Review of relevant methods</td><td>28</td></tr><tr><td>1.2. Selected examples of application</td><td>31</td></tr><tr><td>1.2.1. Polymer</td><td>32</td></tr><tr><td>1.2.2. Mixture virtual separation</td><td>36</td></tr><tr><td>1.2.3. Supramolecular chemistry</td><td>38</td></tr><tr><td>1.3.4 Aggregates</td><td>40</td></tr><tr><td>2. Reaction monitoring by NMR</td><td>45</td></tr><tr><td>2.1. The sampling methods</td><td>45</td></tr><tr><td>2.1.1. Aliquoting</td><td>45</td></tr><tr><td>2.1.2. In-situ</td><td>46</td></tr><tr><td>2.2. Flow methods</td><td>55</td></tr><tr><td>2.2.1. Online monitoring</td><td>55</td></tr><tr><td>3. Fast DOSY NMR sequence</td><td>70</td></tr></table>
<table><tr><td>3.1.</td><td>Why do classic DOSY experiments take time?</td><td>70</td></tr><tr><td>3.1.1.</td><td>QNMR and flow effect</td><td>71</td></tr><tr><td>3.2.</td><td>Methods to accelerate Diffusion experiment</td><td>73</td></tr><tr><td>3.2.1.</td><td>Oneshot methods</td><td>73</td></tr><tr><td>3.2.2.</td><td>Spatial parallelization</td><td>74</td></tr><tr><td>3.2.3.</td><td>Sliding window and TR-DOSY</td><td>80</td></tr><tr><td colspan="2">Part B Method</td><td>83</td></tr><tr><td>4.</td><td>Methods for processing, analyzing and evaluating DOSY</td><td>83</td></tr><tr><td>4.1.</td><td>The DOSY workflow</td><td>83</td></tr><tr><td>4.1.1.</td><td>Data acquisition</td><td>83</td></tr><tr><td>4.1.2.</td><td>Data processing</td><td>84</td></tr><tr><td>4.1.3.</td><td>Data analysis</td><td>85</td></tr><tr><td>4.1.4.</td><td>The DOSY display</td><td>87</td></tr><tr><td>4.2.</td><td>Methods</td><td>88</td></tr><tr><td>4.2.1.</td><td>Sample</td><td>88</td></tr><tr><td>4.2.2.</td><td>Processing software</td><td>89</td></tr><tr><td>4.2.3.</td><td>Analysis software</td><td>90</td></tr><tr><td>4.3.</td><td>Qualitative comparison</td><td>90</td></tr><tr><td>4.3.1.</td><td>Integration methods</td><td>90</td></tr><tr><td>4.3.2.</td><td>Thresholding/intensity methods</td><td>91</td></tr><tr><td>4.4.</td><td>Quantitative comparison</td><td>93</td></tr><tr><td>4.4.1.</td><td>Metrics</td><td>93</td></tr><tr><td>4.4.2.</td><td>Graphical representation</td><td>96</td></tr><tr><td>4.5.</td><td>Comparing DOSY pulse sequences</td><td>97</td></tr><tr><td>5.</td><td>Experimental part</td><td>100</td></tr><tr><td>5.1.</td><td>-Part 6 methods</td><td>100</td></tr><tr><td>5.1.1.</td><td>Oneshot methodology</td><td>100</td></tr><tr><td>5.2.</td><td>Part 7 methods</td><td>101</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>5.3. Part 8 methods</td>
      <td>102</td>
    </tr>
    <tr>
      <td>5.3.1. Chemistry experiment setup</td>
      <td>102</td>
    </tr>
    <tr>
      <td>5.3.2. NMR experiment setup</td>
      <td>102</td>
    </tr>
    <tr>
      <td>Part C</td>
      <td>104</td>
    </tr>
    <tr>
      <td>6. Accelerating DOSY experiments</td>
      <td>104</td>
    </tr>
    <tr>
      <td>6.1. The Oneshot approach</td>
      <td>104</td>
    </tr>
    <tr>
      <td>6.1.1. Coherence selection using parallel gradients</td>
      <td>104</td>
    </tr>
    <tr>
      <td>6.1.2. Coherence selection using orthogonal gradients</td>
      <td>107</td>
    </tr>
    <tr>
      <td>6.1.3. Comparison between the two</td>
      <td>108</td>
    </tr>
    <tr>
      <td>6.2. Multivariate processing of ultrafast DOSY experiments</td>
      <td>110</td>
    </tr>
    <tr>
      <td>6.2.1. Multivariate processing methods for diffusion NMR</td>
      <td>110</td>
    </tr>
    <tr>
      <td>6.2.2. Methods<sup>178</sup></td>
      <td>112</td>
    </tr>
    <tr>
      <td>6.2.3. DECRA analysis of SPEN DOSY data</td>
      <td>113</td>
    </tr>
    <tr>
      <td>6.2.4. SCORE UF</td>
      <td>114</td>
    </tr>
    <tr>
      <td>6.2.5. UF DOSY for flow NMR monitoring</td>
      <td>116</td>
    </tr>
    <tr>
      <td>6.3. Conclusion</td>
      <td>116</td>
    </tr>
    <tr>
      <td>7. DOSY NMR in continuous flow</td>
      <td>118</td>
    </tr>
    <tr>
      <td>7.1. Presentation of the apparatus</td>
      <td>118</td>
    </tr>
    <tr>
      <td>7.1.1. The tubbing</td>
      <td>118</td>
    </tr>
    <tr>
      <td>7.1.2. The pumps</td>
      <td>121</td>
    </tr>
    <tr>
      <td>7.2. Flow compensation and effect</td>
      <td>123</td>
    </tr>
    <tr>
      <td>7.2.1. Methods</td>
      <td>124</td>
    </tr>
    <tr>
      <td>7.2.2. flow effect on diffusion</td>
      <td>124</td>
    </tr>
    <tr>
      <td>8. Monitoring a flowing reaction with DOSY</td>
      <td>130</td>
    </tr>
    <tr>
      <td>8.1. Prerequisite for Reaction monitoring</td>
      <td>130</td>
    </tr>
    <tr>
      <td>8.1.1. Solvent suppression</td>
      <td>130</td>
    </tr>
    <tr>
      <td>8.1.2. Presaturation</td>
      <td>130</td>
    </tr>
    <tr>
      <td>8.1.3. Spectral and diffusion resolution</td>
      <td>134</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>8.2.</td>
      <td>The model reaction</td>
      <td>135</td>
    </tr>
    <tr>
      <td>8.3.</td>
      <td>Methods</td>
      <td>137</td>
    </tr>
    <tr>
      <td>8.3.1.</td>
      <td>The pulse sequence</td>
      <td>137</td>
    </tr>
    <tr>
      <td>8.3.2.</td>
      <td>Experimental</td>
      <td>138</td>
    </tr>
    <tr>
      <td>8.4.</td>
      <td>Results and discussion</td>
      <td>139</td>
    </tr>
    <tr>
      <td>8.4.1.</td>
      <td>Monitoring's data and processing</td>
      <td>139</td>
    </tr>
    <tr>
      <td>8.4.2.</td>
      <td>Estimated diffusion coefficients</td>
      <td>142</td>
    </tr>
    <tr>
      <td>8.4.3.</td>
      <td>Some challenges of reaction monitoring</td>
      <td>143</td>
    </tr>
    <tr>
      <td>8.4.4.</td>
      <td>Repeatability</td>
      <td>145</td>
    </tr>
    <tr>
      <td>8.5.</td>
      <td>Conclusion and perspective</td>
      <td>146</td>
    </tr>
    <tr>
      <td colspan="2">Conclusion</td>
      <td>148</td>
    </tr>
    <tr>
      <td colspan="2">References</td>
      <td>149</td>
    </tr>
    <tr>
      <td colspan="2">Annexe</td>
      <td>162</td>
    </tr>
    <tr>
      <td colspan="2">A-1 DOSY plot</td>
      <td>162</td>
    </tr>
    <tr>
      <td colspan="2">Sequence</td>
      <td>166</td>
    </tr>
    <tr>
      <td colspan="2">"AMstebposgc Grad phycy v2"</td>
      <td>166</td>
    </tr>
    <tr>
      <td colspan="2">"AMdsteosgic GradZ phycy"</td>
      <td>172</td>
    </tr>
    <tr>
      <td colspan="2">"AMwetstebposgc GradX phycy v2"</td>
      <td>182</td>
    </tr>
    <tr>
      <td colspan="2">"AMwetdsteosgic GradX phycy"</td>
      <td>186</td>
    </tr>
  </tbody>
</table>
Notation et abbreviation

1D: one dimension

2D: two dimensions

NMR: nuclear magnetic resonance

DOSY: diffusion ordered spectroscopy

MRI: magnetic resonance imagery/imaging

RF: radiofrequency

STE: stimulated echoes

DSTE: double stimulated echoes

LED: longitudinal eddy current delay

SEC: size exclusion chromatography

D: Diffusion coefficient

DFT: density functional theory

DNA: deoxyribonucleic acid

PFG: pulsed field gradient

PTFE: polytetrafluoroethylene

PEEK: polyether ether ketone

CTP: coherence transfer pathway

BW: band width

DECRA: Direct Exponential Curve Resolution Algorithm

EPSI: Echo-Planar Spectroscopic Imaging

FID: free induction decay

FOV: Field Of View

FT: Fourier Transformation

SW: Spectral Width

UF: UltraFast

SPEN: SPatially ENcoded

SCORE: Speedy Component Resolution.

NUS: non uniform sampling

p-DOSY: permutated DOSY

TMS: tetramethylsillane
Introduction

Nuclear magnetic resonance spectroscopy is a powerful analytical tool with a large range of applications. For high-resolution solution-state NMR of small molecules, these notably include the analysis of organic compounds, especially their structures, the study of molecular interactions, and the analysis of mixtures, which will be the focus of the present work.

While there are many methods to study mixtures of chemicals, few have the non-disruptive nature of NMR. It is often a requirement to first separate the components of a mixture and analyse them afterwards. There are some cases, however, when this is not possible or would have an unwanted impact. One of those cases is the monitoring of chemical reactions. Chemical reactions are mixtures for which the components interact and cannot by definition be physically separated without impairing their properties. Many pieces of information are of interest for reacting mixtures: what is the outcome of the reaction? How is this outcome reached? Can it be controlled? Real-time reaction monitoring is a powerful approach to help answering these questions, and NMR spectroscopy has many advantages for that.

Diffusion NMR makes it possible to achieve virtual separation of components in a mixture, through the measurements of translational diffusion coefficients for a mixture's components. Diffusion is the subtle random motion of particles or molecules within a sample, that results from Brownian motion. Since translational diffusion depends on the size and shape of the diffusing object, if all the analytes have sufficiently distinct sizes and/or shapes then diffusion NMR can be used to separate their 1D NMR spectra. Diffusion NMR is also referred to as diffusion-ordered spectroscopy (DOSY), which originally described a specific data representation. Diffusion NMR is very useful for mixture analysis in general, and for reaction monitoring in particular.

Real-time reaction monitoring by NMR is most often achieved using a classical 5 mm tube, which is rather different from a typical flask in organic chemical synthesis. Notably, sample stirring is absent from the NMR tube, the sample volume is different, and so is the accessibility of the medium for, e.g., light irradiation or the progressive addition of a reactant. Those elements have pushed chemists towards new ways to monitor reactions. One such method is online monitoring by flow NMR, which consists of flowing the reacting medium from its typical flask toward the spectrometer and back. Flow NMR is being increasingly used for reaction monitoring. However, several key NMR methods are not directly applicable in continuous flow. In the case of diffusion NMR, it may appear as difficult to measure the subtle motion of diffusion, and use it for virtual separation, while the medium undergoes a not-so-subtle motion that is flow.

In this work, we have characterised the impact of sample flow on diffusion NMR experiments, and developed methods for accurate diffusion NMR in continuous flow. These rely on the use of a
diffusion encoding axis that is orthogonal to the main direction of the flow, and of a double stimulated
echo pulse sequence. For reaction monitoring, the duration of NMR experiments is also a key
consideration; fast experiments are useful to adapt to a large array of possible reactions. We have
developed fast diffusion NMR methods that rely on gradient-based coherence pathway selection, and
are also applicable in continuous flow. We have also assessed the resulting methodology with the
monitoring of a model organic chemical reactions. In order to achieve these goals, we found it
necessary to propose an approach for the quantitative comparison of diffusion NMR experiments.
Overall, the resulting methodology should be useful for a broad range of reaction monitoring
applications.
# Part A bibliographic and theory work

## 1. Diffusion in NMR

### 1.1. Diffusion by NMR

#### 1.1.1. What are diffusion, self-diffusion and restricted diffusion.

Diffusion is a physical phenomenon that can take several forms. It is important to give the definition we will be using throughout this whole document. In this work we will consider translational diffusion, and use the term “diffusion” to refer to self-diffusion, which is different from mutual diffusion. We will focus on this motion within liquids.

Diffusion is a passive motion of the molecules, and is the result of Brownian motion, the random motion of particle in a fluid. This random motion was a major discovery back in 1827 when it was first described by the botanist Robert Brown.¹,² It was the topic of one of the first theoretical work of Albert Einstein³ in 1905 and it was demonstrated experimentally in 1908 by Jean Perrin (Nobel prize 1926). Diffusion is quantified through the diffusion coefficient. Consider particles that diffuse during a time $\Delta$, the diffusion length ($D_l$) of the particles in n dimensions, measured as their mean square displacement will be:

$$D_l = \sqrt{2nD\Delta} \qquad 1-1$$

Where $D$ is the diffusion coefficient.

Just like Brownian motion, the diffusion coefficient is a function of temperature. It is an intrinsic property of a solute in a given solvent at a given temperature and this will be the main reason why we want to discuss and study diffusion.

The principles of diffusion were first described for microscopic particles, i.e., particles that were visible under the microscope but several order of magnitudes larger than molecules. It was shown that the diffusion coefficient in this case is described by the Stokes-Einstein equation:

$$D = \frac{k_b T}{6\pi\eta r} \qquad 1-2$$

where $k_b$ is the Boltzmann constant, linked to Brownian motion. $T$ is the temperature, $\eta$ is dynamic viscosity, $r$ is the radius of the molecule. The Stokes-Einstein equation is in principles only valid for hard and perfect-bead shaped particles that are far from each other (no mutual collision) and much larger than the solvent molecules. It can therefore only be applied in sufficient dilution condition to molecules with relatively simple interaction with the solvent. One can find it a bit surprising that we consider the size rather than the weight, not following classic inertial laws. Indeed Stokes, a major contributor in the field of fluid mechanic toward the end of the 19th century, has given his name to a law that allow to retrieve the drag force exerted on a sphere in a viscous fluid. This apply to individual
molecules which mass is negligible in regard of this drag. The dependence on the temperature captures the effect of thermal agitation, which can be seen as a random motion of molecules.

The Stokes-Einstein molecules is not generally valid in the situation encountered in typical diffusion NMR experiments, in which several of its assumptions are not verified. Still, it can provide a useful guide to analyse diffusion NMR data. The radius “r” will change depending on the kind of molecule/solute and its specific interaction with different solvent,⁴,⁵ it is sometimes noted R<sub>h</sub> for hydrodynamic radius.

While this work, and the majority of NMR-based studies of diffusion, focus on self-diffusion, it is interesting to consider its relation with mutual diffusion. Diffusion is also the process through which, in a closed space, through their random motion, molecules will homogenously fill the space given enough time. It was originally described by Fick.⁶ Fick's second law describes the propagation of the solute within the solvent, in the presence of a concentration gradient:

$$ \frac{\delta\phi(x, t)}{\delta t} = D \frac{\delta^2\phi(x, t)}{\delta x^2} \qquad 1-3 $$

Where D is the diffusion coefficient, φ is concentration. This diffusion law governs local concentrations and describe how a solute spread into a solvent. It explains how a local increase of solute concentration lead, even if undisturbed to an homogenic concentration.

#### 1.1.1.1. Mutual diffusion

Mutual diffusion, in contrast with self-diffusion, is not the motion of a particle seen as alone in a matrix-like inert solvent but rather the relative motion of solute and solvent particle.⁷ The mutual and self-diffusion coefficient are only different in that the mutual diffusion take thermodynamic forces and solvent back flow into account, knowing that a corrected mutual diffusion coefficient $\tilde{D}$ exist

$$ \tilde{D} \equiv D_m / \left[ \left( \frac{M}{RT} \right) \left( \frac{\partial \Pi}{\partial c} \right) (1 - \bar{v}c) \right] \qquad 1-4 $$

Where M, c and $\bar{v}$ are respectively molecular mass, concentration, partial specific volume of the solute, R is the gas constant, T the absolute temperature, Π the osmotic pressure and $D_m$ the mutual diffusion coefficient. The effects of the thermodynamic force and the solvent back flow are taken into account by the factors $(M/RT)(\partial\Pi/\partial c)$ and $(1 - \bar{v}c)$, respectively.⁸

The problem of equivalence between mutual ($\tilde{D}$) and self-diffusion (D) coefficients is an important topic as mutual diffusion is measured by light scattering while self-diffusion is more often taken from NMR data. It seems that from the general stand, globular macromolecules and rigid polymer have a good equivalence between the two Ds but flexible or entangled polymer seems to behave otherwise.⁸,⁹ As mutual diffusion is much more complex to study for small molecules and is not the outcome that NMR methods yield, we will mostly set it aside during this work. Nonetheless it is a
good reminder that concentration and diffusion are linked therefore we will consider that solutions we look at are always homogeneously concentrated and there is no gradient of concentration.

Diverting a bit from the subject we will briefly discus of a special case in diffusion studies, named restricted diffusion. The term is used when the duration needed by a diffusing molecule to travel the length of its enclosure is comparable to the diffusion time for its analysis. In this case it is possible to retrieve the size of the enclosure.¹⁰ Restricted diffusion is a term mostly used in the MRI/NMR field, and refers to measurement method as well as the actual motion. One usually speaks about restricted diffusion in either droplets, pores or any other small enclosure.

Restricted diffusion was first characterised using NMR by Tanner and Stejskal¹¹ for colloid and size determination of droplets. It was then used in the field of geology for the determination of pores sizes in rocks.¹² This usage to determine porosity will be decisive as it is used for determination of cellular porosity¹³ and generally to study water in confined biological environment.¹⁴ In an important yet somewhat controversial paper for MRI¹⁵ it is also used for diagnostic purposes. The attentive reader may have noticed that this part on restricted diffusion, mix diffusion focused study and relaxation focus studies. It is not uncommon in this field, as interaction with the enclosure's walls generates changes in relaxation that can help retrieve the relevant information. Indeed, nowadays porosity of the cells is a key point in diagnostic by MRI and rely mostly on relaxation far more than diffusion.

#### 1.1.1.2. Fick law and chemical potential

So far, we have described diffusion as a phenomenon consequence of Brownian motion and thermal motion. Other ways to describe this phenomenon exist, in our case of reaction monitoring, the chemical potential aspect is interesting.

Chemical potential is Gibbs free energy at constant temperature and pressure when moles are considered to count particles. In a description that lies on chemical potential the drive for diffusion is not thermal motion but rather lowering G or chemical potential of the solution. In a solution at thermal equilibrium i.e. homogenous and non-reacting the Gibbs energy and chemical potential is a its minimum. Yet, diffusion still happen and diffusion rate can still be measured the difference is that they will not be defined as a flux but rather as a passive motion.

To use and describe diffusion with chemical potential one would use the diffusion flux defined in Fick laws. A flux that goes in the direction of the concentration gradient, from most concentrated to low concentrated area. This is illustrated by the Fick law of diffusion $J = -D \frac{dc(x)}{dx}$ with D the diffusion coefficient, J the diffusion flux, c the concentration and x the position.

The main interest for us, that work on homogeneously concentrated solution, is about the change of Gibbs energy that could happen with the reactant/product. Let's describe a molecule that need energy E to move at a certain rate.
$$ Rate \propto e^{-(E_c^0-E_1^0)/RT} - e^{(E_c^0-E_2^0)/RT} \qquad 1-5 $$

With $E_c^0$ is the 0 point of energy for the transition step, $E_1^0$ for the initial step and $E_2^0$ for the final step. Rate is therefore a measure of the energy needed to start from a point $E_1$ and go to $E_2$ by passing in $E_c$. So, $G^a = E_c^0 - E_1^0$ with $G^a$ the activation energy, and $\Delta G = E_2^0 - E_1^0$ with $\Delta G$ the change in internal energy. Henceforth we have

$$ Rate \propto e^{-G^a/RT}\{1 - e^{\Delta G/RT}\} \qquad 1-6 $$

From this we can obtain the Arrhenius rate equation for kinetically controlled process. We can also extract 1-7 in the case of $|\Delta G| \ll RT$, which correspond to a thermo controlled process.

$$ Rate \propto e^{-G^a/RT} \left| \frac{\Delta G}{RT} \right| \qquad 1-7 $$

We have now the tool to understand what link Flick's law to Gibbs energy and chemical potential. Let's imagine two compartment such as x the most concentrated one and x+a the less concentrated one. We are in a case such that the concentration is the driving force of the chemical potential $\mu$ and only $\mu$ contribute to $\Delta G$. This will be the simplest case possible. In a reaction contribution to $\mu$ are mainly concentration and $\Delta G$ can be more complex. Yet for reaction to happen molecules need to encounter each other and so need to move, so the simplest step is a motion that decrease chemical potential, diffusion.

<figure><img src="image_2.png" /><figcaption>Figure 1.1 illustration of diffusion from a position x to x+a. Diffusion here is from the most concentrated to the low concentrated, henceforth go for the reduction of the chemical potential. This part and figure are strongly inspired from the lectures of Pr L. Zang of Utah university available online.</figcaption></figure>

We can now define $\Gamma$ the number of jumps like step a, with $\nu$ the vibrational frequency.

$$ \Gamma = \nu \times e^{-\Delta G^a/RT} \qquad 1-8 $$

Therefore, in a 3-dimensional space with 6 equivalent direction (±x, ±y, ±z) we get
$$ \Gamma = \frac{v}{6} \times e^{-\Delta G^a/RT} \qquad 1-9 $$

Which lead to a rate of this form

$$ rate = \frac{v}{6} \times e^{-\frac{\Delta G^a}{RT}} \left(-\frac{a}{RT} \times \frac{d\mu}{dx}\right) \qquad 1-10 $$

Assuming $\frac{d\mu}{dx}<0$ which is the situation illustrated in figure 1.1. We can use this to define a flux J that will be depending on the concentration at x, c(x) and the length of the displacement along x, named a.

$$ J = rate \times (a \times c(x)) \qquad 1-11 $$

$$ J = -\frac{a^2 v}{6} \times e^{-\frac{\Delta G^a}{RT}} \times \frac{c(x)}{RT} \times \frac{d\mu}{dx} \qquad 1-11' $$

By definition the chemical potential driven by concentration can be written as such

$$ \mu(x) = \mu^0 + RT\ln y c(x) \qquad 1-12 $$

With $\gamma$ the activity coefficient constant. We can deduct from 1-12

$$ \frac{d\mu}{dx} = \frac{RT}{c(x)} \times \frac{dc}{dx} \qquad 1-13 $$

Injecting 1-13 into 1-11' we get

$$ J = -\frac{a^2 v}{6} \times e^{-\frac{\Delta G^a}{RT}} \times \frac{dc(x)}{dx} \qquad 1-14 $$

By having D the diffusion coefficient in the from

$$ D = \frac{a^2 v}{6} \times e^{-\frac{\Delta G^a}{RT}} \qquad 1-15 $$

We can change 1-14 into

$$ J = -D \times \frac{dc(x)}{dx} \qquad 1-16 $$

1-16 is the Fick law of diffusion that link concentration/chemical potential to the diffusion. As we have seen it is best to describe two compartment that have different concentration, a case that we will not encounter in our studies. It is also useful as it uses notion of Gibbs energy that are key in reactivity. This links the motion of diffusion with the idea of diffusion as the motion necessary for the compound to encounter each other.

It happens that recently a controversy in the NMR diffusion community¹⁶,¹⁷ centred about a possible acceleration of diffusion in reaction setting. The acceleration is theorized to be linked to chemical potential and chemical activity. They discuss the possible energy transfer from the reaction solvent molecule that would enhance molecular mobility.¹⁶ Yet, the controversy in the NMR communities showed that the evidence for such boosted mobility is coming from artefact in measurement.¹⁸ Therefore, it seems that there is no acceleration or change of speed coming from reaction. Thus, the two descriptions by either Einstein-Stokes that lie on the Brownian motion or the Fick's law and Gibbs function are seemingly equivalent. Reactions that have complex setting such as polymer's growth and increase medium viscosity, reduce molecular mobility. It could be relevant to use Fick's law and chemical potential related descriptions.
Note that very recently a new paper continued the controversy by defending boosted diffusion
so the debate is still relevant.¹⁹

1.1.2. Measuring diffusion by NMR

1.1.2.1. *Self-Diffusion and diffusion coefficient*

In the previous section we have discussed about diffusion at large, here we propose to focus on how
this phenomenon is analysed by NMR. We are going to focus on self-diffusion, and on the main ways
we used diffusion NMR in this work. Diffusion analysis by NMR relies heavily on magnetic-field
gradients and relatively simple pulse sequences. It often works by incrementing a gradient amplitude
or a delay within the sequence. Unlike most 2D NMR experiment (COSY, HSQC, NOESY...), it does not
rely on 2D FT and other so-called indirect dimension. It usually uses only one dimension of frequency
(chemical shift or spectral dimension) and the second dimension will be the diffusion coefficient.

To understand what is happening we will describe the stimulated echo pulse sequence, shown
in figure 1.1, which consists of 3 90° RF pulses and 2 gradients pulses. From there on, the word
"gradient" will be used to refer to a magnetic-field gradient unless stated otherwise. Consider the
equilibrium magnetization of an ensemble of uncoupled spins, which may be described by a vector
aligned along the B₀ field direction. To simplify we will not consider the effects of precession, diffusion
and relaxation.
<figure><img src="image_3.png" /><figcaption>Figure 1.2: Stimulated echo (STE) sequence with monopolar gradient pulses. At each important step the magnetization is drawn. According to RGB additive colour model, red and blue make purple. Step 1) after the 90°$_x$ pulse, the magnetization is along Y. Step 2) after the first gradient pulse, the magnetisation forms a helix. Step 3) The 2nd 90°$_x$ pulse returns the Y component of the magnetization to the Z axis, while the X component stays and will be discarded by other means. Step 4) The 3rd 90°$_x$ RF pulse rotates the Z magnetization back to the transverse plane. 5) The gradient refocuses a helix by unwrapping it. In the presence of diffusion, the resulting magnetization is imperfectly refocused due to the helix being disturbed. The spread of magnetization causes a loss of signal.</figcaption></figure>

In the STE pulse sequence, a first 90° pulse is applied to rotate the magnetization to the transverse plane, orthogonal to the B₀ field (step 1 in figure 1.2). Then, a first gradient pulse is applied. When a gradient is applied, the sample is no longer in a spatially homogeneous magnetic field. The magnetic field experienced by the sample is that of the main homogeneous field (B₀) and a small additional spatial variation coming from the gradient coil:

$$B_{tot} = B_0 + gz \qquad 1-17$$

Where z is the position and g is the gradient amplitude. As a result, the precession frequency of the magnetisation is no longer identical everywhere and it becomes

$$\omega(z) = -\gamma B_0 - \gamma gz \qquad 1-18$$

Where γ is the gyromagnetic ratio. If the gradient is applied during a time δ, the precession of the magnetisation will be of an angle of γgzδ, in the rotating frame, resulting in:

$$M_{\vec{y}} \xrightarrow{\gamma gz\delta} M_{\vec{y}} \cos(\gamma gz\delta) + M_{\vec{x}} \sin(\gamma gz\delta) \qquad 1-19$$

With such change of their phase depending on the position z, the magnetisation vectors form a helix,²⁰ as illustrated in step 2 of Figure 1.2. This helix pattern depends on the strength and duration of the
gradient which will modify its pitch $\Lambda = \frac{2\pi}{\gamma g \delta}$, the number of turns $NT = \frac{L}{\Lambda}$, L being the length of the sample.⁵

As soon as the gradient pulse allows the helix to complete enough turns the magnetization averages to zero over the length of the sample and there would be no detectable signal. As it is, it seems we have just described a way to kill the signal (which in itself can be useful), yet this helix-gradient concept is key in what will follow.

In the STE pulse sequence, once the first gradient pulse is applied, a second RF pulse is applied to return the magnetization along the longitudinal axis. This is important to avoid $T_2$ relaxation and J-modulation during the rather long diffusion delay. The RF pulse transforms the y-component of the magnetization into a z-component leaving only the x-component in the transverse plan, as see in step 3 figure 1.1. The remaining transverse magnetization (shown in blue in Figure 1.1) will be suppressed, either using a gradient pulse that will make another helix that gives no signal, or using phase cycling.

The magnetisation of the second RF pulse can then be written:

$$M_{\bar{y}} \cos(\gamma g z \delta) \xrightarrow{\pi/2} M_{\bar{z}} \cos(\gamma g z \delta) \qquad 1$$

The third RF pulse returns the magnetization to the transverse plan, giving:

$$M_{\bar{z}} \cos(\gamma g z \delta) \xrightarrow{\pi/2} M_{\bar{y}} \cos(\gamma g z \delta) \qquad 1-21$$

If we rewrite the above equation differently using Euler formula we have:

$$M_{\bar{z}} \cos(\gamma g z \delta) \xrightarrow{\frac{\pi}{2}} M_{\bar{y}} \frac{\exp(i\gamma g z \delta) + \exp(-i\gamma g z \delta)}{2} \qquad 1-22$$

Which can be seen as the sum of two helices of opposite signs.

The second gradient pulse is applied which refocuses the helix by cancelling out its now reversed phase,

$$M_{\bar{y}} \cos(\gamma g z \delta) \xrightarrow{\gamma g z \delta} [M_{\bar{y}} \cos(\gamma g z \delta) + M_{\bar{x}} \sin(\gamma g z \delta)] \cos(\gamma g z \delta) \qquad 1-23$$

Using Euler formula, we got:

$$[M_{\bar{y}} \frac{\exp(i\gamma g z \delta) + \exp(-i\gamma g z \delta)}{2} + M_{\bar{x}} \frac{\exp(i\gamma g z \delta) - \exp(-i\gamma g z \delta)}{2i}] \frac{\exp(i\gamma g z \delta) + \exp(-i\gamma g z \delta)}{2} \qquad 1-24$$

Which after some steps give

$$\frac{M_{\bar{y}}}{2} + M_{\bar{y}} \frac{\exp(2i\gamma g z \delta) + \exp(-2i\gamma g z \delta)}{4} + M_{\bar{x}} \frac{\exp(2i\gamma g z \delta) - \exp(-2i\gamma g z \delta)}{4i} \qquad 1-25$$

If we use Euler formula again in the other direction we have the blue part that is a double helix as such,

$$\frac{M_{\bar{y}} \cos(2i\gamma g z \delta)}{2} + \frac{M_{\bar{x}} \sin(2i\gamma g z \delta)}{2} \qquad 1-26$$

which signal is null while the recordable magnetisation in red have been divided by two.
In summary the first gradient pulse creates a spatial organization of the magnetisation, which forms a helix. After being stored as an amplitude modulation, this organization is refocused by using a second gradient pulse.

We have introduced a spatial dependency along z within the helix thus it is sensitive to motion along its main axe. The motion will come from diffusion that makes molecules (and their respective spin) move in a stochastic way. As we are interested in the z dependency the spin can be illustrated as moving from one slice to another. The result is that upon refocusing, there will be an additional loss as not all the spin will undergo the right refocusing because they are not in their initial slice. Without diffusion or motion the slice are expected to refocus and finish in the same state as they started, see step 1) figure 1.2. Instead, due to diffusion, some of the spins have changed slice, those will then be under a different gradient strength than they were initially encoded with. Instead of properly refocusing each slice will have a residual phase shift. The result is a phase spread of the magnetization. The consequence is the loss of signal. A random undirected motion such as diffusion induce a loss that is proportional to the level of organization. The tighter the helix, the more significant the loss. The original model of what was discussed here can be found in Ref.²¹ together with an analytical description of the effect of diffusion using the Torrey-Bloch equation²² a deeper and more mathematical definition of this can be found in ref.²¹⁻²⁵

Solving the Torrey-Bloch equation for the STE pulses sequence gives a signal dependency in the form,

$$S = S_0 e^{-(D g^2 \gamma^2 \delta^2 \Delta')} \qquad 1-27$$

where $\delta$ is the time of the gradient pulse, $g$ is the power of the gradient, $\Delta'$ is the main delay when diffusion happen, corrected to account for the finite width of the gradient pulses, $S$ is the resulting signal, $S_0$ is the signal in the absence of diffusion, and $D$ is the diffusion coefficient. Eq 1-27 is called the Stejskal-Tanner equation, and describes the attenuation of NMR signals under the effect of diffusion, for a pair of gradient pulses separated by a delay.

In practice, diffusion coefficients are measured by acquiring a series of 1D spectra for different degrees of diffusion attenuation. The data is then fitted with Eq 1-27, by non-linear least square optimization. Three parameters may in principle be varied to record experiments with different degree of diffusion attenuation, the power of the gradient, the pulse duration and the storage delay. In this whole work we mostly made the power vary as it is simpler on our hardware and has less consequence in the sequence.

#### 1.1.2.2. Diffusion editing

The principle of diffusion NMR are also used for methods named diffusion-filtered NMR. Their purpose is not to retrieve information on diffusion coefficients but rather to have 1D spectra where small (fast diffusing) molecules are filtered out. This can also be used as a fast method to have a qualitative idea
on the size of molecules or on their binding abilities. This method uses the same kind of sequence and principle as regular diffusion-NMR but usually do not require increments, as no data fitting is performed. Diffusion weighting is also sometimes used to improve solvent suppression.²⁶ Solvent molecules being most of the time small and fast diffusing, the solvent signal can be strongly attenuated by using diffusion encoding gradients. It is mostly used in metabolomics and other fields that study biological fluids or extract.²⁷⁻³¹ Another use of this technique is for screening or rapid determination of binding interaction between a slow-diffusing molecule and a fast-diffusing one. It is used in the pharmaceutical field and in study of protein.³²⁻³⁵

Two examples of such uses from the literature are shown below. Figure 1.3a) and b) shows two spectra of 1 mg of strychnine in a mixture of d₆-DMSO and water. Here diffusion is used as a mean to suppress the fast-moving molecules of solvent²⁹ and is an interesting alternative to solvent suppression. It can suppress the solvent and the other small molecules present (here water) with it and do not require much knowledge on how to create special multi-signals RF pulses.

<figure><img src="image_4.png" /><figcaption>Figure 1.3. The 500-MHz ¹H spectra of 1 mg of **1** [strychnine] in DMSO-d₆. (a) Conventional spectrum acquired with 16 transients and (b) diffusion-filtered using the BPPLED sequence with a gradient length of 3.61 ms acquired with 512 transients. The signal-to-noise ratios are (a) 2183 and (b) 25. Reprinted with permission from Esturau et Espinosa²⁹ Copyright © 2006, American Chemical Society</figcaption></figure>

In figure 1.4 the authors³² are interested in a mixture of compounds and their potential interactions with hydroquinine 9-phenantryl ether. The mixture of 9 compounds including the hydroquinine is shown in figure 1.4a). Figure 1.4b) shows a diffusion edited spectrum in the absence of the hydroquinine there is no signal left and figure 1.4c) the same diffusion-edition conditions but with the hydroquinine. Results are quite striking and allows to quickly identify which compound has binding interactions with the hydroquinine and which has none. The reduction of mobility due to the
association is a rapid mean to show that there are interactions between the molecules and can be used
to screen a whole mixture rather than testing each molecules two-by-two.

<figure><img src="image_5.png" /><figcaption>Figure 1.4 (a) 1D 400 MHz ¹H NMR spectrum of the nine-component mixture in CDCl₃. The concentration of each component is 10 mM. Components: (1) dl-isocitric lactone, (2) (S)-(+)-*O*-acetylmandelic acid, (3) dl-*N*-acetylhomocysteine thiolactone, (4) (±)-*sec*-butyl acetate, (5) propyl acetate, (6) isopropyl butyrate, (7) ethyl butyrylacetate, (8) butyl levulinate, (9) hydroquinine 9-phenanthryl ether. (b) 1D PFG ¹H NMR spectrum of the mixture without hydroquinine 9-phenanthryl ether using LED sequence. (c) 1D PFG ¹H NMR spectrum of the nine-component mixture. Chemical shifts arising from compounds 1 and 2 are labeled. All other shifts are from compound 9. The PFG conditions were the same as in the middle spectrum. Reprinted with permission from Bleicher et al.³² Copyright © 1998, American Chemical Society</figcaption></figure>

1.1.2.3. SEC (Size Exclusion Chromatography) and DOSY for molecular size determination

The gold standard for measuring molecular size and weight in solution, especially for polymers, at this time is chromatography using SEC rather than NMR. It is especially powerful in analysing different polymers, because of its ability to determine weight distribution. Yet, it seems to be less repeatable for getting average or absolute mass determination. It also needs to be coupled with detection method
such as multi-angle laser light scattering to do so. The operative cost in terms of diversity of columns and solvent as well as pumps can also be summoned as a limitation but NMR also suffer akin cost and solvents limitations. At last, compatibility with certain kind of polymer can be limited³⁶ which is rarer for NMR and organic polymers. The SEC capability for mass determination is highly dependent on prior calibration, usually done with polystyrene polymers of know size and weight.

This dependence to polystyrene standards is problematic as accurate calibration with polystyrene is not so easy to get and small difference between experiments and results yield poor inter-lab repeatability. The work of P.-J. Voorter et al.³⁷ propose a method to make universal calibration corrected for the solvent viscosity using DOSY NMR methods for polymer weight determination.³⁷ Using the empirical Rouse–Zimmmodel model they can use Stoke-Einstein equation to link average molecular weight and hydrodynamic radii, D = b'M⁻v. Where b' is an empirical factor and v an arbitrary shape parameter. Another way to write this equation is

$$ \log(D)+\log(\eta)=\log(c)-v\times\log(M) \qquad 1-17 $$

With η the viscosity and c the new proportionality parameter. Knowing the viscosity of the various deuterated solvents and the factor v for polystyrene, they can make calibration curve using DOSY. Those curves are expected to give accurate result independent of the labs, apparatus and solvent viscosity. As shown in figure 1.5 once corrected for viscosity molecular weight are very close in all solvents even in those deemed “a bad solvent for polymer” such as acetone.³⁷ This can be used to create a double calibration system. The first SEC calibration done with polystyrene can be corrected to match the result of the DOSY (using same standard) thus limiting the actual problem of inter-lab lack of repeatability. They conclude that a few tests should be done in various lab to assess the claim of improving inter-lab repeatability but this is expected to work as NMR usually does not suffer from repeatability troubles.
<figure><img src="image_6.png" /><figcaption>Figure 1.5 Diffusion coefficients determined via DOSY for polystyrene standards in a series of solvents (top) and viscosity-corrected data for the same measurements (bottom). Reprinted with permission from Voorter et al.³⁷ Copyright © 2021 Wiley-VCH GmbH</figcaption></figure>

### 1.1.3. Review of relevant methods

In the previous section we have described the monopolar STE pulse sequence as it is the basis for most of the diffusion experiments in high-resolution NMR. Historically, the first method described for diffusion studies is the Hahn or spin echo. It consists of a 90° pulse followed by a 180° pulse, both RF pulses being followed by a gradient pulse. In this work we did not use spin-echo based pulse sequences. We will now review extensions of the monopolar STE pulse sequence that are important for diffusion NMR and especially to understand the work reported here.

#### 1.1.3.1. Eddy/Foucault currents

Eddy currents (also called Foucault current) are electric currents created within electrical conductors by changes of an external magnetic field. Those electric currents in turn generate a magnetic field, that is usually opposite to that of the perturbation. In NMR spectroscopy such currents can happen in the probe when a gradient pulse is applied. Currents inside the coil are created and oppose the shutting down of the gradients. They can have different effects, overall negative, on the quality of the signal. The main effect is the apparition of a residual gradient field that will extend the duration and decrease the quality of the gradient pulse³⁸,³⁹. Those effect depend highly and the kind of hardware that is used.

Several methods have been described to counter the effect of eddy currents in diffusion NMR. The most used is called LED, for "longitudinal eddy current delay". It consists of two 90° pulses with a
delay in between. The idea is to avoid that the residual gradient extends during the acquisition when
it could be very harmful to the signal. The LED block stores the magnetization along the longitudinal
axis during a time Te, during which the residual gradient dispels. Once this delay is over the second 90°
pulse puts back the magnetization in the transverse plan where it can be recorded. A representation
of LED block within a STE is shown in figure 1.6.

Putting the magnetization along the longitudinal axis is often a problem. If the longitudinal
storing happens for too long T1 relaxation can happen thus reducing the signal strength. Small errors
in calibration of the Rf pulse will also lead to artefact as all the magnetization may not be put on the
longitudinal axis. Sometimes a gradient is put in-between the LED block to limit this. It remains a bit
counter-intuitive to add more gradient to a sequence's part made to avoid unwanted gradients effects.
Nowadays modern hardware is very well shielded and LED is less mandatory than it used to be.

<figure><img src="image_7.png" /><figcaption>Figure 1.6 : the STE mono-pulse with the LED. The red curve after gradient pulses shows the possible eddy current induced gradient.</figcaption></figure>

1.1.3.2. Bipolar gradient pulses

This method consists of using bipolar gradient pulses instead of monopolar ones. To do so and keep
the same effect as with a monopolar gradient pulse, a 180° RF pulse is inserted between the two halves
of the bipolar gradient pulse. In analogy with what is explained in 1.1.2.1, and as explained in Ref. 21;
the 180° pulse inverts the magnetisation helix, such that the second half of the gradient pulse, of
opposite polarity, further tightens the helix. The total dephasing is equivalent to that obtained with
two consecutive pulses of the same polarity. The sequence is illustrated in figure 1.7. There are several
reasons to use bipolar gradient pulses.

A first reason is again eddy/Foucault currents. The effect of those residual currents will be
reduced due to the opposite polarity of the bipolar gradient pulses, which compensate each other. A
second reason is the stability of the lock signal. Most NMR systems use locking systems. It consists of
a continuous-wave NMR system that focuses on the frequency of another nucleus than the one of
interest, mostly ¹⁹F or ²H. The lock system makes it possible to monitor changes of the main magnetic
field and continuously compensate them. It includes the field value, its homogeneity, and outside
interference (Rf signal and vibration). It is very important for spectrometer stability.

Locking is a key aspect of NMR spectroscopy, and is required to achieve good repeatability and
for the automation of any experiments. The problem is that when gradients are used, unlike RF pulses,
they are not selective of a nucleus. It happens that gradients will defocus the signal of any nuclei inside
the sample including those that are used to lock the signal. Gradients pulses will disrupt the signal for
the time of the experiment making the experiment more sensitive to outside nuisances.

Bipolar gradient pulses make it possible to avoid this problem. The 180° pulse does not affect
the locked nuclei and in this case the two gradients effectively cancel out for the locked nuclei and not
for the analysed one. It greatly helps to keep experiments running smoothly. Interestingly, in the
standard sequence provided by the manufacturer on our system, the benefit of this effect is lost,
because spoiler gradients are uncompensated.

The main drawback of using bipolar gradient pulses is that the additional RF pulses increase the complexity of the sequence. 180° pulses are more susceptible to mis-calibration and RF inhomogeneity issues, and the selection of the relevant coherence transfer pathway only has to be ensured.

<figure><img src="image_8.png" /><figcaption>Figure 1.7 : the STE pulse sequence with the bipolar pulse strategy. Black rectangle in the upper axis are 90° RF pulse, white ones are 180°. The lower axis white pulse are gradients pulses.</figcaption></figure>

1.1.3.3 Double Stimulated Echo (DSTE)

Diffusion results from molecular motion on a small scale, and its analysis by NMR lies on the fact that
this motion disturbs the organization of the spin's magnetisation created by the magnetic-field
gradient. For this to occur, the sample ideally needs to be steady. No unwanted motion should be
present, no gradient of concentration nor inhomogeneity. One type of motion that is difficult to avoid
in NMR experiments is convection.⁴⁰ It appears in any liquid when there is a gradient of temperature,
which results in a convection cell. Convection cells are usually characterized by motion of cold denser
fluid moving below a portion of warm lighter fluid. Convection is particularly a problem in low-viscosity
fluids like most organic solvents, and in the presence of a strong temperature gradients. Such temperature gradients are supposed to be avoided by the temperature regulation system of NMR probes, but in low viscosity solvent convection is nearly unavoidable.⁴¹ Convection is very detrimental to the diffusion analysis as it will disrupt magnetisation helices, adding its effect to that of diffusion and leading to overestimated diffusion coefficient.

To remove this effect a sequence was proposed in 1997⁴² and is still very much used nowadays. The double stimulated echo (DSTE) pulse sequence relies on the fact that the disruption by convection is not random like diffusion. Instead, it results in the coherent acquisition of a supplementary phase by the magnetisation. In the DSTE pulse sequence one performs two diffusion-encoding steps with opposite coherence pathways, so that the phase is added during the first part and subtracted during the second. This DSTE sequence is a useful method to have reliable results in solvents such as chloroform or acetonitrile (two very low viscosity solvent). The sequence is represented in figure 1.8.

One major drawback is that the storage along the longitudinal axis reduces the sensitivity by a factor 2 so doing it twice reduces sensitivity by a factor 4. This and the effect of gradient that already lessen the sensitivity make DSTE a sequence difficult to use for low concentration samples or if time constrain does not allow to accumulate enough scan/signal.

<figure><img src="image_9.png" /><figcaption>Figure 1.8 : DSTE sequence with coherence pathway.</figcaption></figure>

## 1.2. Selected examples of application

Our work focuses on methods development. It aims to give tools and methods that may be applied to interesting topics/mixture/medium/sample. In this section we will show the diversity of research areas and uses for which diffusion NMR and DOSY are relevant.
1.2.1. Polymer

The polymer field is mostly interested in two pieces of information that DOSY experiments can provide, molecular weights and polydispersity. Let us consider first polydispersity. Until now we have focused on the classical diffusion model for NMR with monoexponential decay, yet it is not the only one. In case of polydispersity, a very common occurrence for polymers, this model fails to describe the data.⁴³ Multiexponential decay is far more difficult to characterize, and requires inverse Laplace transformation (ILP). Such transformations are not as straightforward as Fourier transform and require complex algorithms. To our knowledge the most commonly used algorithm in the context of diffusion NMR is CONTIN⁴⁴,⁴⁵ (general purpose constrained regularization program for inverting noisy linear algebraic and integral equations). Other algorithms such as NLREG (nonlinear regularization) can be found.⁴⁶,⁴⁷ The main problem is that the ILT is an ill-posed problem. Those ILT methods are often used in routine, yet they appear to be very sensitive to SNR as well as any other perturbations that could occurs.

Polydispersity is an important information, with the PolyDisperse Index (PDI) being an interesting data to obtain in a polymer sample. To get this information different models for multi-exponential decay can be used. The models used often derivate from either the log-normal models⁴⁸ used in size-exclusion chromatography (SEC) and NMR or the gamma distribution model.⁴⁹ Using those models gives gaussian distributions (or gaussian-like) results and from the shape and width of the gaussian one can extract the molecular weight distribution⁵⁰,⁵¹ and thus polydispersity. These methods have a large range of different applications that will depend on the different properties of the polymer.⁴³,⁵²,⁵³ It is to be noted that simpler analyses can sometimes be successfully used for polymer samples. For example, if the different parts of the chain (the core and the extremities) can be well resolved then comparing the spread and the coefficient diffusion of each part can allow to retrieve polydispersity.⁵⁴

Diffusion NMR is not the reference method for size determination or polydispersity, it is rather SEC that predominates especially for commercially available polymers. For research purposes NMR and diffusion-NMR are rising due to their high reliability and reproducibility. It gives similar result as SEC⁵¹ and timewise it is comparable if not faster. SEC needs to be coupled with a detector and like diffusion NMR, only gives information relating to hydrodynamic radius rather than mass. Polydispersity is not always easy to access and can ask for a great deal of various columns and mathematical models, for this reason diffusion NMR for polymer seems to be good alternative/complement despite its drawbacks.

Let us now consider what can be learnt on the molecular weight of polymers using diffusion NMR. Molecular weight for a polymer is directly linked to the number of monomers that are attached
together and is likely to be linked to the size of the polymer and thus to its hydrodynamic radius. As explained in section 1.1, the diffusion coefficient is linked to this radius. The determination of molecular weight from diffusion NMR data is then straightforward, using multiple monodisperse samples of known masses to make a calibration curve. This calibration curve then allows to place the diffusion coefficient of an unknown sample and access its molecular weight.⁴⁴,⁵⁵

For weight determination to work the polymer needs to verify a number of criteria. The form of the polymer in solution is important as the hydrodynamic radius is defined for mostly globular molecules (or bead shaped). Polymer being macromolecules different effects can intervene such as folding to minimize interaction with solvent or linearization to maximize it. Other phenomena such as aggregation, binding, reticulation can happen and make the model not so relevant. Thus, it is important to monitor the dilution condition⁴⁴ and sometimes it is necessary to have more complex models to describe the polymer. One relation often seen in diffusion NMR for polymer is $M \propto D^{-df}$ where df is the fractal dimension, a measure that help understand how the polymer extend in solution.⁵⁶

Consider Ref.⁴⁴ as an example. The authors aim at using diffusion NMR and DOSY to determine the molecular weight of a special family of polymers called conjugated polymers. The team explains that such polymers are hard to characterize using SEC, the standard and most general method for polymer size characterization, hence the need for another way. They use multiple equations and different known models to describe such kind of polymer. We are not going into the detailed equation, briefly they use different information such as chain rigidity, persistence length and the chain shape. Those models are necessary to understand if the polymer fit the condition in which self-diffusion law apply (see part 1.1.1).

Using this they can have two numbers to describe the elongation per monomer. One depends on weight-average molecular weight (Mw in the text) a value suited for polydisperse sample. Another metric, absolute number-average molecular weight (Mn in the text) is suited for low-molecular weight polymers with no polydispersity. Those allow them to make the curve one can see in figure 1.7. The first row shows the Stejskal–Tanner plot obtained with different attenuation in different length of polymers. It shows the quality of the plot and the relation between number of monomer and size-related attenuation of the signal. The diffusion analysis is then shown with each diffusion coefficient and its spread, which is a function of polydispersity. Finally, the last row shows how using the diffusion coefficient, they can retrieve the Mw. They show two different polymers, poly(3-hexylthiophene-2,5-diyl) known as P3HP the model, and poly[4-(4,4-dihexadecyl-4H-cyclopenta[1,2-b:5,4-b']dithiophen-2-yl)-alt-[1,2,5]thiadiazolo-[3,4-c]pyridine] known as PCDTPT used for the validation test. They manage to give molecular weight for different sample of different polymer length and polydispersity. They compare it with the standard method: Mw distribution (the spread) is assessed by SEC and its absolute value by NMR end-group analysis (another NMR method to measure Mn that does not use diffusion).⁵⁷
This is rather interesting as it shows that weight can be accessed using size. Yet the distribution
obtained using DOSY is much lesser than expected using SEC, resulting in much narrower curve. The
team blame the ILT and the limited number of points for that, nonetheless the Mw obtained from
DOSY are satisfactory and there is a good qualitative agreement between the two methods. Note that
those kinds of plots are common in the field of polymer studies when diffusion NMR is used albeit
extracted from DOSY data the DOSY classical display is not always shown or used.
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

Figure 1.8 Left column (a-c) is for the polymer used for validation PCDTPT. Right column (d-e) are for the test polymer P3HT. (a) Stejskal–Tanner plot of intensity signal attenuation integrated over δ = 0.5–1 ppm and (b) diffusion coefficient distributions obtained from DOSY analysis for the six batches of PCDTPT, PCDTPT_1 through PCDTPT_6. (c) P3HT-equivalent molecular weight distributions of the six batches of PCDTPT, calculated from the respective diffusion coefficient distributions with the power-law relationship in eq 3 (original text). (d) Stejskal–Tanner plot of intensity signal attenuation at δ = 0.91 ppm of the four batches of P3HT in CDCl3. (e) Absolute weight-average molecular weight of P3HT as a function of diffusion coefficient. (f) Diffusion coefficient distributions obtained from DOSY analysis. (g) Absolute molecular weight distributions (solid lines) and calculated distributions from DOSY analysis (dotted lines) for the four batches of P3HT. adapted with permission from Gu et al.⁴⁴ Copyright © 2018, American Chemical Society.
1.2.2. Mixture virtual separation

Mixtures are ubiquitous, and important in many fields such as natural products and formulation. The analysis of mixtures often requires physical separation of the components. Diffusion NMR is sometimes used for "virtual separation" and compared to chromatography, indeed one can even find it labelled as NMR chromatography.⁵⁸ This analogy originates from one of the very first use of diffusion-NMR⁵⁹, to resolve components in a mixture. Diffusion coefficients are an information of interest, in particular through their relation with size and mass, but they can also be used just as a mean to separate components in a mixture. If we follow the analogy with chromatography the interest is not the interaction with grafted silica but rather the separation of compounds in a mixture by said interaction. DOSY can work with the same principle: as a way to identify different compounds in a mixture, using the relative value of their diffusion coefficients.

Translational diffusion occurs for molecules as a whole, thus the diffusion coefficient measured for every site of a given molecule should be the same. This means that in a diffusion NMR experiment each peak of the same molecule will decay at the same rate. Just like molecular weight, or retention time, diffusion coefficients are unlikely to be exactly the same in two different molecules. Combining all this together makes diffusion NMR a virtual separation method, which gives insight into which peak belong to which molecule, and also on the relative sizes of the molecules.

DOSY NMR is often present in the area where chromatography and Mass Spectroscopy (MS) are present, such as the analysis of natural products.⁶⁰ The information provided by diffusion NMR is analogous to the provided benefit of chromatography coupled with MS. NMR has its own disadvantages such as sensitivity and time requirement but it also has its strength, the non-destructivity and the ubiquity of NMR compatible nuclei. The use of DOSY for identification of molecules in mixture using database is fairly new⁶¹,⁶² but seems promising. It shows both the rises of DOSY methods as well as its capability to give handy tool for identification of complex mixture.

Let us consider an example from the literature. You *et al.* have used DOSY to analyse alkaloid extracts.⁶³ Alkaloids are one of the most ubiquitous classes of molecules in natural extracts, and they have many different uses from medicine such as morphine and vincristine or in food such as piperine and are often used as platform for complex synthesis like indoles.⁶⁴ The main method for their separation is usually chromatography but it happens that because of the basic nitrogen present in their chemical structure, different interactions may rise with the silica particles as well as a strong impact of the pH, which can deteriorate the sample or worsen the separation.

DOSY NMR seems to be an interesting alternative. The spectra of the sample used in this work is quite crowded and poorly resolved because of the complexity of the mixture, and this is a recurrent problem in natural mixtures. The DOSY analysis itself is known to be sensitive to peak overlap, and
limited in terms of the range of diffusion coefficients that can be analysed in a single experiment. There
are also limitations on the resolution that can be achieved in the diffusion dimension. The natural
extract of *Alstonia Mairei* studied seems to have both problems, as can be seen in figure 1.9 (a) . Since
DOSY alone gave unsatisfactory results, the authors decided to use a surfactant capable of making
micelles (SDS for sodium dodecyl sulphate) to make a “matrix-assisted” resolution of the extract. This
makes it possible to increase the resolution in the chemical shift dimension as well as in the diffusion
dimension, as seen in part (b) of the figure. The probable reason being that formation of micelles will
change diffusion of the molecules depending on various binding ability. Micelle might also change
solubility and chemical environment explaining the change of resolution in the chemical-shift
dimension. The matrix-assisted DOSY analysis can be used in conjunction with known alkaloid
databases to identify the alkaloids. This example is interesting as it mixes different possibilities opened
by DOSY. It also gives perspectives for identification and quantification of less known natural samples.
This use of matrix and surfactant is commonly found in the world of natural extract separation⁶³,⁶⁵,⁶⁶
and relies on closely related principle than the use of DOSY in supramolecular chemistry.

<figure><img src="image_16.png" /><figcaption>Figure 1.9 : taken from. DOSY spectra of a mixture of the real total alkaloid extract (20 mg) before (a, upper) and after (b, lower) the addition of SDS (10 mg) in DMSO-d6 (600 µL). Experimental temperature was 298k. reprinted from You et al⁶³ © 2021 by the authors. Licensee MDPI, Basel, Switzerland. (open access CC BY license).</figcaption></figure>
Formulation is a rather wide term that we will use here to describe mixtures that are finished commercial products. Such products can range from food to medicine, and this underlines the fact that all the things that we use and buy are often mixtures.

One application of diffusion NMR is the characterization of emulsions.⁶⁷,⁶⁸ To do so technics a bit different from the classic DOSY are used yet relying in diffusion NMR. This size determination relies on the principle we have talked about in the part 1.2.2.1 under the name restricted diffusion. We don't go in the details as it usually involves a lot of complex theoretical models and algorithms that are more common in the imaging field. Just to mention it they use diffusion into the small enclosure that is the droplet to determine their size. It is interesting as it allows to characterize the emulsion without disturbing it. Alternatively in such mixtures that have a high content of fat or big molecules the diffusion-filter explained in the part 1.2.2.2 can be used.⁶⁹

Fraud detection is also very important in formulation and often chromatography is the most common way to separate compounds in a formulation and check if they match the original product or a forgery. DOSY having close capability is also used for such investigation in medicine formulation⁷⁰,⁷¹, it can also be used in the same kind of compounds for quality control.⁷²

### 1.2.3. Supramolecular chemistry

Supramolecular chemistry can be defined as a field that focuses on supramolecular interactions between molecules and the resulting molecular assemblies. More specifically on relatively weak interactions (compared to covalent bonding) between molecules, such as coordination bonds, ionic bonds, hydrogen bonds, etc. Those bonding can lead to assemblies of molecules that can take complex shape and undergo dynamic processes. One of the most studied processes is the encapsulation of molecules, in this case the host-guest paradigm is used. The host being the cage and the guest what resides inside it. Diffusion NMR is a very interesting tool for such assemblies as the nature of supramolecular bonds is weak and often sensitive to many parameters (temperature, solvent, salt...), NMR takes advantage of its capability to study such fragile objects without interfering whilst in solution.

Cohen and coworkers.⁷³,⁷⁴ have written several reviews about diffusion NMR and cavities/cages, stressing the information that diffusion NMR can bring. To illustrate a typical use of DOSY in the field of molecular cages we are going to take an example from another review of Anna J. McConnel⁷⁵. The work focuses on supramolecular cages that use metal centers, and here the metal is gallium. The cage formula is $[Ga_4L_6]^{12-}$ with L = 1,5-bis(2,3-dihydroxybenzamido)naphthalene, represented in the figure 1.10. The study itself focuses on the stability of the cage and its mobility with different counter-cation.⁷⁶ On figure 1.10 we can see the DOSY spectra of this cage with its guest $NEt_4^+$ and we see that they are able to differentiate two populations of the guest, exterior and interior. The team take
advantages of the chemical shift separation that is common in such assembly as the chemical
environment is different in the cage and free in the solvent. The diffusion of the cage components and
the guest being at the same diffusion rate is characteristic of a stable host-guest complex.⁷³,⁷⁵ In the
paper the team also investigates using diffusion NMR complex interactions with counter-cation, and
the rate of diffusion of the complex, to learn about the inclusion mechanism.

<figure><img src="image_17.png" /><figcaption>Figure 1.10 : ¹H and DOSY spectra of Raymond's [NEt₄CGa¹¹⁻₄L₆]¹¹⁻ host-guest complex where the encapsulated NEt₄⁺ guest is in slow exchange with “free” NEt₄⁺. Signals marked with + correspond to the cage, * the encapsulated NEt₄⁺ guest and # the “free” NEt₄⁺. Adapted with permission from Pluth et al.⁷⁶ Copyright 2008 American Chemical Society.</figcaption></figure>

NMR is particularly efficient at studying dynamical and/or weak interactions in solution.
Diffusion NMR was used to determine the size, elongation and overall bulkiness of complex structures
like helicates.⁵⁹ Many of the supramolecular assemblies show dynamic equilibrium that will be
dependent on the concentration of the species in solution. Those species are often crystallised and
studied by X-ray to have the first insight of the shape in solid-state. Diffusion NMR is one of the rare
technics that allows some determination of size and shape in solution. Merget et al.⁷⁷ report a usually
large molecular cage that self-assembles from macrocycle monomers. Figure 1.11 shows a comparison
of the evolution of diffusion coefficients as a function of the concentration of the monomers. It shows
the rapid decrease of diffusion as the monomer is added as well as the diminution of the hexamer's
coefficient (figure 1.11b). This hints at a mechanism of self-assembly and exchange between the
monomer and the hexameric cages, especially at low concentration where the hexamer is effectively
absent. On figure 1.11c) the quicker diminution of the hexamer's diffusion coefficient compared to other known macrocycle, that are also known to hexamerise, hint at it being much larger. Those kinds of assemblies are often very dependent on the solvent and thus NMR analysis within their medium show that diffusion-NMR can give information on complex equilibrium in solution.

<figure><img src="image_18.png" /><figcaption>a) Related Macrocycles</figcaption></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

Figure 1.11: a) Related macrocycles: pyridinearene 4, octamethylated resorcinarene derivative 5, resorcinarene 6 and pyrogallarene 7, and their respective diffusion coefficients in CDCl₃. b) Concentration dependence of the diffusion coefficients of the monomeric species 1a and the hexameric species I (1 mM –50 mM in CDCl₃). c) Comparison of the diffusion coefficients of the related hexameric assemblies based on macrocycles 1a, 6 and 7 at different concentrations (1 mM –50 mM in CDCl₃). Reprinted with permission from Merget et al.⁷⁷ © 2020 Wiley-VCH GmbH

Diffusion NMR is a powerful tool for supramolecular chemistry. Here we have focused on cages as the applications of diffusion NMR to those kinds of assemblies are particularly striking. Other kind of assemblies can be studied by NMR. We can mention gelators⁶¹, ionic pairs⁶² and various shaped complex.⁷³⁻⁷⁵,⁷⁸

### 1.3.4 Aggregates

Aggregates could also be defined as supramolecular entities, they share the weak bonds that is the core of their nature. We decided to make a separate part for them because they are found in very different contexts.

The use of catalysts is very common in modern chemistry and many key-steps in modern reactions involve different kinds of interactions between the catalyst and its substrate. Diffusion NMR
can be useful in the case of reactive intermediates. As we have seen it can access the size of those
intermediates and thus give information on their stoichiometries and shape. Unfortunately, those
intermediates are often too short-lived to appear on the spectra and do not build-up sufficient
concentration to be seen by NMR. If one aims to see those steps, it is needed to trap the intermediate
species. This species might get weakly bonded to the catalyst thus forming a reactive aggregate that
could be analysed by NMR.

Reducing the temperature is often an efficient way to trap transients species. For example, Qiao et al.⁷⁹ have used this approach. They used ¹H and ¹⁹F NMR and diffusion-NMR to characterize intermediates aggregates at low temperature, -55°C. They used ¹⁹F DOSY to avoid the overcrowding of the spectra, typical of glycochemistry. DOSY experiments allows two things, to observe that the catalyst is indeed bound to the reactant of interest, and to validate their hypothesis on the kind of aggregates by comparison between diffusion coefficients recorded and predicted. They conclude on different intermediates/reactive pathway depending on the catalyst used which allow them to propose a new catalyst.⁷⁹

Other ways to stabilize intermediate aggregates can be found, such as trapping them by
chemical means⁸⁰ or using a test-solution to recreate the conditions of the reaction with a more stable
aggregate. Such is the work of Matador et al.⁸¹ The reaction they are interested in is summarized in
Fig. 1.12. The thiourea is the reactant of interest while the benzoic acid is the catalyst, in the reaction
it is present in catalytic quantity. To understand better the mechanism the two are added here in equal
molarity. As one can see on figure 1.13, this led to the formation of an aggregate with NMR signal of
both species present in the spectral dimension, albeit slightly shifted and larger typical for the
formation of an aggregate. The two compound signals correlate at the same coefficient diffusion. This
resulting coefficient is smaller than that the two reactants it is made of, which strongly hints at an
aggregate formation. This rules that the active catalytic specie is the ion-pair Ia/PhCOO⁻. Its weak bond
allows to be temporally broken to let the substrate enter (see figure 1.12) and is strong enough to
resume its initial paired state and continue the catalytic cycle. The DOSY analysis is an important step
in the catalytic cycle unravelling process, it is part of a package of methods that includes DFT calculation
and X-ray, which is relevant with aggregates and weakly bounded molecules as well as any
mechanistical study.
<figure><img src="image_21.png" /><figcaption>Figure 1.12. The reaction of interest. Reproduced from Matador et al.⁸¹ with permission from the Chinese Chemical Society (CCS), Shanghai Institute of Organic Chemistry (SIOC), and the Royal Society of Chemistry.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Figure 1.13. ¹H DOSY NMR (500 MHz, 0.2 M, toluene-d₈) of benzoic acid (left), thiourea Ia (right) and Ia/PhCOOH 1 : 1 mixture (middle). Reproduced from Matador et al.⁸¹ with permission from the Chinese Chemical Society (CCS), Shanghai Institute of Organic Chemistry (SIOC), and the Royal Society of Chemistry.</figcaption></figure>

We have seen intermediate-aggregates in the course of a reaction. Another kind of reactive aggregates exists, those for which the aggregation state can plays a role as intermediate but also in
their initial state, on their availability as reactive species. This is mostly the case for very reactive
species with difficult storage. In particular, diffusion NMR has been extensively used to characterize
various form of lithium aggregate. Those compounds are known for their extreme reactivity even in
mild conditions.⁸² Studies on lithium aggregates can focus on a range of questions, such as availability
in solution,⁸³ basicity,⁸⁴ impact on selectivity⁸⁵,⁸⁶ (chiral and chemio-), and one of the most hot topic
battery and electrolyte.⁸⁷,⁸⁸ Note that some of those studies take full advantage of the fact that ⁶Li or
⁷Li are both active NMR nucleus, yet when lithium is used with organic compounds most study rather
study ¹H proton NMR as it is more convenient.

Another interesting consequence of aggregation is found in the study of biological molecules.
Indeed, it happen that quite a few health issues come from aggregation of chemicals endogen or
exogen⁷⁴ that once aggregated cannot be removed/metabolized.⁸⁹,⁹⁰ MRI and solid NMR are out of our
scope but they are often used to study such assemblies.

They are multiple examples of aggregation studies in the living, common topic includes,
understanding aggregation in amyloid fiber formation⁹¹,⁹² and allosteric protein.⁹³ An interesting
example is this review⁹⁴ by Dehner and Kessler that showcase examples of interest for DOSY and
diffusion-NMR in the study of the protein p53. They are interested in folding and aggregation in the
p53 protein using diffusion NMR. They illustrate the binding ability of different DNA-binding domains
for variants of p53 with its associated consensus-DNA (con2x25). This consensus-DNA is expected to
link with the p53 Wild-Type (WT on the figure 1.14) protein through those DNA-binding sites. As we
have seen in previous parts a strong association lead to an aggregate with a reduced diffusion
coefficient. Using simulations, they can estimate that a reduction of 33% of the coefficient hint at a
strong association while a reduction of 18% is a single-site association. The results are shown in figure
1.14 It allows to study binding ability of several mutated domain versus wild-type, as well as its possible
binding mechanism. By changing amino-acid of the protein they can identify which amino-acid does
have an impact of this bounding here hinting at importance of the pair E-R (glutamine-asparagine) in
the protein at 180/181.
<figure><img src="image_23.png" /></figure>

Figure 1.14 Reduction of the diffusion coefficients of p53 DBD, p63 DBD, and the p53 DBD dimerization mutants upon complexation with consensus DNA, as measured by pulsed-field gradient NMR spectroscopy. Hydrodynamic simulations with a cooperative p53 DBD–DNA model predict a theoretical re-duction of 33 %, while a single-site binding of DNA should result in 18 % reduction. Adapted with permission from Dehner et Kessler⁹⁴ Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
## 2. Reaction monitoring by NMR

There are many different spectroscopic methods to monitor reactions, such as Raman,⁹⁵ Infrared⁵⁵, NMR, UV-vis spectroscopy, and mass spectrometry.⁹⁶ Those methods have different pro and cons. NMR is a very powerful method for structure elucidation, often mandatory to characterize any new product (NMR characterization is actually mandatory to report new structures). If NMR is so common, it is for the great amount of information it can provide from molecular dynamics to structural studies. The fact that NMR relies on a ubiquitous probe (nuclear spins), as well as its non-destructive nature make it a great technique for many kinds of analyses. A monitoring analysis should be able to provide extensive information on a system in an innocuous and reproducible way. It should not impact the reaction and it should be usable in variety of experimental conditions. NMR seems to fit all those criteria. It may therefore seem straightforward to characterize species as they appear.

Despite all of these advantages, NMR monitoring is not as common as it could be. The reasons for this are multiple. They include limited sensitivity, and cost of operation and other more specific reasons that we will describe this chapter.

### 2.1. The sampling methods

NMR seems a very well-suited spectrometric method for monitoring, thanks to the innocuity of analysis and its large array of obtainable information. Yet a number of challenges arise when monitoring is the focus.⁹⁷,⁹⁸ One of those questions is how to observe the reaction medium without disturbing it. This question is not specific to NMR. Yet the NMR environment with a magnetic field, a need for homogeneity (of magnetic-field and medium), motion dependency, etc. creates specific challenges. It is hard to be exhaustive as each reaction can call for its own specificities. In this part we will describe the sampling methods for NMR analysis rather than the NMR analysis itself.

#### 2.1.1. Aliquoting

Aliquoting a reactive medium is a common strategy, which is not specific to NMR.⁹⁹,¹⁰⁰ It is relatively straightforward to implement. It consists of taking small samples (aliquots) of the reactive medium as the reaction progresses, and analysing them. Yet nowadays to our knowledge and by looking at the recent literature it seems this method is not very widespread, at least in NMR field. It seems to be restricted to matters that specifically needs such methodology because they might not be compatible with another.

Examples can be found in polymer chemistry, which sometimes require very specific reactors that, e.g., are very tight to prevent oxygen to enter, or are able to sustain various temperatures and
pressures that play a role in the degree of wanted polymerization.<sup>101,102</sup> In such cases, it is hard or meaningless to try the reaction elsewhere, and aliquoting make sense.

Aliquoting poses multiple problems. First getting the aliquot out of the medium can be an issue. If pressure is highly controlled or oxygen/air exposition is an issue, getting an aliquot can be hard and pose a significant risk of disturbing the reaction. Another problem can be that the reaction may continue in the aliquot. To have a perfect snapshot at the right moment of the reaction, one need a non-evolving sample of the reaction medium. The aliquot can be quenched,<sup>103</sup> and for that many different means can be used. A drop in temperature such as using liquid nitrogen or cold-water bath can be used to freeze the solution and stop the reaction.<sup>97</sup> Adding large amount of solvent,<sup>104</sup> the same solvent as the reaction or another where the reagents are less soluble than the product, is also a possibility. In NMR it is an especially good solution as it can serve as well to add deuterated solvent, whilst the reagent will be in too low concentration to react at any meaningful rate. Finally, another approach can be to use an active chemical, for example a base that will counter the acid that makes the medium react, or an oxidant/reducer, this kind of quenching is for example seen in polymer chemistry where radical traps are sometimes used.<sup>105</sup>

From the NMR point of view, aliquoting is a labour-intensive option. Every aliquot needs to be transferred into an NMR tube and the spectrometer needs to be calibrated for each tube (shimming, tuning and matching, pulse calibration...) which can be long. Assuming the reaction is not so long, it can play a huge role on the maximum number of aliquots that can be taken, as they should not be stored for too long. For this reason and the others, this method is also used to check the initial and final condition by taking only two aliquots.<sup>105</sup>

Understandably all those manipulations of the sample are unwanted. They try to be as neutral to the main interest but any modification of the sample even as simple as change of volume, can be unwanted. The perfect monitoring should be like a picture whereas aliquoting is more like taking sample of an historic site in order to rememorate it better. It can directly impact the subject and can give information of a flawed system.

### 2.1.2. In-situ

To our knowledge the most common way of monitoring by NMR is "in-situ monitoring", meaning that the reagents are put into the NMR tube and the reaction happens in the spectrometer. The NMR magnet is usually seen as a reasonable place for reactions to take place, since most spectrometers provide temperature regulation, and the in-situ analysis is non-destructive as well as non-invasive. However, NMR tubes are in fact not ideal chemical reactors. Some of the main reasons include: incompatibility with solid and precipitate, need for homogeneity (droplets or multiple phases are best avoided), problems with highly exothermic reactions, lack of agitation/stirring, small reactive volume,
etc. Foley et al.⁹⁸ did an extensive work on the difference of kinetics between *in situ* NMR and the
insightMR flowtube they helped to develop. Showing meaningful differences between the kinetic
profiles on the tube and online, they even tried a method to stir the tube, by inverting it twice at
regular intervals, and still see major differences.

Despite all this, *in situ* monitoring is fairly used, and the main reason is the simplicity to do it. It
does not require anything more than what a routine analysis would require. There are countless
examples of its use and it is the default monitoring technic with NMR. In this section, we are going to
discuss three publications and what *in situ* monitoring allowed them to do. We chose mostly exotic
examples that extend the reach of *in situ* NMR. We also have chosen them because they focus on both
the NMR apparatus and the system studied.

Sollogoub and coworker¹⁰⁶ in a relatively simple *in situ* monitoring setting, studied the
capabilities of a new metallo-pocket molecule for catalysis. They created, from cyclodextrin, a cavity
with a metal center. This approach aims at creating new catalyst for known reactions. Those new
catalysts would show better selectivity for their ligand. The cavity or pocket size and interactions within
it govern which substrate can enter and react in an enzyme-mimetic fashion.¹⁰⁷ The reaction being
relatively fast (~35 min), ¹H 1D NMR seems a good way to monitor it. They can integrate the peaks of
interest with good resolution and obtain the results shown in figure 2.1 and figure 2.2 that give the
concentrations based on a reference in the tube. In figure 2.1 they monitor the cycloisomerization with
their catalyst (β-ICyD)AuCl. They can determine an initial rate of 1.2 10⁻⁶ mol L⁻¹ s⁻¹. Figure 2.2 shows
the same information but with the conventional catalyst. The rate is higher for the conventional one,
which is expected as the cyclodextrine-based one is bulkier, yet the cyclodextrine-based one gives
same product at the same concentration with turnover rate and relative stability of the same order.¹⁰⁶
NMR allows to have a straightforward method of monitoring that does not ask for specialized NMR
knowledge or settings, an easy way to setup a monitoring that give information on a complex system.
This is an example of the classic way for *in situ* monitoring, we will now look at more exotic setups, to
show the large range of possibilities with such methods.
<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /><figcaption>Figure 2.1 : Cycloisomerization catalyzed by β-ICyDAuCl at 300K in CD 2Cl2: a) Stacking of ¹H NMR spectra at different reaction times; b) Plot of the concentration as a function of time. The concentrations were determined by integration of different signals of the enyne and of the cyclized product. The internal reference was used for calibration. The slope at c = 0 for the cyclized product (blue line) gives r₀ of ca. 1.2 10⁻⁶ mol L⁻¹ s Adapted with permission from Sollogoub and coworkers,¹⁰⁶ Copyright © 2017 Elsevier Inc.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>Figure 2.2: Cycloisomerization catalyzed by (IPr)AuCl at 300K in CD 2Cl2. Plot of the concentrations as a function of time. The slope at c = 0 for the cyclized product (blue line) gives an initial rate r₀ of ca. 41.6 10⁻⁶ mol L⁻¹ s⁻¹. Adapted with permission from Sollogoub and coworkers,¹⁰⁶Copyright © 2017 Elsevier Inc.</figcaption></figure>

Leutzsch and co-workers¹⁰⁸ have used benchtop NMR to monitor a hydrogenation reaction on 1-octane, catalyzed with a porous material, using ¹H 1D NMR and T₁/T₂ measurement.¹⁰⁸ While the analysis of solid catalysts requires solid-state NMR methods, liquid-state NMR methods can provide extensive information on their reactivity for heterogeneous catalysis. In Ref. ¹⁰⁵, a rather exotic setting is used, as the NMR tube is filled with pellets and monitored under a flow of hydrogen gas. This is made possible because the solid has no proton (Pd/TiO₂), as well as the reduced magnetic susceptibility line broadening coming from the homogenous orientation of the pellet in the 5mm tube. The way to have an acceptable line broadening is to have the same orientation of the solid catalyst, that can be seen as well-ordered in the 5 mm tube, see figure 2.3. The coupling constant in ppm are expected to differ vastly from low field to high field yet this effect is compensated by the less important broadening effect from anisotropy at low field. Thus, the two sites of interest 1 and 2 despite being relatively close can still be separated and integrated at low field in those exotic conditions. It can be seen that the spectra at high and low fields are not as different as one could expect in normal condition because of those effects.

¹H 1D spectra are used to monitor the isomerization/reduction. Interestingly, the relaxation information is used to distinguish two different environments for the same molecule. Unreactive alkanes indeed tend to have longer relaxation time than those at the surface of the catalyst, which have shorter relaxation time. This is illustrated in Figure 2.4 where one can see the two populations of differently relaxing molecules. Before the reaction two populations are observed showing that the
surface alkenes and the free alkene are not in a fast exchange system. Then only one peak can be seen hinting at a fast exchange rate between free and surface. At about 50 % of the conversion two peaks can be seen once again. The peak with T₂ = 192 ms could be the alkene that has yet to react and is adsorbed on the surface, whilst the other peak shows the reacted alkenes that lost their affinity with the catalyst surface. Overall, this information makes it possible to monitor the reaction and access the turnover rate of the catalyster. It shows an interesting example of using NMR in unusual and challenging conditions by taking advantage of what is often considered a drawback (low field).

<figure><img src="image_27.png" /></figure>

Figure 2.3 : ¹H NMR spectra of 1-octene in a heterogeneous TiO₂ support acquired at 59.7 MHz (1.4 T) (-) and 299.84 MHz (7 T) in a 5 mm (-) and 10 mm NMR tube (-). The chemical structure of 1-octene is shown on the top left and the corresponding assignments are shown above the peaks in the spectra. The right image shows the respective 5 mm and 10 mm sample used for the acquisition of the data. Adapted with permission from Leutzsch et al,¹⁰⁸ Copyright © 2018 Published by Elsevier Inc.
<figure><img src="image_28.png" /><figcaption>Figure 2.4 T₂ distributions obtained after Laplace inversion at different time points during the hydrogenation of 1-octene in 0.3 wt% Pd/TiO₂. Adapted with permission from Leutzsch et al.<sup>108</sup> Copyright © 2018 Published by Elsevier Inc.</figcaption></figure>

Reacting mixtures are often complex. Starting materials can go through multiple changes before becoming the final product. Secondary products can also be formed. NMR, being a very powerful tool for structural analysis, can be used to identify and monitor the formation of the different species of interest and sub-products. This will most of the time be critical in understanding the mechanism of the reaction. In Ref.<sup>109</sup> Kallman *et al.* proposed to study a reaction that may seem simple at first glance but that involves a complex mixture of species and equilibria (see Figure 2.5 a). For this application, they chose to use <sup>19</sup>F NMR, for two main reasons. First, <sup>19</sup>F NMR is highly sensitive and this makes it possible to acquire spectra in a short time. Second, <sup>19</sup>F has a large chemical shift range. Since multiple species that come from the same reaction condition can be closely related in their structure, <sup>1</sup>H NMR spectra can be plagued with overlapping problems.<sup>110</sup>

The authors also used the capability of NMR probes to reach high temperature levels. In order to have good monitoring condition, they raise the temperature up to 75 °C. In this work, monitoring is key to better optimize the reaction and understanding the reaction condition that will favour one product over another. The proposed mechanism is seen on figure 2.5b and shows a great extent of different species evolving throughout times. The capability of NMR to study mixtures is here the key point, all those equilibria and species present can be analysed at the same time to give a complete picture of the ongoing reaction. If the reaction were to be left unmonitored only two species could be
seen the aminopyrazol and the hydrazinylpyrazole (see figure 2.5). Here 3 more transient species can be seen, which is a great way to propose and understand the mechanism. This reaction is stated as useful but "underutilized",¹⁰⁹ the main reason being probably the difficulty to resolve such a complex mixture resulting in a lack of recent studies.¹⁰⁹ The articles show a very good example of what a classic *in situ* studies with relatively simple technic (1D NMR) can yield, deep insight into the chemical pathway and intermediate species of a complex reaction.

<figure><img src="image_29.png" /><figcaption>Figure 2.5 a) proposed mechanism for the conversion of 5-(4-fluorophenyl)isoxazole (1b) into 3-(4-fluorophenyl)-1H-pyrazol-5-amine (2b). b) Reaction profile of 1b with hydrazine. Adapted with permission from Kallman et al.¹⁰⁹ Copyright © 2016, Rights Managed by Georg Thieme Verlag KG Stuttgart • New York</figcaption></figure>

Thus far we have chosen examples that show the capability of NMR to study, in a simple setup, complex phenomenon, which is the general idea of *in situ* monitoring. Nonetheless some solutions exist for reactions that could not be monitored with such simple setups. Ideally those setups should remain compatible with classic NMR experiments, so that they can be used by non-NMR specialists. In
Ref. ¹¹¹, Dolinski *et al*. propose to study photoreaction with *in situ* monitoring, for that they need a light to shine onto the sample. It seems a bit unreliable to shine a powerful light down the NMR shim cannon, they actually tried and record lack of repeatability, probably coming from the difficulty to aim precisely at the sample and the distance with the LED. To overcome this the team made the apparatus presented in figure 2.6a. They used an optically dense medium (opaque) that turns into a clear medium upon illumination, as it contains a “photoswitch” that photoisomerizes. With this approach, they can know which slice of the tube is getting shined on, thus they have a good understanding of the amount of light received by the reactants. The idea is that the light-impacted portion of the tube will go down as the reaction progress in a linear pattern (see figure 2.6c). This also allow precise control of the reaction of interest, here the team chose a light driven polymerization.¹¹¹,¹¹² As seen above, polymerization can be a quick and sensitive reaction that is unsuitable to conventional means of monitoring. The use of a photoswitch allows to reduce the rate as well as to better control the reaction and the amount of light received. This peculiar method allows to gather the kinetic of reaction as well as its quantum yield which is a very important data for photochemistry. Adding this photoswitch to other light-catalysed reactions could allow to gather the same kind of information. The setup here makes the NMR capability shine as there is no need for NMR specialist in order to have information rich experiments while having very controlled condition. It pushes the boundaries of *in situ* monitoring by allowing to control the trigger of the reaction (light) within the spectrometer without compromise for the analysis.
<figure><img src="image_30.png" /><figcaption>Figure 2.6. a) the NMR tube setup, note that they state that in reality there is only a small gap of air between the tube and the insert. DASA photoswitching in an NMR tube B) Chemical structures for tetrahydroquinoline barbituric acid DASA in the open, colored triene form (1) and the closed, colorless cyclopentenone form (2). c) An optically dense sample of 1 in toluene (10 mM) forming a switching front upon exposure. Adapted with permission from Dolinski et al.¹¹¹ Copyright © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim</figcaption></figure>

Those examples do not show the average setup of *in situ* NMR monitoring, that is usually doing the reaction in the tube while monitoring the rise and fall of peaks in 1D NMR. It shows that it can be available in a wide range of setups, reaction conditions or NMR experiments while being relatively simple especially for chemists who specialize in synthesis. The main advantages of *in situ* monitoring is its simplicity and availability. Yet several drawbacks exist. Some are common to all the setups for NMR monitoring, such as spectral resolution and time resolution. Others are specific to *in situ* monitoring, such as the lack of stirring and the scale. Reaction monitoring and kinetic are usually very dependent of good homogeneity and of stirring/mixing. The lack of stirring/mixing in the NMR tube can be a problem especially coupled with the thin nature of the NMR tube.⁹⁸ The scale of reaction is important, it is well known that scaling up of reaction can be a real challenge but a worthy one as
industrial scale is well above benchwork scale. What happens is that often reactions are instead scaled
down in order to fit the tube volume. *In situ* monitoring is also more difficult to combine with the use
of specific reaction methods such as light illumination.

## 2.2. Flow methods

We have seen that there are different ways to monitor reactions using NMR in a static way. Yet those
methods have a few drawbacks. The lack of access to the reacting medium is one, as it does not allow
to act on the medium during the reaction, by adding reagents or solvent for example. The lack of clear
correspondence between a thin volume without stirring, as in an NMR tube, and the benchwork
condition is a problem that could lead to misconception.⁹⁸ In general the low volumes that have to be
used are a major drawback for everything related to scaling-up the reaction and thus a severe drag on
any industrialization process. Finally, we have seen several setups where the team developed their
own specific apparatus for a kind of reaction, which may be difficult to reproduce in other labs. A
common methodology that allows for adjustment during reaction or prior to it would be much
preferable.

In this work we are particularly interested by flow-monitoring NMR, it seems a good alternative
to *in situ* monitoring. It allows to have all the benchwork advantages with the NMR analysis at hand.
Different ways of using flow for monitoring exist and are easy to implement once the apparatus is
installed. The possibility to have a general setup that could work on multiple benchwork-like conditions
was our main goal. We decided to lean toward flow to be able to be under the fumehood while
analysing our medium at the same time using flow as a way to have insight into the reactive medium.

There are many different definitions for flow methods and the type of monitoring used, they
can get rapidly confusing. It seems that definitions may slightly vary from authors to authors. In this
section we will describe a range of flow methods, trying to use a consistent nomenclature.

### 2.2.1. Online monitoring

Online monitoring is the main method we have used during this work to monitor reactions. Generally, online monitoring refers to a continuous observation of the medium (here reactive medium) without interruption and as much as possible in a non-invasive way. In chemistry, it often refers to flow methods. Online monitoring can refer to virtually any analytical method, and here we will focus on its use with NMR. In NMR specifically, it can be defined as a flow of the studied medium in a loop-like system where the medium, whole or part of it, is flowed back and forth from the benchwork to the magnet.
2.2.1.1. Flowtubes, historical aspects

In this work we mostly used an apparatus known as the flowtube made and sold by Bruker in their InsightMR package. This flowtube is mostly inspired by the work of Foley *et al.*<sup>98</sup> Before going into an in-length description we will briefly review older apparatus, that could be considered the ancestor of our flowtube. To our knowledge one of the first attempt to achieve online monitoring with NMR dates from 1982.<sup>113</sup> The apparatus is already quite mature, as they use big reactor (up to 6 L) to mimic the big tank that are used in industrial plants. The sequence along with pump usage is summarized in figure 2.8. The apparatus consists of a by-pass pump that brings the liquid to the flowtube and back to the reactor. This by-pass pump is quite powerful in order to fill and empty the by-pass loop of 100 mL in 6 s and should be stopped during the NMR experiment. This time, needed for emptying and refilling the loop, defines the possible temporal resolution. Due to NMR limitations, mostly the need for a build-up magnetization and to wait for all flow effect to dissipate, they need to wait 10 s then the experiment is done with solvent suppression for both <sup>31</sup>P and proton for a duration of 95 s; then the medium is flown again back and forth for 30 s to have a good homogeneity. The true time resolution is then 135 s, and the result of the monitoring is shown in figure 2.7.

This apparatus is astonishingly modern for its time and even uses a computer to control another pump called the dosing pump, that control intake of reactant, hinting at a possible foreseen retroactive loop control. It uses <sup>31</sup>P and <sup>1</sup>H NMR to monitor an important industrial reaction,<sup>114</sup> the synthesis of retinoic acid (colloquially vitamin A) by a Wittig reaction, the reaction is figure 2.8 and the monitoring's result are shown in figure 2.9. If we refer to our first definition, the online monitoring should be as uninterrupted as possible. Here the need to stop the flow for 135 s for NMR experiment is a major drawback.
<figure><img src="image_31.png" /></figure>

Figure 2.7: A) Schematic diagram of a chemical reactor coupled to a 360 MHz Bruker NMR spectrometer. The dosing and by-pass pumps are controlled by the Aspect 2000 computer via interfaces. Reactor volumes between 0.5 and 6.0 l are available, large enough in comparison with the by-pass volume of approximately 0.1 l. A complete circulation of the reaction medium takes about 6 s. Commonly used control devices such as a thermocouple, pH electrode, gas-flow detectors and the corresponding chart recorders are installed but not shown in the diagram. B) Pulse sequence for ³¹P/¹H measurements: D1, build-up time of the spin equilibrium, 10s; AQ, acquisition time for ³¹P and ¹H, 93 s; D3, solvent saturation, and D2, circulation time, 30 s. Adapted with permission from Neudert et al.¹¹³ Copyright © 1986 John Wiley & Sons, Ltd.

<figure><img src="image_32.png" /></figure>

Figure 2.8. The last two steps of the retinoic acid synthesis. Step B, a semi-batch reaction, was investigated by ³¹P NMR. Compounds 1 and 2 and TPPO are observable simultaneously. Adapted with permission from Neudert et al.¹¹³ Copyright © 1986 John Wiley & Sons, Ltd.
<figure><img src="image_33.png" /></figure>

Figure 2.9. Areas of the ³¹P resonance signals as a function of time. The integral values are given in arbitrary units and have not been corrected with the corresponding response factors. After correction, the sum of the 31P signal areas at the beginning is equal to the sum at the end of the reaction. Phases 1 and 3 belong to the region with non-linearity between the rate of FCA addition and the reaction rate, whereas during phase 2 the reaction rate is proportional to the addition of FCA. Adapted with permission from Neudert et al.¹¹³ Copyright © 1986 John Wiley & Sons, Ltd.

The work of Bernstein *et al*. described in Ref.¹¹⁵ in 2007 also aimed at large-scale reactors. Their aim was to re-create large-scale conditions at the benchwork. This is useful in pharmaceutical companies, in order to closely monitor impurities and perform overall quality control. Large-scale reactors can be hard to sample, so doing the reaction at the benchwork scale on the same condition is a good way to analyse it in real time. To do that they create a benchwork-compatible reactor that can mimic and adjust the reaction condition, stirring, temperature, pressure, air exposition etc. The reactor is linked by PTFE capillaries to the NMR magnet. The apparatus, shown in figure 2.10, is used to monitor two kinds of reactions, one being in a classical setting but with a new green solvent,¹¹² the other being in heterogenous conditions. Scaling up is relevant for these two types of reactions.

The team chose a special flow-NMR probe usually employed for LC-NMR of supercritical fluid, the pressure and flow-speed they reach being incompatible with regular (and already specific) flow-probe. This can be considered as a drawback as those probes are not that readily available. The condition of pressure and temperature they want seems incompatible with more common NMR gears, which can be a huge drawback, not all labs have use for such specialized probes.
<figure><img src="image_34.png" /><figcaption>Figure 2.10. The flow-reactor apparatus shown (A) as a schematic and (B) a photograph. Adapted with permission from Bernstein et al<sup>115</sup> Copyright © 2007 John Wiley & Sons, Ltd.</figcaption></figure>

Moving closer to the present in 2010 Khajeh et al.<sup>116</sup> did make an apparatus for flow NMR. Their focus is on the part that goes into the probes rather than the piping. They aim at making an apparatus that is compatible with various flow conditions, either stop-flow or continuous, in a relative simplicity for non-flow specialist. They call it the flowcell and the whole diagram of it is shown in figure 2.11. It consists of various capillaries that can be dipped into the reacting medium and bring the medium to the magnet. In the magnet lies a normal NMR tube that has the flowcell headpiece seen in figure 2.12, this headpiece has inlet and outlet capillaries as well as pieces to fit the top of the tube/spinner. The apparatus seems to aim at providing an easy access flow reaction monitoring. It includes anti-leak safety, a liquid sensor linked to a safety system that can cut the flow in case of leakage. It also includes spacers and stabilizers for the capillaries to stay still while the reaction happens, number 19-20 on the Figure 2.11. All those systems show a thoughtful process that seem to simplify or avoid lot of flow-related liquid handling challenges. The apparatus is tested in various condition including heterogenous reaction, done by using a filter to stop the solid to enter the flowcell. Interestingly it is one of the first system that is aiming to handle small volumes of liquid, excluding micro-fluidic approach, as the whole apparatus need a volume in the scale of millilitres. A problem may rise nonetheless since the capillaries that come from the medium to the magnet seems a bit bare. They might not be protected enough, especially in terms of temperature. Capillaries this size are known to change temperature very fast because of their small radius and the small volume per section.<sup>117</sup> Nonetheless the apparatus seems sturdy and well-thought enough to be aimed at non-NMR or non-flow chemists.
<figure><img src="image_35.png" /><figcaption>Figure 2.11: Structure of the flow system used. (1) flowcell headpiece; (2) inlet and outlet pipe bushes; (3) and (5) O-rings; (4) NMR tube retaining bush; (6) NMR tube; (7) optical liquid sensor; (8) inlet pipe; (9) outlet pipe; (10) reaction vessel; (11) reaction vessel outlet pipe; (12) and (15) unions; (13) PTFE peristaltic tubing; (14) peristaltic pump; (16) glass tube, glued to turbine (17); (18) long grooved PTFE spacers; (19) short grooved PTFE spacers; (20) cross-section of spacers; (21) safety cutoff. Adapted with permission from Khajeh et al.<sup>116</sup> Copyright © 2010 John Wiley & Sons, Ltd.</figcaption></figure>

<figure><img src="image_36.png" /><figcaption>Figure 2.12: Scale drawing (left) and photographs (right) of the flowcell headpiece assembly. (1) headpiece; (2) inlet and outlet pipe bushes; (3) and (5) O-rings; (4) NMR tube retaining bush. The left part of the composite photograph shows the inlet and outlet pipes and their respective bushes and O-rings, together with the liquid sensor cable, the latter and the inlet pipe running continuously through the headpiece. The top right shows the top view, and the bottom right the bottom view, of the headpiece. Adapted with permission from Khajeh et al.<sup>116</sup> Copyright © 2010 John Wiley & Sons, Ltd.</figcaption></figure>
2.2.1.2. Rapid-injection and stop-flow

Stop-flow, in contrast to continuous flow, refers to methods where the flowing is not perfectly continuous throughout the line. Here we will refer to stop-flow only when done in a non-loop or in-line fashion and if it includes systems that are meant to stop actively the flow. This definition aims at differentiating stop-flow from turning off the pump briefly.

The rapid-injection strategy is a strategy where the medium injected from a suitable place and put in the NMR tube in a rapid fashion. It often has flow-related challenges like having to wait for homogenization of the solution. Those two methods, stop-flow and rapid injection, are often used to see or monitor species that are either short-lived. Note that so called stopped flow NMR methods are as old as 2D NMR.<sup>118</sup>

To illustrate the rapid injection NMR method we will use an example from one of its pioneers.¹¹⁹
The goal is to see a particularly unstable intermediate known as a primary ozonide and see if the
secondary ozonide is present, according to the scheme shown in figure 2.13. The apparatus is quite
complex and consists of a syringe's-controlled piston that pours the liquid from pores that limit the
motion of liquid and its inertia. The apparatus rests on the top of the shim-cannon, with the NMR tube
already in the magnet. The part of the reaction that is supposed to be refrigerated lies already in the
tube, here the ozone solution. The other reagent (tetramethylethylene) is injected quickly in a
controlled way. As the solution is poured, an automatic switch starts the NMR experiment. The result
is a reaction at -85°C within the spectrometer. Figure 2.14 shows a time series of spectra obtained
during the monitoring experiments. The authors estimate that they need a minimum of 92 ms to make
one spectrum and waiting time of 40 ms for the homogeneity within the solution. They estimate that
they can obtain 16 spectra per injection and need 3 injections for their study. The volume and reagents
being well controlled, several injections were done and their data regrouped to follow the kinetics of
this reaction. The modest spectral resolution comes from the very short time of acquisition, 72 ms (2K
point per spectra) and the homogeneity trouble due to fluid motion.
<figure><img src="image_37.png" /><figcaption>Figure 2.13 : the oxonolyse reaction. Adapted with permission from McGarrity et Prodolliet¹¹⁹ Copyright © 1984 American Chemical Society</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>Figure 2.14 Spectra showing the decomposition of 2 at -85°C in CD₂Cl₂. Adapted with permission from McGarthy et Prodolliet¹¹⁹ Copyright © 1984 American Chemical Society</figcaption></figure>

The study has several features that could be considered unusual in kinetics, such as using multiple identical reactions to make one plot. The apparatus is heavy, and sits on top of the magnet, which may seem inconvenient, but this allows to have a pre-magnetized sample without waiting time. They are looking for new intermediate and species, using NMR as a qualitative rather than quantitative tool. From Figure 2.14 you can see the peak of the species labelled C, this peak rises quickly in the first seconds of the reaction and then becomes very faint. This indicates the formation of the first ozonide, however the rearrangement that can lead to secondary ozonide is not seen. This can be used as strong hint that it is not formed within those conditions, probably due to the lack of stabilizing effect from
the methyl substituent. Seeing the peak of such unstable intermediate that can only be spotted in such
harsh conditions was an impressive feat and indeed to our knowledge one of the first-time short-lived
intermediates were seen by high-field NMR.

The next example also uses stop-flow but it is a much more modern setup.<sup>120,121</sup> The general
diagram of typical modern stop-flow device is showed in figure 2.15, where one can see that the
reagents are stored in different syringes that allow a precise yet quick delivery. The flow is stopped
quickly by the stopping syringe mitigating the motion of the fluid while the analysis is proceeding. The
aim here is to illustrate the capability of a stop-flow cell to see the very beginning of a reaction while
providing good temperature and mixing conditions. Dunn et Landis<sup>120,121</sup> use this device to study a
polymerization reaction, that is sensitive to air and moisture, which also shows that the probe is air
and moisture-free. The initial conditions of the reaction are important and can change the kinetic
model. Using different techniques including stopped-flow, quenching the reaction at different point
and retrieving the samples for other analyses (gel permeation chromatography mostly), they discuss a
new model.

In figure 2.16 we see the epimerization of rac-lactide to meso-lactide in the first second of the
reaction that play an important role on the mechanism. Indeed, they state that this epimerisation is in
a kinetic competition with the polymer formation. This effect is only seen in the beginning of the
reaction and will have a decisive importance on the rest of the mechanism and on the monomer
availability during the reaction. This ability to see such rapid epimerization at the very beginning of the
reaction, underlines the importance of stop-flow NMR.
<figure><img src="image_39.png" /><figcaption>Figure 2.15 taken from Generalized diagram of typical stopped-flow NMR instrumentation. Adapted with permission from Dunn et Landis¹²⁰ Copyright © 2016 John Wiley & Sons, Ltd.</figcaption></figure>

<figure><img src="image_40.png" /><figcaption>Figure 2.16 Direct, in situ [the author states in the text that it is “monitored using SF NMR spectroscopy” SF NMR being Stopped-Flow NMR] observation of meso-lactide growth and disappearance during time course of reaction in toluene at room temperature. The bottom spectrum is at reaction time 1 s, with each subsequent spectrum 9 s later. Concentrations plotted with reaction time clearly show growth of meso-lactide and its subsequent disappearance. Initial concentrations: 30 mM l-lactide; 6 mM IMes. All concentrations are calculated from integration of an unreactive internal standard, bis(trimethylsilyl)benzene (BTMSB). No meso-lactide is observable by NMR prior to addition of catalyst. Adapted with permission from Dunn et landis¹²¹ Copyright © 2017 American Chemical Society</figcaption></figure>

Finally, let us consider an example of stop-flow NMR that is a bit more exotic from the point of view of reaction monitoring. In the work of Keifer *et al.*¹²² the goal is not to monitor a reaction as it
unravels, but rather to analyse quickly the outcome of a large number of reactions, using combinatorial organic synthesis of a chemical library. Different cyclic anhydrides were made to react with various primary amines in a combinatorial fashion. The result is placed in wells (one compound per well) with solvent. The content of each well is flowed in an automated way into the NMR magnet using a LC-NMR probe, analysed and handled back to its well. Figure 2.17 shows the apparatus, with the reaction and handling of the wells happening in the Gilson 215 liquid handler, and the flow regulated by N₂ gas (50-100 psi ≈ 3.4-6.9 bar). The flow stops during the acquisition and allows a very efficient handling of the samples. The mains advantages versus the classic NMR automation, with a robot that handle the NMR glass tubes, are less costly container, lesser volumes are needed and overall a better reliability as glass-tube NMR automatic-sampler are known to break tubes once in a while.¹²³

<figure><img src="image_41.png" /><figcaption>Figure 2.17: A block diagram of the VAST (versatile automated sample transport) DI-NMR (direct-injection NMR) system. II.1.3.2.1 Continuous-flow in-line monitoring, adapted with permission from Keifer et al.¹²² Copyright © 2000 American Chemical Society.</figcaption></figure>

#### 2.2.1.3. Continuous flow in-line monitoring

In-line flow monitoring, like online monitoring, consists of monitoring a medium on flow, it differs from online monitoring in that the medium is not analysed in a loop-fashion. The sample once analysed might be discarded or retrieved for other purposes.

Continuous in-line monitoring is notably used to monitor the outcome of reactions that happen on flow. It is less common at high field but it has become a conventional NMR method at low field. Flow chemistry is a rapidly expanding area, and is particularly beneficial for reactions such as heterogenous catalysis where the supported catalyst is fixed in some part of the line, and reaction
triggered by a physical mean whether heat or light-wave and a combination of both. This is by no mean
an exhaustive list but it corresponds to our knowledge to the most common cases.

Heterogenous catalysis in flow chemistry is an important topic, for applications that include
chiral synthesis and hydrogenation. In this approach, a solid catalyst is put in the line, often supported
on a resin/plastic or charcoal.<sup>124-126</sup> Tijssen et al.<sup>124</sup> have developed an in-line apparatus for NMR
monitoring of hydrogenation reactions. The hydrogenation of alkynes can be a problem especially if
there are multiple oxidation/reduction states (like alkyne to alkene to alkane) or sites that can be
reduced. The hydrogen pressure, catalyst and other parameters should be adjusted to get the desired
result. In this case in-line monitoring seems like an especially well fitted method. The principle,
summarized in Fig. 2.18, is conceptually simple: a mix of liquid, the reaction medium, and gas, the di-
hydrogen, is pumped through a solid catalyst cartridge then into an NMR probe, in the same line. The
apparatus allows to monitor the quantity of dissolved hydrogen which is the important parameter
regarding the hydrogenation. The authors tested it with 3 compounds having different possible states
and confirm the importance and possibility to monitor the amount of hydrogen in the solvent in flow
by NMR. This process allows the whole line to be under 5 bar of pressure on a flow speed of 80 µL/min
in a specialized microfluidic NMR probe.<sup>127</sup> We are not going to review here the benefit of microfluidic
but it is especially useful in in-line process because it allows very precise handling of small volumes at
very well monitored pressure.

<figure><img src="image_42.png" /><figcaption>Figure 2.18 Schematic drawing of the stripline NMR reaction monitoring setup for heterogeneously catalyzed hydrogenation reactions. From Tijssen et al.<sup>124</sup> Anal. Chem. Licensed under CC-BY-NC-ND 4.0</figcaption></figure>

Another use of continuous flow in-line monitoring is when the reaction is triggered or trigger a
physical stimulus like heat or light. Reaction that are exothermic usually have complex kinetic as the
heat created by the reaction accelerate it. To better control this having a small volume of reaction at
once, as is the case in the capillaries used in flow chemistry, can allow for a better monitoring and
control of the temperature. Schotten et al.<sup>128</sup> have shown such application, using the insightMR flow
tube in an in-line fashion. The exothermic reduction of TMSCF₃ to TMSCF₂H was conducted in a capillary good for heat control and monitored using high ¹⁹F field NMR.

The in-line monitoring is also quite popularized by new generation of medium-field benchtop spectrometers.¹²⁹ The relative portability of the spectrometer makes it highly useable under benchwork in a setup that does not require to be a flow expert or an NMR one which is highly valuable for synthesis chemist. Several benchtop spectrometers include flowing apparatus such as a flow-cell in their standard configuration. The main drawback of benchtop spectrometers is limited sensitivity and resolution, but this can be counter-balanced by the ease of analysis and the fact that reactive medium is often well concentrated.

#### 2.2.1.4. The Bruker InsighMR flowtube

We have described the ancestor of our apparatus and we tried to highlight their advantages and disadvantages. The commercial Bruker InsightMR flowtube is a variation of the device described by Foley et al.⁸⁴ It aims to be as efficient and capable as earlier devices while being more accessible to chemists that are not flow specialists. It includes several features such as a special NMR-tube able to sustain up to 8 bar of pressure, other feature includes a thermoregulation that allow to thermostat the reaction within the capillaries, it is also very well fitted for the Bruker spectrometer, diverging little to a standard NMR analysis. One of the drawbacks is the lack of system to monitor pressure or leaks as the device is covered in a jacket any leak could be hard to detect before it became catastrophic (liquid in the probe).

We have already seen a few of its use in literature such as Dunn et Landis¹⁰⁸ and Foley et al⁸⁴,¹¹⁸ that developed the apparatus, Said et al.¹¹⁷ also reviewed the engineering aspect of this flowtube, underlining the poor quality of the by default pump. Recently Hall et al.¹³⁰ used the flowtube to get chemical insight into the mechanism of a Noyori–Ikariya-like asymmetric hydrogenation. Their study focuses on the analysis of ruthenium catalyst that allow a transfer of hydrogen. They are able to see hydride species which are usually transient very reactive species through the use of the flowtube with 1D ¹H NMR. The same team previously worked on practical aspect of this device¹³¹ for reaction monitoring, illustrating its usefulness and making it available for a broader audience. Recently the flowtube has been used in various study including important topic like C-H activation¹³² or sulfonyl compounds.¹³³

Another study using the flowtube is that of Hall et al.¹³⁴ in the conventional setting of this apparatus the flowtube is used as a way to observe continuously an ongoing reaction using flow. The study underlines one of the main advantages of this setup which is availability of the medium. If we look back at part 1 and the study of Dolinski et al.¹¹¹ they have photochemistry too and because the medium is not easily available they use a smart way to have illumination but also to control the reaction
with a photoswitch, while information rich it is not realistic benchwork condition. Here the goal is to
have realistic condition NMR analysis with the medium available. The reaction is shown in scheme 2.1,
compound 1 can give three products with the help of a catalyser that is light activated, Eosin Y.

<figure><img src="image_43.png" /><figcaption>Scheme 2.1 Structure of Eosin Y and photocatalytic oxidation of allylic amines. From Hall et al.¹³⁴ Chem. Comm. Licensed under CC-BY-NC 3.0</figcaption></figure>

They are interested in the reaction pathway that leads to the formation of the products. Eosin
being known to form oxygen singlet under light they also question the importance of air and oxygen
in this reaction. They test their hypothesis by using online monitoring and thus can monitor the impact
of the condition on the reactivity live. To do so they try to activate light at some time in the reaction
and observe that product seems to form, and reactant to disappear only at the interval where light is
shined upon them. It indicates the importance of light for the making of any of the three products as
seen in Figure 2.19, also that the active species that allow the reaction to happen is transient, short-
live and only exist under the light.

Another interesting thing that highlights the advantages of having the medium accessible is to
test the air condition. As they try casting light on the sample on anaerobic and aerobic condition and
can monitor the result with no interruption, as seen in figure 2.20. This would have been complicated
otherwise as aliquoting a medium in pure anaerobic condition may prove to be a hard task. They
conclude that **2** and **3** are created in anaerobic condition but not **4** which make sense as **2** and **3** are
hydrolysis resistant. Those manipulation of the reaction medium allow to propose a reaction network
for this example that start by the formation of **2** that can react with the reactant to form **3** or get
oxidized to form **4**.
<figure><img src="image_44.png" /></figure>

Figure 2.19 ¹H FlowNMR reaction profiles of N-allylbenzylamine (1) in MeCN (6.4 mM) at 20°C in the presence of Eosin Y catalyst (1 mol%) under chopped green LED illumination (633 mW) to form **2**, **3** and **4** (100 mL, 4 mL/min flowrate, WET solvent suppression, 1.46 s acquisition time, 3 s relaxation delay, 12 scans). From Hall et al.¹³⁴ Chem. Comm. Licensed under CC-BY-NC 3.0

<figure><img src="image_45.png" /></figure>

Figure 2.20, ¹H FlowNMR reaction profiles of N-allylbenzylamine (1) in MeCN (6.4 mM) at 20°C in the presence of Eosin Y catalyst (1 mol%) under chopped green LED illumination (633 mW) and different atmospheres (argon to dry air) to form **2**, **3** and **4** (50 mL, 4 mL/min flowrate, WET solvent suppression, 1.46 s acquisition time, 3 s relaxation delay, 16 scans). From Hall et al.¹³⁴ Chem. Comm. Licensed under CC-BY-NC 3.0
## 3. Fast DOSY NMR sequence

Reaction monitoring by NMR classically relies mainly on ¹H 1D experiments. The reasons for that are simplicity of acquisition and processing, speed, and straightforward access to concentrations and structural information. Yet 1D methods are limited and have known problems such as overlapping, especially with ¹H and usually does not allow efficient assignment of peaks especially in the case of mixture or complex molecule. To go beyond those limitations 2D NMR methods are used to gather more information. Yet they remain underused outside of their routine usage for the characterization of purified products, the main reason being their duration. Experiment duration is a key aspect for reaction monitoring, as it sets a limit on the range of kinetics that can be studied. A series of means to accelerate 2D NMR experiments have been described, with reaction monitoring as one of the motivations for their development. We will here propose a brief overview of those methods, focusing on DOSY NMR experiments.

### 3.1. Why do classic DOSY experiments take time?

Consider the simplest possible 1D NMR experiment: the pulse-acquire experiment. The parameters that define its duration are the number of scans, the acquisition time (which governs the resolution) and, if multiple scans are collected, the inter-scan delay needed for the recovery of longitudinal magnetization. The simplest 1D experiment, if sensitivity is sufficient, requires just 1 scan, with an acquisition time that can range from a few tens of milliseconds to a few seconds. Any conventional 2D NMR requires more time, because increments are needed to construct the so-called indirect dimension. Those increments are acquired consecutively, and separated by inter-scan delays. Another issue is that 2D experiments select complex coherence transfer pathway. Several methods can be used for this, and if phase cycling is used then multiple scans need to be acquired for each increment.

In classic DOSY experiments, several increments are collected in order to have enough points for the diffusion fitting, and phase cycling is used to select the desired coherence transfer pathways. In the STE experiment described in part 1, a minimum of 8 scans per increment is needed. As for the number of increments, it is highly dependent on the required accuracy and on the spread of diffusion coefficients within the sample. To our knowledge the number of increments usually varies from 8 to 32 for standard diffusion-NMR sequence such as the stimulated-echo (STE) sequence. Accurate fitting of the data also requires that diffusion only attenuates the signals. If inter-scan delays are too small, different consecutive scans can yield a decrease in intensity due to T₁ relaxation not being complete. This will lead to inaccurate diffusion coefficients. Different methods exist such as using dummy scans to reach an equilibrium with a smaller inter-scan delay but they are also time-consuming. Considering all of these criteria together, and assuming that the sample is sufficiently concentrated so that signal
averaging is unnecessary, a typical experiment will have 8 x 16 scans separated by an inter-scan delay of about 5 s, resulting in an experiment time of around 10 min. Realistically speaking DOSY experiment average around 15-20 min extra delay coming from acquisition, dummy scan and experiment time. When the DSTE pulse sequence is used, to compensate for convection effects, the minimum duration of the experiment is doubled, as 16 scans per increment are needed.

### 3.1.1. QNMR and flow effect

One of the most important ideas of quantitative NMR is to get a proportionality coefficient between the peaks and the spins they come from. The goal is to measure the relative quantity of molecules in a sample. It is an important concept to do kinetics by NMR as the goal is to see changes in those quantity indicatives of the species relative concentration. This can be written $I_x \propto N_x$ so $I_x = K_x \times N_x$. Where $K_x$ are parameters related to the spectrometer, $I_x$ is the signal intensity (measured preferably in peak area), and $N_x$ the number of nuclei.

For the relation of quantitativity to work a few conditions are necessary. The main condition that one will encounter usually is $T_1$ related. The relation between recycle time being $\approx 5 \times T_1$ for the magnetization to be back to equilibrium is important especially if scans are done in sequence. Note that other problems may arise involving NoE effect, shaped pulse, decoupling etc. We are not in a setting where those will matter and the level of accuracy needed for relative concentration usually does not need to account for them.

The recycle time can be increased to meet the $T_1$ relation thus lengthening the experiment. Other way such as dummy scans can be used. The problem is that each site has its own $T_1$ value and sites with extreme $T_1$ may break the condition of quantitativity under rapid sequence of scans. This could explain why a lot of kinetics studies from the literature mostly focus on one site to access the concentration of a molecule. As a site well identified both in NMR terms ($T_1$, SNR...) and checked for being indicative of one compound only, is enough to access the molecule concentration.

Other parameters are important for the quantitativity of NMR such as a sufficient acquisition length and number of points. Good practice of gain, tunning and matching. Overall, a signal of good quality with sufficient SNR... Those parameters albeit important are usually relevant in our NMR condition anyway and the level of quantitativity wanted will not demand to look deep in those parameters.

These phenomena are relatively straightforward in normal condition and are usually responsible for the lengthy duration of most NMR experiment. Indeed, the waiting time need to be applied both between experiment but also between scans/increments in the case of a 2D NMR experiment. Hence, in the DOSY experiment the delay should be put between each scan. In general, for any 2D experiment or suite of experiment the spectrometer spend most of its time idle because of this waiting time.
The sample flow also has consequences for the recovery of the magnetisation. In a static NMR experiment, the sample is all the time at high magnetic field, and magnetisation relaxes towards its equilibrium value at high field, with a time constant T₁. In flow NMR, especially with shielded magnet, the time that the sample spends in a high-field region before excitation is more limited, and depends on the flow rate. Figure 3.1 show a schematic of an on-flow shielded spectrometer setup. Three area are there; area A before the magnetic field (B = 0); area B magnetic field is not the strongest (0 < B < B₀); area C magnetic field is B₀. The effective recovery delay, τB, becomes shorter when the flow rate increases. The condition that should be verified to acquire NMR spectra in quantitative conditions applies to τB rather than the recovery delay. For this reason, spectra that are acquired on flow are rarely acquired from fully relaxed magnetisation.

<figure><img src="image_46.png" /><figcaption>Figure 3.1 Schematic illustration of magnetization build-up effects in flow, resulting in non-quantitative results for nuclei with long T1 relaxation times or for high flow rates, where τB < 5 × T1. B = magnetic field strength, τB = residence time of sample in magnet prior to entering detector. Note: For the purpose of clarity, the sample is shown as exiting through the base of the instrument in this diagram, whereas in reality the sample returns by a path parallel to that it entered the instrument by (see Fig. 1). Stray field effects are ignored in this example. Hintermair and coworkers¹³⁵ propose a simple way to do so by using to formula one can straightaway correct the peak intensity as such. Reproduced from Ref. 135 with permission from the Royal Society of Chemistry.</figcaption></figure>

The correction can be expressed as:

$$I_{corr} = CF \times I \qquad 3-1$$

$$CF = \frac{I_{static}}{I_{flow}} \qquad 3-1'$$

With I the peak intensity/integral (depending on the case) and CF the correction factor. If needed one can also measure the apparent T1 on flow as such

$$\frac{1}{T_{1,flow}^*} = \frac{1}{T_{1,static}^*} + \frac{1}{Tb} \qquad 3-2$$

Tb should be calculated as the residence time within the spectrometer (area B and C).
Note that on our case we take advantage of the unshielded nature of our magnet. Although it
can be responsible for other trouble the unshielded magnet has a much larger area B that allow to
have a build-up of magnetization akin to the one in static condition due to the elongated Tb.

To apply the correction a few things can be done. The author recommends to do analysis to measure static peaks integrals at the end of the reaction, the beginning and whenever intermediaries of interest form. This would allow to have a CF for every species and correct flow effect. Note that if those flow effect arise, it could be somehow beneficial. As the nuclei do not stay long enough to be fully magnetized, they also would leave too fast to suffer T₁ saturation. Applied correctly this correction would allow to increase the speed of experiment by reducing recycle time needed.

## 3.2. Methods to accelerate Diffusion experiment

Now that we have seen the factors that determine the duration of diffusion experiments, we are in a position to understand methods to reduce them and speed-up the process. We will describe the most commonly found and those that were considered (some only in theory) for this work.

3.2.1. Oneshot methods

The Oneshot (or one-shot) DOSY method was introduced by Pelta et al. in 2002.<sup>136</sup> It refers to a diffusion NMR sequence for which only 1 scan per increment is needed. This reduces the duration of an experiment from 10-20 min to ~1 min. The possibility to use just one scan per increment is achieved by getting rid of the phase cycling and using pulsed-field gradients instead for coherence transfer pathway selection. However, since PFGs are also used for diffusion encoding, CTP selection and diffusion attenuation can be inter-dependent and this needs to be accounted for.

In the work of Pelta et al. unbalanced gradient pairs are used to achieve simultaneously CTP selection and diffusion encoding. The sequence they used is shown in figure 3.2. It is based on a regular STE pulse sequence, in which the bipolar gradients that flank the 180° pulse are unbalanced by a factor called α. The bipolar gradients being unmatched, they will suppress any coherence that arise from the imperfect 180° pulse. Starting from this base, they later described several modifications of the pulse sequence. For example, in order to mitigate the effects of J-modulation they added a 45° pulse thus the name Oneshot45<sup>137</sup>. They also combined the Oneshot45 with the DISPEL (Destruction of Interfering Satellites by Perfect Echo Low-pass filtration) methods to suppress <sup>13</sup>C satellites without broadband decoupling<sup>136</sup>. Those methods show the good versatility and ease-of-use for this Oneshot method. It is interesting to mention that despite proof that it works better than conventional method in the same number of scans, to our knowledge few examples are reported using 1 scan per increment.
<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /><figcaption>Figure 3.2. Radiofrequency (RF) and gradient (G) pulse sequences for DOSY. (a) Bipolar pulse pair stimulated echo (BPPSTE) sequence; (b) the proposed one-shot sequence using (solid line) the stimulated antiecho and (dotted line) the stimulated echo. The diffusion delay is the time between the mid points of the two diffusion-encoding periods and that between the midpoints of the antiphase field gradient pulses within a given diffusion-encoding period. The outward/inward facing arrows indicate gradient pulses which are incremented/decremented as the diffusion weighting is changed. The gradient prepulses in (b) are most conveniently given a duration of 2μs. Adapted with permission from Pelta et al.<sup>136</sup> Copyright © 2002 John Wiley & Sons, Ltd.</figcaption></figure>

The use of PFGs for CTP selection in diffusion experiments becomes easier when more than 1 gradient axis is available. This was for example described by Sarkar et al,¹³⁸ who underlined the possibility to use other axes to have a better coherence selection/filter as well as different others possibility such as easy implementation of solvent suppression. It does not mention the possibility to use it in a oneshot fashion but it checks all the boxes for such use.

### 3.2.2. Spatial parallelization

Several methods have been reported for the single-scan acquisition of complete diffusion NMR data sets. They rely on spatial parallelization to replace the sequential acquisition of gradient increments. The spatial parallelization for DOSY follows two different close pathways. The first path starts in the UK with the work of Loening et al.¹³⁹ They described a STE experiment with a twist: the $z^2$ field from the shimming console is used in addition of the conventional z gradient. They relied on the fact that a field with a non-linear variation (such as $z^2$) causes the diffusion-dependent signal loss to vary along the different parts of the sample. Once the gradients are well mapped, for fitting purposes, the experiment can carry on. The principle is to do a simple STE with a $z^2$ gradient continuously active during the pulses and to read the data using a weak-readout gradient. The result although fast were not so good compared to the conventional version. The figure 3.3 show the 2D DOSY yielded by such
methods, also the use of a gradient during acquisition cause broadening of the peak. The method
demands to use a lot of tools to fit the data or to map the gradients which makes it hard to implement
yet it is very innovative and crafty. This can be defined as a first attend at 1 scan diffusion-NMR that
will lead to further study and improvement.

<figure><img src="image_49.png" /></figure>

Figure 3.3, DOSY spectra constructed using data from (a) a conventional (stimulated-echo) two-dimensional DOSY experiment and (b) a one-dimensional DOSY experiment. The diffusion coefficients given in Table 1 are shown as dotted lines across (b); these values were used to construct (a). For the conventional DOSY spectrum, the intensities of the peaks correspond to the first increment of the DOSY experiment. For the one-dimensional DOSY spectrum, the intensities correspond to the one-dimensional spectrum shown in Fig. 7a. In the diffusion dimension, both spectra consist of Gaussians centered at the diffusion coefficient estimated by the fitting procedure and with widths corresponding to the standard deviations of the fits. For both spectra, the contour lines correspond to 1, 2, 5, 10, 20, and 50% of the maximum intensity of the spectrum. Adapted with permission from¹³⁹. Copyright © 2001 Academic Press. All rights reserved.

Taking advantage of the rising use of swept pulse in NMR studies, the same team latter
developed a new sequence aiming at the same one-scan goal. This was described by Thrippleton et
al.¹⁴⁰, using the sequence shown in figure 3.4. The encoding step consists of the simultaneous
application of a 180° CHIRP pulse and a magnetic-field gradient. The 180° CHIRP pulse purpose is to
make the spin evolve under a gradient pulse for which the effective length varies linearly across the
sample.¹⁴¹ This replaces the needs for multiple gradient-increments or the need for non-linear
gradients as the spins within the sample will experiment different effective gradients depending on
their position. The diffusion-attenuated signal resulting from such pulses vary across the sample, the
only thing left needed is a way to read it.
<figure><img src="image_50.png" /></figure>

Figure 3.4: (a) The stimulated echo (STE) pulse sequence, commonly used for measuring diffusion coefficients. (b) The basic 1D DOSY pulse sequence, which permits the measurement of diffusion coefficients in a single scan. The required coherence transfer pathway is shown below each pulse sequence. The filled rectangles on the line marked RF represent 90° pulses and the hollow boxes with diagonal lines represent 180° CHIRP pulses. z-Gradients are displayed on the line marked G. Adapted with permission from Thrippleton et al¹²⁹ Copyright © 2003 John Wiley & Sons, Ltd.

In the work of Thrippleton et al., they kept the same acquisition method with a weak gradient-readout. The spectra yielded by such sequence is shown in figure 3.5. The principle is to record a 1D spectra with larger peaks; the line shape of which give a diffusion attenuation curve as seen in Figure 3.5c). This curve can be fitted to retrieve the diffusion coefficient like a normal DOSY but in 1 scan and no increments.
<figure><img src="image_51.png" /><figcaption>Figure 3.5 taken from¹²⁹. (a) Conventional 1D proton spectrum of a sample containing camphene, a zinc(II) porphyrin and chloroform in CDCl₃. (b) 1D DOSY spectrum of the same sample; the diffusion coefficient for each resonance is encoded in its lineshape. (c) Expansions of the 1D DOSY spectrum, showing a zinc(II) porphyrin (1), camphene (6) and chloroform (4) peak. Visual inspection of the peaks gives a qualitative indication of the relative diffusion rates of the three molecules and a quantitative analysis of the lineshapes yields estimates of the diffusion coefficients. Adapted with permission from Thrippleton et al.¹⁴⁰ Copyright © 2003 John Wiley & Sons, Ltd.</figcaption></figure>

The application of a weak gradient will broaden the peaks while making their diffusion-shape
linewidth appear. This broadening depends on the gradient strength, a good balance must be reached
between intensity, diffusion-lineshape and overlapping/resolution. Hence, using this method the
peaks become a diffusion-weighted image of the sample. One must be careful with the gradient
strength as it dictates the broadening of the linewidth. If it is too small, the curve cannot be resolved,
if it is too large, the chemical-shift information and overall resolution of the spectra are lost.

The paper shows impressive result, with the possibility to acquire in 1 s > with result quality akin
of a conventional STE experiment. A major drawback is the broadening of peaks as it does reduce the
resolution, more caution should be taken for no overlapping as the diffusion attenuation curve would
be unreadable. It is also interesting to note that linewidth analysis of a peak to fit for diffusion
coefficient is not a straightforward operation, it calls for specialized software and knowledge in order
to retrieve accurate values.

Another path for one-scan DOSY comes from Israel with the methodology reported by Frydman et al,¹⁴² the so-called ultrafast (UF) NMR spectroscopy. In 2008 Frydman and coworkers¹⁴³ developed a one scan DOSY using this ultrafast methodology. Their UF DOSY sequence is illustrated in figure 3.6. The sequence is similar that one on the figure 3.4. The only difference is the acquisition scheme known as EPSI (echo planar spectroscopic imaging). The EPSI is a special scheme for acquisition first developed for MRI to have chemical insight in the MRI image by mapping the chemical shift,¹⁴⁴ and mostly used
to create voxel where the third dimension is of chemical shift.¹⁴⁵ In UF DOSY, EPSI is used to map the magnetization as a function of Z for each peak of the spectrum. The main advantage of EPSI over the weak gradient readout is that it increases the spatial resolution and thus the possible quality of the fit, yet it limits the time of the acquisition thus the possible spectral resolution attainable.

<figure><img src="image_52.png" /><figcaption>Figure 3.6 Results obtained for a TPP, Benzaldehyde and Diphenylether solution (≈50 mM each) in CDCl₃ at 25°C. (A) Pulse sequence and parameters employed in the ultrafast 2D DOSY implementation; notice that unlike the sequence in Fig. 3 (see original paper) this relies on an anti-echo coherence transfer pathway, associated now with equally-sensed p-frequency sweeps. (B) High-resolution spectrum afforded by this sequence along the ¹H shift dimension. Adapted from Frydman and coworker¹⁴² with permission, Copyright © 2008 Elsevier Inc. All rights reserved.</figcaption></figure>

In diffusion NMR experiments that involve spatial parallelization, the data is analysed with a modified Stejskal Tanner equation:

$$S(z) = S_0 \exp(-D(K(z))^2 \Delta') \qquad 3-1$$

Where $\Delta'$ is the corrected diffusion delay $z$ is the position $S$ the signal intensity and $K(z) = \frac{\partial\varphi}{\partial z}$ the spatial derivative of the spin's phase. The processing and analysis of UF DOSY data (also called SPEN DOSY) is summarized in figure 3.7 We can see that the data recorded are a train of sinc-shaped echoes rather than an FID this comes from the peculiar acquisition scheme. To process those data, they are reshaped to fit in the k-space, a concept often found in MRI. The idea is to have a space that depends on the time-dimension of the acquisition and one that depend on the gradient. The k dimension being a function of gradients area and gyromagnetic ratio¹⁴¹ such as, $k = \int_0^t \gamma G(t') dt'$. The FT of such a space yields an image, where each peak is spread in a spectral dimension and diminish along the z (real-space) axis.
<figure><img src="image_53.png" /><figcaption>Figure 3.7: Principle of the SPEN DOSY processing. Adapted with permission from Lhoste et al.¹⁴⁶ under a license Creative Commons CC-BY-NC-ND, Published by Elsevier B.V.</figcaption></figure>

This UF method for DOSY was used in a few different cases. The main disadvantage of having a one-scan experiment is often the sensitivity. It is thus a logical pathway for it to be used with hyperpolarization method especially if the hyperpolarization allows only one scan to be done. Two examples with different hyperpolarization methods exist.¹⁴⁷,¹⁴⁸ It is also used to accelerate otherwise lengthy 3D experiment,¹⁴⁹ for monitoring of reaction,¹⁵⁰ and to accelerate restricted diffusion experiment.¹⁵¹
### 3.2.3. Sliding window and TR-DOSY

Non-uniform sampling (NUS) is a strategy that focuses on the reconstruction of a multidimensional NMR spectra from a reduced number of acquired increments. Instead of acquiring increments on a regular grid, only a subset is acquired, and non-Fourier reconstruction algorithms are used.¹⁵²⁻¹⁵⁵ The validity of the approach relies on the fact that multidimensional NMR spectra are typically sparse. NUS can significantly shorten the time needed to obtain a full spectrum but may ask for careful optimization in the amount of sampling as a compromise between quality and rapidity.

2D DOSY experiments are not really compatible with such NUS strategies because they do not rely on the Fourier transform to process the indirect dimensions. NUS has been used to accelerate 3D DOSY experiments,¹⁵⁶,¹⁵⁷ but we will not describe them in detail. We will focus here instead on 2D DOSY accelerated using NUS-like strategy

A NUS-like strategy was developed at first in the team of Urbańczyk et al.¹⁵⁸ It relies on an older work done by Oikonomou et al.¹⁵⁹, the permutated DOSY (p-DOSY) approach. It can be explained as using a list of randomly permutated gradient to remove the bias coming from changes of concentration within an out-of-equilibrium mixture. We have seen (part 1.1) that unwanted rise or fall of the peaks unlinked to diffusion-attenuation will compromise the accuracy of the fitting and lead to erroneous results. Rise and fall of the peaks can happen if concentration change such is expected in a reaction medium. The goal would be to separates those concentration changes from the diffusion-attenuation and thus having better DOSY results for the study of evolving medium. The team demonstrates that it can be done using random gradient ramps instead of monotonous ramp. The principle is to avoid any correlation between the experiment time, during which the system may evolve, and the gradient sampling.

Using the classical way, a decrease of signal while the gradient is increasing lead to a bias that increase the recorded diffusion coefficient. The impact of the gradient on the attenuation of the signal is exaggerated. If the gradient sampling goes from least to highest than the opposite happens, the coefficient is recorded inferior. The randomization of the gradient makes it so that the peak's time-variation is separated from the gradient evolution. With permutated DOSY, changes in concentration result in higher apparent noise, and the estimated error for the fit is larger, especially if the evolution is really too important at the scale of diffusion, but it will remove any bias, resulting in improved trueness for the estimated diffusion coefficient. In summary Using random gradients transforms the concentration change into a noise-like artefact rather than a bias.¹⁵⁹

Knowing that p-DOSY approach we can go deeper into Time Resolved NUS (TR-NUS) strategy. Developed first by Urbańczyk et al.¹⁵⁸ in this approach the number of increments is not reduced, but rather increments are acquired using an uninterrupted series at randomly varying gradients. This series
can be analysed by creating a window that should encompass enough increments to allow for a good fit. It was used in the monitoring of polydispersity, using Laplace transformation in a combination of TR-NUS and technics seen in part 1.3.1. The same team also worked on an interesting comparison for restricted diffusion¹⁴⁰ (see part 1.1.1). Those restricted diffusion study can be quite long and so they tried different methods to accelerate them using the previously seen ultrafast approach and the TR-NUS methods. The implementation of both methods was successful as restricted diffusion is not the point of this work, we will simply explain their conclusion. The gain of time is around 1-2 order of magnitude using both methods, the UF methods seems completer and more accurate but is more demanding for the hardware and less easy to adapt to inhomogeneities in the sample compared to the TR-NUS.¹⁵¹

The principle of TR-NUS as we are interested in are illustrated in figure 3.8 from the work of MacDonald et al.¹⁶⁰ They study the variation of a single compound, methanol, during a rapid (5min) change of temperature from 304.5 to 306.5 K. One can see the different windows that allow the determination of diffusion coefficient along the continuum of scans (red crystal in figure 3.8a) using random gradient value (black boxes in figure 3.8a). Reporting the result of those windows in figure 3.8c, shows the increase of diffusion due to temperature shift in less than 2min. This process uses the same kind of fitting as conventional methods with here 8 random increments by fitted diffusion point.

<figure><img src="image_54.png" /></figure>

Figure 3.8 Moving average analysis of time-resolved diffusion NMR data. a) Continuous rapid acquisition of spectra using a random gradient list (grey bays) generates an array of NMR spectra over time from which peaks can be integrated (red). Diffusion coefficients are then obtained by fitting the Stejskal-Tanner equation to a subset of [integral, b] points (8 points here) centered about time t. b) Time-dependent diffusion information D(t) is found by advancing this fit over the dataset by a moving series of non-linear fits. c) Combining the fast PGSE experiment allows changes in diffusion (black) induced by temperature changes (red) to be followed over sub-minute timescales. 1H PGSE (δ = 1.2 ms, Δ = 45 ms, ns = 2, 5 s repetition time), methanol capillary placed in DMSO-d6, 304.5 – 306.5 K, 500 MHz. Adapted with permission from MacDonald et al.¹⁶⁰ © 2019 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
They also monitor a *in situ* polymerization, extracting concentration and the changes of diffusion coefficient of the resulting polymer with a time resolution of 40 s per gradient's value and 12 slices per fit so an average of 8 min per spectra/diffusion calculation. It is to be noted that they use a slightly unusual NMR experiment, they have a spin echoes with a spoiler gradient during the inter-scan delay that allow them an inter-scan delay of 1.5s. (see supplementary information of the paper¹⁶⁰) thus explaining the very fast rate at which they record each increment.

Note that in the first article on tr-NUS DOSY by Urbańczyk et al.¹⁵⁸ they too studied polymer and polymerization. They looked at their capability to get the polydispersity index of standard samples. They also delved in the *in situ* polymerisation by looking at the depolymerisation of heparin by enzymes.
## 4. Methods for processing, analyzing and evaluating DOSY

### 4.1. The DOSY workflow

In the previous chapters we have described the basic principles of diffusion NMR and DOSY, as well as the associated challenges. In this chapter, we will describe the DOSY workflow, discuss the qualitative evaluation of DOSY results, and introduce quantitative metrics to assess and compare DOSY experiments.

#### 4.1.1. Data acquisition

The first step of the workflow is to acquire the data. It is an important step as the quality of the acquired data strongly influences the subsequent steps. The key points are the attenuation of the signal that should go to around 1 to 5% of its initial strength. To reach this target, on multiple analytes that behave differently, we run the experiment with 2 steps/transients. The lightest gradient strength (most signal) and the strongest gradient (least signal). This helps us to check if the compound reaches the attenuation objective we have. In general, this is not done *ex nihilo* as knowledge of the solvent, viscous or not, and of the solute's nature will guide the parameters. Temperature should be known and as stable as possible, stirring/spinning or any kind of motion should be avoided.

The spectral width used for acquisition is also an important parameter. It often the case that the edge of the spectrum can be problematic. It is advisable not to have any peak in the edge of the spectrum. Notably, in Bruker systems the baseline at the extremities is known for going up or down due to digital filtering issues. DOSY being sensitive to baseline distortion/problems it is advisable to take a wide spectral width.

The spectra are acquired by repeating the same experiment multiple times with increasing gradient amplitudes. Gradient increase, in its simplest way, is done following a linear ramp. The list of gradient amplitudes increases linearly from the lowest value to the strongest value. Figure 4.1 shows the resulting FID from such experiment. The first increment gives the strongest signal and is very close to the 1D spectrum that would be obtained with a pulse-acquire sequence. On the other hand, the last increment is barely readable due to low SNR.
<figure><img src="image_55.png" /><figcaption>Figure 4.1, List of FIDs obtained in a DOSY experiment. Each Fid represent an acquisition with increasing gradient power. The gradient powers are illustrated by the area of each rectangle associated with its experiment.</figcaption></figure>

### 4.1.2. Data processing

Once the data are acquired each data sets is a stack of N FIDs, N being the number of increments. In figure 4.1, one can see 16 FIDs for 16 increments. The Fourier transform is done only in the so-called direct dimension (F2), which means that every FID is converted into a spectrum but there is no 2D Fourier transform as for other 2D NMR experiments (like TOCSY, COSY, HMQC etc.). Apodization happens just like for 1D spectra, and is a balance between resolution, linewidth and lineshape. We tried a few apodization function at different weights but it does not appear to play a major role. Indeed, if the data are not good enough to be analyzed without apodization there is little to no chance that it will improve it for the rest of the DOSY analysis.

Here we chose to use the Topspin program for data processing. The reason why we decided to use Topspin, despite it not being made specially for DOSY, is because processing steps are also common in NMR. It therefore made more sense to use a software well known and robust while reserving the analysis part specific to DOSY data to a software made specially for such use.¹⁶¹,¹⁶²

Another major point of importance for the processing is phase correction. The NMR signal can be written as:¹⁶³

$$S(t) = S_0 \exp(i\Omega t) \exp\left(-\frac{t}{T_2}\right) \times \exp(i\phi') \quad 4-1$$

The term $\phi'$ corresponds to the phase, that can be adjusted in order to have good lineshape. After Fourier transform the signal $S(t)$ take the form:
$$S_0[A(\omega) + iD(\omega)] \times \exp(i\phi + \phi_{corrected}). \qquad 4-2$$

Where $A(\omega)$ and $D(\omega)$ are absorption and dispersion part of the spectrum. We have to adjust the $\phi_{corrected}$ value to cancel the exponential and get a pure absorption lineshape in the real part of the spectrum, this is colloquially called “phasing the spectrum”.

In a 1D spectrum this is straightforward, and can be carried out using a graphical interface or by automated means. In a 2D data set (or pseudo 2D), it can be trickier, since a single value of $\phi_{corrected}$ might not be suitable for all the spectra simultaneously. For example, the first FID may have a good lineshape but as the gradient increase, due to hardware reasons the phase shift on the last increment might have a different value. This makes the phase correction step a double compromise, the peak should have a Lorentzian shape but also share this shape throughout the increments as much as possible. When the compromise gets difficult the decision is to phase as good as possible the first one (or least attenuated spectra) that carry the more signal strength and try to improve the following spectra without degrading it too much. Albeit this might seem complicated, we rarely if ever suffered from a problem or an inconsistency as long as the spectrum are correctly phased and phasable.

### 4.1.3. Data analysis

We have seen in part 1 (equation 1-13) the form and meaning of the Stejskal-Tanner equation, that describes signal attenuation in NMR due to translational diffusion and pulsed-field gradients. Once the DOSY data are processed, they are fitted with this equation. Least-squares methods are used to fit the signal strength as a function of the gradient amplitude, to yield the estimated diffusion coefficient for each peak that we choose to analyze. This option to choose peaks on the spectrum rather than taking the whole spectrum is the most easy and straightforward and is called univariate. There are others methods, called multivariate, that analyze the spectrum as a whole. They will be briefly described in part 6, here we will focus on univariate processing using least-squares methods.

There are two main methods of data selection that exist for univariate analysis of DOSY data: using integrals of selected spectral regions, or using intensities for all the peaks above a certain threshold. Those methods have different advantages and disadvantages that we are going to discuss in the context of complex mixtures.

The thresholding method relies on a peak picking tool, and then uses the intensity of the selected peaks. Peak picking can be of varying complexity depending on the software used. In the simplest case a threshold is set, anything above is a peak the rest is not accounted for. In most cases the peak-picking/thresholding will not consider a multiplet as a single peak, and instead picks each sub-peak separately. It can also miss-identify two close peaks as one or a slight lineshape distortions as a whole peak. Despite this it has many advantages, such as its speed (it is almost instantaneous), and the fact that it is less user dependent. Using thresholding may also be mandatory when the spectrum is too crowded.
The use of integrals of selected spectral regions is another option available to analyze the data. It does not depend on any peak-recognizer and is set by the experimenter by hand, which means that it is user-dependent.

Whatever the technic we use it will yield a set of numbers that can be referred as the signal (S in the Stejskal-Tanner equation) a function of the gradient strength. For each peak, whether decided by threshold or by the user, such values will be regrouped, creating a peak set for the DOSY experiment. With those values we can make the fit, each peak will be fitted and all the peaks of the set once fitted form the DOSY result.

Note that even if a spectrum is acquired in good conditions and well processed, some challenges still arise during analysis. Overcrowding of a spectrum, especially common for a mixture, could pose multiple problems. It is known¹⁶⁴ that two overlapped peaks will give an intermediate value of the two diffusion coefficients when single exponential fits are used. Bi-exponential fitting only gives correct values when SNR is very high.

Overlapping is often encountered in two different ways, some overlaps are complete and it is impossible to see or guess each peak, sometimes one can guess that there is two or more but not decipher them. Some are less straightforward; the peaks do mingle, yet they might be resolved, the peak only overlap at their extremities for example. This is the hard case as different way to process the spectra might or might not allow you to retrieve the right value, almost always with some drawback. Finally, another phenomenon is overlapping with smaller peaks, from impurities for example. Those small peaks can be invisible to the user but remain hidden under the peak of interest or close to it and thus hinder the analysis.

This fitting results in two numbers for each peak, the estimated value of the diffusion coefficient, and the associate estimated uncertainty. Figure 4.2 shows two DOSY displays with their respective fits, one being considered as good and one bad. The sample is the same in both cases. It is comprised of three different species. For the “good” example, one can see that the fitting curve for a same molecule almost superimpose both together and with the corresponding experimental points. While the other spectra considered bad is messier and even if some fitting curve slightly align, they do not match the experimental data point well.
<figure><img src="image_56.png" /><figcaption>Figure 4.2 same sample with two different DOSY experiment and their display. Each species has its color and the fit's curve match the species color.</figcaption></figure>

#### 4.1.4. The DOSY display

The DOSY display has become a standard method to represent the result of diffusion NMR experiments on mixtures. In the context of mixture analysis, DOSY experiments should ideally give us information that makes it possible to associate peaks together as belonging to the same species, and hint on the size of the molecules relative to one another. As illustrated with the "bad spectrum" shown in figure 4.2, the peaks should not only be well aligned, but their widths (the uncertainty from the fit) should also be as small as possible; otherwise, it is difficult to know which molecule it belongs to. In this "bad" example it seems that there are 2 species instead of three, while the three species are well separated in the "good" example.

The display takes a form that is akin to the classic 2D NMR but it is only apparent as there is no spectral indirect dimension or 2D Fourier transform. Instead, the display shows peaks which value on the horizontal dimension match the frequency (in ppm) of the peak in the 1D spectra usually displayed on top of the map. The vertical value is then the value of the estimated diffusion coefficient belonging to the specific peak. Another important information that we retrieve from the fit is the uncertainty, derived from the differences between the experimental data points and the fitted ones.
This is represented as the vertical width of the peak. The horizontal width does not hold strong
meaning except the size of the integration decided by the user or by the peak picking.

The display in itself is represented as a contour map, just like a map or most 2D NMR plot. Figure 4.2 shows two examples of this display. One of the main advantages of this display is that it is really simple to read, a simple look can help to determine where the fit worked well, and, if it did, which peak belongs to which species. It also provides the relative sizes of the different species. This is based on the reasonable assumption that translational diffusion happens for molecules as a whole, and therefore the estimated diffusion coefficient should be the same for all the peaks. One disadvantage is that it is easy to manipulate, as the choice of contour levels that show the topography, as well as the level of zoom, can give false impressions.

## 4.2. Methods

### 4.2.1. Sample

In order to assess existing and new DOSY methods, we worked mainly with a sample of sucrose, 2-butanol and pyridine in deuterated water. This sample was used for its convenience as it shows three species in three different areas of the spectra. Figure 4.3 shows the 1D ¹H spectra of such a mixture. In this spectrum not all the peaks were considered. We decided to select well-resolved peaks, to limit the contributions of peak overlap and of the choice of integration region. We also chose to work with a concentrated sample, to limit the effect of sensitivity. This made it possible to focus on other sources of error in the DOSY experiments.

The three selected peaks of pyridine and sucrose are not overlapped and relatively well resolved. For butanol, the peak at 3.51 ppm may seem slightly overlapped with the sucrose but in practice it is easily separable from the sucrose. The multiplet at 1.25 ppm is of high multiplicity and the total SNR is a bit low this coupled with a slight overlap. This overlap with iPrOH, that is a solvent commonly found in the flowtube, because it is the storage solvent, being problematic we discarded this peak.
<figure><img src="image_57.png" /><figcaption>Figure 4.3, the 1D ¹H spectrum of the mixture most commonly used throughout this work. The wide peak at 4.7 is water mostly from the residual DOH and brought by both pyridine and sucrose that are not fully dry.</figcaption></figure>

### 4.2.2. Processing software

The processing and analysis of DOSY data was done using multiple software. The Topspin software was used for the processing part, that is the same as for 1D NMR. Apodization was done often using very weak factor for the weighting functions. In general, we used the most classical exponential function, or no apodization at all. In this work all 2D data are shown without apodization except if specified and 1D data have a 0.5 Hz apodization using the exponential function.

For zero filling, all the 2D data sets were processed with 4 times their original number of points. This is because it was found to play a role in the analysis steps, when using peak picking. Zero filling is known to bring additional information when using 2 times the original number of points.¹⁶³ Beyond that, it simply acts as a form of interpolation. We observed empirically that, visually, the DOSY display was of higher quality when using zero-filling up to 4 time the points number rather than 2. This might be because peak picking with thresholding works better with a high degree of interpolation.

Baseline correction was performed with the default parameters of the automatic baseline correction functionality in topspin.
### 4.2.3. Analysis software

To analyze the data, we chose to use the General NMR Analysis Toolbox (GNAT).¹⁶¹ It is a free toolbox developed with MATLAB, MATLAB being itself a commercial software. GNAT¹⁶¹ is a software developed by the Manchester NMR methodology group to process and analyze all kinds of diffusion NMR experiments. It merges different analytical technics surrounding DOSY¹⁶⁵,¹⁶⁶ or general NMR (baseline correction, apodization, reference shifting etc.). It also includes relaxation¹⁶⁷ NMR technics and analysis/processing tools for various special cases like a pure-shift chunks editor. It lacks detailed documentation but the code is fully available and well commented. Note that the InsightMR flow tube comes with software such as Dynamic Center but we found it not that convenient compared to GNAT, that is open-access version and that we could modify in various ways.

## 4.3. Qualitative comparison

In this section, we will discuss a few processing parameters and their impact on the general quality of the results of DOSY experiments, based on visual inspection of the DOSY display. Before doing so it is important to define what is expected from such a display in the context of complex mixture analysis. The measured diffusion coefficient is used as a mean to achieve a so-called virtual separation of the NMR spectra. Such separation is achieved only if the peaks are thin enough to not overlap in the diffusion dimension with those of others species. At the same time, the peaks of the same molecule should overlap in the diffusion dimension and not get scattered too far apart from each other.

### 4.3.1. Integration methods

To analyze the data, one needs a way to retrieve the signal S for the different peaks, so that it can be fitted. To do so, one can use the area under the peak by integrating the spectrum. In this case, the user chooses two points on the spectrum which determines the length of the integration region. Such integration regions can be stored and retrieved, allowing the user to re-use the area and hence use consistent integration regions across several experiments. It remains user-dependent, and the quality of the fit can be impacted heavily by the choice of integration region. One should remember that having peak with low error (small vertical width) that align with each other is unlikely to happen, if the user poorly integrates their data.

This method has some advantages. It can help untangle two peaks that happen to slightly-overlap by narrowing the integration region to fit the peak tightly. In theory the contribution of a noise region to an integral should not depend strongly on its size, so it is advisable to use large integration region if possible. In the real case low concentrated species or various phenomena can quickly lead to taking unwanted signal and thus heavily worsen the fit. In almost all cases the integration regions that we used remained tightly around the peak. This method also has the advantage of being straightforward.
The disadvantages of this method are mostly that it is difficult to perform well if small
signals/peaks are present at the feet of the peak of interest. If those signals are impossible to separate
or to disambiguate while integrating, they will play an adverse role in the fit. Also, a problem of this
method is that it is time consuming: integration of a complex mixture with multiple species can take a
long time. This is true when many species are present, but also if the peaks are close, as finding the
right area that work throughout multiple spectra is not an easy task and may have to be redone
multiple times.

Overall, this method was the most used during this work. It was our default method. When the
analysis is done differently in this manuscript, it will be mentioned.

4.3.2. Thresholding/intensity methods

Another way to analyse data is to use the intensity rather than the integrals of the peaks. To do
so a peak picking is necessary. Usually one chooses a threshold line, and everything above will be
considered a peak, while anything below will be discarded as noise. It is less user dependent as the
user does not decide for each peak, yet it can be tuned and will give different result depending on
where the threshold is placed.

The main advantage of the method is that it is fast. It is virtually instantaneous, and the number
of peaks or interesting area does not play a role in its length. Another advantage is that it is a good way
to get rid of smaller uninteresting peaks those which may overlap with the peak of interest. This is
another way to slightly bypass overlapping. Thresholding seems a better suited method if there is a
crowd of smaller peaks at the feet of the interesting peaks. Conversely, Thresholding fails more often
when the overlap happens between two peaks of similar intensity. A case that while difficult can often
be solved by using integration regions, as long as the peaks can be distinguished. It happens that two
peaks of similar intensity are easier to separate using integration than thresholding. Overall
overlapping has no straightforward answer. To solve it, when possible, is often a trial and error
between the different approach, regions... The use of thresholding/integration is not a solution to
serious overlapping. When heavy or total overlap happens, one should look for other methods that
increase resolution, such as pure-shift NMR.<sup>168,169</sup>

The main problem with peak picking is that it will not consider multiplets as a single entity, but
rather consider each sub-peak on its own. It is a problem as multiplets suffer from lower SNR (relative
to an equivalent singlet). This impact the fit negatively and also gives different values for a single peak.
It increases the spread of the peak and thus the separation is less evident. We often found that, the
actual diffusion value is the average of all sub-peaks. It also means that even if the average is right the
peak might be very stretched in the whole spectrum, which worsen its readability.