Thesis

Influence of Hydrogen-bonding on dynamical properties of ionic liquids

MORA CARDOZO, Juan Francisco

Abstract

Ionic liquids (ILs) are liquids composed entirely of ions, therefore they screen every charged perturbation and present ionic conductivity. Recent studies focus in particular on the so-called room temperature ionic liquids (RTILs), that are organic/inorganic salts with melting point or glass transition below 100 C, whose chemical-physics properties are greatly affected by their ionic character. The dissociation of molecules into ions gives origin to an interplay between multiple interactions such as Coulomb forces, dispersion forces and hydrogen bonding (HB). The latter is crucial for the structural organisation of the liquids, which furthermore is intertwined with proton conduction, a key feature for applications in electrochemical energy conversion devices. In this thesis we show how HB influences the structure, dynamics and proton conduction of prototypical ILs.

Reference

MORA CARDOZO, Juan Francisco. Influence of Hydrogen-bonding on dynamical properties of ionic liquids. Thèse de doctorat : Univ. Genève, 2019, no. Sc. 5365

DOI : 10.13097/archive-ouverte/unige:121811 URN : urn:nbn:ch:unige-1218113

Available at: http://archive-ouverte.unige.ch/unige:121811

Disclaimer: layout of this document may differ from the published version.

1 / 1 UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES Section de Physique Department of Quantum Matter Physics Prof. Christian Rüegg

PAUL SCHERRER INSTITUTE Laboratory for Neutron Scattering and Imaging Dr. Jan Embs

Influence of Hydrogen-bonding on dynamical properties of ionic liquids

THÈSE

présentée à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de Docteur ès Sciences, mention Physique

par

Juan Francisco Mora Cardozo de Bogota (Colombie)

Thèse No. 5365

GENÈVE Atelier de reproduction de la Section de Physique 2019

UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES Section de Physique Department of Quantum Matter Physics Prof. Christian Rüegg

PAUL SCHERRER INSTITUTE Laboratory for Neutron Scattering and Imaging Dr. Jan Embs

Influence of Hydrogen-bonding on dynamical properties of ionic liquids

THÈSE

présentée à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de Docteur ès Sciences, mention Physique

par

Juan Francisco Mora Cardozo de Bogota (Colombie)

Thèse No. 5365

GENÈVE Atelier de reproduction de la Section de Physique 2019 ii He who knows nothing, fears nothing. — Hermes Ortiz

To my parents: Gerardo Mora Torres and Gloria Inés Cardozo Gómez Abstract

Ionic liquids (ILs) are liquids composed entirely of ions, therefore they screen every charged perturbation and present ionic conductivity. Recent studies focus in particular on the so-called room temperature ionic liquids (RTILs), that are organic/inorganic salts with melting point or glass transition below 100 ◦C, whose chemical-physics properties are greatly affected by their ionic character. The dissociation of molecules into ions gives origin to an interplay be- tween multiple interactions such as Coulomb forces, dispersion forces and hydrogen bonding (HB). The latter is crucial for the structural organisation of the liquids, which furthermore is intertwined with proton conduction, a key feature for applications in electrochemical energy conversion devices.

In this thesis we show how HB influences the structure, dynamics and proton conduction of prototypical ILs. Because of their their labile (acidic) proton, most of the efforts in this thesis were devoted to ammonium based ILs. However, methylation of imidazolium-based ILs also has a strong impact on the HB formation ability of these liquids. This is reflected in an increment of viscosity and in a decrement of electrical conductivity of methylated species.

Our study relies on the combination of two complementary methods: Computer simula- tions and neutron scattering experiments. By means of density functional computations we optimized the structure of single ions, neutral ion pairs, small ionic clusters, calculated cohesion energies, characterized the HB’s geometry and computed the frequency of their stretching modes. This information was used to optimize rigid-ion, fixed-topology empirical force fields, which, in a second step, were used to perform classical molecular dynamics simulations. Using the generated trajectories, we calculated macroscopic properties of the liquids such as self-diffusion coefficients, electric conductivity, we estimated the H-bond life time, we computed radial distribution functions, dynamical structure factors and several correlation functions. When possible, we compared the latter with experimentally obtained neutron scattering spectra of the ILs.

The neutron scattering part of our investigations included backscattering experiments and iv quasi-elastic neutron scattering experiments with and without polarization analysis. The ILs considered in our study are hydrogen-rich materials, a property which makes them suitable for neutron spectroscopy. Neutron scattering on selectively deuterated samples, in particular, allowed us to focus on specific dynamical modes of the samples, such as those involving the labile proton of ammonium based ILs. The different dynamical processes were analyzed by models based on stochastic motion, thus diffusion coefficients, confinement radii, activation energies of each process were obtained.

Force fields used in our simulations were optimized for structural properties, not for dy- namical features such as diffusion. The computed properties did not quantitatively coincide with the experimentally determined parameters. However, the temperature dependence of several properties was reproduced. In our search for enhanced conductivity in ILs, we found that our structural optimization approach was very useful to study half-neutralized diamine ILs, which furthermore are rich in hydrogen and therefore suitable for future neutron scatter- ing experiments. In these liquids, non-vehicular proton diffusion was reported and measured by means of pulsed-field gradient-nuclear magnetic resonance (PFG-NMR), but the exact mechanism for the enhanced conductivity is still under debate. In this thesis we present the results of extensive simulations of a family of diamine based ILs, where the idea of ions paths where the proton could jump, overcoming a modest energy barrier, was confirmed.

This thesis validates the combination of simulations and neutron experiments as a pow- erful synergetic tool to explore the influence of H-bonding on the microscopical dynamics of ILs and its effects on their macroscopic properties.

v Résumé

Les liquides ioniques (LI) sont des liquides entièrement composés d’ions, ils masquent donc toute perturbation portant une charge et présentent une conductivitéionique. Des études récentes portent notamment sur les liquides ioniques à température ambiante (LITA), qui sont des sels organiques/inorganiques avec un point de fusion ou une transition vitreuse inférieure

à 100 ◦C et dont les propriétés physico-chimiques sont grandement affectées par leur caractère ionique. La dissociation des molécules en ions donne lieu à une interaction entre de multiples phénomènes telles que forces de Coulomb, forces de dispersion et liaisons hydrogène (LH). Ces dernières sont cruciales pour l’organisation structurale des liquides, qui est en outre liée à la conduction protonique, une caractéristique essentielle pour les applications dans les dispositifs de conversion d’énergie électrochimique.

Dans cette thèse, nous démontrons comment les LH influencent la structure, la dynamique et la conduction protonique de LI prototypiques. En raison de leur proton labile (acide), la plupart des efforts de cette thèse ont été consacrés aux LI à base d’ammonium. Cependant, la méthylation des LI à base d’imidazolium a également un fort impact sur la capacité de formation de LH dans ces liquides. Cela se traduit par une viscosité accrue ainsi qu’une perte de conductivité électrique des espèces méthylées.

Notre étude repose sur la combinaison de deux méthodes complémentaires : Simulations sur ordinateur et expériences de diffusion neutronique. Au moyen de la théorie de la fonctionnelle de la densité, nous avons optimisé la structure d’ions simples, de paires d’ions neutres et de petits clusters ioniques, puis calculé les énergies de cohésion, caractérisé la géométrie des LH et calculé la fréquence de leurs modes d’étirement. Ces informations ont été utilisées pour optimiser des champs de force empiriques à ions rigides et de topologie fixe, qui, dans un deuxième temps, ont été utilisés pour des simulations classiques de dynamique moléculaire. En utilisant les trajectoires générées, nous avons calculé les propriétés macroscopiques des liquides telles que les coefficients d’autodiffusion ainsi que la conductivité électrique. Nous avons estimé la durée de vie des LH et avons calculé les fonctions de distribution radiale, les facteurs de structure dynamique et plusieurs fonctions de corrélation. Dans la mesure vi du possible, nous avons comparé ces derniers à des spectres obtenus lors d’expériences de diffusion neutronique sur des LI.

La partie de diffusion neutroniques de nos recherches comprenait des expériences de ré- trodiffusion ainsi que des expériences de diffusion quasi-élastique avec et sans analyse de polarisation. Les LI considérés dans notre étude sont des matériaux riches en hydrogène, une propriété qui les rend appropriés pour la spectroscopie neutronique. La diffusion neutronique sur des échantillons sélectivement deutérés nous a permis, en particulier, de nous concentrer sur des modes dynamiques spécifiques des échantillons, tels que ceux impliquant le proton la- bile des LI à base d’ammonium. Les différents processus dynamiques ont été analysés par des modèles basés sur des mouvements stochastiques, menant à l’obtention des coefficients de diffusion, aux rayons de confinement ainsi qu’aux énergies d’activation de chaque processus.

Les champs de force utilisés dans nos simulations étaient optimisés pour les propriétés structurales, et non pas pour les caractéristiques dynamiques telles que la diffusion. Les propriétés calculées ne coïncidaient pas quantitativement avec les paramètres déterminés expérimentalement. Cependant, la dépendance en température de plusieurs propriétés a été reproduite. Dans notre recherche de conductivité améliorée dans les LI, nous avons constaté que notre approche d’optimisation structurale a été très utile pour étudier les LI diamines à demi neutralisés, qui sont en outre riches en hydrogène et donc adapté aux futures expériences de diffusion neutronique. Dans ces liquides, la diffusion de protons non-véhiculaires a été signalée et mesurée à l’aide de la technique de résonance magnétique nucléaire à gradient de champ pulsé (RMN-GCP), mais le mécanisme exact de la conductivité améliorée est encore en cours de débat. Dans cette thèse, nous présentons les résultats de simulations approfondies d’une famille de LI à base de diamines, dans laquelle l’idée de chemins ioniques où le proton pourrait sauter, surmontant une barrière énergétique modeste, a été confirmée.

Cette thèse valide la combinaison de simulations et d’expériences neutroniques en tant que puissant outil synergique pour explorer l’influence de la liaison H sur la dynamique microscopique des LI et ses effets sur leurs propriétés macroscopiquesé.

vii Contents

Abstract (English/Français) iv

List of figures x

List of tables xviii

1 Introduction and motivation1

2 Neutron scattering and computational methods8 2.1 Neutron scattering...... 8 2.1.1 Scattering cross-sections...... 8 2.1.2 Correlation functions in nuclear scattering...... 10 2.2 Polarisation analysis...... 11 2.2.1 Scattering length operator...... 11 2.2.2 Coherent and incoherent scattering...... 12 2.3 Incoherent quasi-elastic neutron scattering and stochastic processes...... 13 2.3.1 Fickian diffusion...... 14 2.3.2 Jump diffusion...... 15 2.3.3 Three-fold jump rotation...... 16 2.3.4 Continuos rotational diffusion...... 16 2.3.5 Gaussian model...... 17 2.4 Time-of-flight-spectrometers...... 17 2.4.1 Direct geometry spectrometer...... 18 2.4.2 Backscattering spectrometer...... 18 2.5 Computational chemistry...... 19 2.5.1 Molecular dynamics simulations...... 19 2.5.2 Force field...... 20 2.5.3 Ab-initio simulations...... 20

3 Density functional computations and molecular dynamics simulations of the tri- ethylammonium triflate protic ionic liquid 23 3.1 Methods...... 24 viii Contents

3.2 Classical MD simulations: results...... 25 3.2.1 Dry TEA-TF samples...... 25 3.2.2 The effect of water at low concentration on the structure and dynamics of TEA-TF...... 40 3.3 Density functional computations and ab-initio simulation...... 43 3.3.1 The molecule, the ions, and the energetics of ionisation and ion dissociation 43 3.4 Summary and conclusions...... 46

4 Linking structure to dynamics in protic ionic liquids: A neutron scattering study of correlated and single-particle motions 50 4.1 Materials and methods...... 50 4.1.1 Samples...... 50 4.1.2 QENS experiment...... 51 4.1.3 MD analysis...... 52 4.2 Data analysis...... 52 4.3 Results...... 55 4.3.1 Diffraction with polarisation analysis...... 55 4.3.2 Single particle dynamics...... 57 4.3.3 Collective dynamics...... 60 4.4 Summary and conclusions...... 62

5 Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering 63 5.1 Materials and methods...... 63 5.1.1 Samples...... 63 5.1.2 Differential scanning calorimetry (DSC)...... 64 5.1.3 Quasi-elastic neutron scattering experiments...... 65 5.1.4 Data analysis...... 67 5.1.5 Ab-initio simulations...... 71 5.2 Results and discussion...... 72 5.2.1 Density functional computation...... 72 5.2.2 Dynamics in the solid phase...... 74 5.2.3 Liquid phase...... 79 5.2.4 Summary and conclusions...... 85

6 Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids 87 6.1 Methods...... 88 6.2 Results...... 89

ix Contents

6.2.1 Density functional computation of geometry and hydrogen bonding in neutral ion pairs and small aggregates...... 89 6.2.2 Proton conductivity in model DAEt-TF wires...... 95 6.2.3 Molecular dynamics simulations...... 99 6.2.4 Paths for proton diffusion according to a Grotthuss-type mechanism.. 110 6.2.5 Water effect on the structure and dynamics...... 114 6.3 Summary and conclusions...... 117

7 Methylation impact on the dynamics and structure of imidazolium-based ionic liq- uids 121 7.1 Materials and methods...... 121 7.1.1 Samples...... 121 7.1.2 Differential scanning calorimetry (DSC)...... 122 7.1.3 Quasi-elastic neutron scattering experiments...... 123 7.1.4 Data analysis...... 124 7.1.5 Ab-initio simulations...... 125 7.2 Results and discussion...... 126 7.2.1 Density functional computation...... 126 7.2.2 Dynamics in the liquid phase...... 127 7.2.3 Summary and conclusions...... 131

8 Conclusions and outlook 134

A TEA-TF miscellaneous figures 138

Bibliography 169

Acknowledgements 170

Curriculum Vitae 172

x List of Figures

1.1 Structure and nomenclature of various commonly used cations and anions in the synthesis of RTILs from Ref. [3]...... 2 1.2 Reflectivity curves obtained for silver-coated liquids from Ref. [13]...... 3

2.1 Scattering experiment geometry [74]...... 9 2.2 IN5 disk chopper TOF spectrometer layout [88]...... 18 2.3 IN16B backscattering spectrometer layout [91]...... 19

3.1 Schematic structure of [TEA]+ and [TF]−...... 24 3.2 (a) Average potential energy per ion pair as a function of temperature. The statistical error bar is of the order of 0.5 kJ/mol, smaller than the size of the dots. Green line: linear interpolation to the four lowest-T points. Red line: linear interpolation to the four points of highest T . Inset: deviation of E (T ) from the 〈 〉 high-temperature linear interpolation E (T ) α βT . (b) Average volume 〈 〉hi gh = + per ion pair as a function of temperature. The error bar on the volume is 0.1 ∼ Å3, smaller than the size of the dots. Green and red lines defined as in panel (a). 27 3.3 Radial distribution function of N-O (blue line), N-N (green line) and O-O (red line) pairs in TEA-TF at T 300 K, P 1 atm. Inset: short range portion of = = the running coordination number nNO(r ), obtained by integration of the radial distribution function (see text)...... 28 3.4 Arrhenius plot for the diffusion constant. D and D in [cm2/s]...... 32 + − 3.5 Arrhenius plot for the electrical conductivity at pressure P 1 atm...... 33 = 3.6 Parameter ∆ measuring the pairing of [TEA]+ and [TF]− ions. Estimated error bar of the order of 5% at T 310 K, slightly lower above T 310 K...... 34 ≤ = 3.7 Time auto-correlation function of the N-H direction in [TEA]+ (red lines), and of the C-S bond in [TF]− (blue line)...... 36 3.8 Time correlation function of cation and anion orientations. Dots and squares represent simulation results. Lines are a guide to the eye...... 37

xi List of Figures

3.9 Cumulative number of HB per 100 TEA-TF ions pairs as a function of T , account- ing for the contribution from anions accepting one HB, corresponding to the area below the green line; two HB’s, represented by the area between the green and blue line; or three HBs, corresponding to the strip between the blue and the red lines. Thus, the red line represents the total number of HB per 100 ion pairs. 38 3.10 Cluster consisting of an anion accepting three HBs from neighbouring cations. A thin dash line identifies hydrogen bonds...... 39 3.11 Lifetime of N H O hydrogen bonds as a function of inverse temperature. The − ··· straight lines are a guide to the eye. τHB is measured in ps...... 40 3.12 Typical configuration of a water molecule donating H-bonds to two [TF]− anions, and accepting a third one from a [TEA]+ cation. A thin dash line identifies hydrogen bonds...... 41 3.13 Ground state geometry of TEA-TF from density functional computations. PBE exchange correlation approximation, and Gaussian 09 computation (see Sec. 3.1). The dash line represents a hydrogen bond connecting the cation to the anion. 44

3.14 Energy variation along the constrained coordinate measuring the dH O dis- −− tance. Decreasing dH O means moving the proton towards the nearest [TF]− −− oxygen, giving origin to a neutral TEA and TF pair. Green dots: computations for the TEA-TF molecule. Red filled squares: computation for the periodic structure shown in Figure A.15. The full and dash black curves are a guide to the eye... 46

4.1 Coherent (orange line) and incoherent (blue line) contributions of the diffraction

spectrum of TEA-TF (a) and TEAD-TF (b) measured at T = 320 K. The experimen- tal data are compared to the cross-section weighted structure factor calculated from the MD particle configuration (black dotted line). The component intensi- ties are normalized to I (Q 0) for clarity...... 56 inc → 4.2 Anion-anion (orange), cation-cation (blue) and cation-anion (green) subcom-

ponents of I(Q,t=0) for TEA-TF (a) and TEAD-TF (b) as obtained from the MD particle configuration at T = 320 K. The subcomponent intensities are deter- mined by the neutron coherent scattering lengths of the species and their total number as given in eq 4.3b...... 57 4.3 Temperature dependence of the parameters describing the cation single-particle dynamics in the liquid phase as obtained from the iterative fits of the TEA-TF

and TEAD-TF spectra. (a) Self-diffusion coefficients of the long-range (global) diffusion, Dtr, the localized motions of the N-H proton, DH, and the ethyl chains, Dch. The dashed lines are Arrhenius fits. (b) Sketch of the TEA structure and three groups of dynamically “equivalent” protons. (c) Temperature dependence

of the confinement radii for the N-H proton (RH, red), bridging methylene (R1, blue), and terminal methyl (R2, green) groups. The dashed lines are guides to the eye...... 58 xii List of Figures

1 4.4 Intermediate scattering functions I(Q,t) at Q 1.5 Å− as obtained from the = MD trajectories. The relaxation curves of the N-H proton (gray solid line), the nitrogen atom of the triethylammonium cation (violet dashed line) and the sul- fur of the triflate anion (black dash-dotted line) are practically identical on the picosecond time scale. The intermediate scattering functions of the bridging methelene (light blue solid line) and methyl (green solid line) hydrogens demon- strate a significantly faster decay due to localized motions of the ethyl chains and are presented for comparison. The relaxation of the oxygen intermediate scattering function (orange solid line) is also faster than that of the acidic H, N and S indicating that the breaking time of individual hydrogen bonds is shorter than the relaxation time of the ion pair correlated motion...... 59

coh 4.5 Linewidths of the narrow quasielastic contribution Γtr of TEA-TF (red) and TEAD-TF (blue) as a function of Q at T = 320 K. Short-dashed color lines are the coherent contributions of the diffraction spectra, respectively. The black dashed line is the narrow quasielastic contribution of the incoherent spectrum calculated using Equation 2.21...... 60

4.6 Coherent dynamic structure factor of TEA-TF (dashed red line) and TEAD-TF (dashed blue line) at the charge-charge (a) and adjacency (b) correlation peaks. The incoherent dynamic structure factor of the protonated sample (black solid line) is presented for comparison. The gray dotted line is the resolution linewidth at zero energy transfer for the D7 spectrometer...... 61

5.1 DSC traces of a) TEA-2C, b) TEA-MS, c) TEA-PFBF and d) TEA-PFOS at 1 K/min scan rate...... 66

5.2 Ground state geometry of: a) TEA-2C, b) TEA-MS, c) TEA-PFBF, d) TEA-PFOS from DFT computations. PBE exchange correlation and CPMD calculation. The close contact from H1 and O represent a hydrogen bond...... 73

5.3 Energy variation from the ground state configuration along the restricted vector

joining dAH O. Negative dAH O means moving AH toward the oxygen in the ··· ··· anions. Positive dAH O implies moving away toward N. Dashed curves are guides ··· for the eye...... 74

1 5.4 EFWS and IFWS data of TEA-2C at Q=1.72 Å− . The solid line is the result of the 2D-fit using the three-fold jump-rotation model and the dashed line is the result for the continuous rotation model (Equations 5.9 and 5.10)...... 75

xiii List of Figures

5.5 a) The EFWS and b) the IFWS of TEA-PFBF averaged over the Q-group where no structural maxima were found. At least three different phase transitions can be identified, with corresponding maxima at in the IFWS at T=110 K, a broad bump between 160 K to 220 K. The maximum at T=300 K is a first melting transition as identified with our DSC traces. They reflect the onset of at least two different dynamical processes in the solid phase and a the sample melting with corresponding features in the EFWS...... 77

5.6 IFWS and EFWS intensities for a PIL/d-PIL pair and IAH as in Equation 5.3. a) Experimentally (not normalized) measured IFWS of TEA-MS (scaled to f ) and 1 TEAD-MS at Q=1.79 Å− . b) Corresponding EFWS and in the inset the zoom of the dynamical phase transition. c) Calculated and normalized elastic/inelastic intensity of AH as a function of the temperature...... 78

5.7 IFWS of TEAD-2C a) and of TEA-2C in b). The partially deuterated sample shows a Q-dependent peak maxima from T>220 K indicating long-range dynamics at low temperatures. In TEA-2C no Q dependency is seen in the temperature domain 110 K T 220 K...... 79 ≤ ≤ 1 5.8 QENS spectrum at Q=1.4 Å− of TEAD-MS at T=390 K along with the fit curve (blue line) given by Equation 5.5. Long-range and localized contributions are plotted in red and green, in dashed and dot dashes lines are R(Q,E) and bg (Q,E) respectively...... 80

5.9 Temperature and anion dependence of the AH confinement Radii. The filled symbols correspond to the fitted data (Equation 5.5), whereas the dashed lines are an eye-guide. The confinement radii increase with temperature...... 81

5.10 Arrhenius plot for the diffusion coefficients of DH. The filled symbols correspond to the fitted data (equation 5.5). Solid lines correspond to the Arrhenius fits DH, Equation 5.7...... 81

5.11 Temperature dependence of the diffusion coefficients Dtr (filled symbols) and DCH (open symbols) for the different PILs. The solid lines correspond to the fit of an Arrhenius behaviour, Equation 5.7...... 83

5.12 Temperature dependence of the confinement radii for the methyl group R2 (filled symbols) and the methylene group R1(open symbols) for the different PILs. The dashed lines are a guide to the eyes...... 84

6.1 Ground state geometry of the gas phase cations. (a) [DAEt]+; (b) [DAPr]+; (c) [DABu]+...... 88 6.2 Lowest energy configuration of: (a) DAEt-TF; (b) DABu-TF.Dash lines represent hydrogen bonds...... 90 xiv List of Figures

6.3 Variation of the potential energy on moving the proton out of the ground state

position along the direction joining the two N-atoms in the same [DAEt]+ cation. Green line: computed on the gas-phase cation. Blue line: computed on the

cation joined to a [TF]− anion in a neutral ion pair. The reaction coordinate x is the difference of the proton distances from the two N atoms...... 93 6.4 Energy variation on moving the proton out of the equilibrium position along the direction leading the proton to the non-covalently bonded partner in inter- ion HBs. Panel (a): primary cation-anion HB. The reaction coordinate x is

the distance between the proton on: [DAEt]+ (blue line); [DAPr]+ (green line); [DABu]+ (red line) and the oxygen on [TF]−. Panel (b): cation-cation HB in the model DAEt-TF wire (see text). The coordinate x is the distance between the proton from NH + and the nitrogen on the neighbouring NH . Red line: − 3 2− single proton displacement. Blue line: in-phase displacement of all equivalent protons. In the latter case, the energy per moving proton is displayed...... 95 6.5 Variation of the potential energy on moving the proton out of the ground state

position along the direction joining the two N-atoms in the same [DAEt]+, com- puted by PBE and by B3LYP on the cation joined to a [TF]− anion in a neutral ion pair. The reaction coordinate x is the difference of the proton distances from the two N atoms...... 96

6.6 Chain-like arrangement of [DAEt]+ cations (a), (b), (c), with: (b) bridging by [TF]− and (c) bridging by [TF]− and by water. Possible paths for proton jumps are indicated by dash lines and arrows. Blue dots: N; red dots: O; yellow dots: S.

For clarity, the CF moiety of [TF]− is omitted...... 97 − 3 6.7 Linear chain built to investigate the stability and energy profile of hydrogen bonds joining cations...... 98 6.8 Average potential energy E and average density ρ as a function of temperature 〈 〉 〈 〉 from MD simulations of DAEt-TF at NPT conditions. In both panels the inset reports the plotted quantity minus its linear interpolation for T 330 K. Data ≥ collected on cooling...... 100 6.9 Density-density and charge-charge structure factors at T 350 K of: (a) DAEt-TF, = and (b) DABu-TF.The experimental melting point of DAEt-TF is T 351 K [73]. 102 m = 6.10 Radial distribution functions of ions in (a) DAEt-TF and in (b) DABu-TF..... 103

6.11 Probability distribution for the N N distance within [DAEt]+ and [DABu]+ ··· cations computed by classical MD at T = 350 K...... 104 6.12 Average number of N H O HB per cation (or, equivalently, per anion) as a func- − ··· tion of temperature. HBs are defined by N O separation 3.2 Å and N H O ··· ≤ − ··· angle 150◦. The line is a guide to the eye...... 105 ≥ xv List of Figures

6.13 Arrhenius plot of the diffusion coefficient of cations and anions in DAEt-TF.Full lines represent the linear interpolation to the low-and high-temperature data for

[DAEt]+...... 106 6.14 Arrhenius plot of the electrical conductivity. Full dots: simulation results from Eq. 3.6. Empty squares: Nernst estimate of conductivity, Equation 3.7. The straight lines represent the linear interpolation of the high and low temperature portions of the conductivity data...... 108 6.15 Time autocorrelation function of ion orientation in DAEt-TF at T 350 K. The = full lines give the interpolation of the simulation data with a stretched exponential.109 6.16 Relaxation time τ for rotations, estimated from the fit of simulation data by a stretched exponential in Equation 6.6. The straight lines represent the linear interpolation of the low- and high-temperature values of the relaxation times of cations and anions...... 110 6.17 Logarithm of the concentration c(n) of chains length n, expressed in number of chains per inverse cubic micron. The main panel reports the results considering

the possibility of oxygen atoms on [TF]− shuttling protons between two [DAEt]+ cations, see text. Inset: results considering only the HBs linking cations directly, see text...... 111 6.18 Chain of 12 cations and 10 bridging anions (see text) forming a connected set in which the longest link is less than 3.6 Å . Two further bridging anions have been omitted for clarity...... 113 6.19 (a) Radial distribution function of water in samples of 216 DAEt-TF ion pairs and

25 water molecules at T 350 K. Green line: OW - ammonium N on [DAEt]+; = OW - oxygen on [TF]−; blue line (inset): OW-OW. (b) Typical configuration of a water molecule donating H-bonds to two [TF]− anions and accepting a H-bond from a [DAEt]+...... 116 6.20 Comparison of the concentration of chains in dry and in water contaminated DAEt-TF samples at T 350 K...... 117 =

7.1 a) Chemical structure of 1-Ethyl-3-methylimidazolium and b)1-Ethyl-2,3-dimethylimidazolium (methylated) cations. The numbers label the different positions within the imi- dazolium ring...... 122 1 7.2 DSC traces of a) EMIM-SCN, b) C2C1C1IM-SCN at 1 Kmin− scan rate...... 123 1 7.3 DSC traces of a) EMIM-DCA, b) C2C1C1IM-DCA at 1 Kmin− scan rate...... 124 1 7.4 DSC traces of a) EMIM-TCM, b) C2C1C1IM-TCM at 1 Kmin− scan rate...... 125

7.5 Ground state geometry of: a) EMIM-SCN, b) C2C1C1IM-SCN. PBE exchange correlation and CPMD calculation. The close contacts represented by doted lines are hydrogen bonds...... 126 xvi List of Figures

7.6 Ground state geometry of: a) EMIM-DCA, b) C2C1C1IM-DCA. PBE exchange correlation and CPMD calculation. The close contacts represented by doted lines are hydrogen bonds...... 127

7.7 Ground state geometry of: a) EMIM-TCM, b) C2C1C1IM-TCM. PBE exchange correlation and CPMD calculation. The close contacts represented by doted lines are hydrogen bonds...... 128

7.8 Temperature dependence of the global diffusion coefficients Dtr. In filled sym-

bols the results for the C2C1C1IM based ILs and in open symbols the results for the EMIM based ILs. The solid lines correspond to the fit of an Arrhenius behaviour, Equation 5.7...... 129

7.9 Temperature dependence of the diffusion coefficients Dalkyl. In filled symbols

the results for the C2C1C1IM based ILs and in open symbols the results for the EMIM based ILs. The solid lines correspond to the fit of an Arrhenius behaviour, Equation 5.7...... 129 7.10 Temperature dependence of the confinement radii for the alkyl chain. In filled

symbols the results for the C2C1C1IM based ILs and in open symbols the results for the EMIM based ILs. The dashed lines are a guide to the eyes...... 130

A.1 Running coordination number nNO(r ) at intermediate range. The vertical dash line points to the inflection point in nNO(r ), corresponding to a weak shell closure of 8-fold coordination...... 138 A.2 Radial distribution function g (r ) at three different temperatures, P 1 atm. 139 NO = A.3 Radial distribution function g (r ) at three different temperatures, P 1 atm. 139 NF = A.4 Density-density structure factor at T 320 K. See text for the definition..... 140 = A.5 Charge-charge structure factor at T 320 K. See text for the definition...... 140 = A.6 Mean square displacement of cations and anions as a function of time. Red lines: T 360 K; Blue line: T 300 K; Green line: T 240 K. The vertical scale is the = = = same in the two panels...... 141 D¯P ¯2E A.7 Time dependence of the operator: Π(t) ¯ i qi [ri (t t0) ri (t0)]¯ entering = + − t0 the determination of the electrical conductivity. e is the atomic unit of charge. The sum extends over all atoms in the system...... 142 A.8 Logarithm of the angular correlation function of cations (Θ ) and anions (Θ ) + − as a function of time. See main text for the definition of Θ(t). The function has been normalised in such a way that Θ(0) 1...... 142 = A.9 Probability distribution for the breaking time of individual H-bonds in TEA-TF at T 300 K...... 143 = A.10 Probability distribution for the three principal momenta of inertia of [TEA]+ and [TF]− at T 300 K. Masses are measured in atomic mass units (a.m.u.), and = coordinates in Å...... 144

xvii List of Figures

A.11 Intermediate scattering function Fq (t) on a semi-logarithmic scale computed at T 280 K. Time is measured in ps. At any time, curves of higher F value = q correspond to lower q...... 145 A.12 Filled squares and red line: Average potential energy as a function of temperature for a system made of 125 [TEA][Tf] ion pairs and 17 water molecules. The total potential energy is divided by the number of ion pairs. The result for the dry sample (solid dots and green line) is reported for a comparison. The difference of the two sets of data is reported in the inset. All lines are a guide to the eye... 146

A.13 Radial distribution function of the water oxygens (gOW OW (r )) in samples of 125 − TEA-TF ion pairs and 17 water molecules. The T 300 K and T 400 K curves = = have been shifted along the vertical direction by 2 and 4 units, respectively, for the sake of clarity...... 147

A.14 Typical configuration of a water molecule donating H-bonds to two TF− anions. 147 A.15 Lowest energy configuration of a periodic geometry constructed from the ([TEA][TF])4 ground state cluster geometry...... 148

xviii List of Tables

3.1 Diffusion constant of [TEA]+, [TF]− and water molecules as a function of tem- perature in a system made of 125 TEA-TF ion pairs and 17 water molecules (wet samples). Values for dry samples made of 125 ion pairs are reported for a 2 1 comparison. All values in [cm s− ]...... 42 3.2 Electrical conductivity as a function of temperature computed by simulation (Sim., Eq. 3.6) and estimated by the Nernst-Einstein approximation (NE, Eq. 3.7) in a system made of 125 TEA-TF ion pairs and 17 water molecules (wet samples). Values for dry samples made of 125 ion pairs are reported for a comparison. All values in Siemens/m...... 42

4.1 Summary of the Neutron Cross Sections σi. The cross-sections σi are given in 24 2 barns (1 b 10− cm ) at a wave-length λ 5.70 Å...... 51 = = 5.1 Neutron Cross-Section and Chemical Structures of the studied Cations. The 24 2 cross-sections σ are given in barns (1 b 10− cm ) at a wave-length λ 5.5 Å.. 64 = = 5.2 Neutron Cross-Section and Chemical Structures of the studied Anions. The 24 2 cross-sections σ are given in barns (1 b 10− cm ) at a wave-length λ 5.5 Å.. 65 = = 5.3 Experimental Ratios between d-PIL and PIL Number of Molecules...... 69 5.4 Hydrogen-bond characterization in the ground state geometry of the different TEA based PILs...... 73 5.5 Atomic charges of the terminal groups for the different anions...... 74 5.6 Fit results of the FWS measurements for the different protiated samples accord- ing to the three-fold jump-rotation and continuous rotation model...... 75

5.7 Temperature dependence of localized diffusion coefficients (DH), confinement 10 2 1 radii (RH) and characteristic time (τAH). DH is given in 10− m s− , RH in Å and τAH in ps...... 82 5.8 Activation energy for AH localized dynamics following an Arrhenius behaviour 82

5.9 Temperature dependence of the global diffusion coefficient (Dtr), residence time 10 2 1 (τa), and alkyl chain diffusion coefficient (DCH). D is given in 10− m s− , τ0 in 10 2 1 ps and DCH in 10− m s− ...... 83

xix List of Tables

5.10 Temperature dependence of the methyl R2 and methylene R1 radii of confine- ment expressed in Å...... 84 5.11 Activation energy for the global and the alkyl chain dynamics following an Arrhe- nius behaviour...... 85

6.1 Geometric parameters and N-H stretching frequency for the intra-ion H-bond in the gas-phase cations. Distances are in Å , the angle is in degrees and the 1 stretching frequency is in cm− ...... 89 6.2 Geometric parameters for the primary H-bond joining cation and anion. A weaker HB is also present. Distances are in Å and the angle is in degrees..... 92 6.3 Geometric parameters for the intra-cation H-bond measured on the ground state geometry of the neutral ion pair. Distances are in Å and the angle is in degrees...... 93 6.4 Diffusion constants and electrical conductivity of dry DAEt-TF and DABu-TF samples. Data for DAEt-TF at 1 % weight water contamination are given for a comparison. Diffusion constants in cm2/s; electrical conductivity in S/m.... 115

7.1 Neutron cross-sections and chemical formulas of the studied ILs. The cross- 24 2 sections σ are given in barns (1 b 10− cm ) at a wave-length λ 5.75 Å. The = = abbreviations cat. and an. stand for cation and anion, respectively...... 122 1 7.2 Thermal transitions of the investigated ionic liquids at 1 Kmin− scan rate. Tc: crystallization temperature; Tg: glass transition temperature; Tcc: cold crystalliza- tion temperature; Tm: melting point; Tss: solid-solid transition. All temperatures are given in K...... 123 7.3 Activation energy for the global and the alkyl chain dynamics following an Arrhe- nius behaviour...... 128 7.4 Temperature dependence of localized and global diffusion coefficients (D),

confinement radius (R) and residence time (τ0). Dtr and Dalkyl are given in 10 2 1 10− m s− , R in Å and τ0 in ps...... 131 7.5 Temperature dependence of localized and global diffusion coefficients (D),

confinement radius (R) and residence time (τ0). Dtr and Dalkyl are given in 10 2 1 10− m s− , R in Å and τ0 in ps...... 132 7.6 Temperature dependence of localized and global diffusion coefficients (D),

confinement radius (R) and residence time (τ0). Dtr and Dalkyl are given in 10 2 1 10− m s− ,Ralkyl in Å and τ0 in ps...... 133

xx 1 Introduction and motivation

Ionic liquids (ILs) are compounds entirely constituted of ions, thus, presenting ionic conduc- tivity [1]. The term ILs includes traditionally known liquids like molten or fused salts such as NaCl, KCl, LiCl, etc., which have high melting points [2]. However, during the past lustra the term ILs has been mainly reserved for those liquids whose melting points or glass transitions falls below 100 ◦C. In particular, those ILs which are liquid at or around room temperature are called room temperature ionic liquids, RTILs [3]. Aqueous solutions of salts are not be considered as ILs, since they are not exclusively made up of ions.

ILs have received special attention from the scientific community because of a variety of reasons [2]. They have opened the path for the research of ionic systems in chemistry at room temperature. This topic, pioneered by Walden and Wilkins, reported the discovery of ionic organic compounds of low melting temperature 12 ◦C [4,5]. The mixture of two ILs is also an IL, thus, the number of possible ILs is in principle unlimited which makes them appealing for many types of applications and research. At present, the number of RTILs synthesised and characterised exceeds 500. Earl and Seddon estimated the total number to be over one billion [6]. ILs do not go over redox reactions within wide electrochemical windows. A narrow electrochemical window ( 2 V) limits the role of standard electrolytes in energy conversion ∼ electrochemical devices. RTILs have electrochemical windows of up to 5 V, as shown by experiments [7,8] and by density functional theory computations [9]. In addition, ILs can be used as catalyst or reaction media for a multiple number of new chemical reactions [10,11].

RTILs usually include a bulky (with linear alkyl chains) and not very symmetrical cation, and a weakly-coordinating anion [3]. Figure 1.1 shows some of the most common cations and anions used in the synthesis of RTILs. In fact, the low charge density and low molecular symmetry of the ions are responsible of the low melting points of RTILs [12]. This, in addition to their negligible vapour pressure, thermal stability and wide liquid range has made ILs suitable for the construction of very specialized types of materials, such as mirrors for telescopes working

1 Chapter 1. Introduction and motivation in the outer space [13]. The deposition of metal films on the IL 1-ethyl-3-methylimidazolium ethylsulphate has demonstrated to improve the reflectivity as compared to usual polymer substrates (see Figure 1.2). Having a better reflectivity is a key factor for the investigation of the infrared regionElectrochemistry of the spectrum in Room Temperature in Astronomy. Ionic Liquids ... 1249

Scheme 1. The structures and nomenclature of various cations and anions commonly em- Figure 1.1 – Structureployed in the and synthesis nomenclature of second, third of variousand forth generation commonly RTILs. used cations and anions in the synthesis of RTILs from Ref. [3]. asupportingelectrolytein,forexample,acetonitrile[7].Theuseofatri- The chemicalfluorotris(pentafluoroethyl)phosphate structure of the ionic liquids exerts [FAP]− abased strong ionic influence liquid significantly on their physical and widened the anodic component of the electrochemical window of acetonitrile, chemical properties, arising from the interplay of Coulomb forces, dispersion forces and hydrogen bonding (HB) [14–16]. As already stated, the low melting point of ILs is achieved by a proper combination of cation and anion. LowBrought cation to symmetryyou by | Lib4RI and Eawag-Empa low hydrogen bonding Authenticated Download Date | 5/4/19 5:27 PM 2 LETTERS NATURE | Vol 447 | 21 June 2007

100 Ag on Cr on ionic liquid 0.79535 Ag on PEG 80 µm 0.75805 60 64 Ag on ionic liquid 40 mm Reflectivity (%) 20 51 0 58 mm 71 0 500 1,000 1,500 2,000 2,500 Wavelength (nm) Figure 2 | Three-dimensional map of a small section of a silver-coated liquid mirror. The 1.25 cm2 area is made of a 30-nm-thick silver layer Figure 1.2 1 | –Reflectivity Reflectivity curves curves obtained obtained for for silver-coated silver-coated liquids liquids. fromWe Ref. [13]. deposited on a 5-nm-thick chromium layer deposited on an ionic liquid. It conducted a number of coating experiments by vaporizing in vacuum a shows a respectably small peak-to-valley deviation of only 0.0373 mm, which reflective silver layer on to liquids. The figure shows our best reflectivity is a hundredth of a wave at 4 mm. This is close to the standard deviation of the curve with a hydrophilic block polymer (PEG). We then successfully coated 0.03 mm error of measurement of our interferometer. The measurements ability combined with sizeable anions usually decreases the ILs melting point. The thermal an ionic liquid, an important milestone because ionic liquids have negligible were made with a Mach–Zender interferometer operating at a wavelength of stabilityvapour of ILs is pressures. limited by The the figure strength shows of their a reflectivity intramolecular curve bonds obtained and for the a strength silver- of the632.8 nm. hydrogencoated bond ionic network. liquid Higher and for thermal silver stabilites deposited can on be chromium obtained by deposited proper anion on an selection, thus many ILs have been shown to be thermally stable up to 400 C [17]. For imidazolium- ionic liquid. The silver on chromium on ionic-liquid coating◦ is a noticeable showed that the film is made of colloidal particles having diameters of based ILs,improvement the density over is inversely the silver proportional coating on to PEG. the The length curves of the do alkyl not chain extend and can be a few tens of nanometres. Indeed, ionic liquids have been reported to furtherbeyond tuned as 2.2 a functionmm because of the that counter is the anion sensitivity [18]. The limit viscosity of our of equipment. the ILs is determined by induce stable colloid formation25–27. This appears to be the reason the strengthPresumably of the dispersion one can extrapolate forces and by that the the tendency reflectivity to hydrogen increases bonding further formation in the [19]. why the reflectivities seen in Fig. 1 are lower than the reflectivity of Apart frominfrared. the already We also mentioned noted that properties, as the temperature ILs exhibit of large deposition heat capacities was lowered, and fast heat both the quality of the film and its infrared reflectivity improved. metallic silver. Our next successful attempt to improve film reflectiv- transfer, some are highly water stable, have high conductivity and large electrochemical ity involved the initial deposition of a chromium film, followed by potential windows [20–25]. This manifold of characteristics make ILs a highly interesting subsequent deposition of a silver layer on the chromium layer. The researchof topic a reflective and suitable metal for on the liquids. described We applications experimented and further mostly more. with silver, which possesses the high reflectivity needed for an LLMT. Before nucleation density is greater for chromium than it is for silver, so Dependingidentifying on the nature cryogenic of the liquids cation, the suitable ILs can for be an classified LLMT, in one two must groups: deter- Protic ionicchromium is far easier to deposit than silver. The thickness of a liquidsmine (PILs) the and physical aprotic ionic characteristics liquids (AILs). needed PILs are for produced successful by an coating. equimolar To neutral-chromium layer deposited on an ionic liquid grows significantly izationour of a knowledge,Brønsted acid liquids with a Brønsted had never base, been where vacuum a proton coated is transferred before, from so we the acidfaster than an analogous silver layer, and a silver layer deposited on to the basesampled [26] leading the parameter to an explicit space protonation using a variety of the cation. of liquids. This Most allows experi- the formationthis intermediate chromium layer grows substantially faster than a of highlyments oriented were hydrogen-bonds unsuccessful, failingand the to existence coat the of liquids competing with hydrogen-donor a reflective andsilver layer directly deposited on an ionic liquid. Figure 1 shows the hydrogen-acceptorlayer, but we sites did [27 succeed–29]. AILs, in in coating contrast, a consistsilicone of oil non (although explicitly protonated it gave an cationsreflectivity curve of a silver-on-chromium-on-ionic-liquid mirror, and anionsunusable [2]. wrinkled skin). Then we performed two important experi- which is significantly better than the reflectivity curve of a silver- ments. First, building on our experience with nanoparticles16,17, we on-ionic-liquid mirror. Figure 2 shows the three-dimensional map In this context,successfully HB appears coated to the be one hydrophilic of the most block important copolymer directional PPG–PEG–PPG intermolecular interac-of a small (1.25 cm2) section of a mirror made of a 30-nm-thick silver tions [30(50%]. HB is PEG; essential PEG, to determine polyethylene the structure, glycol; function PPG, polypropylene and dynamics of glycol) many systems.layer deposited on a 5 nm chromium layer deposited on the HBs can stabilize the transition states for catalysis in fuel cell materials and enzymes [27,31–33], with silver. The observed reflectivity curve is shown in Fig. 1 and [emim][EtOSO3] ionic liquid. The optical quality of the surface is drive thewhile self-assembly being clearly of biomolecules inadequate [34] for in supramolecular our purpose, chemistry, it was a [significant35] and determineexcellent. the orderingimprovement in domains on (from the micellescoatings to on liquid silicone crystals) oil. [27,30,36]. Furthermore, the HB Although the reflectivities shown in Fig. 1 are not yet adequate, it is From the abovementioned coating and related results, it was clear now only a matter of technological improvement. This will require 3 that the ideal liquid to form the base for a highly reflective, uniform better vacuum facilities and more experiments to improve the coat- metal film would have effectively zero vapour pressure, high viscosity ing technique and reflectivity. We have already found that the reflec- and a low melting point, while being effectively involatile in vacuo. tivities shown in Fig. 1 can be improved by increasing the thickness of This property set is found for some members of a suite of fluids the silver layer. However, heating of the metallic layer from the heat- known as ionic liquids18,19. Ionic liquids are salts which are liquid ing element prevents us from increasing the thickness at present. We at temperatures below 373 K, composed entirely of ions, and usually are thus experimenting with cooling techniques, but for technical possess no significant vapour pressure at room temperature or reasons, they are difficult to implement in a vacuum tank. We will below20–22. They are also often highly viscous, and may be either also be experimenting with different coating techniques. hydrophilic or hydrophobic. Following this logic, we successfully We have shown here that various liquids can be successfully coated coated a hydrophilic commercially-available ionic liquid, 1-ethyl- with a reflective metal surface. Moreover, for the coated liquid to 3-methylimidazolium ethylsulphate ([emim][EtOSO3]; commer- function as a liquid primary telescope mirror on the Earth’s moon, it cially known as ECOENG 212), which solidifies at 175 K (ref. 23). is essential that the liquid have a low vapour pressure as well as a low This was a transformational breakthrough: Fig. 1 shows a reflectivity freezing temperature. These two requirements have been met by curve obtained for silver-coated [emim][EtOSO3]. There is substan- using an ionic liquid. In fact, the metal coating of an ionic liquid tial improvement with respect to the curve obtained using PEG- has been a defining demonstration, since it is essential for the poten- derived liquids as a substrate. Moreover, as there are at least a million tial implementation of an infrared LLMT—an instrument which will (106) simple ionic liquids, and a trillion (1018) ternary ionic liquid revolutionize astronomical observations of the early Universe. systems24, there is a phenomenally wide choice for optimizing the properties of the liquid substrate, to minimize melting point and Received 15 November 2006; accepted 4 May 2007. volatility, while obtaining optimal infrared reflectivity. 1. Gardner, J. P. et al. The James Webb Space Telescope. Space Sci. Rev. 123, A major problem that we encountered with the direct deposition 485–606 (2006). of silver on an ionic liquid is that it tends to diffuse in the liquid 2. Borra, E. F. The case for liquid mirror in a lunar telescope. Astrophys. J. 373, 317–321 (1991). substrate, making it difficult to obtain a thick layer. We note, how- 3. Girard, L&. Borra, E. F. Optical tests of a 2.5-m diameter liquid mirror. II. Behavior ever, that this appears to be a problem only during deposition. After under external perturbations and scattered light measurements. Appl. Opt. 36, deposition, the surface coating is stable. Indeed, electron microscopy 6278–6288 (1997). 980 © 2007 Nature Publishing Group Chapter 1. Introduction and motivation tendency of the anion usually determines the IL-water miscibility. For example, the selection of fluorinated anions defines the hydrophobicity of the IL [37]. Usually, HBs in ILs are stronger for PILs and weaker or absent for AILs, thanks to the explicit protonation of the cation of the former.

At this point a formal definition for HB is needed; we refer to the general explanation proposed by Steiner [30]: An X H Y interaction is called a "hydrogen bond" if 1. it constitutes a local − ··· bond, and 2. X H act as a proton donor to Y. Thus, the X H group is called the donor and Y − − the acceptor. The strength of the HB can be classified regarding its geometrical disposition. Symmetrical, "linear" and highly directional HBs are customarily indication of strength, i.e. similar X H and H Y distances, and the XHY angle close to π [27]. − ··· 6 HB and the above mentioned properties of ILs are studied by a broad array of experimental methods. By means of differential scanning calorimetry, it is possible to determine the phase boundaries of these liquids [38–41]. Electrochemical properties, such as the width of the electrochemical potential window are usually measured by cyclic voltametry [3,21, 42,43]. Numerous studies on the structure in bulk and in solution, and diffusion coefficients deter- mination are obtained via pulsed field gradient nuclear magnetic resonance (PFG-NMR) as well as with neutron scattering [44–49]. Information regarding the chemical bonding in ILs are usually accesible via infrared and Raman spectroscopy [14,15,50 –52]. Furthermore, the ILs bulk structure is routinely determined via X-ray diffraction [38,53,54], colloidal aggregation properties of ILs in water have been estimated by dynamic light scattering [55–58]. Last but definitely not least, via molecular dynamics and ab initio simulation it is possible to determine ground state structures of dimers, small clusters, bulk IL properties which are a key element in the interpretation of experimental measurements on these liquids [43,59–63].

The idea of the present thesis is to study the microscopic details of HB and proton conduc- tivity in ILs by means of neutron scattering in combination with computational methods. Understanding the connection between proton conduction and HB is vital to respond to the increasing demand for high power, high capacity electrochemical energy conversion devices such as batteries, supercapacitors, fuel and photovoltaic cells. Thanks to their multiple and beneficial properties, ILs are leading candidates for innovative electrolytes for energy con- version applications [64–70]. In this regard, this thesis presents succinctly in Chapter 2 the basics of neutron scattering and computer simulation. The investigation was motivated in a first stage by the characterisation of dynamical properties of the triethylammonium-triflate (TEA-TF) PIL by elastic and quasi-elastic neutron scattering QENS of Ref. [71]. In this study, a protiated and a partially deuterated sample of TEA/TEAD-TF were used to enhance the ability of neutron scattering to focus on specific dynamical modes [72]. The analysis of the neutron signal revealed a variety of wide amplitude, sub-diffusive motions, whose precise nature could not be unambiguously determined from the available experimental data [72].

4 In Chapter 3, we tackled this issue using ab initio and molecular dynamics simulations (MD) based on empirical force fields, in particular, we have analyzed a variety of properties rang- ing from thermodynamic functions to diffusion coefficients and electrical conductivity, to the structure, distribution and dynamics of HBs and the influence of water contamination throughout the system [72]. Eventually, we found that molecular rotations account for the fast dynamics measured in the experimental paper and we discarded the possibility of having Grotthuss like charge transport mechanisms in TEA-TF.

In Chapter 4 we complemented the interpretation of our simulations by comparing the find- ings of Chapter 3 with the outcomes of neutron measurements on TEA-TF and TEAD-TF with polarization analysis. In this way, we could experimentally separate the coherent and nuclear spin-incoherent scattering contribution of the samples, and state the relation between the structure and the dynamics of this sample PIL. Utilizing the coherent signal we could describe the correlations affecting the collective dynamics at different length-scales in a ps time-window. The nuclear spin-incoherent scattering was used to quantify the diffusion coefficients of the single-particle dynamics, which appeared to be faster than for Ref. [71]. The fast mode of TEA-TF in the liquid phase was associated to the confined dynamics of the ion pair.

In Chapter 5, we addressed the question of the anion influence on the dynamics of the TEA cation. For this, we performed scans of the elastic and inelastic intensity, quasi-elastic neutron scattering experiments and ab initio simulations for samples of TEA and TEAD with four differ- ent types of hydrogen free anions, which varied in size and, thus, in structure. With the elastic and inelastic scans we could observe the onset of the methyl (R CH ) group rotation, alkyl − 3 chain librations and the start of the ions rotations as proposed in Chapter 3. In the liquid phase, correlations between localized and long-range diffusion with physicochemical properties of these liquids such as viscocity, conductivity and density were found. The calculated potential energy surface (PES) of our ILs ion pairs pointed to the presence of strong HB between the ions which make unlikely non vehicular charge transport mechanisms for this type of systems.

In our search for Grotthuss like charge transport mechanisms in PILs, we studied in Chapter 6 diamine-based PILs systems, as the one proposed in Ref. [73], combined with the TF anion. We performed computational simulations to study these PILs, i.e. ab initio simulations of the single ions, ion pairs and small clusters together with extensive MD simulations of larger systems based on empirical atomistic force fields. The ab initio simulations revealed that the PES of the proton of the cation has a double minimum along the HB, then opening paths for intra- and inter-cation jumps of the proton in association with the anions. The MD simulations, as in Chapter 3, were based on a rigid-ion force field; they allowed to quantify the available paths for proton conduction independent of vehicular mechanism. The connected paths included up to 80 cations ( 30 Å) and required anions acting as a shuttle between adjacent ∼

5 Chapter 1. Introduction and motivation cations. This made the whole processes relevant and explained the enhancement of the conductivity in the liquid.

Chapter 7 condensed all the methods used among this thesis and serves as an outlook for future research. The chapter presents preliminary results of the study of selected AILs. We investigated the effect of HB on imidazolium based AIL, to this aim, we methylated the donor site and compared the dynamics to the non-methylated species. In addition, we studied the influence of the anion selection in the whole dynamics of the AILs and performed simulations to optimize the ground state geometry of the ILs, which helped interpret our QENS data.

The results obtained during the PhD are summarized within this thesis and where published in peer-reviewed scientific journals as listed below.

(i) Juan F. Mora Cardozo, J. P.Embs, A. Benedetto, and P.Ballone, Equilibrium Structure, Hydrogen Bonding, and Proton Conductivity in Half-Neutralized Diamine Ionic Liquids, The Journal of Physical Chemistry B 2019 (accepted), DOI: 10.1021/acs.jpcb.9b00890

(ii) Tatsiana Burankova1, Juan F. Mora Cardozo1, Daniel Rauber, Andrew Wildes, and Jan P. Embs, Linking Structure to Dynamics in Protic Ionic Liquids: A Neutron Scattering Study of Correlated and Single-Particle Motions, Scientific Reports 2018 8 (1), 16400, DOI: 10.1038/s41598-018-34481-w

(iii) Juan F. Mora Cardozo, T. Burankova, J. P. Embs, A. Benedetto, and P. Ballone, Density Functional Computations and Molecular Dynamics Simulations of the Triethylammo- nium Triflate Protic Ionic Liquid, The Journal of Physical Chemistry B 2017, 121 (50), 11410-11423, DOI: 10.1021/acs.jpcb.7b10373

(iv) Tatsiana Burankova, Giovanna Simeoni, Rolf Hempelmann, Juan F.Mora Cardozo, and Jan P. Embs, Dynamic Heterogeneity and Flexibility of the Alkyl Chain in Pyridinium- Based Ionic Liquids, The Journal of Physical Chemistry B 2017, 121 (1), 240-249, DOI: 10.1021/acs.jpcb.6b10235

Publications in preparation:

(i) Juan F.Mora Cardozo, Tatsiana Burankova, Daniel Rauber, Frederik Philippi, Dina Klip- pert, Rolf Hempelmann, Jacques Ollivier, Bernhard Frick and J. P.Embs. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

1Equal contribution

6 (ii) Juan F. Mora Cardozo, Tatsiana Burankova, Daniel Rauber, Rolf Hempelmann and J. P. Embs. Methylation impact on the dynamics and structure of imidazolium-based ionic liquids

(iii) N. C. Forero-Martinez, R. Cortes-Huerto, Juan F.Mora Cardozo, and P.Ballone. Thermodynamics and kinetics of water absorption and evaporation through the surface of the half-diamine triflate room temperature ionic liquid. A molecular dynamics study

7 2 Neutron scattering and computational methods

Neutrons have specific characteristics that distinguish them from other particles. They are uncharged units with spin 1/2 that penetrate deeply the matter, and come close to the nuclei as they do not need to overcome the Coulomb barrier. Therefore, neutrons are scattered by nuclear forces and for some nuclide such as hydrogen, they can be ample. This chapter will explain the basic theory and terminology of neutron scattering and computational chemistry.

2.1 Neutron scattering

2.1.1 Scattering cross-sections

In a neutron scattering experiment, a beam of neutrons is incident to a target or scattering system (Figure 2.1), which is usually a set of atoms organized in a crystal, a polymer, a liquid, a gas, etc. The incoming neutrons are represented by a plane wave traveling in the direction of the wave vector k (Equation 2.1), and normally, just a small fraction of them interacts with the scattering system. The scattered neutrons are subsequently detected and expressed in terms of a quantity called the cross-section. In our experiments, we measured quantities proportional to the so called double-differential cross-section which is defined in Equation 2.2.

ik r Ψ ve · (2.1) incident =

8 2.1. Neutron scattering

Direction θ, φ dS

r φ

dΩ Incident k θ neutrons axis Target

Figure 2.1 – Scattering experiment geometry [74].

Number of neutrons scattered per second into the solid angle

d 2σ dΩ in direction θ,φ with final energy between E 0 and E 0 dE 0 : + (2.2) dΩdE = Number of incident neutrons per unit area per second dΩdE 0 × 0 Due to the short range of the interaction between neutrons and the atoms of the target, the scattered neutrons at the point r are described by a spherical wave:

b Ψ exp(ik0r ), (2.3) scattered = − r

where k0 is the norm of the wave vector of the scattered neutrons and b is the scattering length. The latter is independent of the scattering direction and represents the effective range of the nuclear potential; it varies from atom to atom, even if the target is composed by a single element, as b depends upon two factors: the isotope proportion and the nuclear-neutron spin state [74,75]. Therefore, it is more convenient to express Equation 2.2 as the sum of two terms:

d 2σ µ d 2σ ¶ µ d 2σ ¶ , (2.4) dΩdE 0 = dΩdE 0 coh + dΩdE 0 inc where the first summand considers the scattering coming from an average scattering length

9 Chapter 2. Neutron scattering and computational methods

2 (σcoh 4πb ) or also called coherent scattering and the second term accounts for the de- = ³ 2´ viations of the scattering length from the mean value (σ 4π b2 b ) and is called the inc = − incoherent scattering.

2.1.2 Correlation functions in nuclear scattering

The functional form of the double-differential cross-section can be written in terms of the so called correlation functions. They are expressions directly related to the nature of the scattering system, thus numerous properties of it can be calculated. Equation 2.4 can be stated in terms of the so called coherent and incoherent dynamical structure factor,

2 d σ N k0 (σcohScoh(Q,E) σinc Sinc (Q,E)), with (2.5a) dΩdE 0 = 4π k + Z µ ¶ 1 1 X ­ ¡ ¢ ¡ ¢® iE Scoh(Q,E) dt exp iQ R j (0) exp iQ R j (t) exp t , and (2.5b) = 2π N − · 0 · − ħ j j 0 ħ Z µ ¶ 1 1 X ­ ¡ ¢ ¡ ¢® iE Sinc (Q,E) dt exp iQ R j (0) exp iQ R j (t) exp t , (2.5c) = 2π N − · · − ħ j ħ

where N is the number of nuclei comprising the target, Q is the scattering vector (Q : k k0), = − E the neutron energy change (E : E E 0) and ... is the thermal average of the Heisenberg = − 〈 〉 operators, which embrace the position of all the atoms of the scattering system and its energy state [74]. The summation in Equation 2.5b runs over all pairs of nuclides, thus it provide us with information of the self and pair position correlation of the nuclei as a function of the time, so it is originated from interference effects. In contrast, the summation in Equation 2.5c runs on a single index and gives information of the self position correlation of a nucleus as a function of the time, which can be associated with single particle dynamics [76].

In addition, the coherent and the incoherent scattering functions are the Fourier transform in space and time of the Van Hove pair (Gpair(r,t)) and self (Gself(r,t)) correlations functions respectively, which are proportional to the conditional probability of finding a particle at position r 0 at a time t 0 if at the time t 0 (such that t t 0) a particle was at position r [77]. = <

Z 1 X 3 ­ ¡ ¢ ¡ ¢® Gpair(r 0,t 0) d r 00 δ r 0000 R j (0) δ r 0000 r 0 R j (t) , (2.6a) = N − 0 + − j j 0 Z 1 X 3 ­ ¡ ¢ ¡ ¢® Gself(r 0,t 0) d r 00 δ r 0000 R j (0) δ r 0000 r 0 R j (t) (2.6b) = N j − + −

10 2.2. Polarisation analysis

2.2 Polarisation analysis

In neutron scattering experiments with polarisation analysis, the spin state, the energy and the momentum of the neutron are determined. This delivers us additional information about the scattering system, and furthermore separates the coherent scattering contribution from the incoherent part.

2.2.1 Scattering length operator

Consider a target composed by identical nuclei and spin I 0. The system formed by a neutron 6= (spin angular momentum 1/2) and a nucleus have a total spin t, which can take two values: t I 1/2 or t I 1/2. Each t has a specific scattering length b+ and b−, respectively. If = + = − |+〉 and are eigenstates of I 1/2 and I 1/2, accordingly, the scattering length operator (bˆ) |−〉 + − should satisfy the following conditions:

bˆ b+ , (2.7a) |+〉 = |+〉 bˆ b− , (2.7b) |−〉 = |−〉

In addition, the square of the neutron-nucleus system spin operator can be written as:

µ σˆ ¶ µ σˆ ¶ σˆ 2 tˆ2 Iˆ Iˆ Iˆ2 σˆ Iˆ, (2.8) = + 2 · + 2 = + 4 + · where σˆ is the spin operator composed of the Pauli spin matrices and the states and |+〉 |−〉 are eigenfunctions of tˆ2, Iˆ2 and σˆ 2/4, furthermore their respective eigenvalues (in units) are: ħ t(t 1), I(I 1) and 1/2(1 1/2) [74]. Simultaneously, these two states are eigenfunctions of + + + σˆ Iˆ and their eigenvalues are I for and (I 1) for , so the scattering length operator · |+〉 − + |−〉 read as:

bˆ A Bσˆ Iˆ, (2.9a) = + · bˆ b+ (A BI) , (2.9b) |+〉 = |+〉 = + |+〉 bˆ b− (A B(I 1)) , (2.9c) |−〉 = |−〉 = − + |−〉

11 Chapter 2. Neutron scattering and computational methods

b+(I 1) b− I b+ b− where A 2+I 1+ and B 2I− 1 . To evaluate the spin-state cross-section, we have to =­ ¯ + = + ¯ ® calculate σ ¯bˆ σ for all the initial ( σ ) and final (¯σ ) neutron spin state combinations. If 0 | 〉 | 〉 0 we denote the spin-up state of the neutron with , and with the spin-down state of the |↑〉 |↓〉 neutron we get [74]:

bˆ A BI bˆ A BI (2.10a) 〈↑| |↑〉 = + z 〈↓| |↓〉 = − z bˆ B(I i I ) bˆ B(I i I ) (2.10b) 〈↑| |↓〉 = x − y 〈↓| |↑〉 = x + y

2.2.2 Coherent and incoherent scattering

Coherent scattering

Coherent scattering is proportional to the average of the scattering length (Equation 2.4). So, if we consider the spin transition from to (non spin-flip), from Equation 2.10a b is: |↑〉 |↑〉

b A BIz s-s isotope (2.11) |↑〉→|↑〉 = 〈〈 + 〉 〉 where ... denotes two different averages. ... is the average over the 2I 1 eigen- 〈〈 〉s-s〉isotope 〈 〉s-s + values of I and ... is the average over the isotopic composition of the system. A and B z 〈 〉isotope are isotope specific (Equation 2.9), moreover if the scattering system has the nuclear spins ran- domly oriented, i.e. I , ­I ® and I are equal to zero, then from Equations 2.10a and 2.10b 〈 x 〉 y 〈 z 〉 we conclude that the coherent scattering does not change neutron spin-state,

2 1 ³ 2 2 ´ 2 b b b A isotope (2.12) = 2 |↑〉→|↑〉 + |↓〉→|↓〉 = 〈 〉

Incoherent scattering

2 In contrast to the coherent scattering, the incoherent scattering is proportional to b2 b . Lets − consider once more a system with random oriented nuclear spins, then using Equations 2.10a and 2.12 we can write the neutron-spin transition from to as follows: |↑〉 |↑〉

³ 2´ 1 b2 b ­A2® A 2 ­B 2I(I 1)® , (2.13) − = isotope − 〈 〉isotope + 3 + isotope |↑〉→|↑〉

12 2.3. Incoherent quasi-elastic neutron scattering and stochastic processes which in addition, is the same result for the transition. For the spin-flip transition |↓〉 → |↓〉 (Equation 2.10b) we have that:

³ 2´ 2 b2 b ­B 2I(I 1)® (2.14) − = 3 + isotope |↑〉→|↓〉 ∨ |↓〉→|↑〉

Finally, for a monoisotopic scattering system we have: ­A2® A 2 , thus replacing isotope = 〈 〉isotope this in Equation 2.13 we notice that the cross-section for the spin-flip process doubles the one for the non spin-flip.

2.3 Incoherent quasi-elastic neutron scattering and stochastic pro- cesses

The term quasi-elastic neutron scattering (QENS) refers in a wide manner to those inelastic processes that are very close in energy to the elastic scattering (E 0) and are outside the = Bragg reflections [78]. In general, QENS is originated from stochastic processes and has in principle a coherent and an incoherent part. The former provide us with information on interference effects and correlated motion of the atoms, whereas latter yields information about the single-particle dynamics [79]. From now on, we will focus on the single-particle dynamics and refer to the incoherent quasi-elastic neutron scattering as QENS.

Diffusion processes and vibrations originate the QENS signal, however, they are in general dynamically independent since they occur at different time scales [78]. Therefore, they are separable processes, and the scattering function (Equation 2.5c) is written as the convolution of these two independent processes,

S (Q,E) Svib (Q,E) Sdiff (Q,E), (2.15) inc = inc ⊗ inc where denotes the convolution operator. Usually, the vibrational processes (Svib (Q,E)) ⊗ inc accessible by QENS do not change the shape of the spectra, but they reduce the signal’s intensity as a function of Q. This effect is summarized in a term called the Debye-Waller factor (exp( 2W ))[78]. Furthermore, the term Sdiff (Q,E) encloses the contributions originated from − inc rotational and translational processes. Rotations are a spatially restricted type of motions, they are usually faster than the spatially unrestricted dynamics. Therefore, they can be separated

13 Chapter 2. Neutron scattering and computational methods and we can rewrite Equation 2.15 as:

S (Q,E) exp( 2W )¡S (Q,E) S (Q,E)¢. (2.16) inc = − global ⊗ r ot

Mathematical models describing stochastic motions have to be substituted in Equation 2.16in order to get meaningful information about the dynamical processes in the scattering system. They are constructed by solving differential equations or a system of differential equations of the Van Hove self-correlation function (Equation 2.6b) and then Fourier transformed to have, when possible, an analytical expression for the incoherent scattering function.

2.3.1 Fickian diffusion

Translational diffusion can be imagined as a cyclical process, i.e. starting from an arbitrary origin a particle is found at r0 at time t0, then it travels through an unspecified mechanism a distance l1 in a time t1, at this point the particle starts a new move l2 in a time t2 which is uncorrelated with the previous one, an so on indefinitely. This process can be modelled 3 by the rate of change of Gs(r ,t) with respect to time, where Gs(r ,t)d r is interpreted as the conditional probability of finding a particle at r around d 3r on a time t 0 if the same particle > was at the origin at t 0, G (r ,t) satisfies a diffusion equation: = s

∂Gs(r ,t) 2 Ds Gs(r ,t), (2.17) ∂t = ∇

where Ds is the self-diffusion coefficient. A solution for 2.17 must fulfil two conditions: At time t 0 it should behave as a delta function (G (r ,0) δ(r )) and have probability one over = s = the space (R G (r ,t)dr 1). A function fulfilling this two boundary conditions has a Gaussian s = shape:

1 µ r 2 ¶ G (r ,t) exp (2.18) s = 3 − (4πDs t) 2 4Ds t

14 2.3. Incoherent quasi-elastic neutron scattering and stochastic processes

Fourier transforming 2.18 in time and space, we get the dynamical structure factor for diffusion:

2 1 DsQ S(Q,E) ħ , (2.19) = π E 2 ¡ D Q2¢2 + ħ s which is a Lorentzian function L(Γ,E) with full-width at half maximum (fwfm) Γ 2 D Q2, = ħ s

Γ 1 2 L(Γ,E) 2 . (2.20) = π E 2 ¡ Γ ¢ + 2

2.3.2 Jump diffusion

Fickian diffusion is adequate to describe motions over long distances and times (r,t) in comparison to the time and and length of the individual diffusion steps ti and li , respectively. However, if we were able to measure S(Q,E) for small values of r and t, close to the individual diffusion steps, the scattering law for the jump diffusion will differ from Equation 2.19. The so called jump diffusion model considers that a diffusing particle stays at a given place for some time τ0 [80], where it vibrates around its equilibrium position. After this time has elapsed, the particle moves instantaneously to a new equilibrium position, at a distance l from its original site, where it starts again to vibrate for a given time before performing a new jump to another equilibrium position, and thus, repeating the process in a cyclic way. Furthermore, the diffusion jumps are assumed to be not correlated, as τ t is considerable larger than the 0 À i time that the particle needs for the individual jumps. The shape of the scattering function for ¡ ¢ the jump diffusion is the Lorentzian L Γglobal ,E , however, its hwhm accounts for the jumps being isotropic and having an exponential probability distribution function for the length.

2 DsQ Γglobal ħ (2.21) = 1 D Q2τ + s 0

For τ 0, we recover the DQ2 behaviour for the Fickian diffusion, whereas for larger Q values, 0 → Γglobal ħ , so we can measure the residence time of the particle. → τ0

15 Chapter 2. Neutron scattering and computational methods

2.3.3 Three-fold jump rotation

This model is a special case of jump rotation among N energetically equivalent sites [78]. Motivated by molecular symmetry, the diffusing particle visits a finite number of spots under its rotation, the dynamical structure factor is composed of a delta function (accounting for the restricted nature of the dynamical process) and a broadening L(Γres,E). If the sample target has no preferred orientation, i.e. is not a single crystal, the scattering function has to be averaged over all the possible directions of Q in the solid angle Ω (powder average), thus S(Q,E) can be written as follows:

3 1 ³ ³ ´´ 2 ³ ³ ´´ 2ħτ S(Q,E) 1 2j0 p3QR δ(E) 1 j0 p3QR (2.22) = 3 + + 3π − ¡ 3 ¢2 2 ħ E 2τ +

th where R is the radius of rotation, jk (x) the k order spherical Bessel functions, τ is the residence time. Furthermore, the factor accompanying the delta function is called the elastic incoherent structure factor (EISF) and contains all geometrical information of the restricted dynamics.

2.3.4 Continuos rotational diffusion

Similar to the long range diffusion, if we consider a particle to perform a small angular diffusive step θ in a time τr with respect to an arbitrary origin, the particle orientation distribution function G(Ω,Ω0,t), where G(Ω,Ω0,t)dΩ is defined as the conditional probability of finding a particle with orientation centred in Ω around dΩ at time t provided that it was at Ω0 at 1 t0 t, follows Equation 2.17 with Dr [81]. This distribution is analogous to the Van Hove < = 6τr self-correlation function for Fickian diffusion and the dynamical structure factor for this type of motions can be written as:

l(l 1) + ħ 1 X∞ 6τr S (Q,E) j 2(QR)δ(E) (2l 1) j 2(QR) (2.23) cont 0 l ³ ´2 = + π + l(l 1) 2 l 1 + ħ E = 6τr + where R is the radius of rotation, j (x) the l th order spherical Bessel functions and l(l 1) is l + the rotational angular momentum playing the role of Q2 as in Equation 2.19.

16 2.4. Time-of-flight-spectrometers

2.3.5 Gaussian model

The so called Gaussian model describes confined translational motion of particles in a finite volume. Thus, in contrast to previously described models, it explicitly considers the spatial boundary conditions of the processes through a Gaussian well, which in addition is a continuos and an infinitely derivable function. Therefore, it imposes a soft boundary where the particle is confined to diffuse [82]. Moreover, the model does not assume jumps among isoenergetic sites, and make the particle displacements to be self-correlated with joint probability density:

  2 2 1 r1 r2 2r1r2ρ1,2 p(r1,r2,ρ1,2) exp + − , (2.24) q ­ ®³ ´ = 2π­r 2® 1 ρ2 − 2 r 2 1 ρ2 − 1,2 − 1,2 where r and r are two displacements from a fixed origin at time t and t respectively, r 2 1 2 1 2 〈 〉 is the size of the region where the particle is confined, and ρ1,2 is the correlation coefficient between the two mentioned displacements. For a stationary random processes, the correlation coefficient is a function of time and its simplest form is an exponential:

µ t ¶ ρ1,2 ρ(t) exp , (2.25) = = −τ0

where τ0 is the correlation time of the displacements, and represents the mean time for a 1/2 particle to explore a segment of length 2­r 2® . Finally, the dynamic structure factor for this model is written as:

 n D  ¡­ 2® 2¢n ħ loc 2 2 1 r Q r 2 r Q  X∞  S(Q,E) e−〈 〉 δ(E) 〈 〉 , (2.26) =  + π n! ³ n D ´2  n 1 ħ loc E 2 = r 2 + 〈 〉

r 2 where Dloc 〈 〉 is the diffusion coefficient of the confined dynamics. = τ0

2.4 Time-of-flight-spectrometers

The use of time-of-flight (TOF) spectrometers allows us to measure the intensity of scattering processes as a function of the neutron energy E and momentum transfer Q.

17 P1: JYS Trim: 189mm 246mm × JWST068-18 JWST068-Boudenne July 7, 2011 12:50 Printer: Yet to come

Chapter 2. Neutron scattering and computational methods Characterization of Multiphase Polymer Systems by Neutron Scattering 721

Detectors

4 m

Beam stop

Choppers Focusing neutron guide Choppers Monitor Sample Radial collimator 8 m 1.2 m

Figure 18.11 Time of flight spectrometer: Schematic layout of the instrument IN5 at the ILL [15]. Figure 2.2 – IN5 disk chopper TOF spectrometer layout [88].

thus selects a certain neutron energy or wave length:

h h λ (18.49) = mv = m L 2.4.1 Direct geometry spectrometer τ where L is the distance between the chopper disks and τ the flight time of the neutrons for this distance. The In thephase direct between geometry the two spectrometer, disks is defined modulo a pulse 2π ofand incident a third chopper neutrons with the with same well rotational defined speed energy is is producedneeded to by filter a for set higher of choppers harmonics. or A fourth a crystal chopper monochromator. rotating at a lower frequency This hits is filtering the sample intermediate and the pulses and assures a certain time interval between the pulses long enough to get a complete time analysis of scatteredthe different neutron pulses portion and prevent flight overlapping are timed of subsequent over a specific ones. distance L, where they are detected. The detectorThe secondary bank spectrometer is usually consists spherically of the sample arranged table and with the detectors the sample covering placed a large angular at its center; volume. the From the difference of the flight time of the inelastic neutrons in comparison to the flight time of the elastically scatterscattered angle neutrons is measured the energy with transfer respect can be calculated: to the incoming beam so that Q can be correctly determined (Figure 2.2). The resolution of this type of spectrometer range from ∆E 10– mn 2 1 1 = 100 µeV. ∆E is limited by the accuracy$E in theL neutronPD 2 velocity2 measurement, i.e. the maximum(18.50) = 2 τel − τinel possible chopper spinning frequency, and the uncertainties! " of the flight paths L. In this project we performedHere LPD experimentsis the distance between on the the following sample andcold-neutrons the detector, τinel the direct-geometry flight time of the inelastically spectrometers: and τ el that of the elastically scattered neutrons. FOCUS [83–85] at the Swiss spallation source SINQ at the Paul Scherrer Institute (PSI), IN5 [86] and D718.3.2.4 (in TOF Triple mode) Axis – [87 Back] at Scattering the Institute Laue-Langevin in France. On a triple axes spectrometer (Figure 18.12) a certain wave length is selected with a monochromator out of the white spectrum in the neutron guide. The energy analysis after the sample is done with a rotatable crystal 2.4.2analyzing Backscattering the outgoing wave spectrometer length under a certain angle or Q value. On a backscattering instrument both monochromator and analyzer are used in backscattering condition. The mainThe resolution idea for of this these type kinds of of instrument instruments is (see essentially Figure given 2.3 by) is the to monochromator, use a Bragg angle the analyzerθ close crystal to π to and the angular divergence. At both crystals the neutrons are Bragg scattered. The energy uncertainty in the 2 select and analyse (using typically a crystal) neutrons with wavelength λ so that the detected (reflected) neutron band ∆λ gets very narrow.

λ 2d sinθ with (2.27a) = ∆λ ∆d ∆θ , (2.27b) λ = d + tanθ

18 www.nature.com/scientificreports/ 2.5. Computational chemistry

Figure 1Figure. Scheme 2.3 of – the IN16B IN16B backscattering spectrometer in spectrometer BATS confguration. layout [91].

Equation 2.27a is the famous Bragg’s law, where d is the distance between reflecting planes of the analyzer. By differentiating and dividing this equation by λ, we explicitly observe that for θ π the angular part of Equation 2.27b vanishes, thus very high energy resolution can → 2 be obtained. We performed experiments on the IN16B backscattering spectrometer at the Institute Laue-Langevin in France, where we recorded the scattered intensity at specific fixed energies [89,90].

2.5 Computational chemistry

The term computational chemistry refers to the use of computational techniques in chemistry. It involves ab initio approaches based on quantum mechanics as well as empirical methods to study the structure and properties of diverse materials. Figure 2. Distance vs. time diagrams of neutron pulses in the BATS confguration for the (a) Si 111 LRR mode and (b) Si 111 HRR mode. 2.5.1 Molecular dynamics simulations

In a typical molecular dynamics simulation of a liquid, N atoms are placed in a box (usually a resolution spectrometer at a reactor source8. In the following, we will extend the basic concept reported for BATS cube) within corresponding ref.7 and present initialthe details velocities of a much drawn more fromversatile a Maxwell chopper system distribution with a variable at temperature energy resolution extend- T , and guaranteeinging down to 1.2 a zero µeV. totalTe resulting linear momentum design is supported of the by system. extensive Then, ray-tracing Newton’s simulations equations and is the base for a of motionf (exibleEquation 4-disk 2.28 chopper) are numericallysystem that was solved developed, in small built time and installed steps, thus over the the timelast years. evolution Hot commissioning of BATS is scheduled for spring 2018. of the interacting system can be simulated. This method depends on a force field (FF), which models theInverted inter- and TOF intra-molecular Mode and Requirements interactions offor the the liquid, BATS and Chopper the system System physical propertiesWhile can bethe calculated incident neutron as averages energy in over a conventional a constructed backscattering statistical spectrometer ensemble [is92 de].fned and modulated by a moving crystal monochromator on a Doppler drive, in BATS mode, it is determined by the diferent fight times of neutrons propagating from a short, quasi-white neutron pulse created by the chopper system. In both cases, the energy of neutrons scattered from the sample is analysed with crystal analysers. Figure 1 shows the IN16B 2 BATS confguration with the beam structure created at the pulse chopper system, propagating through the wave- ∂ rilengthFi band limiting1 neutronN velocity selector to the background (BG) chopper and fnally into the secondary 2 i VN (r ), (2.28) ∂t spectrometer.= mi = −mi ∇ Te analyser of backscattering spectrometers like IN16B have spherical geometry with the sample in the centre to attain best energy resolution. As a consequence, the incoming neutron beam must19 be pulsed with a duty cycle of at most 50% to distinguish neutrons scattered into the detector with and without energy analy- sis at the backscattering crystals. Te possible pulse repetition rates are related to the distance between sam- ple and analyser of dSA = 2m. With Si 111 analysers, the wavelength is λ0 = 6.271 Å corresponding to a neutron −1 velocity of v0 = 630.8 ms . Tis yields a fight time from sample to analyser and back of tSAS = 6.34 ms, which defnes the maximum length of the neutron pulses at 50% duty cycle. Te corresponding repetition rate is thus −1 f0 = (2tSAS) = 79 Hz. Figure 2a depicts this pulse structure in a time vs. distance plot. Short pulses with fre- quency f0 are created by the chopper system, the wavelength spectrum being restricted by the following velocity selector to a distribution with ∆λ/λ ≈ 12% full width half maximum (FWHM). Te BG chopper operates at the same frequency f0 and transmits the central part of the spread pulse onto the sample (green), blocking out the overlapping tails of subsequent pulses (red). Note that the detector appears twice in this representation to indicate the two possible fight paths ‘Sample-Detector’ and ‘Sample-Analyser-Detector’, respectively. Te time periods when energy analysed neutrons arrive on the detector are indicated by grey boxes. Te width of the

SCIENTIFIC REPORTS | (2018) 8:13580 | DOI:10.1038/s41598-018-31774-y 2 Chapter 2. Neutron scattering and computational methods

2.5.2 Force field

The force field describing the interactions in liquids consists of the sum of bonded Vb and non-bonded Vnb contributions [72]:

V V V (2.29) = b + nb

Non-bonded interactions are the sum of pair contributions, corresponding to Coulomb inter- actions and Lennard Jones short range repulsion and dispersion energy:

à 2 µµ ¶12 µ ¶6¶! X X qi q j e σi j σi j Vnb 4²i j , (2.30) = i j i ri j + ri j − ri j > where the qi are the partial atomic charges. Coulomb forces are assumed to act in vacuum, σi j and ²i j are the coefficients for the dispersion interaction. This interaction is computed intermolecularly as well as intramolecularly, in the latter case, for atoms separated by at least three bonds.

The bonded energy Vb is given by the contribution of the harmonic bond stretching term, the angle bending term and the torsional term:

1 X str. 0 2 1 X bend. 0 2 1 X tor. h 0 i Vb Ki j [Ri j Ri j ] Ki jk [θi jk θi jk ] Ki jkl 1 cos(nφi jkl φi jkl ) = 2 i j − + 2 i jk − + 2 i jkl + − (2.31)

str. bend. tor. 0 0 0 Ki j , Ki jk and Ki jkl are force constants, Ri j , θi jk and φi jkl are the length, bending and dihedral angles of unstrained bonds [93].

2.5.3 Ab-initio simulations

In a pragmatic and consistent form, the matter can be modelled as a set of atoms, which create an assembly of electrons and nuclei interacting quantum-mechanically. The Hamiltonian describing this system can be written, in a non-relativistic framework, as the sum of the kinetic energy of the nuclei (Tion) and electrons (Te) plus the Coulomb energy associated with ion-ion

20 2.5. Computational chemistry

(Vion–ion), electron-electron (Ve–e) and ion-electron (Vion–e) interactions:

Hˆ T T V (R) V (r ) V (R,r ), (2.32) 0 = ion + e + ion–ion + e–e + ion–e

If we assume the system being described by a many-body wave function Ψ(r ,R;t), its time evolution is given by the Schrödinger equation:

∂Ψ(r ,R;t) i Hˆ0Ψ(r ,R;t). (2.33) ħ ∂t =

In addition, due to the large mass difference between the electrons and the nucleons, the temporal evolution of electrons and ions can be separated (Born-Oppenheimer approxima- tion) [94,95]; in this approximation Equation 2.32 can be written as:

Hˆ Hˆ T , (2.34) e = 0 − ion where the nuclei are treated as the source of an effective potential acting on the electrons. Application of Equation 2.34 to computer simulations (ab-initio methods), refers mainly to the development of the so-called density functional theory (DFT), and more specifically in the Hohenberg-Kohn and Kohn-Sham (KS) formulation [96,97]. In it, the ground state electron density ρ(r ) is defined by an auxilliary set of N non-interacting electron orbitals ϕi (r ), also called KS orbitals:

n X ρ(r ) ϕi∗(r )ϕi (r ), (2.35) = i 1 = where we have to account for the different and unknown potential acting on the interacting and non-interacting electrons to replicate the exact system density. Thus, the KS energy (EKS) is a functional of the density and its minimum corresponds to the ground state energy of a

21 Chapter 2. Neutron scattering and computational methods

system with n electrons and N ions fixed at Rk positions. EKS is given by:

n Z N Z £ ¤ 1 X ­ ¯ 2 ¯ ® 1 ρ(r )ρ(r 0) X ρ(r )dr £ ¤ EKS ρ R ϕi ¯ ¯ϕi dr dr 0 ZN EXC ρ , (2.36) | = −2 i 1 ∇ + 2 r r 0 −k 1 r Rk + = | − | = | − |

£ ¤ where EXC ρ is the exchange-correlation energy, which accounts for the antisymmetry (ex- change) of ϕi (r ) and the gain in kinetic energy of the interacting (correlations) electrons. The selection of orthonormal ϕi (r ) for Equation 2.36 maps the many-body problem into a set of coupled partial differential equations. The method to solve this equation is the goal £ ¤ behind DFT, and its accuracy depends both on the way EXC ρ is modelled and the choice of ϕi (r ). Conventional description of the exchange-correlation energy uses the Perdew-Burke- Ernzerhof (PBE) [98] functional or the hybrid functional B3LYP [99], the orbitals are selected from a plane wave basis or Gaussian functions.

22 3 Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

The following chapter presents the results published as: Juan F.Mora Cardozo, T. Burankova, J. P.Embs, A. Benedetto and P.Ballone, Density functional computations and molecular dynam- ics simulations of the triethylammonium triflate protic ionic liquid, J. Phys. Chem. B 2017 121, 11410-11423. In this paper, systematic molecular dynamics simulations based on an empirical force field have been carried out for samples of triethylammonium trifluoromethanesulfonate (triethylammonium triflate, TEA-TF), covering a wide temperature range 200 K T 400 ≤ ≤ K and analysing a broad set of properties, from self-diffusion and electrical conductivity to rotational relaxation and hydrogen-bond dynamics. The study was motivated by quasi-elastic neutron scattering and differential scanning calorimetry measurements in Ref. [71] on the same system, revealing two successive first order transitions at T 230 K and T 310 K (on ∼ ∼ heating cycle), as well as an intriguing and partly unexplained variety of sub-diffusive motions of the acidic proton. Simulations show a weakly discontinuous transition at T 310 K, and = highlights an anomaly at T 260 K in the rotational relaxation of ions, that we identify with = the simulation analogue of the experimental transition at T 230 K. Thus, simulations help = identifying the nature of the experimental transitions, confirming that the highest temperature one corresponds to melting, while the one taking place at lower T is a transition from the crys- tal, stable at T 260 K, to a plastic phase (260 K T 310 K), in which molecules are able to ≤ ≤ ≤ rotate without diffusing. Rotations, in particular, account for the sub-diffusive motion seen at intermediate T both in the experiments and in the simulation. The structure, distribution and strength of hydrogen bonds are investigated by molecular dynamics and by density functional computations. Clustering of ions of the same sign, and the effect of contamination by water at 1 % wgt concentration are discussed as well.

23 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

3.1 Methods

The bulk of our computations consisted of molecular dynamics simulations based on an empirical force field for the TEA-TF ion pair, whose schematic structure is shown in Figure 3.1.

Figure 3.1 – Schematic structure of [TEA]+ and [TF]−.

The force field is of the all-atom OPLS/Amber type [100, 101]. The starting point for its parametrisation was provided by the potential of Ref. [93] for [TF]− (see also Ref. [102]), while [TEA]+ can be described using the extensive tabulation of force field parameters given in Ref. [103]. Fine tuning of the potential, and of the [TEA]+, [TF]− cross interaction has been carried out using the results of our density functional computations (see Sec. IV) for the ground state geometry and harmonic dynamics of the TEA-TF molecule. Both vibrational eigenvalues and eigenvectors have been used to this effect. Atomic charges have also been verified and re-tuned using the electrostatic potential (ESP) [104,105] values provided by our density functional computations for the isolated ions and for the neutral TEA-TF pair. The full list of parameters is reported in the supplementary information of Ref. [72].

Simple chemical considerations suggest that no atom in TEA-TF has the simultaneous H- donor and H-acceptor ability needed for the onset of a Grotthus proton conduction channel. This observation is the major justification for our usage of a fixed-topology force field model, avoiding the complications of a reactive force field approach. [106]

All classical simulations with the empirical force field have been carried out in the isothermal- isobaric (NPT) ensemble using the Gromacs package. [107] Constant temperature was en- forced using the Nosé-Hoover thermostat with a characteristic relaxation time of 2 ps, while the constant pressure of 1 atm was enforced using the Parrinello-Rahman extended Lagrangian formulation, again with a characteristic time of 2 ps. All samples are periodic in space, and the long range Coulomb potential and forces are computed using particle-particle-particle-mesh Ewald sums. [108] Bond distances, bending and, of course, dihedral angles are all flexible.

Simulations have been carried out for dry TEA-TF,and for samples slightly contaminated by water. The TIP4P model was used for water, whose cross interactions with [TEA]+ and [TF]− has been estimated using Berthelot’s rule.

Our force field and molecular dynamics set up are equivalent to those of Ref. [109,110], despite a few different choices. The most important one is the rescaling of ion charges, summing up to

24 3.2. Classical MD simulations: results some 80% of the formal value, adopted both in Ref. [109] and in Ref. [110], but not used here. Rescaling has been shown to improve the value of linear dynamical coefficient compared to experiments [111], but, despite some intuitive justification, it is still an ad-hoc adjustment. Moreover, we did not rescale charges because the equilibrium density of the simulated samples already slightly underestimates the experimental value (see following section). Remarkably, the underestimation of transport coefficients by our model does not seem to affect the location and quality of the transitions that represent the real interest of our study.

Our level of ab-initio corresponds to density functional theory, with the Perdew-Becke-Ernzerhof (PBE) approximation for the exchange and correlation energy [98]. Computations have been carried out using primarily the Gaussian 09 package [112], which uses Gaussian basis functions, and, as such, is suitable for all-electron computations. In all Gaussian 09 computations, a 6- 311++G(2d,2p) basis has been used. Gaussian 09 has been used also to check total energies and especially energy differences among the different species using the B3LYP approximation [99] for the exchange correlation function. Lacking a precise experimental thermo-chemical bench- mark, the results of BPE and B3LYP turn out to be broadly equivalent. Other computations have been carried out using a different computer package, i.e., CPMD [113], based on plane waves and soft pseudopotentials [114]. CPMD is especially optimised for molecular dynamics simulations, that have been extensively used in our computations.

Ground state geometries were optimised by the so called eigenvector following method [115] in Gaussian 09, and by simulated annealing [116] in CPMD. This last approach, more intuitive than the first one, is, however, computationally time consuming.

Dispersion interactions have been included at the empirical level [117] in our CPMD compu- tations, and neglected in the Gaussian 09 computations, upon verifying by CPMD that their exclusion did not change significantly the equilibrium geometry nor the cohesive properties. By and large, and despite the slight differences in their approach, the results of CPMD and Gaussian 09 are mutually compatible whenever a comparison is possible.

3.2 Classical MD simulations: results

3.2.1 Dry TEA-TF samples

Simulations have been carried out for samples of 125 ion pairs, enclosed in a cubic box periodically repeated in space. The sample size, although relatively small, is sufficient to investigate properties of homogeneous systems. At the same time, the limited sample size allows us to extend simulations to the long time ( 100 ns) required to investigate diffusion ∼ and electrical conductivity in a disordered system that exhibits long relaxation times up to fairly high temperature.

25 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

In our study we first equilibrate our sample at T 400 K and P 1 atm during 15 ns. The = = equilibrated sample is apparently liquid-like, and it is used to start a cooling stage down to T 200 K, with a cascade of equilibration runs of 5 ns at T 380 K, 360 K, 340 K, 320 K, 310 = = K, 300 K, 290 K, 280 K, 270 K, 260 K, 240 K, 220 K, 200 K. Each of the samples obtained in this way is propagated in time in 5 ns blocks repeated until equilibration has been achieved, and sufficient statistics has been accumulated. The change from equilibration to production runs is decided by monitoring the drift of diagnostic properties such as volume and potential energy. Needless to say, equilibration is longer at low T than at high T , and longest at the intermediate temperatures around T 300 K, where thermodynamic and dynamical anomalies manifest = themselves.

All simulations are carried out with a time step of 1 fs, and configurations are stored on the trajectory file every 5 ps. Shorter runs (from 300 ps to 900 ps) with more frequent sampling (one configuration every 0.1 ps) have been performed to monitor fast processes such as the re-orientation of H bonds. In all cases, statistics runs lasted at least 40 ns. At each temperature below T 300 K, the sum of equilibration and production stages lasted more than 100 ns. = We emphasise that all the results presented below concern the cooling of the sample from the liquid phase. No heating simulations have been attempted because no crystal configuration at low T is available. Ab-initio searches for the crystalline ground state have been carried out (see Figure A.15) but the result is not sufficiently validated to justify extensive simulations of its melting.

The average potential energy per ion pair E as a function of T is shown in panel (a) of 〈 〉 Figure 3.2. The E (T ) relation is remarkably linear both at high and at low T , with however a 〈 〉 weak anomaly at T 310 5 K (the a subscript stays for anomaly). The anomaly represents a = ± a quantitatively small but nevertheless clear drop in the average potential energy below its linear extrapolation (from high temperature), taking place at at 310 K, accompanied by an equally slight change in the constant-pressure specific heat Cp (T ), that on cooling across Ta decreases from C 0.41 kJ/mol/K to C 0.39 kJ/mol/K. To highlight the tiny anomaly in p = p = the average potential energy, in the inset of Figure 3.2 we plot the difference δE(T ) between E (T ) and the high-temperature linear interpolation α βT of the average potential energy, 〈 〉 + showing that δE is virtually zero above T 310 K, and drops to about 0.8 kcal/mol below the ∼ − transition temperature.

The slight discontinuity in the average potential energy at Ta identifies a weakly first order transition. We anticipate that the analysis of dynamical transport coefficients shows that Ta also corresponds to the quenching of diffusion and electrical conductivity, thus suggesting that the transition at T T 310 K is in fact melting, joining a liquid and a solid-like phase. a = m = We emphasise that in this context solid-like is not equivalent to crystal-like. We also anticipate that the structure of the solid just below Tm is highly disordered, partly because of the sluggish

26 3.2. Classical MD simulations: results

360 0.5 30 0.0 350

T [kJ/mol] -0.5 〉 −α−β E 〈 ]

0 -1.0 3 340 200 250 300 350 400 T [K] [A 〉 V 〈 330 (T) [kJ/mol] 〉 -30 E 〈

320

-60 (a) (b) 310 200 250 300 350 400 200 250 300 350 400 T [K] T [K]

Figure 3.2 – (a) Average potential energy per ion pair as a function of temperature. The statistical error bar is of the order of 0.5 kJ/mol, smaller than the size of the dots. Green line: linear interpolation to the four lowest-T points. Red line: linear interpolation to the four points of highest T . Inset: deviation of E (T ) from the high-temperature linear interpolation 〈 〉 E (T ) α βT . (b) Average volume per ion pair as a function of temperature. The error 〈 〉hi gh = + bar on the volume is 0.1 Å3, smaller than the size of the dots. Green and red lines defined as ∼ in panel (a).

dynamics and slow relaxation due to the molecular nature of the ions, but, even more, because the equilibrium phase resulting from cooling below Tm lacks the orientational ordering of a genuine crystal phase.

The observation of the anomaly in E (T ) is remarkable. First order transitions are rarely 〈 〉 observed on cooling molecular liquids by computer simulations, whose likely result is to turn the sample into a glass [118], even for systems less complex than TEA-TF (see, for instance, the cooling branch in Figure 2, Ref. [119] for SiO2).

A completely analogous behaviour is displayed by the average volume V (T ), shown in panel 〈 〉 (b) of Figure 3.2. We note in passing that the density of the simulated sample is ρ(T ) 1.34 = g/cm3 at T 200 K, and ρ(T ) 1.20 g/cm3 at T 400 K, compared to the experimental value = = = in the liquid phase at 403 K of ρ 1.33 g/cm3 (Ref. [73]) or ρ 1.16 g/cm3 (Ref. [120]). 403K = 400K = The underestimation of the density by our model is one major reason why we do not re-scale the charges to a value below the nominal one. No clear sign of a second transition at T 310 K < is apparent in either E (T ) or V (T ). 〈 〉 〈 〉 The microscopic structure has been characterised primarily through the radial distribution functions. Both ions are fairly large and somewhat flexible, and we decided to represent cations by the coordinates of their nitrogen atom, and to look at correlations among N-O, N-N

27 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

3

6

4 (r) (r) NO 2 n 2 OO

0 (r), g 2 3 4 5

NN r [A]

(r), g 1 NO g

T=300K 0 0 4 8 12 16 r [A]

Figure 3.3 – Radial distribution function of N-O (blue line), N-N (green line) and O-O (red line) pairs in TEA-TF at T 300 K, P 1 atm. Inset: short range portion of the running coordination = = number nNO(r ), obtained by integration of the radial distribution function (see text).

and O-O. The results are shown in Figure 3.3.

By and large, the set of three distribution function are recognisable as the radial distribution functions of an ionic system, with the N-O (cation-anion) component displaying the strongest correlation (highest peak), in opposition of phase with the N-N and O-O functions, reaching their maxima where gNO(r ) has its minima. The molecular nature of the ions, however, gives origin to a variety of sharp details that are not found in the radial distribution functions of simpler ionic systems. The N-O radial distribution function, for instance, displays a remarkable peak at short range (r 2.72 Å ) corresponding to the N-O distance in their tight hydrogen ∼ bonding.

The running coordination number nNO(r ) is defined as:

Z r 2 nNO(r ) 4πρk r gNO(r )dr. (3.1) = 0

When computed with ρ ρ it gives the average number of oxygen atoms around each N k ≡ O atoms. When computed with ρ ρ ρ /3 it gives the average number of nitrogen atoms k ≡ N = O around each O atom.

The running coordination n (r ) has a plateau for 3 r 3.6 (inset of Figure 3.3), correspond- NO ≤ ≤ 28 3.2. Classical MD simulations: results

ing to the deep minimum in gNO(r ) following the H-bonding peak. When computed with ρ ρ , the plateau value measures the average number of NH terminations engaged in a k = O hydrogen bond. At T 300 K this value is nearly exactly n 1.00, and its dependence on T = NO = is mild. The nearly full saturation of all H-bonding sites and the weak dependence of the nNO plateau on T emphasise the relevance of the H-bonding mechanism. The secondary peak on the side of the main N-O peak at r 5.22 Å is a geometric consequence of the presence of = three oxygen atoms on the SO3 side of [TF]−.

On a slightly longer length scale and at low temperature (T 310 K), an inflection point in ≤ n (r ) at r 5.4 Å marks a second weaker shell closing (see Figure A.1), corresponding to NO = the minimum in g (r ) following the main broad peak at r 4.7 Å . The n coordination of NO ∼ NO nearly 8 at the shell closing, together with the next-nearest neighbour peak at r p2 4.7 7 = × ∼ Å suggests an NaCl-type geometry for the distribution of cations and anions in space. This structural hint is supported by visual inspection of simulation snapshots and by the density functional computations reported in Sec. 3.3.

Of the three radial functions displayed in Figure 3.3, gNN (r ) displays the widest correlation hole, partly because of the like-charge repulsion among the N-H termination of [TEA]+, and, more importantly, because of the N-H location at the centre of a tightly packed crown of ethyl chains. The O-O radial distribution function displays a prominent intra-molecular peak at r 2.63 Å , that has been removed from Figure 3.3 because of its partial overlap with the short ∼ range N-O peak attributed to H-bonding.

All these major structural features display a relatively weak temperature dependence from T 400 K down to T 200 K, see Figure A.2, although below T 310 K sharper features start = = = to develop especially in gNO(r ), pointing to the propagation of partial ordering to the medium length scales covered by simulation [121]. Nevertheless, all g (r )’s look closer to those of glassy systems than to those of crystalline samples.

Weaker features in the radial distribution functions are more sensitive to temperature. For instance, down to T 310 K, the N-F radial distribution function does not display any clear ∼ peak at short range that could be attributed to a N-F hydrogen bond, however weak. Below T = 300 K such a sharp peak starts to develop at r 4.7 Å , becoming apparent and prominent NF = at T 200 K (see Figure A.3). This feature, probably due to the low negative charge on the = F atoms, could point to a weak H-bond joining N H F atoms, and the analysis of triplet − ··· configurations of this type indeed finds a few candidates within a cut-off N-F distance of

5.2 Å and N H F angle 30◦. The long bond distance, and the sensitivity to temperature, 6 − ··· < however, suggest that this bonding mechanism has little effect on structural and dynamical properties of the system.

Analysis of all other gXY (r ) shows no other sharp feature at H-bonding distances in the radial

29 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid distribution functions, confirming that the N H O case, and the very weak N H F case at − ··· − ··· low T , are the only H-bonding possibilities in TEA-TF.

The structural counterpart of the radial distribution function closer to experimental data is the set of partial structure factors Si j (Q), where {i, j} are atom-type indices. Of the multitude of possible {i, j} combinations in TEA-TF,we selected again the N-O, N-N and O-O pairs to characterise the arrangement of ions in reciprocal space.

To identify the role of packing and of Coulomb interactions, we display in Figures A.4 and A.5 the density-density and the charge-charge combination of the three Bathia-Thornton structure factors [92,122]:

X Sρρ(Q) Sαβ(Q)and (3.2) = α,β

X SZZ (Q) ZαZβSαβ(Q), (3.3) = α,β where {α,β N,O}, S (Q) are partial structure factors, with the fictitious charges Z 1, and ≡ αβ = Z 1/3 attributed to N and O, respectively, to identify them as the cation and the anion of a = − globally neutral system.

Inspection of Sρρ(Q) and SZZ (Q) clearly shows the prominent role of Coulomb forces in determining the structure of the system. The vanishing of SZZ (Q) at low Q is due to the perfect screening of charge in this ionic system [123]. The low value of S (Q) in the same Q limit ρρ → is due to the low compressibility of this ionic system not far from its triple point [92]. More 1 intriguing is the sizeable pre-peak displayed by S (Q) at Q 0.7 Å − , that highlights the ρρ ∼ formation of ion clusters, dynamically modulating the density and temporarily breaking the system homogeneity.

The third function SρZ , describing density-charge cross correlations, is less prominent than the first two functions, pointing to a rather weak coupling of density and charge fluctuations that is found in many molten salts systems.

The computation of linear dynamical coefficients confirms the presence of slow relaxation processes at all simulated temperatures, and the glassy translational dynamics of the system below T 310 K. = The diffusion constant of both ions has been computed from the time dependence of their

30 3.2. Classical MD simulations: results mean square displacement, which is defined as:

1 X 2 MSDα(t) ri (t t0) ri (t0) t0 , (3.4) = Nα i α〈| + − | 〉 ∈ where α labels the ion type. In our computation, in particular, α 1 labels the coordinates of = the N atom in [TEA]+, while α 2 identifies the coordinates of the three oxygen atoms in [TF]−. = The average over the reference t0 spans the entire time interval covered by the simulation (i.e., at least 40 ns minus the time t itself). Typical results for the {MSD (t), α 1, 2 } at T 360 K, α = = T 300 K and T 240 K are shown in Figure A.6. The diffusion coefficient is computed from = = the Einstein relation:

1 Dα lim MSDα(t), (3.5) = t 6t →∞ where the limiting slope is in fact approximated by the linear coefficient of the linear inter- polation over the 10 t 12 ns range. The choice of the time interval is crucial, and in our ≤ ≤ computation it has been selected upon inspecting the MSDα(t) curves at all T (See again examples in Figure A.6). Beyond 12 ns, long-time fluctuations in MSDα(t) appear at the lowest temperatures. At intermediate temperatures 260 K T 310 K, MSD (t) displays a ≤ ≤ α non-negligible curvature up to 8 ns. Remarkably, the onset of the linear behaviour is faster at ∼ T 260 K than at intermediate temperatures (see the T 240 K MSD (t) again in Figure A.6). ≤ = α These observations will become relevant in the discussion of molecular rotations reported below. Because of the downward curvature of MSDα(t) on the ns time scale, moving the range of the fit to lower times increases, even significantly, the computational estimate of the diffusion constant. In a similar way, the diffusion coefficients estimated by neutron scattering are systematically higher than those measured by PFG-NMR, since the time probed by the former approach is much shorter than for the latter. To be precise, the neutron scattering estimates should be referred to as short-time diffusion coefficients. Given this dependence of the diffusion coefficients on the measurement time scale, and because of the systematic underestimation of Dα by unpolarisable, formal-charge force field used in our simulations, we will not comment in detail on the quantitative correspondence of experimental and compu- tational results. For our purposes, the analysis of diffusion scaling with temperature is more significant.

The results for the diffusion constants D and D of cations and anions are shown in Figure 3.4 + − in a form immediately amenable to an analysis of activation (free) energy estimated by an Arrhenius relation.

To give an idea of the diffusion rate of ions in liquid TEA-TF, we observe that, despite the

31 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

-6 10

-7 10

-8 10 ]

- -9 10

log[D -10 10

-11 10

-7 10

-8 10 ] + -8 10 log[D -9 10

-10 10 2.5 3.0 3.5 4.0 4.5 5.0 1000 / T [K-1]

Figure 3.4 – Arrhenius plot for the diffusion constant. D and D in [cm2/s]. + − similarity of the melting temperatures, at T 320 K the diffusion coefficient of cations is three = orders of magnitude slower than that of H2O in liquid water at the same temperature, while each ion is roughly six times heavier than H2O. In agreement with NMR measurements [73], we also observe that the cation diffuses somewhat faster than the anion. This might be due to the fact that the anion is slightly heavier than the cation, but the ratio of the square root of the masses accounts for only 20% of the difference, implying that molecular interactions play a relevant role in slowing down [TF]−.

In Figure 3.4, once again, we find two different linear ranges at low and at high temperature, with a non-strictly-monotonic behaviour in a temperature interval centred on the transition temperature T 310 K. For cations, the high temperature branch corresponds to an activa- a = tion free energy of 41.5 kJ/mol, that decreases to 16 kJ/mol at low T . For anions, the high temperature branch corresponds to an activation free energy of 45 kJ/mol, that decreases to 25 kJ/mol at low T .

32 3.2. Classical MD simulations: results

0 10

-1 Nernst-Einstein 10 Simulation -2 10

-2 10 [S/m] κ -3 10

-4 10 2.5 3.0 3.5 4.0 4.5 5.0 1000 / T [1/K]

Figure 3.5 – Arrhenius plot for the electrical conductivity at pressure P 1 atm. =

It might be useful to remark that the anomaly in D , D on cooling through Ta does not + − unambiguously correspond to the drop of diffusion rate expected at solidification. Also the decrease of the activation energy on cooling from the liquid to the solid phase are somewhat counter-intuitive, and we think that the precise determination of D , D around and below + − Ta is affected by transient effects and by the short time scale of simulations. Nevertheless, the low value of the diffusion constants at Tm still identifies the low temperature phase as a solid.

A second crucial linear dynamical coefficient is the electrical conductivity, computed from the simulation trajectories according to:

*¯ ¯2+ 1 1 1 1 ¯X ¯ κ lim Π(t) lim ¯ qi [ri (t t0) ri (t0)]¯ , (3.6) t t ¯ ¯ = kB TV 6t = kB TV 6t ¯ i + − ¯ →∞ →∞ t0 where V is the system volume and kB is the Boltzmann constant. Because of the partial cancellation of contributions from anions and cations, the time dependent average in Eq. 3.6 is more noisy than the mean square displacement in Eq. 3.5 (see examples in Figure A.7), and, at equal simulation length, the linear range of Π(t) is restricted to a narrower time interval than in the MSD(t) case. Nevertheless, to avoid biasing the result, we fit the time dependent average in Eq. 3.6 on the same 10 ns t 12 ns already used to estimate diffusion constants. ≤ ≤ Once again the result is reported in the form of an Arrhenius plot, see Figure 3.5, displaying the same two linear ranges of the diffusion constants. The activation free energy for the electrical conductivity turns out to be 18 kJ/mol at low T , and 41 kJ/mol at high T .

An important aspect of linear transport is represented by the well known relation of diffusion

33 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

1.0

0.8

(T) 0.6 ∆

0.4 κ = κ ∆ NE(1 - )

0.2 200 250 300 350 400 T [K]

Figure 3.6 – Parameter ∆ measuring the pairing of [TEA]+ and [TF]− ions. Estimated error bar of the order of 5% at T 310 K, slightly lower above T 310 K. ≤ = constants and electrical conductivity. The so-called Nernst-Einstein (NE) relation, in particular, provides a simple estimate of the electrical conductivity based on the diffusion coefficients:

2 F ρ ¡ 2 2 ¢ κNE ν z D ν z D , (3.7) = RT Mw + + + + − − −

where F is the Faraday constant, R is the gas constant, ρ is the mass density and Mw the molecular weight, ν , ν are the number of cations and anions in a formula unit, z and z + − + − are the corresponding ions’ charge. Such a relation assumes that ions diffuse independently, performing uncorrelated random walks (see Sect.10.5 in Ref. [92]). Of course this is a very idealised approximation, and the deviation of the actual conductivity with the NE estimate is a measure of correlation. Following the time honored practice, this correlation, or "pairing" is quantified by the parameter ∆, defined as:

κ κ (1 ∆) (3.8) = NE −

The results are shown in Figure 3.6. From the picture it is apparent that cation-anion pairing is always a relevant aspect in the dynamics of TEA-TF over a broad range of temperatures, at least up to T 400 K. AT T 310 K the pairing ∆ has a sudden change, paralleling the behaviour = = 34 3.2. Classical MD simulations: results observed in most other observables. Below T 310 K pairing reaches up to 95 % of the ions. ∼ At these low temperatures, however, both diffusion and conductivity are already reduced to very low rates by the sluggish dynamics of TEA-TF.

A preliminary and partial summary of the results presented up to this point could be stated as follows. The analysis of thermodynamic functions, of diffusion and electrical conductivity point to T 310 K as the temperature at which our simulated systems turn solid on cooling a = from the liquid state. Above this temperature ions diffuse relatively freely, and carry electric current, despite non-negligible ions’ pairing. Below this temperature diffusion and electrical conductivity are both very low, and the sudden change of activation free energy tells that the molecular mechanism underlying ions’ translations has changed across the transition.

Besides translations, the rotational relaxation of ions represents another basic aspect of the system dynamics. Because of the ions flexibility, rotations are not uniquely defined. Our choice is to characterise this property by analysing the orientation of the N-H termination of (i) [TEA]+ and of the C S covalent bond of [TF]−. To this aim, we associate a unit vector (o1 ) − (j) to the N-H covalent bond in [TEA]+ and another one (o ) to the C S bond at the centre of 2 − [TF]−. In the definition above, (i) and (j ) refer to individual ions in the sample. The rotational relaxation time is estimated by first defining the time correlation functions:

1 X Θα(t) oi (t t0) oi (t0) t0 , (3.9) = Nα i α〈 + · 〉 ∈ where Nα is the (equal) number of cations or anions in the system. Typical results are displayed in Figure 3.7.

A better insight into these properties might be obtained by looking at the logarithm of the autocorrelation function, that becomes a straight line in the case of a simple exponential relaxation. An example of such plot is given in Figure A.8. Beyond a relatively short time of the order of 0.2 ns, the logarithm of Θα(t) is indeed a straight line, pointing to a relatively 1 long-time (up to 10 ns at T 310 K) exponential relaxation process. The 10− ns width ∼ = of the short-time feature is covered by vibrational modes affecting dihedral angles in the covalent backbone of the ions (see Sect. 3.3). For this reason, we think that this fast relaxation channel corresponds to rotations of the single N H or C S bond within each ion, although a − − completely unambiguous identification is not available, and perhaps cannot be found. Then, it is tempting to identify the longer time relaxation with the rotation of the defining N-H and C-S bonds as part of the whole ions.

The analysis of this feature is completed by performing a fit of the linear portion of logΘα(t).

35 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

1.0 1.0 T=280 K

(t) 0.5 T=320 K (t) - + Θ Θ

0.5 T=360 K

(t); T=400 K

+ 0.0 0 2 4 6 Θ t [ns]

T=360 0.0 0 2 4 6 t [ns]

Figure 3.7 – Time auto-correlation function of the N-H direction in [TEA]+ (red lines), and of the C-S bond in [TF]− (blue line).

The inverse of the linear coefficient represents the opposite of a relaxation time τ that we report again on an Arrhenius-type plot in Figure 3.8.

The result is similar to all the other plots obtained in our study up to now, with distinct low-T and high-T ranges. The crossing between the two regimes, however, takes place at a temperature 50 K lower than the melting of the simulated samples. In other words, ∼ both ions are still able to rotate well below the temperature at which the centre of mass of cations and anions is no longer able to diffuse significantly. The picture provided by the simulation, therefore, is that of a plastic phase arising from the solid some 50 ◦C below the melting transition, being replaced at T 310 K by the homogeneous liquid phase. A similar m = sequence of transformations is fairly common in molecular systems, and it has been studied by computational approaches since the early days of computer simulation [124]. Plastic crystal (or, equivalently, rotor phases) are well known in ionic liquids [38], and in protic ionic systems [125] in particular, and TEA-TF thus joins the list of such systems.

Ion association and rotational relaxation are likely to be greatly affected by the distribution and properties of hydrogen bonds in the TEA-TF system. In our analysis of simulation trajectories, hydrogen bonding (HB) is defined purely in terms of geometry. We aim at characterising the N H O hydrogen bonds joining cations and anions, and the g radial distribution function − ··· NO already provides an estimate ( r 2.75 Å at T 300 K) of the N O separation in a typical 〈 NO〉 ∼ = − 36 3.2. Classical MD simulations: results

3 10

τ+ 2 10 τ−

[ns] 1 τ 10

0 10 2.5 3.0 3.5 4.0 4.5 5.0 1000 / T [K-1]

Figure 3.8 – Time correlation function of cation and anion orientations. Dots and squares represent simulation results. Lines are a guide to the eye.

H-bond. In our definition, a triplet of atoms consisting of N H on the cation side, and an − oxygen on the anion side, is a HB if the distance N O is less than 3.2 Å , and the angle between # » # » − the separation vectors N H and H O is less than 30◦. Analysis of trajectories shows that at − ··· very low T (T 200 K) nearly all N-H terminations are engaged in an HB and the number = of hydrogen bonds decreases only slowly with increasing temperature, consistent with an estimated strength of about 40 kJ/mol (see Sec. 3.3), significantly higher than k T 2.5 kJ/mol B = at T 300 K. = Based on the complementary structure of cations and anions, and on intuition, it is tempting to think of the system as made primarily of cation-anion unique pairs. The analysis of simula- tion snapshots, however, identifies anions with more than one hydrogen bond stretching to different cation partners [126–128]. To quantify this qualitative observation, we compute the fraction of anions having 0, 1, 2 and 3 HBs. The cumulative number of HB per 100 TEA-TF ion pairs and its partition in multiple-bond contributions is displayed in Figure 3.9. The figures shows that with increasing temperature the largest change is due to fraction of anions forming three simultaneous HBs. An example of a triple-bonded cluster is represented in Figure 3.10

In our force field model, N in [TEA]+, with its low positive charge q 0.025 e, is unlikely to N = act as the acceptor in an additional H-bond besides the one donated to oxygen, as discussed in the previous paragraphs. In fact, no close association of N and H is found in the simulation trajectories besides the pair connected by a primary covalent bond. Because of this observa- tion, it is difficult to imagine proton transport paths going beyond vehicular transport, and approaching the Grotthus mechanism familiar from proton mobility in water. This aspect will

37 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

100 3-HB 80 2-HB 60 HB (100)

n 40

20 1-HB

0 200 240 280 320 360 400 T [K]

Figure 3.9 – Cumulative number of HB per 100 TEA-TF ions pairs as a function of T , accounting for the contribution from anions accepting one HB, corresponding to the area below the green line; two HB’s, represented by the area between the green and blue line; or three HBs, corresponding to the strip between the blue and the red lines. Thus, the red line represents the total number of HB per 100 ion pairs.

be discussed in some more detail in the density functional section.

Besides the static properties discussed up to now, molecular dynamics gives us access to the kinetics of H-bond formation and dissociation. The probability distribution of the breaking time for individual H-bonds has been computed by identifying all N H O hydrogen bonds − ··· at a given reference time t , and monitoring the persistence of the bond at time t t , until it 0 + 0 breaks. Similarly to what has been done with the the other time-dependent properties, the result is averaged over the initial time t0.

Also in this case, it is possible to distinguish a fast relaxation channel in the 0.2 ns time range, and a slower relaxation channel stretching over a few ns. More in detail, the analysis of snapshots shows that up to T 400 K ions connected by H-bonds stay close to each other for = a fairly long time. The H-bond itself, however, is broken and reformed at a much faster rate as a result of intra-ion vibrations [129,130]. To decrease the effect of this flickering noise on our analysis, we disregarded all breaking events of H-bonds that reform within 0.4 ps. The result of this mild filtering is shown in Figure A.9. Only the slowest relaxation process is retained, whose time evolution appears to be a simple exponential. The time constant of the exponential is identified with the genuine lifetime of hydrogen bonds τHB , whose temperature dependence is displayed in Figure 3.11. Remarkably, the crossover between the low-T and the high-T regime in τ takes place at T 260 K, consistently with the fact that the freezing of rotations, HB = 38 3.2. Classical MD simulations: results

Figure 3.10 – Cluster consisting of an anion accepting three HBs from neighbouring cations. A thin dash line identifies hydrogen bonds.

and the stabilisation of HBs are two aspects of the same dynamical transition.

Our protocol to compute τHB is similar to what is currently used in the analysis of H-bonding by simulation, extensively discussed especially in the case of water. Also our results are qualitatively similar to those obtained and discussed in classical papers on this subject [131, 132], with only a somewhat longer time scale due to the larger size and mass of TEA-TF ions with respect to water.

To monitor possible gradual changes, or even sudden transformations of the geometry of ions as a function of T we computed the principal momenta of inertia of cations and anions at all temperatures. The results confirm basic information already apparent from visual inspection of snapshots. At all temperatures [TEA]+ is globular, and [TF]− is only somewhat more elongated, justifying the classification of the intermediate phase of TEA-TF as a plastic solid instead of a liquid crystal. More in detail, [TF]− is a prolate ellipsoid, with I 200 15, 1 = ± I I 360 15 where masses have been expressed in atomic mass units and lengths in Å . 2 ∼ 3 = ± [TEA]+ is somewhat less symmetric than [TF]−, and strictly speaking it should be classified as a spheroid. However, there is a clear separation between the two lowest momenta of inertia and the highest one, and for this reason we we still consider it to be an oblate ellipsoid, with I I 230 3, and I 380 8. The probability distributions for the three momenta of 1 ∼ 2 = ± 3 = ± 39 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

2 10

1 10 [ps] HB τ

0 10 2.5 3.0 3.5 4.0 4.5 5.0 1000/T [K-1]

Figure 3.11 – Lifetime of N H O hydrogen bonds as a function of inverse temperature. The − ··· straight lines are a guide to the eye. τHB is measured in ps.

inertia of [TEA]+ and [TF]− are shown in Figure A.10. This information could provide a basis for a coarse grained modelling of the system.

3.2.2 The effect of water at low concentration on the structure and dynamics of TEA-TF

Most if not all RTILs are hygroscopic, including those that are listed as hydrophobic when dissolved in water [133]. It is crucial, therefore, to investigate the effect of water at relatively low concentration on a wide range of TEA-TF properties. To this aim, we added 17 water molecules to our samples, corresponding to 1 % weight concentration, placing them at random positions within the simulation box, only taking care of avoiding close atomic contacts.

These new samples have been equilibrated and simulated following precisely the same pro- tocol used for the dry samples, practically doubling the number of simulations and the CPU time requested by our computations. The results largely conform to our expectations, but they are nevertheless useful to fully characterise the properties of TEA-TF.

First of all, the average potential energy and volume per ion pair follow closely the behavior seen for the dry samples, apart from a nearly parallel shift due to the extra cohesion and volume due to the added water molecules. Because of this similarity, the results are shown in Figure A.12. Then, the OW-OW radial distribution function (OW being the water oxygen) show that at 340 T 400 K water molecules are distributed homogeneously throughout ≤ ≤ 40 3.2. Classical MD simulations: results

Figure 3.12 – Typical configuration of a water molecule donating H-bonds to two [TF]− anions, and accepting a third one from a [TEA]+ cation. A thin dash line identifies hydrogen bonds.

the system, without a clear tendency to segregate. To be precise, up to T 400 K g (r ) = OW OW shows a sharp peak at r 2.72 Å , due to water-water hydrogen bonding (see Figure A.13). The ∼ computation of the average coordination number, however, shows that H-bonding among water molecules is quantitatively modest, and only one or two H-Bonded water dimers are typically found at any given time in our samples of 125 TEA-TF and 17 water molecules.

Below T 310 K a liquid-like modulation appears at intermediate range (6 r 16 Å ) in the ∼ ≤ ≤ gOW OW (r ) radial distribution function, while the sharp peak due to HBs is somewhat reduced. Below T 300 K, however, a sudden transition takes place, changing the shape of the radial = distribution function and completely suppressing the water-water HB peak. More detailed analysis of simulation trajectories shows that water molecules form stable associations with pairs of anions, in which water is the HB donor (see Figure A.14). A minority of water molecules forms even more complex structures made of two [TF]− anions and one [TEA]+ cation acting as proton donor, as shown in Figure 3.12.

The structural features described in the previous paragraphs are reflected in (or, equivalently, reflect) the dynamical properties of the simulated samples. First of all, at T 340 K,water ≥ diffuses significantly faster than [TEA]+ or [TF]−, as can be seen in Table 3.1. At T 300 K, ≤ however, the tight association of water and [TF]− anions implies that the two species diffuse at the same low rate.

At all temperatures, however, cations and anions diffuse faster in water contaminated samples than in dry samples (see again Table 3.1), and the enhancement of diffusion increases with

41 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

Table 3.1 – Diffusion constant of [TEA]+, [TF]− and water molecules as a function of tempera- ture in a system made of 125 TEA-TF ion pairs and 17 water molecules (wet samples). Values 2 1 for dry samples made of 125 ion pairs are reported for a comparison. All values in [cm s− ]

Wet samples Type T 240 K T 280 K T 300 K T 320 K T 360 K = = = = = 9 9 9 8 7 [TEA]+ 2.1 0.3 10− 5.1 0.2 10− 7.1 0.2 10− 2.2 0.1 10− 1.2 0.1 10− ± × 10 ± × 9 ± × 9 ± × 8 ± × 8 [TF]− 5.1 0.5 10− 2.3 0.2 10− 3.8 0.2 10− 1.0 0.1 10− 6.3 0.1 10− ± × 10 ± × 8 ± × 8 ± × 7 ± × 7 H O 5.2 0.3 10− 2.5 0.2 10− 4.3 0.1 10− 2.1 0.1 10− 8.7 0.1 10− 2 ± × ± × ± × ± × ± × Dry samples Type T 240 K T 280 K T 300 K T 320 K T 360 K = = = = = 9 9 9 8 8 [TEA]+ 2.5 0.4 10− 4.4 0.2 10− 4.9 0.2 10− 1.9 0.1 10− 9.7 0.1 10− ± × 10 ± × 9 ± × 9 ± × 8 ± × 8 [TF]− 5.1 0.5 10− 2.3 0.2 10− 3.8 0.2 10− 1.0 0.1 10− 6.3 0.1 10− ± × ± × ± × ± × ± ×

Table 3.2 – Electrical conductivity as a function of temperature computed by simulation (Sim., Eq. 3.6) and estimated by the Nernst-Einstein approximation (NE, Eq. 3.7) in a system made of 125 TEA-TF ion pairs and 17 water molecules (wet samples). Values for dry samples made of 125 ion pairs are reported for a comparison. All values in Siemens/m.

Wet samples Method T 240 K T 280 K T 300 K T 320 K T 360 K = = = = = 3 3 3 Sim. 1.1 0.4 10− 4.5 0.4 10− 5.3 0.2 10− 0.155 0.01 0.35 0.01 ± × 3 ± × 2 ± × 2 ± 2 ± NE 6.3 0.5 10− 1.5 0.1 10− 2.05 0.1 10− 5.5 0.1 10− 0.271 0.05 ± × ± × ± × ± × ± Dry samples Method T 240 K T 280 K T 300 K T 320 K T 360 K = = = = = 4 3 3 3 Sim. 7.3 0.5 10− 1.6 0.3 10− 1.75 0.2 10− 9.7 0.4 10− 0.103 0.05 ± × 2 ± × 2 ± × 2 ± × 2 ± NE 1.1 0.4 10− 2.3 0.2 10− 2.6 0.2 10− 6.6 0.3 10− 0.198 0.01 ± × ± × ± × ± × ± increasing temperature. As a result of the increased diffusion rate, also electrical conductivity is enhanced by the addition of water. Remarkably, the increase of conductivity is even larger than the increase of diffusion, as can be seen in Table 3.2. Moreover, we find that in wet samples above T 310 K, the conductivity computed by MD exceeds the Nernst-Einstein estimate. = This result, that does not violate any strict condition, is increasingly found by simulations [134]. It could be rationalised by thinking that at sufficiently hight density and fluidity (low viscosity), the motion of one ion along a given direction forces the motion of neighbouring counter-ions in the opposite direction, enhancing electric current beyond diffusion. A similar effect in quantum systems is known as backflow [135]. We point out, however, that this discussion is elementary and based on intuition. Rigorous statistical mechanical definitions and concepts might affect both the result and its interpretation. All together, the results on diffusion and

42 3.3. Density functional computations and ab-initio simulation conductivity show that water addition changes the properties of the hydrogen-bonding pattern, affecting the degree of ion pairing in their diffusion at medium and high temperature.

3.3 Density functional computations and ab-initio simulation

The analysis of the simulation trajectories raises many questions about details of the structure, relative strength of the hydrogen bonding and of Coulomb forces, stability of multiply charged clusters, etc., that we address here through the usage of density functional computations and a limited set of ab-initio (Car-Parrinello) simulations.

3.3.1 The molecule, the ions, and the energetics of ionisation and ion dissocia- tion

Computations have been carried out to determine, first of all, the ground state geometry of the different species; the energetics of the neutral versus ionic state of TEA and TF and their combination in the TEA-TF molecule; the geometry and strength of the hydrogen bond contributing to the cation-anion binding energy (together with Coulomb and dispersion forces).

A picture of TEA-TF in its gas-phase equilibrium configuration as determined by Gaussian 09 is shown in Figure 3.13. The closest contact between the two ions corresponds to a short and presumably strong hydrogen bond connecting the nitrogen atom on [TEA]+ to one of the oxygen atoms on [TF]−. The corresponding N O distance is 2.63 Å according to Gaussian 09, − and 2.59 Å according to CPMD. The N H O angle is 172◦ or 168◦ according to Gaussian 09 − ··· and CPMD, respectively. Such a short bond length suggests that the potential energy surface for the proton in the HB has a single minimum, in contrast to the double well potential of longer and looser hydrogen bonds [136]. In experiments, such a feature could be probed by vibrational spectroscopy, and it could also affect the proton conductivity at low and interme- diate temperature. The computational verification of the single-minimum property of the proton energy is illustrated below.

The analysis of vibrational frequencies carried out by CPMD shows that the frequency of the 1 1 N H stretching goes from 3357 cm− in the [TEA]+ ion to 2206 cm− in the TEA-TF molecule. − Together with the short N O distance in TEA-TF,this very large downwards shift emphasises − 1 the strength of the hydrogen bond. This is further confirmed by the fact that at 1550 cm− the N H O mode is the stiffest of all bendings. For the sake of completeness, we mention that 15 − ··· 1 1 C H stretching modes give origin to a narrow band from 2950 cm− and 3100 cm− , bending − 1 modes involving N H pairs are found between 1150 and 1450 cm− . Modes localised on [TF]− − tend to have lower frequency than those on [TEA]+. C F stretching modes, for instance occur −

43 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

Figure 3.13 – Ground state geometry of TEA-TF from density functional computations. PBE exchange correlation approximation, and Gaussian 09 computation (see Sec. 3.1). The dash line represents a hydrogen bond connecting the cation to the anion.

1 1 1 at 1050 - 1140 cm− , while S N stretching is found at 820 - 900 cm− . Below 550 cm− the − spectrum is made of a variety of modes affecting primarily dihedral angles.

While the hydrogen bond is the most apparent structural feature, the cohesive energy of the ionic TEA-TF molecule seems to be dominated, as expected, by Coulomb forces. This statement is supported by the following analysis, representing the formation of the ionic TEA-TF pair out of the neutral TEA and TF molecules in terms of a few more elementary steps.

According to G09, the energy of the reaction: TEA + TF TEA-TF (gas phase) −→ is ∆E 1.19 eV, or 27.4 kcal/mol. In our convention, positive ∆E means that the reaction runs = spontaneously from left to right. This relatively modest binding energy results from balancing the energy required to move one proton from the gas phase neutral TF molecule to the gas phase neutral TEA molecule, and the larger gain of Coulomb energy in bringing the two gas phase ions together, making one globally neutral but ionic TEA-TF molecule.

The proton transfer reaction, in particular, could be seen as the combination of two simpler steps:

TF [TF]− +p (gas phase) −→ and:

44 3.3. Density functional computations and ab-initio simulation

TEA + p [TEA]+ (gas phase) −→ where p is a proton, and the combination of these two steps requires ∆E 2.88 eV, or 66.4 = − − kcal/mol.

Then, the energy gain in joining [TEA]+ to [TF]− according to the reaction: [TEA]+ + [TF]− TEA-TF (gas phase) −→ is ∆E 4.07 eV, or 93.9 kcal/mol. This last and large ∆E, in particular, can be seen as the = Coulomb interaction of the two ions, and apparently determines the stability of the ionic TEA-TF gas-phase molecule.

The computed stability of the two neutral and isolated TEA and TF molecules with respect to the gas phase ions [TEA]+ and [TF]− is expected, since the ionised state of even the most ionic compounds (NaCl, for instance) is always due to the mutual interaction of the two ions. Additional details on the stability of the ionic versus the neutral state of TEA and TF units are given below.

All the energies reported in this sub-section have been computed by G09. Computations carried out by CPMD give results fully compatible with those of G09, but somewhat more uncertain for some residual difficulty in treating globally charged systems by plane waves.

Moreover, all cohesive energies do not contain the zero-point contribution from vibrations. However, all vibrational frequencies have been computed and we verified that addition of the zero-point energy does not change significantly the results for the cohesive energy.

Consistently with the room temperature ionic liquid character of TEA-TF, the molecular cohesive energy ∆E 1.19 eV is modest on the scale of covalent or ionic systems, and larger = than typical cohesive energies of H-bonds, however strong. On the other hand, this energy is still large on the scale of thermal energies at about room temperature.

The analysis of the charge distribution provided by CPMD for all neutral and anionic species confirms that N tends to have a slightly positive charge, and supports our previous statement saying that N is unlikely to act as a proton acceptor in a H-bond. This, in turn, makes it difficult to imagine proton transfer paths in TEA-TF reminiscent of the Grotthus mechanism in water. The picture is different in closely related compounds based on di-amines, like those discussed in Ref. [73,137].

An alternative way for the proton to escape strict vehicular motion on board of [TEA]+ would require its transfer back to a [TF]− ions, producing a neutral TEA and TF pair, with the proton moving together with TF before being transferred to a different neutral TEA unit. To determine whether the proton transfer is energetically possible and the associated barrier not overwhelm- ing in the temperature range of interest (200 T 400 K), the molecular energy of TEA-TF ≤ ≤

45 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid

15

10

5 E [kcal/mol] ∆

0 0.8 1.2 1.6 2.0

dO--H [A]

Figure 3.14 – Energy variation along the constrained coordinate measuring the dH O distance. −− Decreasing dH O means moving the proton towards the nearest [TF]− oxygen, giving origin −− to a neutral TEA and TF pair. Green dots: computations for the TEA-TF molecule. Red filled squares: computation for the periodic structure shown in Figure A.15. The full and dash black curves are a guide to the eye.

has been computed upon constraining the distance of the hydrogen bound to N in [TEA]+, progressively moving it towards the closest oxygen on [TF]−. All other degrees of freedom are relaxed to their minimum energy. Whenever the two ions [TEA]+ and [TF]− are in close contact, E(H O) has a unique minimum, corresponding to the equilibrium distance in the −− TEA-TF ground state (see Figure 3.14). In other terms, the presence of TEA at short distance from TF,destabilises the neutral pair, which is instead metastable when the two ions are well separated (not shown in the figures).

The single minimum in the E versus dH O distance (see Figure 3.14) is one further point sup- −− porting the strict vehicular mechanism as the only relevant proton conductivity mechanism in TEA-TF.

3.4 Summary and conclusions

Molecular dynamics simulations based on a simple, unpolarisable force field model, covering the 200 K T 400 K temperature range, and lasting 100 ns provide crucial insight to identify ≤ ≤ ∼ the transitions in TEA-TF seen by calorimetry and in neutron scattering measurements [71].

The experimental results, in particular, reveal two transitions on cooling, taking place on

46 3.4. Summary and conclusions heating at T 230 K and T 310 K, and at T 260 K and T 210 K on cooling. Calorimetry = = = = shows that both transitions are first order, and connect the liquid phase at T 310 K to the ≥ crystal phase at T 210 K, with an intermediate solid phase of uncertain identification in ≤ between. The macroscopic time scale of experiments makes the two transitions broadly reversible, despite sizeable hysteresis.

Simulations of TEA-TF on cooling from T 400 down to T 200 K show that the homogeneous = = liquid undergoes a weakly first order transition at T 310 K. At the transition temperature the = diffusion coefficient of both ions and the electric conductivity are simultaneously reduced to very low rates, while the rotation of the ions still represents an effective relaxation channel. These properties identify T 310 K as the melting temperature (T 310 K) of the simulated = m = system, and the phase at 260 K T 310 K as a plastic solid. The freezing of the system into a ≤ ≤ solid configuration is confirmed by quantitatively modest but qualitatively revealing changes in the structure as described by radial distribution functions. The observation of solidification by simulation is remarkable, especially for a molecular system of the TEA-TF complexity, that usually become glassy on cooling at the high rates of molecular dynamics.

No other discontinuous transition is apparent in the thermodynamic functions of the simu- lated sample down to T 200 K. Simulation of the heating cycle is prevented by the lack of an = experimentally determined crystal structure.

In the simulated samples, however, T 260 K marks the change in the rotational diffusion of = ions, that virtually stops at this temperature. The significance of this observation is emphasised by the change of the activation energy for rotational diffusion, pointing to a qualitative change in the rotational dynamics of the ions. We conclude that these effects are the simulation coun- terpart of the first order transformation seen in the experiment 50 K below melting, since ∼ the change from discontinuous to continuous transitions is a rather common consequence of the high cooling rates of molecular dynamics.

The atomistic resolution of the force field model then provides a wealth of additional micro- scopic information on the thermodynamic functions, the structure, and the linear dynamical coefficients of TEA-TF samples. For instance, comparison of electrical conductivity computed during the simulations with the estimate based on the Nernst-Einstein model allows us to quantify the effect of correlation in the diffusion of ions, that we express in terms of ion pairing. An important aspect in the system properties is represented by the structure and kinetics of the population of hydrogen bonds in TEA-TF that greatly affect measurable properties of the system. Also in this case, molecular dynamics trajectories allow to quantify a variety of parameters, that could be compared with experiments, and also with previous computa- tions on the same system [109]. Most of the quantities that we analyse depend on activated processes, that can be easily identified by their characteristic dependence on temperature. Arrhenius-type plots on the log-(1000/T) plane, in particular, show that these properties dis-

47 Chapter 3. Density functional computations and molecular dynamics simulations of the triethylammonium triflate protic ionic liquid play piecewise-linear ranges, whose linear coefficient allows us to estimate activation free energies for a variety of processes in the three phases displayed by the simulated samples of TEA-TF.

Detailed analysis of simulation snapshots reveals the formation of unexpected complexes made by up to three cations connected by H-bonding to a single anion. In the condensed phase, overall neutrality is enforced by screening from the neighboring ions, and locally charged clusters are thermodynamically stable. Density functional computations for gas-phase species show that only the smallest multiply charged clusters are stable or at least metastable, but also highlight sizeable stabilising effect arising from ions’ correlation, and from the formation of hydrogen bonds. In this respect, and despite quantitative differences, our results are reminiscent of those from previous studies, devoted to similar charged complexes in other protic room-temperature ionic liquids [126,127].

Vibrational properties of protic ionic liquids closely related to TEA-TF have been measured experimentally [14,50,138]. The quantitative comparison of computational and experimental data on vibrational properties would be highly valuable, but would also require a focused effort to quantitatively analyse the relative infrared or Raman weight of each mode, and to include anharmonic effects, that are all important for the low-frequency modes that carry information on inter-ion interactions. Such a detailed analysis has not been carried out yet, but remains as an appealing direction of quantitative research for the near future.

The role of water contamination on the properties of TEA-TF sample has been investigated by simulations, revealing no major effect on the thermodynamics of the system, but providing an intriguing view of characteristic changes in transport coefficients and in the structure due to the water ability to form strong H-bonds donated to the [TF]− anion, and, to a lesser extent, accepted from the [TEA]+ cations. It is found, for instance, that water enhances the ion mobility down to the solidification point, increasing the diffusion coefficient of ions, and, even more, the electrical conductivity. Analysis of simulation snapshots reveals intriguing local clusters made of [TEA]+ and, again, multiple [TF]− anions, joined by a bridging water molecule.

Besides these positive aspects of our study, it is important also to mention the limitations. It is well known that unpolarisable force field models are certainly only a first approximation to the potential energy surface of the system. Quantitative inaccuracies and even qualitative failures due, for instance, to the lack of polarisability in the model are apparent, and are not easy to overcome. The fixed bonding topology adopted by the force field limits the simulation ability to analyse proton transport mechanisms besides vehicular. This limitation might not be crucial for TEA-TF, since ab-initio analysis shows that a change of bond topology from TEA-TF is indeed very unlikely even for the acidic N-H termination, but, in general it is a strong drawback of the rigid ion model. Approaches to overcome the problem range from reactive

48 3.4. Summary and conclusions force fields [106], to ab-initio simulations. These last, however, are still expensive and limited to time scales orders of magnitude shorter that needed for a system such as TEA-TF at its triple point.

49 4 Linking structure to dynamics in pro- tic ionic liquids: A neutron scattering study of correlated and single-particle motions

The following chapter presents the results published in first co-authorship as: Tatsiana Bu- rankova, Juan F.Mora Cardozo, Daniel Rauber, Andrew Wildes and J. P.Embs, Linking Struc- ture to Dynamics in Protic Ionic Liquids: A Neutron Scattering Study of Correlated and Single- Particle Motions, Sci. Rep. 2018 8, 16400. The spot of the study is the structure-dynamic relationship in the protic ionic liquid TEA-TF characterized by strong hydrogen bonds be- tween cations and anions [72]. The site-selective deuterium/hydrogen-isotope substitution was applied to modulate the relative contributions of different atom groups to the total co- herent and incoherent scattering signal. This approach, in combination with the molecular dynamics simulations performed in Chapter 3, allowed us to obtain a sophisticated descrip- tion of cation self-diffusion and confined ion pair dynamics from the incoherent spectral component by using the acidic proton as a tagged particle. The coherent contribution of the neutron spectra demonstrated substantial ion association leading to collective ion migration that preserve charge alteration on picosecond time scale, as well as correlations of the localized dynamics occurring between adjacent ions.

4.1 Materials and methods

4.1.1 Samples

The sample of TEA-TF ([NH(C2H5)3][SO3CF3] see Figure 3.1) and its partially deuterated ana- logue TEAD-TF ([NH(C2D5)3][SO3CF3]) were synthesized and characterized at the Department of Physical Chemistry, Saarland University [139]. The neutron scattering (coherent and in-

50 4.1. Materials and methods

Table 4.1 – Summary of the Neutron Cross Sections σi. The cross-sections σi are given in barns 24 2 (1 b 10− cm ) at a wave-length λ 5.70 Å. = =

σinc System σscatt [b] σ [b] σinc [b] σ [b] [%] abs coh σscatt H 82.02 1.05 80.26 1.76 0.98 D 7.64 0.00 2.05 5.59 0.27 TF 31.33 1.80 0.01 31.32 0.04 TEA 1357.27 23.16 1284.83 72.45 94.66 TEA-TF 1388.60 24.96 1284.84 103.77 92.53

TEAD 241.48 7.23 111.53 129.95 46.19 TEAD-TF 272.81 9.03 111.54 161.27 40.89

coherent) and absorption cross sections for the cation and for the anion are summarized in Table 4.1.

4.1.2 QENS experiment

QENS experiments [140] in conjunction with polarization analysis were conducted on the D7 diffuse scattering spectrometer [141] with the wavelength of incident neutrons of 5.7 Å 1 covering the Q-values in the range of 0.3–2.0 Å− . The measurements were performed both in the diffraction and time-of-flight modes. The polarization efficiency of the instrument was determined by measuring an amorphous quartz standard. The detectors efficiency was calibrated by measuring a vanadium standard. The frequency of the Fermi chopper used in the time-of-flight mode was equal to 145 Hz, providing the resolution function of 98 µeV (FWHM) [142]. The low temperature incoherent TEA-TF spectra (T = 10 K) were used for the estimation of the linewidth of the instrument resolution. In order to minimize absorption and multiple scattering effects, an annular hollow cylindrical sample holder made of aluminum was used. The distance between the inner and outer cylinder was equal to 0.20 mm. Such a sample thickness guaranteed that neutron beam transmission through the sample exceeds 90%.

The standard data reduction of the D7 spectra was performed in the LAMP software pack- age [143]. The raw data were corrected for empty cell, cryostat and time-independent (am- bient neutrons/electronic noise) background contributions, sample geometry dependent self-attenuation and detector efficiency, converted to energy scale and finally binned into 1 several Q-groups with ∆Q=0.1 Å− to ensure adequate data statistics. After the separation of the coherent and nuclear spin-incoherent scattering [141,144], simultaneous fitting in the (E, Q)-domain was performed in a program module [145] based on the MPfit procedure [146].

51 Chapter 4. Linking structure to dynamics in protic ionic liquids: A neutron scattering study of correlated and single-particle motions

4.1.3 MD analysis

The details of the MD simulation were presented in Chapter 3. The comparison of the MD trajectories with respect to the neutron scattering experiment was carried out using the nMol- dyn/MDANSE software [147]. In particular, weighted incoherent and coherent intermediate scattering functions were calculated for all the particles in the simulation as well as for selected groups of atoms (bridging methylene groups, terminal methyl groups, N-H proton etc). The 2 weights of the terms are defined from the neutron scattering lengths and proportional to bα,inc and bα,coh bβ,coh for the incoherent and coherent contributions, respectively.

4.2 Data analysis

As it follows from the theoretical principles of the polarization analysis [141,148], the experi- mental scattering intensity can be separated into the coherent and nuclear spin-incoherent contributions, which are directly related to the corresponding dynamic structure factors,

Scoh(Q,E) and Sinc (Q,E)(Equations 2.5b and 2.5c), defined as Fourier transforms of the intermediate scattering functions, Icoh(Q,t) and Iinc (Q,t):

1 Z∞ µ E ¶ Scoh/inc(Q,E) Icoh/inc(Q,t)exp i t dt (4.1) = 2π − ħ ħ −∞

The next expressions demonstrate the connection between the intermediate scattering func- tions and the position operators in a system of identical particles:

1 D E X iQ R (0) iQ Rj (t) I (Q,t) e− · j0 e · and (4.2a) coh = N j,j 0 1 D E X iQ Rj (0) iQ Rj (t) Iinc (Q,t) e− · e · , (4.2b) = N j where N is the total number of scatterers in the system; the angular brackets denote a 〈···〉 thermodynamic average. We recall that the coherent contribution is determined by the corre- lation between the positions of different nuclei (j, j 0) at different times and originates from interference effects, while the incoherent contribution provides information on single-particle relaxations. In the case of different types of nuclei the intermediate scattering functions have to be averaged with weights depending on their neutron scattering lengths, bi :

52 4.2. Data analysis

D E X iQ R (0) iQ Rj (t) I (Q,t) b b e− · j0 e · and (4.3a) coh ∼ j,coh j 0,coh j,j 0 D E X 2 iQ Rj (0) iQ Rj (t) Iinc (Q,t) bi,inc e− · e · . (4.3b) ∼ j

These formulas enable calculation of neutron spectra from MD trajectories [147] and, hence, a direct comparison with the experimental scattering functions.

The model description of cation single-particle dynamics on a picosecond time scale gen- erally implies a superposition of two relaxation processes [71, 149, 150]. The first one is the long-range diffusion, the second one comprises entangled localized motions of side groups (conformational changes of alkyl groups, librations). To resolve the third subpicosecond component reported for ILs [150–152], the probed dynamical range has to be expanded by decreasing the wavelength of incident neutrons. With the applied experimental setting in the present study the fast relaxation is detected only as a flat background contribution.

Since the characteristic linewidths of the confined and long-range processes differ by ap- proximately a factor of ten, the incoherent dynamic structure factor can be presented as a convolution of the independent global, Sglob(Q,E), and localized, Sloc(Q,E), dynamic structure factors, multiplied by a Debye–Waller factor, exp( 2W ). −

S (Q,E) exp( 2W )S (Q,E) S (Q,E) (4.4) inc = − glob ⊗ loc

The adequate modeling of the long range process in ILs is based on the jump-diffusion model [153], where Sglob(Q,E) has a Lorentzian shape with the half-width Γtr(Q,E;Dtr,τ0) as defined in Equation 2.21. Dtr is the self-diffusion coefficient and τ0 is the residence time. It is necessary to mention that, because the time scale of the discussed QENS measurements does not exceed tens of picoseconds, Dtr has the meaning of a short-time diffusion constant. Experiments in a broader time window clearly show that the formalism of the jump-diffusion model is not strictly valid and the so-called stretched exponential function is required to characterize the long-range process [150–152]. For this reason diffusion coefficients evaluated by other methods such as PFG-NMR [73, 137] are usually slower than those obtained from QENS experiment.

G To describe various localized cation motions we applied the Gaussian model S (Q,E;Dloc,R), see Equation 2.26[82], which considers particles moving inside a confinement with a “soft” boundary. Dloc stands for the self-diffusion coefficient of the localized motion and R is the

53 Chapter 4. Linking structure to dynamics in protic ionic liquids: A neutron scattering study of correlated and single-particle motions variance of the particle displacement and characterizes the size of the domain, in which the particles are diffusing. Taking into account that the incoherent dynamic structure factor does not contain any cross-correlation terms and, hence, is an additive function, Sloc(Q,E) for the whole cation can be given as a simple sum of the three terms accounting for the motions of “ equivalent” hydrogens diffusing in a confinement with the corresponding characteristic radius

(RH, R1, and R2 for the N-H proton, bridging methylene, and end methyl groups, respectively). The contribution of the other elements (C, N, S, O) can be neglected [139]. The three terms of

Sloc(Q,E) have to be weighted with respect to the total number of particles in each group and the incoherent neutron cross sections of H and D.

prot 1 G 6 G 9 G S (Q,E) S (Q,E;DH,RH) S (Q,E;D ,R1) S (Q,E;D ,R2) and (4.5a) loc = 16 H + 16 1 ch + 16 2 ch deut σH G 6σD G S (Q,E) S (Q,E;DH,RH) S (Q,E;Dch,R1) loc = 15σ σ H + 15σ σ 1 + D + H D + H (4.5b) 9σD G S (Q,E;Dch,R2), + 15σ σ 2 D + H where the superscripts “prot” and “deut” are used for the TEA-TF and TEAD-TF samples, σH and σD are the neutron incoherent cross sections of the hydrogen isotopes H and D, respectively. The diffusion coefficients for the hydrogens of the ethyl group are considered to be equal to each other (Dch). Although it is obvious that the flexibility of the alkyl groups may result in a distribution of both radii of confinement and diffusion coefficients, as it is suggested, for example, from MD simulations, we had to apply this approximation to ensure the stability of the fit parameters.

Finally, the model dynamic incoherent structure factor (Equation 4.4 including Equations 2.21 and 4.5) convoluted with the resolution function of the instrument, R(Q,E), is fitted to the measured scattering intensity:

I S (Q,E) R(Q,E) bg(Q) (4.6) meas ∼ inc ⊗ + where bg (Q) is a flat background accounting for faster relaxations unresolved in the accessible experimental time window.

The fits of a pair of the TEA-TF and TEAD-TF spectra were performed in an iterative way at each measured temperature point. In the initial parameter set for the TEA-TF sample, the contribution of the acidic proton was neglected. This provided the first estimates for the other

54 4.3. Results

parameters Dtr, Dch, R1, and R2, which were used in the next step of fitting of the TEAD-TF spectrum. The procedure was repeated until the difference in the parameters values of two successive iterations was significantly less than the error margins (5-6 times).

The number of known analytical models applicable for coherent scattering is significantly smaller than that for the simpler case of incoherent scattering. For example, correlated reorientational motions can be characterized in the systems of non-interacting identical ions/- molecules [47,154]. There are also examples of a more general description such as Vineyard’s static approximation [155] and Sköld’s ad-hoc ansatz [156]. However, these approaches cannot be directly and unambiguously transferred to the coherent scattering of ILs, where differ- ent type of both intra- and intermolecular correlations lead to the appearance of diffraction peaks [157,158] in the Q-range accessible by QENS and have impact on dynamics [144,159]. For this reason, in the present work we will use a model-independent approach assuming that the total coherent structure factor is a convolution of the correlated long-range (subscript tr) and localized (subscript loc) relaxation processes:

  coh coh 1 Γtr (Q) Γloc (Q) Scoh(Q,E) S(Q)exp( 2W ) 2 A (Q)δ(E) (1 A(Q)) 2  = − π ¡Γcoh(Q)¢ E 2 ⊗ + − ¡Γcoh(Q)¢ E 2 tr + loc + (4.7)

coh coh where S(Q) is the coherent structure factor, the other parameters Γtr (Q), Γloc (Q) and A(Q) are modulated by S(Q) and do not have an explicit analytical description. The qualitative picture of correlated motions in TEA-TF provided by eq 4.7 will be interpreted in terms of anion-anion, cation-anion, and cation-cation contributions (eq 4.3) with the help of the MD simulations.

4.3 Results

4.3.1 Diffraction with polarisation analysis

Using the D7 diffuse scattering spectrometer in the diffraction mode we determined the nuclear spin-incoherent and coherent parts of the diffraction pattern as presented in Figure 4.1. The nuclear spin-incoherent scattering dominates the TEA-TF spectrum, whereas the coherent signal of the partially deuterated TEAD-TF is comparable and even stronger than the self- correlation contribution in the probed Q-range. Energy redistribution due to high-frequency vibrations (Debye-Waller factor) leads to a gradual decay of the incoherent component with Q. The mean square displacement (MSD, u2 ) associated with these vibrations can be estimated 〈 〉

55 Chapter 4. Linking structure to dynamics in protic ionic liquids: A neutron scattering study of correlated and single-particle motions

a) b)

TEA-TF TEAD-TF

Figure 4.1 – Coherent (orange line) and incoherent (blue line) contributions of the diffraction spectrum of TEA-TF (a) and TEAD-TF (b) measured at T = 320 K. The experimental data are compared to the cross-section weighted structure factor calculated from the MD particle configuration (black dotted line). The component intensities are normalized to I (Q 0) inc → for clarity. from the formula exp( 2W ) exp¡ u2 Q2¢. The fast vibrational motions of the ethyl protons − = −〈 〉 significantly change the total msd of TEA-TF ( u2 = 0.12 Å2 at T = 320 K) in comparison to 〈 〉 TEA -TF ( u2 = 0.05 Å2 at T = 320 K) . D 〈 〉 The coherent part of the diffraction pattern exhibits a pattern typical for other ILs [157,158] 1 1 with two correlation peaks at about Q= 0.9 Å− and 1.3–1.8 Å− . The latter is the so-called adjacency peak [158], the position of its maximum shifts with the deuteration of the ethyl chain pointing out to the intra- and intermolecular origin of the feature. The low-Q peak at 1 0.9 Å− is a signature of the unique charge ordering in ILs and referred to as the charge-charge correlation peak. Its position is not influenced by the isotope substitution in the cations. The data are compared with S(Q) I (Q,0) calculated from the MD trajectories using the = coh intermediate scattering function Equation 4.3. The experimental and theoretical results show a relatively good agreement, especially for the peak positions, allowing us to use the results of the MD analysis in the interpretation of the experimentally observed dynamics. For example, it is possible to dissect contributions of different atom groups and construct anion-anion (an-an), cation-cation (cat-cat) and cation-anion (cat-an) subcomponents of S(Q) by adding up corresponding cross-section weighted terms in eq 4.3 (Figure 4.2).

1 All the subcomponents exhibit intense peaks or antipeaks at Q= 0.9 Å− . This picture is typical for systems of two species distributed with equal periodicity [158]. The adjacency 1 correlation peak at Q=1.3–1.8 Å− of the neutron spectrum is mainly formed by the cation cross-correlation functions in both TEA-TF and TEAD-TF. The main difference is that the carbon skeleton contributes largely to the total S(Q) of the protonated sample, whereas the

56 4.3. Results

a) b)

TEA-TF TEAD-TF

Figure 4.2 – Anion-anion (orange), cation-cation (blue) and cation-anion (green) subcompo- nents of I(Q,t=0) for TEA-TF (a) and TEAD-TF (b) as obtained from the MD particle configu- ration at T = 320 K. The subcomponent intensities are determined by the neutron coherent scattering lengths of the species and their total number as given in eq 4.3b.

deuterium atoms are responsible for the dominating part of S(Q) in TEAD-TF.

4.3.2 Single particle dynamics

Long-range translation, localized conformational and librational motions of the ethyl chains as well as the restricted dynamics of the acidic proton (AH) have been previously described on a picosecond time scale in TEA-TF [71]. The interpretation of the results has been, however, based on the assumption that any interference effects of the inter- and intramolecular pro- cesses relax fast enough and do not distort the incoherent signal originating from the localized ion motions, as it was previously observed for a pyridinium-based IL [144]. Experimental separation of coherent and nuclear spin-incoherent scattering allows us to estimate the limits of validity of this approach for TEA-TF.

As can be seen from Equation 4.5 comparison between the completely protonated and paritally deuterated samples enables evaluation of a more complete set of parameters. The correspond- ing temperature dependencies are presented in Figure 4.3. The long-range process of TEA-TF and TEAD-TF is characterized by the same value of the self-diffusion coefficient, Dtr, suggest- ing that the isotope effect is minimal for the transport properties in the liquid state [71]. The obtained values of Dtr are in excellent agreement with the previously published data measured on the FOCUS time-of-flight spectrometer at SINQ, Switzerland with a similar resolution func- tion [71]. The temperature dependence of D follows the Arrhenius law D D exp( E /RT ) tr = 0 − A with the activation energy E 15.4 0.5 kJ/mol. The existing quantitative and qualitative A = ± difference with the PFG-NMR results [73,137] is the consequence of the significantly shorter

57 Chapter 4. Linking structure to dynamics in protic ionic liquids: A neutron scattering study of correlated and single-particle motions

a) Dtr b) c) Dch R 1 R DH H

R2 R

Figure 4.3 – Temperature dependence of the parameters describing the cation single-particle dynamics in the liquid phase as obtained from the iterative fits of the TEA-TF and TEAD-TF spectra. (a) Self-diffusion coefficients of the long-range (global) diffusion, Dtr, the localized motions of the N-H proton, DH, and the ethyl chains, Dch. The dashed lines are Arrhenius fits. (b) Sketch of the TEA structure and three groups of dynamically “equivalent” protons. (c) Temperature dependence of the confinement radii for the N-H proton (RH, red), bridging methylene (R1, blue), and terminal methyl (R2, green) groups. The dashed lines are guides to the eye.

time scale probed by QENS.

Various entangled localized motions of the ethyl chains are the source of the quasielastic component characterized by the parameters R1, R2, and Dch. After removing the coherent contribution, the diffusion coefficients turn out to be approximately twice as fast as the corresponding values obtained for the total, unseparated spectra on FOCUS [71]. Broader linewidths and consequently faster localized dynamics were also observed for the “pure” incoherent contribution of the aprotic pyridinium-based IL [144]. However, in the present case the effect is more pronounced indicating a greater impact of correlated dynamics of the three ethyl chains in the triethylammonium cation.

The restricted dynamics of the N-H proton discussed in Ref. [71] are also present in the refined incoherent contribution of TEAD-TF, corroborating the earlier observations. The absolute values for DH and RH have yet changed significantly after the subtraction of the coherent component. To explain the nature of this process we addressed the DFT computations and MD simulations in Chapter 3[72]. A close contact between the triethylammonium cation and the triflate anion in the gas-phase equilibrium corresponds to a strong hydrogen bond, the potential energy surface for the N-H proton exhibiting a single minimum, see Figure 3.14. Thus, it is not highly probable that the observed localized process is related to a direct proton exchange between the cation and anion. In this regard, the MD simulations can offer some insights, because the N-H incoherent scattering function can be directly compared with those of the other atom groups. It should be mentioned, however, that the MD relaxation processes appear to be significantly slower as compared to the experiment. This is a major drawback

58 4.3. Results

O F

O S F

O F

H3C

NH

H3C CH3

1 Figure 4.4 – Intermediate scattering functions I(Q,t) at Q 1.5 Å− as obtained from the MD = trajectories. The relaxation curves of the N-H proton (gray solid line), the nitrogen atom of the triethylammonium cation (violet dashed line) and the sulfur of the triflate anion (black dash-dotted line) are practically identical on the picosecond time scale. The intermediate scattering functions of the bridging methelene (light blue solid line) and methyl (green solid line) hydrogens demonstrate a significantly faster decay due to localized motions of the ethyl chains and are presented for comparison. The relaxation of the oxygen intermediate scattering function (orange solid line) is also faster than that of the acidic H, N and S indicating that the breaking time of individual hydrogen bonds is shorter than the relaxation time of the ion pair correlated motion.

of non-polarizable force fields [72,109,110]. Moreover, while a sum of several exponents is a good approximation for the QENS intermediate scattering functions, the corresponding MD curves are decidedly “stretched”, requiring, for example, Kohlrausch-Williams-Watts (KWW) functions for modeling. Under these conditions only qualitative comparison between the MD simulations and the QENS data is possible.

Figure 4.4 reveals a remarkable similarity between the intermediate scattering functions of the N-H proton, the nitrogen atom of the triethylammonium cation and the sulfur atom of the triflate anion during the first tens of picoseconds (the corresponding pair-correlation functions remain almost constant). This time-range is roughly equivalent to the experimental one including the discussed localized dynamics of the acidic proton. It means that the fast spatially restricted component of the TEAD-TF incoherent spectrum may reflect the localized dynamics of the anion-cation pair. According to the MD simulation, this correlated motion of the cation-anion pair persists over a longer time period than the lifetime of an individual hydrogen bond between them, as can be seen from a faster decay of the oxygen intermediate scattering function.

59 Chapter 4. Linking structure to dynamics in protic ionic liquids: A neutron scattering study of correlated and single-particle motions

TEA-TF

TEAD-TF coh

coh Figure 4.5 – Linewidths of the narrow quasielastic contribution Γtr of TEA-TF (red) and TEAD-TF (blue) as a function of Q at T = 320 K. Short-dashed color lines are the coherent contributions of the diffraction spectra, respectively. The black dashed line is the narrow quasielastic contribution of the incoherent spectrum calculated using Equation 2.21.

4.3.3 Collective dynamics

Although the difference between the H and D neutron coherent cross sections is less significant than that between the incoherent ones, the isotope substitution changes the sensitivity of the coherent QENS to different cross-correlation contributions (Figure 4.2). Thus, Scoh(Q,E) of TEAD-TF is mainly affected by cation-cation inter- and intramolecular correlated motions, while the coherent spectrum of TEA-TF contains all components. The influence of collective 1 cation-anion dynamics is most pronounced at the charge-charge diffraction peak (Q= 0.9 Å− ).

In general two quasielastic contributions are required to describe the coherent spectra of both samples (Equation 4.7 and Ref. [139]). The slower relaxation process is related to the coh long-range ion transport as can be seen from Figure 4.5, where the linewidths Γtr (Q) are compared with the Q-dependence calculated from the jump-diffusion model (Equation 2.21) for the incoherent spectrum. The typical narrowing of the quasielastic lines at the diffraction correlation peaks, referred to as de Gennes narrowing [160], can be seen for both TEA-TF and TEAD-TF.This effect literally means that there exist long-lived local arrangements of ions diffusing collectively on the picosecond time scale. The strength of the line modulation is comparable for both samples within experimental errors suggesting that the cat-cat, an-an, and cat-an cross-correlation components are characterized by similar or close relaxation times.

In contrast to the case of the pyridinium-based IL [144], Scoh(Q,E) of TEA-TF exhibits the

60 4.3. Results

inc TEA-TF inc TEA-TF Q = 0.9 Å-1 Q = 1.5 Å-1 coh TEA-TF coh TEA-TF

coh TEAD-TF coh TEAD-TF resolution resolution

a) b)

Figure 4.6 – Coherent dynamic structure factor of TEA-TF (dashed red line) and TEAD-TF (dashed blue line) at the charge-charge (a) and adjacency (b) correlation peaks. The inco- herent dynamic structure factor of the protonated sample (black solid line) is presented for comparison. The gray dotted line is the resolution linewidth at zero energy transfer for the D7 spectrometer.

second broader component, which allowed us to characterized the loss of coherence through localized dynamics. Fast intramolecular motions determine the shape of the QENS spectra in the energy transfer range of [-1, 1] meV (Figure 4.6) and the observed effect strongly depends ∼ on the type of dominating correlations (cat-cat, cat-an, an-an), which can be highlighted by means of deuterium labeling. The dynamics of the ethyl chains (carbon and deuterium 1 atoms) in TEAD-TF are mainly observed at the adjacency peak (1.3–1.8 Å− ). In this Q-range it is, therefore, possible to formally apply the Gaussian model as in the case of the incoherent spectra (Equation 2.26). The estimates of the effective diffusion coefficient are very close to the Dch-values (Figure 4.3, a) and the characteristic confinement size is of order R1 (Figure 4.3, c). The quasielastic linewidths of the totally protonated sample are narrower due to the cat-an and an-an contributions, which slow down the average relaxation times. Thus, the coherence in local ion arrangements may be maintained despite fast stochastic intramolecular motions. This effect may arise from the stronger interaction between ions due to the hydrogen bond in the PIL, as well as it may depend on the ion size and shape. For example, in regard to internal dynamics the structures of the bis(trifluoromethylsulfonyl)imide anion and 1-butylpyridinum cation allow more degrees of freedom. As a result, the coherent contribution of this aprotic IL did not feature the second broader component [144] seen in the present case. The charge- 1 charge correlation peak at Q = 0.9 Å− corresponds to the length scale longer than that of the adjacency peak. It inevitably leads to a faster decay of the cross-correlation terms due to localized internal motions and, consequently, to a significantly broader QENS spectrum in the energy transfer range of 1 meV of TEA-TF as compared to TEAD-TF (Figure 4.6, a). Moreover, the observed difference may also originate from overall faster anion relaxation, because mainly

61 Chapter 4. Linking structure to dynamics in protic ionic liquids: A neutron scattering study of correlated and single-particle motions the an-an component forms the charge-charge correlation peak of TEA-TF (Figure 4.2).

4.4 Summary and conclusions

In summary, an extensive understanding of picosecond dynamics of the model protic ionic liquid TEA-TF has been achieved by means of a synergistic approach combining QENS with the polarization analysis and MD simulations. The experimental separation of coherent and nuclear spin-incoherent scattering permits a sophisticated descriptions of collective and single-particle processes, while the MD analysis provides the tools to disentangle cross- correlation terms between selected groups of atoms.

Long-range diffusion as well as spatially restricted dynamics of the ethyl chains and the acidic proton have been characterized for the refined nuclear spin-incoherent spectra. Although the subtraction of the coherent contribution leads to significant changes in the estimates of the diffusion coefficients for localized dynamics, the qualitative picture of molecular motions seen with QENS on the picosecond time scale remains the same as has been previously inferred from the total dynamic structure factor. The enhanced localized dynamics of the acidic proton have been observed as well. Based on the analysis of the MD trajectories we assume that this process reflects the spatially restricted dynamics of cation-anion pairs in the liquid state.

The coherent QENS spectra have provided evidence of highly correlated picosecond motions in TEA-TF.The long-range diffusion can be considered as a collective process of ion associations. Their characteristic size is at least as large as the charge-charge periodicity of the PIL structure. Owing to the strong interaction between adjacent ions, the localized dynamics also turn out to be partially of collective nature, but motion coherence becomes gradually less significant at larger distances. Correlated long-range diffusion of ions on the picosecond time scale appears to be a common feature of both aprotic and protic ILs, whereas the nature of spatially restricted dynamics strongly depends on the ion structure and interaction between the ions. A complex interplay of single-particle and collective motions underlies the dynamical heterogeneity of ILs and accounts for their time scale-dependent transport characteristics.

62 5 Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

This chapter represents a manuscript in preparation, to be submitted as: Juan F. Mora Car- dozo, Tatsiana Burankova, Daniel Rauber, Frederik Philippi, Dina Klippert, Rolf Hempel- mann, Jacques Ollivier, Bernhard Frick and J. P. Embs, Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering. The aim of the study was to investigate the influence that different anions have on the dynamics of the acidic hydrogen in TEA-based PILs. We have used site selective deuteration of the cation, as we have done for the experiments in Chapter 4, to modulate the relative contributions of different atom to the total coherent and incoherent scattering signal. This approach together with ab initio computations for the ground state geometry of the samples and potential energy surface calculations for the hydrogen bond break confirmed the relative strength of this bond for all TEA samples (anion indipendent). It also allowed us to correlate physicochemical properties of the samples such as: viscosity, conductivity and density with the cation global and localized dynamics. The plastic phase proposed for TEA-TF in Chapter 3 was measured by backscattering experiments having the acidic hydrogen of the proton as a probe of the ion rotation.

5.1 Materials and methods

5.1.1 Samples

Four PILs with the triethylammonium cation (TEA, or NH(C2H5)3) and their partially deuter- ated analogues with TEAD (NH(C2D5)3) were synthesized and characterized at the Chemistry Department of Saarland University [139]. Tables 5.1 and 5.2 summarize the neutron cross-

63 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

Table 5.1 – Neutron Cross-Section and Chemical Structures of the studied Cations. The cross- 24 2 sections σ are given in barns (1 b 10− cm ) at a wave-length λ 5.5 Å. = =

Cations

Name Molecular Formula Acronym σcoh σinc σabs Structure

Triethylammonium NH(C2H5)3 TEA 72.42 1284.79 22.15

d-Triethylammonium NH(C2D5)3 TEAD 129.95 111.52 6.92

sections and acronyms of the ionic species. The large neutron incoherent cross section of hydrogen leads to the dominant incoherent signal from the TEA-cation in the protiated PILs and, thus, allows to investigate its single-particle dynamics. However, it is impossible to com- pletely neglect the correlation effects coming from a non-zero coherent cross-section [139].

For the partially deuterated samples, the neutron incoherent signal is on the same proportion than the coherent one, thus the spectra will reveal the different correlations (seen as peaks or correlation peaks) of the ILs containing their structural information. Each peak reflects a specific type of correlation at a given length-scale. Doing neutron and/or X-ray diffraction in ILs together with MD simulations at least three characteristic correlations in ILs have been identified . The first correlation usually occurs at short length scales ( 4 Å) and is due to the ∼ neighbouring atoms correlations, which can be intra or intermolecular [158]. At intermediate length scales ( 7 Å) a second correlation was found; it is related to charge ordering [139,158], ∼ the benchmark of ionic systems. The third correlation at long length scales in the order of nm, is related to the polar-apolar alternation and mainly depends on the anion size and ∼ symmetry [161].

5.1.2 Differential scanning calorimetry (DSC)

Thermal transitions were measured by means of differential scanning calorimetry (DSC), see Figure 5.1, using a DSC 1 STARe System (Mettler Toledo, Gießen, Germany) with a liquid nitrogen cooling system. Slow scan rates for the dynamic steps were applied to ensure the detection of the complete phase transitions [162]. Samples were dried in oil-pump vacuum and samples of about 25 mg were hermetically sealed in aluminium crucibles and heated to 373.15 K with a heating rate of 10 K/min followed by isothermal heating at 373.15 K for 10 min to remove the thermal history of the sample. Afterwards the sample was cooled with 1 K/min to 153.15 K with subsequent remaining at 153.15 K for 10 min. After the isothermal treatment

64 5.1. Materials and methods

Table 5.2 – Neutron Cross-Section and Chemical Structures of the studied Anions. The cross- 24 2 sections σ are given in barns (1 b 10− cm ) at a wave-length λ 5.5 Å. = =

Anions

Name Molecular Formula Acronym σcoh σinc σabs Structure

Trifluoroacetate C2O2F3 2C 31.88 0.006 0.11

d-Methanesulfonate CD3SO3 MS 36.04 6.16 1.64

Perfluorobutane Sulfonate C4F9SO3 PFBF 72.88 0.02 1.93

Perfluorooctane Sulfonate C8F17SO3 PFOS 127.49 0.03 2.16

a dynamic heating using a heating rate of 1 K/min to 373.15 K was applied. All experiments were performed twice to check reproducibility.

The whole set of PILs showed two phase transitions while cooling with corresponding features in the heating cycle. TEA-2C and TEA-MS have a liquid to solid phase transition around T= 262 K with corresponding melting temperatures close to 312 K. Furthermore, these two samples showed a solid-solid phase transition, in the cooling cycle, at T=260 K for TEA-2C and at T=212 K for TEA-MS, see Figure 5.1a and b. The respective DSC traces for the heating cycle can clearly be seen for TEA-MS close to T=230 K and as a shoulder of the melting peak at 300 K for TEA-2C.

TEA-PFBF and TEA-PFOS DSC traces behave alike as the former samples, they have a solid- solid phase transition at T=293 K for TEA-PFBF and at T=250 K for TEA-PFOS. The temperature transitions of the before mentioned PILs were also identified in Ref. [163], discrepancies in the transition temperatures are linked to thermal history of the liquid, thus to the specific (faster/slower) temperatures scan rates utilized in each experiment [71], which furthermore may result in overlooking of sensible thermal transitions [163].

5.1.3 Quasi-elastic neutron scattering experiments

Neutron experiments were carried out at the Institut Laue-Langevin (ILL, Grenoble, France). The spectrometers IN5 and IN16B were utilized to investigate the dynamics in the largest

65 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

a) b)

c) d)

Figure 5.1 – DSC traces of a) TEA-2C, b) TEA-MS, c) TEA-PFBF and d) TEA-PFOS at 1 K/min scan rate.

possible time-window. The cold neutron backscattering spectrometer IN16B was used with an incoming neutron wavelength of λ= 6.27 Å. This wavelength provided an energy resolution of 0.75 µeV (fwhm) where the nanosecond time-window was studied. The momentum transfer 1 accessible for this configuration, Q= 0.1–1.8 Å− , was covered by 16 detectors. Elastic and inelastic fixed window scans [89], EFWS and IFWS respectively, were performed simultaneously on heating; the scans measured the intensity in narrow channels around E= 0 µeV and E= 2 µeV, correspondingly. The temperature covered was in the range T= 2–370 K at a heating rate not greater than 3 K/min.

IN5 was utilized with an incident neutron wavelength λ= 5.5 Å, and providing a resolution of

66

1 5.1. Materials and methods

60 µeV (fwhm) where the dynamics in the ps time-window were investigated. The accessible 1 energy-window and momentum transfer were E= 1.7 meV and Q= 0.4–1.8 Å− , respectively. ± TEA-2C measured at 75 K was used as the resolution function R(Q,E).

A vanadium standard was used to calibrate the detectors of both instruments. Background effects were corrected by measuring an empty can at different temperatures. The samples were contained into the gap (0.2 mm wide) of a concentric double-hollow thin Aluminum cylinder. The transmission of the filled sample holder was about 90 %, thus minimizing multiple scattering. The raw neutron data were transformed from time-of-fight (TOF) to I(Q,E) S(Q,E)[78] using LAMP [143] in the standard manner. The sample signal was ∝ normalized to the incoming flux followed by the subtraction of the signal of an empty sample holder, then the energy transfer E was calculated. The signal from the data was normalized with respect to the vanadium standard and corrected for the energy dependent detector efficiency. Finally, the momentum transfer Q was calculated and the data was binned into groups of the same momentum transfer width.

Eventually, the individual Q groups were analyzed, using the DAVE [164] software-package, in a model-independent approach. This strategy allowed to identify and separate different dynamical processes accessible in the experimentally probed time and energy windows. In a second step, analytical models were adjusted to the neutron data. They require multiple parameters to describe the neutron data, thus, it was necessary to perform a two dimensional (2D) analysis, i.e., treating Q and E simultaneously as independent variables when adjusting the spectra. The 2D analysis was performed in a program module [145] using the MPFIT procedure [146] and in MATLAB.

5.1.4 Data analysis

Liquid phase

The QENS signal is composed of two dynamically decoupled processes occurring on different time scales [71,139]; a slower and spatially not restricted motion observed in the time window of few picoseconds was interpreted as the self-diffusion of the cation (global motion). In addition, faster dynamical processes characterized by relaxation times in the range of 0.5–1 ps, which appear to be spatially confined (localized motion), and are related to the intramolecular librational and rotational motions.

The measured intensity is proportional to the dynamical structure factor S(Q,E), which is a convolution of the functions describing the long-range (Sglobal(Q,E)) and localized

67 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

k (Slocal(Q,E)) dynamics [78]:

K X k S(Q,E) Sglobal(Q,E) Slocal(Q,E). (5.1) = ⊗ k 1 =

The unrestricted diffusion of the cations can be satisfactorily represented by the jump-diffusion model [153], where Sglobal(Q,E) is given by a Lorentizan with half width at half maximum defined in Equation 2.21. Where Dtr is the self-diffusion coefficient and τ0 is the residence time between successive jumps. For the analysis of the localized motions we applied the G Gaussian model S (Q,E;Dloc,R), see Equation 2.26[82]. It describes the restricted motion of particles in a finite domain with soft boundaries; R characterizes the size of the region where the particle is confined to diffuse and Dloc is the corresponding diffusion coefficient. To illustrate our analysis, the dynamical structure factor of the fully protiated ILs (SPIL(Q,E)) is presented as the convolution of the global motion of the cation with the restricted dynamics of the different hydrogen groups of the alkyl chains (see Equation 4.5),

prot S (Q,E) I(Q) L(Γ ,E) S (Q,E) bg(Q,E), (5.2) PIL = global ⊗ loc +

prot where I(Q) is an intensity factor containing the Debye-Waller factor, Sloc (Q,E) contain the functions describing the restricted dynamics of the acidic hydrogen (AH), the hydrogens of the three methylene groups (CH2) and the three terminal methyl groups (CH3), together with their corresponding diffusion coefficients D{H,ch} and confinement size R{H,1,2}. We recall that prot the pre-factors in each Sloc (Q,E) weight the share of each hydrogen group to the total signal, that for the PIL can be considered to be proportional to the total number of hydrogens (16) in the cation, see Table 5.1. The term bg(Q,E) in Equation 5.2 summarizes all motions faster than the observation time for the given instrumental setting.

Equation 5.2 involves a relative high number of parameters; to reduce them we used RH and DH form the partially deuterated ILs, and substituted these outcomes in Equation 5.2, as explained in Chapter 4 and in Refs. [71, 139]. Nonetheless, to obtain the AH parameters implied to analyze the deuterated IL signal, which unlike the PIL one (that is mainly incoherent and dominated by the hydrogen atoms of the cation) is a mixture of the scattering of all the atoms of the IL. For this reason, a separation of the AH incoherent signal (IAH) is necessary. To accomplish this we used the signal of our PIL and subtracted it from the deuterated IL signal

68 5.1. Materials and methods

Table 5.3 – Experimental Ratios between d-PIL and PIL Number of Molecules

D 15σinc TEAD/TEA 2C MS PFBF PFOS H 16σinc Nd-PIL 0.8812 0.9311 0.9670 0.9786 0.0239 NPIL

and approximated IAH as follows:

I (Q,E,T ) I (Q,E,T ) f I (Q,E,T ), (5.3) AH ≈ d-PIL − · PIL

where Id-PIL is the measured intensity of the partially deuterated IL (d-PIL) and IPIL is the corresponding signal from the protiated PIL. The factor f accounts for the incoherent signal of the protiated PIL to the one coming from the deuterium atoms of the alkyl chains in the d-PIL, therefore we write f as:

15σD N f : inc d-PIL , (5.4) = H · N 16σinc PIL

where Nd-PIL is the number of the d-PIL molecules as obtained form the sample preparation and NPIL the ones of the PIL. For all the cases, the ratio Nd-PIL/NPIL was less than one, re- flecting the mass difference between the hydrogen and its isotope, see Table 5.3. The ratio D between the incoherent scattering cross-sections of deuterium and hydrogen, i.e., σinc and H σinc, respectively, was weighed by the ratio between the number of deuterium atoms in the d-PIL (15 of the deuterated alkyl chains) and the total number of hydrogens in the PIL (16).

Regardless of our approach, the IAH signal will contain information about the collective dynamics of the d-PIL thanks to the relative high coherent scattering cross-section of 15 deuterium atoms and the different carbons (in the alkyl chains and in the different anions)

[139]. Notwithstanding the foregoing, the remaining incoherent part of IAH is dominated by the scattering of AH, and is this highlighted signal that we studied. IAH was composed of two well separable processes, namely the long-range dynamics of the entire cation and the localized dynamics of AH. We decided not to assign any analytical model to the long-range dynamics but to describe it in a phenomenological way with a single Lorentzian, so as its line-width get modulated, de Gennes narrowing [144,160,165,166], at the coherent correlation peaks. Moreover, the localized dynamics are also affected by cross-correlations in certain Q-regions [139, 158, 161], but where possible, they were described by the Gaussian model (Equation 2.26). We can rewrite Equation 5.3 in terms of the dynamical structure factor as

69 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering follows:

S (Q,E) I(Q) L(Γ,E) SG(Q,E;R ,D ) bg(Q,E), (5.5) AH = ⊗ H H H + where as in Equation 5.2, I(Q) is an intensity factor containing the Debye-Waller factor and bg(Q,E) is the background.

Solid phase

If the temperature decreases, at a certain T the ILs changed from the liquid to the solid phase (Figure 5.1), where their long-range dynamics ceased. This caused a drastic narrowing of S (Q,E) together with a steep increase of the intensity around the elastic line (E 0 µeV). global = However, some broadening around this line was still detectable, i.e. not all the ILs dynamics were frozen, some of the localized modes such as the methyl group rotations were ongoing [49,167,168]. The dynamical structure factor for this phase can be written as [76]:

S (Q,E) I(Q)((1 ν)δ(E) νS (Q,E)), (5.6) solid = − + local where I(Q) is an intensity factor including the Debye-Waller factor, a δ(E) function accounts for the cease of the global dynamics and ν is the fraction of mobile particles. Slocal(Q,E) describes the methyl group rotation and its functional forms can be described either by the three-fold jump-rotation or the continuous rotation model, see Equations 2.22 and 2.23[49,167,168]. In th the models R stands for the rotation radius, jk (x) is the k order spherical Bessel functions, τ is the residence time for the three-fold jump model and τr is the relaxation time for the continuous rotation. Moreover, if we consider the localized dynamics as a thermally activated process, the relaxation time (for the simplest case) will follow an Arrhenius behaviour

µ ¶ Ea τ(T ) τ0 exp , (5.7) = −kB T

with activation energy Ea and where kB is the Boltzmann constant. Now, we can combine Equations 5.6 and 5.7 to have an expression where Ssolid(Q,E,T ) depends explicitly on the temperature. Ssolid(Q,E,T ) can be measured via fixed window scans (FWS), a technique where the intensity is registered as function of the sample temperature (gradually changed) in narrow

70 5.1. Materials and methods energy channels. For example, measured around the elastic line E 0 µeV (EFWS) and off = close to the elastic line E 2 µeV (inelastic IFWS). The obtained signal, is the convolution of off = Equation 5.6 with the instrumental resolution R(E):

R R(E 0)Ssolid(Q,E E 0,T )dE 0 I FWS(Q,T ) − . (5.8) = R(E 0) =

For the sake of having an analytical form for I FWS(Q,T ), R(E) was assumed to have a Lorentzian shape [71] with hwhm Γres and the mean squared displacement proportional to the tempera- ture [169,170], so we can rewrite Equation 5.8 as:

2 õ µ ¶¶ FWS CTQ 1 ³ ³ ´´ Γres I (Q,T ) B e− 3 1 ν 1 1 2j0 p3QR 3-Fold = − − 3 + ¡ 2 2 ¢ π Γres Eoff +  µ ¶ 3 1 ³ ³ ´´ Γres 2ħτ ν 1 1 2j0 p3QR +  and (5.9) + − 3 + ³¡ 3 ¢2 2 ´ π Γ ħ E res + 2τ + off

2 Ã FWS CTQ ¡ ¡ 2 ¢¢ Γres I (Q,T ) B e− 3 1 ν 1 j (QR) cont = − − 0 ¡ 2 2 ¢ π Γres Eoff +  k(k 1) Γres + ħ 1 X∞ 6τr ν (2k 1)j 2(QR) + , (5.10) k ³ ´2  + π k 1 + k(k 1) 2 Γres + ħ E = + 6τr + off where B is a scaling factor taking into account the resolution convolution and C a proportion- ality constant.

5.1.5 Ab-initio simulations

Computations were carried out to better understand the outcomes of the performed neutron scattering experiments, thus, the dynamics of our PILs. We performed ab initio computations at the density functional theory (DFT) level to obtain the ground state structure and energy of the ionic pairs. The Perdew-Burke-Ernzerhof [98] approximation for exchange and correlation energy was used, in addition the dispersion interactions were included at empirical level [117], and simulated annealing was employed to optimize the ground state geometries [116]. The calculations were performed using the CPMD [113] software package, which is based on soft

71 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering norm-conserving ab-initio pseudopotentials and plane waves [114]. The calculations included the computation of properties related to the hydrogen-bond such as the N H stretching − frequency, the bond angle and its length. In addition, we computed the energy needed for the jump of a acidic-hydrogen to the anion; we did it by moving progressively the acidic hydrogen towards the closest oxygen in the anion and simultaneously relaxing the other degrees of freedom to their minimum energy, see Chapter 3. These factors were vital to reveal the type of interactions present in our samples and helped to understand the outcomes of the localized dynamics of the acidic hydrogen.

5.2 Results and discussion

The present study was designed to focus on the dynamics of the acidic hydrogen, i.e the hydrogen taking part in the hydrogen-bond of the form N H O. This hydrogen or AH, is the − ··· one covalently bonded to the nitrogen (proton donor site) of the cation and hydrogen bonded to one of the multiple oxygens of the anion (proton acceptor sites).

5.2.1 Density functional computation

The ground state geometries of the different samples are presented in Figure 5.2 and in Ta- ble 5.4. The nearest contact between ions corresponds to a short hydrogen bond connecting the nitrogen in TEA with one of the oxygens of the anion. The corresponding N O distances ··· (dN O) are 2.6Å, the hydrogen bond angle ( N AH O) is close to 180°, suggesting the forma- ··· ∼ 6 − ··· tion of a strong hydrogen bond [27]. This bond become more stable as the anion decreases in size, as it is reflected by the reduction of the N AH stretching frequency (ωN AH) and in the − − increase of the covalent bond length dN H. − We calculated the potential energy surface (PES) of the ionic pairs as a function of the vector joining AH and the nearest O of the anion (dAH O); Figure 5.3 shows that as either the ions ··· get closer or move apart, the energy penalty is large and higher than the available thermal 1 energy ( 3.26 kJmol− at T = 400 K), thus, manifesting the strength of the coulomb forces. The ∼ calculated PES show a single minimum along dAH O, making it very unlikely for AH to jump ··· from the cation to any of the anions. The PES for TEA-PFOS was not calculated, however, due to the similarities in the structural parameters of TEA-PFOS with rest of the samples, we do not expect it to be different than the ones shown in Figure 5.3.

The atomic distribution of charges was calculated using the electrostatic potential (ESP) [104, 105]. In particular we focused on the anion terminal groups. For the MS anion, the hydrogens of the methyl group are positively charged, whereas the oxygens in the CO2 terminal group are mainly negative charged. In contrast, the fluorinated terminal groups of 2C, PFBF

72 5.2. Results and discussion

a) b)

c) d)

Figure 5.2 – Ground state geometry of: a) TEA-2C, b) TEA-MS, c) TEA-PFBF,d) TEA-PFOS from DFT computations. PBE exchange correlation and CPMD calculation. The close contact from H1 and O represent a hydrogen bond.

Table 5.4 – Hydrogen-bond characterization in the ground state geometry of the different TEA based PILs

1 dAH O[Å] dN O[Å] N H O[°] dN H[Å] ωN H[cm− ] ··· ··· 6 − ··· − − TEA - - - 1.03 3357.0 TEA-2C 1.31 2.50 174.7 1.19 1719.6 TEA-MS 1.45 2.58 179.0 1.13 1878.0 TEA-PFBF 1.55 2.64 169.5 1.10 2348.0 TEA-PFOS 1.54 2.63 171.3 1.10 2348.0

and PFOS are negatively charged, and the respective oxygens in the SO3 terminal group are negatively charged too (see Table 5.5). Thus, even though the MS anion as a whole carries a negative charge, it can behave locally as a dipole.

73 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

14 TEA-2C 12 TEA-MS TEA-PFBF 10 8 6 E [kJ/mol]

" 4 2 0 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

d [Å] H...O

Figure 5.3 – Energy variation from the ground state configuration along the restricted vector joining dAH O. Negative dAH O means moving AH toward the oxygen in the anions. Positive ··· ··· dAH O implies moving away toward N. Dashed curves are guides for the eye. ···

Table 5.5 – Atomic charges of the terminal groups for the different anions

2C MS PFBF PFOS q[e] q[e] q[e] q[e] – – O29 -0.66 O38 -0.56 O50 -0.56 O29 -0.81 O30 -0.67 O39 -0.41 O51 -0.46 O30 -0.64 O31 -0.73 O40 -0.53 O52 -0.54 F26 -0.28 H17 0.28 F35 -0.25 F47 -0.23 F27 -0.28 H18 0.30 F36 -0.24 F48 -0.22 F28 -0.30 H19 0.32 F37 -0.25 F49 -0.23

5.2.2 Dynamics in the solid phase

Protiated samples

Elastic and inelastic fixed window scans, EFWS and IFWS, respectively, cover a wide tempera- ture range, enabling to observe the onset of diverse dynamical processes. For example, methyl group rotation in alkyl chains has been measured by means of EFWS in ammonium-based PILs and in other systems [71, 171–173]. The EFWS and IFWS of TEA-2C measured on the backscattering instrument IN16B at the ILL are shown in Figure 5.4. The EFWS displays a "steplike" decrease of the elastic intensity between T=2–230 K together with the appearance of an inelastic bump in the IFWS. The width of this bump mainly depends upon two factors: The activation energy of the dynamical process and the high temperature limit of its relaxation time [89]. Above 230 K the sample starts to melt, and the elastic intensity decreases rapidly until it eventually vanishes at T=290 K.

74 5.2. Results and discussion

#10-2 1.0 3-Fold Cont 1.2

0.8 0.5 IFWS [a.u.] EFWS [a.u.] 0.4

0.0 0 50 100 150 200 250 300 T [K]

1 Figure 5.4 – EFWS and IFWS data of TEA-2C at Q=1.72 Å− . The solid line is the result of the 2D-fit using the three-fold jump-rotation model and the dashed line is the result for the continuous rotation model (Equations 5.9 and 5.10).

Table 5.6 – Fit results of the FWS measurements for the different protiated samples according to the three-fold jump-rotation and continuous rotation model.

Three-Fold Jump-Rotation 1 ν R[Å] τ[ps] Ea[kJmol− ] TEA-2C 0.521(0.008) 1.44(0.02) 6.93(0.81) 6.92(0.12) TEA-MS 0.378(0.021) 1.29(0.15) 4.90(1.09) 6.45(0.21) Continuous Rotation 1 ν R[Å] τr [ps] Ea[kJmol− ] TEA-2C 0.448(0.008) 1.75(0.05) 3.29(0.38) 7.01(0.13) TEA-MS 0.466(0.082) 1.08(0.17) 3.68(0.66) 5.90(0.23)

The temperature dependence of the EFWS and IFWS for TEA-2C and TEA-MS was analyzed using Equations 5.9 and 5.10 in the Q-regions free from Bragg peaks and in the temperature range prior to melting transitions, i.e. T=2–230 K for TEA-2C and T=2–150 K for TEA-MS (Figure 5.6). Fit results are presented in Figure 5.4 and Table 5.6.

Visual inspection of the EFWS of TEA-2C, reveals that both the three-fold jump-rotation model and the continuous rotation model describe equally well the dynamics in the solid phase, however, differences are present in the determination of the IFWS bump maximum. They are caused either by the divergence of τ0 (the high temperature limit of the relaxation time) for each model, to the scattered nature of the inelastic signal or to extra degrees of freedom in the ions (librations). If we assume that the intensity of our FWS is dominated by the 16 hydrogens of the cation, the number of mobile particles found in TEA-2C is 8.3 (ν=0.521) for the three-fold model and 7.2 (ν=0.448) for the continuos rotation model, thus suggesting the rotation of the methyl groups (9 hydrogen atoms) [171,174,175]. However, the calculated radii of rotation

75 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering are larger than the typical C H bond length (1.16 Å), therefore indicating the flexibility of the − ethylene group (CH CH ) that causes an increase in R. These extra motion of the alkyl chain 2− 3 can not be seen as an evident discontinuity of the EFWS, but they are certainly detected in the IFWS, which appears to be more sensitive to this type of dynamics than the customary EFWS.

Another factor influencing the dynamics in the solid phase is the chemical composition and size of the anions. The anions can alter the fraction of mobile particles and can restrict the methyl group rotation. For instance, in TEA-2C (Table 5.6) the radii of rotation obtained by the two models are larger than those for TEA-MS, moreover, they also differ from the outcomes of our previous published data on TEA-TF [71], where a rotation radius of R=1.16 Å and 9.28 mobile particles were found. The anion size, and more specifically the length of their fluorinated chain is a source of extra degrees of freedom in the system, so as their chain can perform librations and their trifluoromethyl terminal groups (CF3) can rotate. For example, we found that for TEA-PFBF,the IFWS displayed a complex temperature dependence (see Figure 5.5 ); in it the onset of at least two different dynamical processes is presented. An inelastic maxima at T=110 K is related to the methyl group rotation of the TEA cation (consistent with TEA-2C, TEA-MS and TEA-TF outcomes) and a broad maxima between T=160 K and T=220 K correspond to the onset trifluoromethyl group hindered rotation, as they have been identified via NMR measurements [176,177]. In addition the EFWS and IFWS of TEA-PFBF shows a melting transition at T=300 K as it was identified on the heating cycle in our DSC characterization (Figure 5.1c)).

Partially deuterated samples

The partially deuterated samples were analyzed applying Equation 5.3; the equation is valid in those Q-regions where no structural maxima are present and where the cross-correlations are less intense. Furthermore, we considered only those pairs of protiated and partially deuterated samples, which show similar thermodynamic behaviour, i.e. those pairs with phase transitions at similar temperatures. As an example of our approach, the EFWS and IFWS outcomes for the

TEAD/TEA-MS sample pair are displayed in Figure 5.6. Three different regions for TEA-MS can be identified: One starting from T= 2 K to 150 K, characterizes the methyl group rotation, followed by a phase transition at T=160 K where additional motions are expected such as alkyl chain librations, take place, and finally, the melting transition at T>300 K. The transition at T=160 K is evidenced as a sharp decrease in the elastic signal (see inset Figure 5.6b), in combination with an increase of the inelastic bump, hence from T= 160 to T=300 K the methyl group rotation are entangled with alkyl chain librations, which makes the inelastic bump in the IFWS to extend further in temperature and to be broader than for TEA-2C (Figure 5.4).

For TEAD-MS in Figure 5.6, the described features observed inTEA-MS are not observable. The difference reflects the effect of deuterium in the scattering signal of the alkyl chain. As a result,

76 5.2. Results and discussion

1.0 a)

0.5 EFWS [a.u.] 0.0 0 100 200 300 T [K]

#10-2 3.0 b)

2.0

IFWS [a.u.] 1.0

0 100 200 300 T [K]

Figure 5.5 – a) The EFWS and b) the IFWS of TEA-PFBF averaged over the Q-group where no structural maxima were found. At least three different phase transitions can be identified, with corresponding maxima at in the IFWS at T=110 K, a broad bump between 160 K to 220 K. The maximum at T=300 K is a first melting transition as identified with our DSC traces. They reflect the onset of at least two different dynamical processes in the solid phase and a the sample melting with corresponding features in the EFWS.

the decrease of the elastic intensity as well as the increase of the inelastic intensity before melting (T<300 K) is mainly caused by the Debye-Waller factor (Figure 5.6a and Figure 5.6b).

Figure 5.6c displays the calculated EFWS and IFWS of AH. The EFWS stays constant in the temperature interval T=2–200 K, while the inelastic intensity remains on average at zero, suggesting no thermal activation of any AH dynamics. From T=220 K and 290 K, the elastic intensity decreases and the inelastic intensity increases, however, the IFWS does not show a bump as for the protiated counterpart, thus, making it difficult to model this behaviour through analytical models. Nonetheless, the decrease in the EFWS together with the complementary increase of the IFWS indicate the activation of a dynamical process, which we consider to be caused by ion rotations without diffusion. The mechanism can be initiated in this temperature range, relaxes in the nanosecond time-scale (partly accessible to our experimental time- window) [72,124], and characterizes plastic solids [38,125].

77 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

1.0 TEA -MS a) TEA -MS b) D D TEA-MS TEA-MS 10-2 0.8 0.6

0.4 IFWS [a.u.] 10-3 EFWS [a.u.] 0.2

0.0 150 200 250 300 150 200 250 300 T [K] T [K] c) #10-2 1.0 2.8

0.8 1.9 AH EFWS 0.5 AH IFWS 0.9 IFWS [a.u.] EFWS [a.u.] 0.3

0.0 0.0 120 140 160 180 200 220 240 260 280 300 320 T [K]

Figure 5.6 – IFWS and EFWS intensities for a PIL/d-PIL pair and IAH as in Equation 5.3. a) Experimentally (not normalized) measured IFWS of TEA-MS (scaled to f ) and TEAD-MS 1 at Q=1.79 Å− . b) Corresponding EFWS and in the inset the zoom of the dynamical phase transition. c) Calculated and normalized elastic/inelastic intensity of AH as a function of the temperature.

For sample pairs with different thermodynamic behaviour such as TEA-2C and TEAD-2C the Equation 5.3 can not be applied, see Figure 5.7. Below T=300 K the IFWS of TEAD-2C show a Q-dependent position of inelastic intensity maxima, whereas for TEA-2C the maxima appears to be Q-independent. This behaviour is related to the activation of different dynamics for each sample, namely the spatial unrestricted dynamics for TEAD-2C and the localized dynamics for TEA-2C. On the one hand, the relaxation time for global diffusion is inversely proportional to 2 Q− (see Equation 2.19), thus the maxima of the IFWS moves towards lower temperatures for higher Q values. On the other hand, the relaxation time for restricted dynamics (Equations 2.22 and 2.23) is explicitly Q-independent, thus the inelastic maxima should be found at the same temperature, so as for TEA-2C. In this case the analysis used for the other samples can not be used, so the phase transition for TEA-2C and TEATEAD-2C is not consistent.

78 5.2. Results and discussion

#10-2 5.0 0.6 Å-1 a) 4.0 1.1 Å-1 1.5 Å-1 3.0 -1 1.8 Å 2.0

IFWS [a.u.] 1.0

0.0 100 150 200 250 300 T[K] # -2 2.5 10 -1 b) 0.6 Å 2.0 1.1 Å-1 1.5 Å-1 1.5 -1 1.8 Å 1.0 IFWS [a.u.] 0.5

0.0 100 150 200 250 300 T[K]

Figure 5.7 – IFWS of TEAD-2C a) and of TEA-2C in b). The partially deuterated sample shows a Q-dependent peak maxima from T>220 K indicating long-range dynamics at low temperatures. In TEA-2C no Q dependency is seen in the temperature domain 110 K T 220 K ≤ ≤

5.2.3 Liquid phase

Partially deuterated samples

We performed QENS experiments on the protiated and partially deuterated ILs using the time of flight instrument IN5 from the ILL. We focused our attention on the AH dynamics (in a ps time-window) and applied Equation 5.3 to the experimental data. Figure 5.8 displays the AH

QENS for TEAD-MS according to Equation 5.5. The background bg(Q,E), summarized mostly the coherent signal from the deuterated ethyl chain dynamics, which for TEAD are expected to 1 1 1 be prominent between Q=1.3 Å− and 1.8 Å− . Correlation peaks at Q below 0.7 Å− are caused by nanosegregation of long fluorinated alkyl chains of the anions [139,161]. Moreover, line- narrowing of the localized component is also expected, so bg(Q,E) can neither completely absorb all the coherent signal nor separate it from the incoherent one. Experimentally such a separation is achieved by performing QENS experiments with polarized neutrons (Chapter 4), which is not the type of performed experiment in this study. The results of our analysis are shown in Figures 5.9 and 5.10, and summarized in Table 5.7.

The localized dynamics of AH are characterized by a confinement radius RH (Figure 5.9) and a diffusion coefficient DH (Figure 5.10), which increase for all anions as a function of

79 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

102 Long-range Localized 101

100 I[a.u.]

10-1

10-2 0.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 E [meV]

1 Figure 5.8 – QENS spectrum at Q=1.4 Å− of TEAD-MS at T=390 K along with the fit curve (blue line) given by Equation 5.5. Long-range and localized contributions are plotted in red and green, in dashed and dot dashes lines are R(Q,E) and bg(Q,E) respectively.

the temperature. These two parameters define a characteristic time τ R2 /D , which AH = H H represents the mean time required for AH to explore a spatial domain of twice the length of

RH (Table 5.7)[82]. During this time the cation and the anion (on average) remain together as neutral ionic pairs before recombining with other ions of the neighbourhood, and coincides with the lifetime of the neutral ionic pair for TEA-TF that was calculated in Chapter 3[72].

The association in ion pairs seems to be thermally stable, so as τAH increases as a function of the temperature, hence reflecting the strength of the hydrogen-bond (N H O) in the liquid − ··· phase too. The increase of τAH as a function of the temperature can be counterintuitive at 2 first glance, but it justified by the rapid increase of RH/DH with temperature, thus, AH needs more time to explore its confined domain. Additional motions, such as reorientations of the hydrogen-bond are not described in this localized component, which are usually faster than our experimentally accessible time-window (sub-ps) and therefore summarized in bg(Q,E).

The anion structure and size are further factors that can influence the AH localized dynamics.

For instance, if we assume that DH follows an Arrhenius behaviour (Equation 5.7) the activation energy of the AH dynamics can be calculated. Figure 5.10 and Table 5.8, show that for TEAD- MS, TEAD-PFBF and TEAD-PFOS the activation energies are very similar, in the order of 1 9kJmol− . The anions of these partially deuterated PILs have three oxygen atoms acting as ∼ hydrogen acceptors sites. Whereas, for TEAD-2C the anion has two oxygen atoms as hydrogen 1 1 acceptors and E 6 kJmol− , requiring an activation energy per oxygen atom of 3 kJmol− . a ∼

DH and RH decrease in the following sequence: TEAD-2C/PFBF/PFOS, in an anion size in- creasing trend. However, TEAD-MS does not follow this order, this d-PIL is the lightest one but simultaneously has the slowest AH dynamics and the strongest hydrogen-bond (Table 5.4).

80 5.2. Results and discussion

TEA -2C 0.7 D TEA -MS D TEA -PFBF 0.6 D TEA -PFOS D 0.5 [Å] H

R 0.4

0.3

300 320 340 360 380 T[K]

Figure 5.9 – Temperature and anion dependence of the AH confinement Radii. The filled symbols correspond to the fitted data (Equation 5.5), whereas the dashed lines are an eye- guide. The confinement radii increase with temperature.

TEA -2C 8 D TEA -MS 7 D

] TEA -PFBF -1 6 D s

2 TEA -PFOS D

m 5 -10

[10 4 H D

3

2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 1000/T [K-1]

Figure 5.10 – Arrhenius plot for the diffusion coefficients of DH. The filled symbols correspond to the fitted data (equation 5.5). Solid lines correspond to the Arrhenius fits DH, Equation 5.7.

We relate this phenomena to the presence of 3 deuterium atoms in the terminal group of MS, which are a positively charged in comparison with the rather negative charge of fluorine in the terminal groups of 2C, PFBF and PFOS; therefore the MS anion behaves as a dipole, whose positive part (deuterium atoms) tend to repulse the cation and diminishes the number of possible energetically favourable packing configurations of the IL. This is reflected in the TEA- 3 3 MS density (ρ=1.12 gcm− at T=298 K [120]), which is lower than for TEA-2C (ρ=1.61 gcm− at room temperature [178]), a similar PIL in size. In addition, we see that having smaller RH and slower DH are footprints of higher viscosities, such as for TEA-MS compared to TEA-2C, and similarities in τAH for TEA-MS (0.0167 Pas [163]) and TEA-PFBF (0.021 Pas [163]) reflect the comparable viscosities of the two samples as reported in the literature [163,179].

81 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

Table 5.7 – Temperature dependence of localized diffusion coefficients (DH), confinement 10 2 1 radii (RH) and characteristic time (τAH). DH is given in 10− m s− , RH in Å and τAH in ps.

T[K] 300 330 350 370 390

RH 0.469(0.001) 0.552(0.002) 0.594(0.002) 0.636(0.003) 0.678(0.004) TEAD-2C DH 4.62(0.05) 5.94(0.06) 7.38(0.07) 7.16(0.08) 8.00(0.09) τAH 4.77(0.06) 5.13(0.06) 4.78(0.06) 5.65(0.09) 5.75(0.10)

RH – 0.334(0.001) 0.394(0.001) 0.451(0.001) 0.505(0.002) TEAD-MS DH – 2.89(0.04) 3.44(0.04) 4.03(0.04) 4.93(0.04) τAH – 3.86(0.06) 4.52(0.06) 5.05(0.06) 5.18(0.06)

RH – – 0.457(0.001) 0.518(0.001) 0.564(0.001) TEAD-PFBF DH – – 4.66(0.05) 6.17(0.05) 6.49(0.05) τAH – – 4.49(0.06) 4.36(0.05) 4.91(0.05)

RH – – 0.370(0.001) 0.430(0.001) 0.499(0.001) TEAD-PFOS DH – – 4.24(0.07) 4.31(0.06) 5.64(0.06) τAH – – 3.23(0.06) 4.29(0.07) 4.42(0.05)

Table 5.8 – Activation energy for AH localized dynamics following an Arrhenius behaviour

TEAD-2C TEAD-MS TEAD-PFBF TEAD-PFOS 1 Ea[kJmol− ] 5.92(0.92) 9.54(0.68) 9.10(3.46) 9.50(4.66)

Protiated samples

The PILs were analyzed using Equation 5.2. Due to the AH low signal and the large number of free parameters in the equation, the outcomes for RH and DH from the corresponding d-PILs (Table 5.7) were substituted in Equation 5.2, and kept fixed in our analysis. Owing to the varied anions size, the coherent proportion of the total scattering exceeded 10% for TEA-PFBF and TEA-PFOS, therefore the line-width of the global dynamics was analyzed independently for all the samples. The results of our approach are presented in Figures 5.11 and 5.12 and Tables 5.9 and 5.10.

For TEA-2C, TEA-PFBF and TEA-PFOS, the global and the ethyl chain diffusion coefficients decrease as the mass of the anion increases. However, for TEA-MS (the lightest of the PILs) the long range diffusion coefficient is similar but lower than for TEA-2C (the second lightest PIL), and markedly faster than those of the heaviest PILs. In contrast, the alkyl diffusion coefficient of TEA-MS is closer to TEA-PFBF than to TEA-2C (Figure 5.11); this behaviour indicates that the MS anion brakes the whole ion pair dynamics, and imposes a harder spatial confinement to the ethyl chain than the other anions. Figure 5.12 displays this behaviour, the methyl group

82 5.2. Results and discussion

TEA-2C TEA-MS TEA-PFBF TEA-PFOS ] -1 s 2 101 m -10 D [10

2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 1000/T [K-1]

Figure 5.11 – Temperature dependence of the diffusion coefficients Dtr (filled symbols) and DCH (open symbols) for the different PILs. The solid lines correspond to the fit of an Arrhenius behaviour, Equation 5.7.

Table 5.9 – Temperature dependence of the global diffusion coefficient (Dtr), residence time 10 2 1 (τa), and alkyl chain diffusion coefficient (DCH). D is given in 10− m s− , τ0 in ps and DCH 10 2 1 in 10− m s− .

T[K] 300 330 350 370 390

Dtr 3.50(0.30) 5.13(0.30) 7.10(0.50) 9.30(0.50) 11.80(0.50) TEA-2C τ0 3.30(0.90) 0.96(0.50) 0.48(0.47) 0.39(0.29) 0.17(0.14) DCH 12.60(0.30) 17.40(0.30) 22.60(0.30) 26.70(0.30) 31.00(0.30)

Dtr – 3.30(0.20) 5.50(0.20) 8.20(0.10) 10.90(0.10) TEA-MS τ0 – 18.80(2.30) 16.00(1.00) 13.10(0.20) 9.00(0.20) DCH – 10.60(0.20) 12.60(0.20) 14.90(0.20) 17.20(0.20)

Dtr – – 4.20(0.30) 5.90(0.60) 7.70(0.50) TEA-PFBF τ0 – – 8.90(0.60) 8.10(1.10) 5.30(2.30) DCH – – 10.00(0.10) 13.00(0.10) 16.20(0.10)

Dtr – – 1.70(0.10) 3.10(0.20) 4.80(0.50) TEA-PFOS τ0 – – 8.40(2.00) 12.70(1.10) 15.10(1.10) DCH – – 8.30(0.10) 12.20(0.10) 14.70(0.20) confinement radii of TEA-MS below 340 K are on the same magnitude as for TEA-PFBF and TEA-PFOS, and the methylene group confinement radii are the smallest of all the PILs. This can be correlated with physicochemical properties and NMR measurements of the PILs available in the literature [163,179,180]. For example, the conductivity of the PILs followed the same trend as our outcomes of the global diffusion coefficients, thus maintaining the idea of a vehicular charge transport, where the AH does not hop between ions. Diffusion coefficients measured by

83 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering

1.5 TEA-2C TEA-MS TEA-PFBF TEA-PFOS 1.0 R [Å] 0.5

0.0 300 320 340 360 380 T[K]

Figure 5.12 – Temperature dependence of the confinement radii for the methyl group R2 (filled symbols) and the methylene group R1(open symbols) for the different PILs. The dashed lines are a guide to the eyes.

means of NMR, regardless of the different time and space window probed, suggested that TEA- MS is indeed slower than similar PILs, i.e comparable in size [163,180]. In addition, viscosity

η shows the same trend as DCH for our PILs [163, 179], if we recall that η is proportional to 1/DCH for a given T ; the increase on viscosity as seen by neutrons reflects a slower dynamics of the alkyl chains of the cation and a more restricted diffusion domains, i.e. smaller R2 of the terminal groups and smaller RH.

Table 5.10 – Temperature dependence of the methyl R2 and methylene R1 radii of confinement expressed in Å

T[K] 300 330 350 370 390 R 0.320(0.010) 0.367(0.008) 0.399(0.007) 0.445(0.007) 0.501(0.006) TEA-2C 1 R2 0.92(0.01) 1.08(0.01) 1.22(0.01) 1.35(0.01) 1.41(0.01) R – 0.140(0.010) 0.319(0.008) 0.404(0.008) 0.456(0.008) TEA-MS 1 R2 – 0.89(0.01) 0.95(0.01) 1.01(0.01) 1.08(0.01) R – – 0.480(0.010) 0.511(0.009) 0.528(0.007) TEA-PFBF 1 R2 – – 0.90(0.01) 1.00(0.01) 1.14(0.02) R – – 0.400(0.010) 0.431(0.008) 0.478(0.007) TEA-PFOS 1 R2 – – 0.80(0.01) 0.90(0.01) 1.02(0.01)

Finally, the temperature dependence of the global and the ethyl chain diffusion coefficients follows an Arrhenius behaviour, the activation energies of the respective processes are pre- sented in Table 5.11. It is noticeable that on average for all PILs the energy needed for the unrestricted dynamics is higher than the energy for the localized dynamics. In particular,

84 5.2. Results and discussion

Table 5.11 – Activation energy for the global and the alkyl chain dynamics following an Arrhe- nius behaviour

i 1 Ea [kJmol− ] TEA-2C TEA-MS TEA-PFBF TEA-PFOS tr Ea 13.70(0.60) 19.20(2.50) 17.60(0.50) 30.70(2.50) CH Ea 9.90(0.40) 8.70(0.10) 13.70(0.30) 15.70(2.80)

TEA-MS has the highest activation energy for the global dynamics and the lowest for the ethyl chain, reflecting the influence of microscopical dynamical properties to the viscosity and conductivity in particular.

5.2.4 Summary and conclusions

Acidic hydrogen dynamics (AH) in a family of protic ionic liquids were investigated via neutron spectroscopy together with DFT calculations, which helped to interpret the experimental data. The PILs were formed by a single type of cation, TEA, a molecule rich in hydrogen atoms. The anions were hydrogen-free species, they vary in size and in structure. To explore the AH dynamics (both in the solid and in the liquid phase), partially deuterated samples as well as fully hydrogenated samples were measured. The solid phase was mainly studied doing backscattering experiments (EFWS and IFWS), which gave us access to dynamics in the ns time-window, where methyl rotation and a plastic phase were observed. In the solid phase, AH dynamics where frozen, whereas in the plastic one, ion rotation without diffusion was identified; this phase takes place in a short temperature range and our DSC identified it as a first melting transition.

In the liquid phase, AH showed two dynamical processes happening in the ps time-window. One of the processes was sufficiently slower compared to the other one so that we could separate them; the slower one was associated to the long range diffusion of the cation and the faster one to the AH localized dynamics. We focused on the AH localized dynamics, which were described by the Gaussian model. The characteristic time defined by this model coincided with the time where the anion and the cation stayed together as a neutral pair. The inter-ionic hydrogen-bond reorientations were much faster than the experimental time-window, and consequently were absorbed in the background of the spectra. The anion structure played an important role in the AH confined dynamics too, their mass and their charge distribution can slow-down/speed-up the AH confined dynamics and are reflected macroscopically as an increase of the viscosity, or as for TEA-MS in its low density as well. The long-range diffusion is also affected by the anion selection and therefore the PIL conductivity; moreover, the PES of the different PILs suggested that the proton jump between the cation and the anion is energetically not feasible, therefore the preferred mechanism for charge transport in our

85 Chapter 5. Acidic hydrogen dynamics in triethylammonium-based protic ionic liquids probed by neutron scattering samples is a vehicular one, providing anhydrous conditions. In view of the considerable coherent share of the signal, neutron experiments with polarization analysis together with extensive classical molecular dynamics simulations could be advantageous.

86 6 Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

The following chapter presents the results published as: Juan F.Mora Cardozo, J. P.Embs, A. Benedetto and P.Ballone, Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids, J. Phys. Chem. B 2019 Article ASAP. The study was inspired in the search of non-vehicular charge transport in ILs together with the recent results of experiments on proton conducting ionic liquids [73]. The latter pointed to half-neutralised diamine-triflate salts as promising candidates for applications in power generation and energy conversion electrochemical devices. In our research structural and dynamical properties of the simplest among these compounds are investigated by a combination of density-functional theory (DFT) and molecular dynamics (MD) simulation based on an empirical force field similar to the approach used in Chapter 3. Three different cations have been considered, consisting of a pair of amine-ammonium terminations joined by a short aliphatic segment (CH ) with n= 2, 3 and 4. First, the ground state structure, vibrational eigenstates and − 2 n− hydrogen-bonding properties of single ions, neutral ion pairs, small neutral aggregates of up to eight ions and molecularly-thin hydrogen bonded wires have been investigated by DFT computations. Second, structural and dynamical properties of homogeneous liquid and amorphous phases are investigated by MD simulations over the temperature range 200 K T 440 K. Structure factors, radial distribution functions, diffusion coefficient and electrical ≤ ≤ conductivity are computed and discussed, highlighting the inherent structural heterogeneity of these compounds. The core investigation, however, is the characterisation of connected paths consisting of cation chains that could support proton transport via a Grotthuss-type mechanism [181]. Since simulations are carried out using a force field of fixed bonding topology, this analysis is based on the equilibrium structure only, using geometrical criteria to identify potential paths for proton conduction. Paths of connected cations can reach a length

87 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

(a) (b) (c)

Figure 6.1 – Ground state geometry of the gas phase cations. (a) [DAEt]+; (b) [DAPr]+; (c) [DABu]+. of 80 cations and 30 Å, provided bridging oxygen atoms from triflate anions are taken into account. The effects of water contamination at the 1 % weight concentration on structure, dynamics and paths for proton transport are discussed.

6.1 Methods

The bulk of our computational study consists of molecular dynamics simulations based on an atomistic force field, whose functional form corresponds to the OPLS/Amber model [101,103], with fixed molecular topology, fixed atomic charges and no explicit atomic polarisability.

Most parameters for [DAEt]+ and [DABu]+ were taken from Ref. [182], while for [TF]− the parametrisation from Ref. [93] has been used. Atomic charges have been computed from our density functional computations, using the electrostatic potential model, ESP, and its refinement, RESP [104, 105].In the present study the rigid ion approximation is the major source of uncertainty in the computation of general chemical physics properties, while the the ability of the model to cover proton transport beyond the vehicular mechanism is limited by the fixed topology, although we endeavour to provide indirect information on the basis of geometrical criteria.

Force-field-based MD simulations have been carried out using the Gromacs package [183] with a time step of 1 fs. NPT conditions have been enforced introducing a Nosé-Hoover thermostat and Parrinello-Rahman barostat, both with a relaxation time constant of 2 ps. Long-range Coulomb interactions are dealt with by the particle-particle-particle-mesh Ewald approach [108]. All degrees of freedom were kept unconstrained, including stretching and bending. To simulate samples contaminated by water, the force field has been supplemented by the TIP4P potential [184].

The exploration of structural features and hydrogen bonding in ion pairs and in very small clusters at the density functional level has been carried out by resorting to the pseudopotential-

88 6.2. Results

Table 6.1 – Geometric parameters and N-H stretching frequency for the intra-ion H-bond in the gas-phase cations. Distances are in Å , the angle is in degrees and the stretching frequency 1 is in cm− .

Compound dN H dN N dN H N H N ωN H − ··· ··· 6 − ··· − [DAEt]+ 1.10 2.56 1.71 129 2465 [DAPr]+ 1.15 2.61 1.53 153 1850 [DABu]+ 1.18 2.63 1.48 163 1721

plane wave approach implemented in CPMD [113, 185]. In our computation we used the generalised gradient approximation of Perdew-Burke-Ernzerhof (PBE) [98], norm-conserving pseudopotentials of the Troullier-Martins type [114] and a kinetic energy cut-off of 120 Ry for the expansion of Kohn-Sham orbitals. Periodic boundary conditions have been applied in all computations concerning neutral species, while open boundary conditions [186] have been used to treat systems with a net electrostatic charge. Dispersion interactions have been included using the empirical approach of Ref. [117].

Molecular dynamics on the ab-initio potential energy surface has been used to optimise structures, mainly by short ( 10 ps) simulated annealing runs. Vibrational eigenvalues and ∼ eigenvectors have been determined by diagonalisazion of the dynamical matrix (i.e., the Hessian with mass factors), computed by the simplest finite-difference approximation to second derivatives. Vibrational frequencies, in particular, have been used to compute the zero- point energy of all species, whose contribution changes reaction energies by a few hundredth of an eV.

6.2 Results

6.2.1 Density functional computation of geometry and hydrogen bonding in neu- tral ion pairs and small aggregates.

To quantify energy and structural properties of half-neutralised diamine salts we carried out density functional computations for single ions, neutral ion pairs, small neutral aggregates with up to eight ions, and molecularly thin hydrogen bonded wires. Three different cations have been considered, consisting of short aliphatic segments terminated by a pair of complementary amine-ammonium groups [H N (CH ) NH + n= 2, 3, 4] in a bola configuration. To fix 2 − 2 n− 3 notation, we refer to the ethyl (n=2) case as [DAEt]+, to the propyl case (n=3) as [DAPr]+, to the butyl case (n=4), as [DABu]+. Each of these ions has been investigated alone and in – combination with the trifluoromethanesulfonate, i.e., triflate anion, CF3SO3 or [TF]−.

89 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

(b)

(a)

Figure 6.2 – Lowest energy configuration of: (a) DAEt-TF; (b) DABu-TF.Dash lines represent hydrogen bonds.

The ground state geometry of the three gas-phase cations optimised at the DFT-PBE level by a short simulated annealing is reported in Figure 6.1. Basic geometrical parameters are listed in Table 6.1. The three structures show a tight pairing of the amine-ammonium group, with a bridging proton in between, forming a kind of ring configuration. The [DAEt]+ structure appears to be fairly strained, and the N H N combination would not be considered a proper − ··· hydrogen bond according to standard criteria used to analyse MD trajectories, since the

N H N angle is 129◦ only. The strain is much less in [DAPr]+ and [DABu]+, whose N H N − ··· − ··· angle rapidly approaches linearity, making the N H N combination a genuine hydrogen − ··· bond. The increasing strength of the HB with increasing n is accompanied (or, one could say, emphasised) by the increasing length of the covalent N H bond, and decreasing length of − the non-covalent H N bond. The n-dependence of the N N distance is somewhat counter- ··· ··· intuitive, since it grows with increasing n, while the HB appears less strained and thus more stable. The longer N N distance, however, is simply the geometric consequence of the ··· increasing linearity of the N H N bond. The strengthening of the intra-cation HB with − ··· increasing carbon content is decisively confirmed by the estimate of the N H stretching − frequency, that decreases monotonically and significantly from [DAEt]+ to [DABu]+. The

90 6.2. Results

1 frequency of this N H stretching mode is low (at 2465 cm− ) already in [DAEt]+. In [DAPr]+ − and [DABu]+ the N H stretching is no longer distinct from H N H bendings, but the highest − − − 1 frequency mode with significant stretching character is computed at 1850 cm− in [DAPr]+ 1 and at 1721 cm− in [DABu]+ (see Table 6.1).

Pairing each of these cations with the [TF]− anion gives origin to very stable neutral ion-pairs, whose structure is illustrated by the ground state geometry of DAEt-TF shown in Figure 6.2 (a) and DABu-TF in Figure 6.2 (b). The ground state structure of DAPr-TF,is not shown, but it is intermediate between these two. In all these pairs, Coulomb forces apparently play the major role, as emphasised by the close contact between the ionic moiety of [TF]−, represented by SO – and the corresponding ionic moiety of the cation, represented by the NH + termina- − 3 − 3 tion, and, to a lesser extent, by NH2. Hydrogen bonds play a secondary but still important − + role. The intra-cation HB, in particular, persists also in the ion pairs, while the H2N – NH3 terminations act like a bidentate functional group donating two protons to [TF]−, forming two HBs of unequal strength, the strongest originating from NH +, the weakest from NH . − 3 − 2 The geometric parameters defining the strongest of these two inter-ion HBs are collected in Table 6.2. The primary role of Coulomb forces and the complementary role of H-bonding is confirmed by similar computations for larger aggregates, up to four neutral ion pairs. In all cases, at T 0 K ions arrange themselves on a somewhat distorted but easily recognisable = NaCl-type lattice. Also in the case of clusters, cations extend at least two HBs to different neighboring anions, giving origin to a connected network of HBs.

The energetics of ionic neutral ion pairs is summarised by the reaction energies that follow, computed by DFT in the PBE gradient corrected approximation.

HTF [TF]− +p ∆E 13.57 eV, → = −

DAEt+ p+ [DAEt]+ ∆E 10.19 eV → = [DAEt]+ + [TF]− DAEt-TF ∆E 5.08, → =

DAPr+ p+ [DAPr]+ ∆E 10.62 eV → = [DAPr]+ + [TF]− DAPr-TF ∆E 5.09 eV, and → =

DABu+ p+ [DABu]+ ∆E 10.76 eV → = [DABu]+ + [TF]− DABu-TF ∆E 4.90 eV, → = where positive energies mean that the reaction runs spontaneously from left to right. Although the triflic acid HTF is one of the strongest acids (a super-acid), its deprotonation to give the

91 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

Table 6.2 – Geometric parameters for the primary H-bond joining cation and anion. A weaker HB is also present. Distances are in Å and the angle is in degrees.

Compound dN H dN O dH O N H O − ··· ··· 6 − ··· DAEt-TF 1.12 2.58 1.47 171 DAPr-TF 1.11 2.58 1.48 170 DABu-TF 1.09 2.66 1.58 170

triflate anion [TF]− requires a sizeable 13.57 eV, only partially offset by the energy gain (about 10 eV) in protonating the diamine to form the cation. A positive energy balance is restored only by pairing the two ions into neutral aggregates, releasing about 5 eV. The overall stability of the ionic pairs is measured by the reaction energy (T 0K including zero-point energies, = zpe):

HTF + DAEt DAEt-TF ∆E 1.47 eV, → =

HTF + DAPr DAPr-TF ∆E 1.76 eV, → =

HTf + DABu DABu-TF ∆E 1.80 eV. → =

Zero-point energy contributions are not negligible, their effect being to shift downwards ∆E, decreasing it from the estimate without zpe: ∆E 1.70 eV for DAEt-TF; ∆E 2.14 eV for = = DAPr-Tf; ∆E 2.09 eV for DABu-TF. = The slow increase of stability of the ion pairs with increasing length of the carbon chain, there- fore, results from the compensation between the increasing energy gain through protonation of the diamine and the decreasing gain in joining cation and anion. Both these competing effects can be seen as primarily due to hydrogen bonding.

All inter-ion HB are relatively unstrained (as shown by the N H O angle, see Table 6.2), but − ··· their loss of cohesion from DAEt-TF to DABu-TF is apparent, and likely to result from the competition of the intra-cation bond, whose antagonistic role is highlighted by the comparison of the geometric data in Tables 6.1 and 6.3. Table 6.1, in particular, reports parameters of the intra-cation HB computed for the gas-phase cation, while Table 6.3 reports the same parameters computed for the neutral ion-pair. In Table 6.3 the non-monotonicity in the N N ··· distance as a function of n is likely to be due to the interplay with the secondary HB joining the cation and the anion in the neutral ion-pairs.

Comparison of the ESP charges computed for all the ions and aggregates described until now

92 6.2. Results

Table 6.3 – Geometric parameters for the intra-cation H-bond measured on the ground state geometry of the neutral ion pair. Distances are in Å and the angle is in degrees.

Compound dN H dN N dN H N H N − ··· ··· 6 − ··· [DAEt]+ 1.05 2.66 1.94 122 [DAPr]+ 1.05 2.74 1.91 133 [DABu]+ 1.10 2.69 1.65 157

5

4

3

2 U [kcal/mol] ∆ 1

0 -0.8 -0.4 0.0 0.4 0.8 x [A]

Figure 6.3 – Variation of the potential energy on moving the proton out of the ground state position along the direction joining the two N-atoms in the same [DAEt]+ cation. Green line: computed on the gas-phase cation. Blue line: computed on the cation joined to a [TF]− anion in a neutral ion pair. The reaction coordinate x is the difference of the proton distances from the two N atoms.

and for different isomers of selected species, reveals a variety of effects not always unambigu- ously due to electrostatic polarisation. A detailed analysis, in fact, points to a sizeable charge redistribution within each ion due to changes in the geometry of bonds, or to the proximity of chemical groups, giving origin to a chemical polarisation effect in addition and beyond electro- static polarisation. For the systems investigated in the present study, the effect is particularly relevant for the cations, due to the flexibility of their structure. The fixed charges of the rigid ion model do not account for these effects. Moreover, to avoid spurious distinctions among atoms formally equivalent such as the three protons on NH or the two protons on NH , the − 3 − 2 assigned charges are somewhat averaged over equivalent atoms and over low energy isomers. We realise that these choices and approximations might affect at least quantitatively features that are discussed in the force-field MD section, including the absolute and relative stability of different types of HBs.

93 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

The basic geometric and bonding properties characterising the ground state structure and isomers of small aggregates are reflected in the energy variations upon moving the protons in HBs from their covalent to the non-covalent partner along each hydrogen bonds. The results are collected in Figures 6.3 and 6.4. Each of the curves on these two figures has been computed by moving the proton (p) towards its non-covalently bonded partner (X) in steps of 0.04 Å . At each step, the p-X distance is kept fixed by a constraint, and the energy minimised with respect to all other degrees of freedom.

By symmetry, the potential energy along the reaction coordinate for the intra-cation HB always has a double minimum. The barrier between the two minima is below 1 kcal/mol for all ∼ gas-phase cations, and decreases slowly along the DAEt-TF,DAPr-TF,DABu-TF sequence. The barrier is somewhat higher, but remains below 5 kcal/mol when measured along the same path in the neutral ion pairs (see again Figure 6.3), partly because the N N distance within ··· the cation increases with respect to the isolated cation, and partly because the proton transfer has to be accompanied by a substantial re-arrangement of the relative orientation of the two ions. Nevertheless, both in the case of gas phase cations and of the ion pairs, the low barrier and proximity of the two minima along the potential energy curve suggest that the amine and ammonium terminations could be more symmetric than implied by their structural formula. Taking quantum effects into account, it is likely that one proton is equally shared between the two nitrogens on the same cation. This picture is compatible with the experimental 1H NMR spectra [73] which are unable to detect the presence of the free amine.

The corresponding energy variations in moving the proton along the cation-anion primary hydrogen bond are collected in Figure 6.4 (a). Also in this case, quantum mechanical effects are not included, although they are expected to be non-negligible. In this case, the reaction coordinate is the H O distance, which is progressively reduced to plot the curves in panel (a) ··· of 6.4. For all choices of cation, the potential energy curve has one minimum only, consistently with the short N O distance [136]. However, the energy needed to move the proton to a ··· covalent bond distance ( 1.1 Å ) from the oxygen is low, and a double minimum could form ∼ whenever cation and anion move further from each other by thermal fluctuation. In particular, the energy to move the proton to about 1.1 Å from the nearest oxygen in a N H O HB is − ··· 4 kcal/mol in DAEt-TF and in DAPr-TF, growing slightly in DABu-TF because the N O ∼ ··· separation is somewhat longer in this last compound.

The computation of chemical reaction barriers by simple exchange-correlation approxima- tions such as PBE might be affected by significant and non-systematic errors [187]. To assess the uncertainty of the PBE barriers computed in our study, we repeated the barrier determi- nation using the hybrid B3LYP functional [99]. Although this method might not be the best one among the many hybrid functionals that are available [188], its Hartree-Fock component represents a significant difference with respect PBE, and the discrepancy between the two

94 6.2. Results

8

O x H +- 6 NH OS H N x O H N + H H 4 U [kcal/mol] ∆ 2 (a) (b) 0 1.6 1.4 1.2 1.6 1.4 1.2 x x

Figure 6.4 – Energy variation on moving the proton out of the equilibrium position along the direction leading the proton to the non-covalently bonded partner in inter-ion HBs. Panel (a): primary cation-anion HB. The reaction coordinate x is the distance between the proton on: [DAEt]+ (blue line); [DAPr]+ (green line); [DABu]+ (red line) and the oxygen on [TF]−. Panel (b): cation-cation HB in the model DAEt-TF wire (see text). The coordinate x is the distance between the proton from NH + and the nitrogen on the neighbouring NH . Red line: single − 3 2− proton displacement. Blue line: in-phase displacement of all equivalent protons. In the latter case, the energy per moving proton is displayed.

barriers is expected to give a fair estimate of the uncertainty on the results we reported. In the case of the intra-cation proton transfer in neutral DAEt-TF discussed above and illustrated in Figure 6.3 (green line), the B3LYP barrier turns out to be ∆E 5.2 kcal/mol, to be compared = to the ∆E 4.46 kcal/mol given by PBE. Although significant, this difference of less than 1 = kcal/mol does not alter the general picture of hydrogen bonding and proton transfer dynamics given by PBE. This assessment is reinforced by considering that the zero-point energy of the 1 proton in between the two nitrogens of DAEt-TF (ω 2565 cm− ) is already nearly 4 kcal/mol. = The full energy profile for the proton transfer computed for this case using PBE and B3LYP is shown in Figure 6.5.

6.2.2 Proton conductivity in model DAEt-TF wires

The positive outlook for proton conduction resulting from the low barriers towards proton displacement along single hydrogen bonds is tempered by the observation that Grotthuss transport across the system eventually requires proton jumps from cation to cation. To make this mechanism relevant, however, cations need to form chains like those schematically depicted in part (a) of Figure 6.6, neutralised by a corresponding number of anions, as already

95 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

6

B3LYP 4 PBE

U [kcal/mol] 2 ∆

0 -0.8 -0.4 0.0 0.4 0.8 x [A]

Figure 6.5 – Variation of the potential energy on moving the proton out of the ground state position along the direction joining the two N-atoms in the same [DAEt]+, computed by FIG. S5:PBE Variation and by B3LYP of the on potential the cation energy joined on to moving a [TF]− theanion proton in a neutral out of ionthe pair. ground The state reaction position coordinate x is the difference of the proton distances from the two N atoms. along the direction joining the two N-atoms in the same [DAEt]+, computed by PBE and by

B3LYPsuggested on the cation in Ref. joined [73]. to a [Tf] anion in a neutral ion pair. The reaction coordinate x is the di↵erence of the proton distances from the two N atoms. The type of hydrogen bond stabilising these chains is apparently less stable than those linking cations and anions, since the former join functional groups of comparable positive charge (assuming that the two terminations are nearly equivalent), while the latter join groups of -0.4 opposite charge, thus enjoying a sizeable stabilisation by electrostatic forces. This qualitative picture is confirmed by the results of our simulations of nano-clusters, in which we observe a number of very stable cation-anion HB, but no cation-cationN2 in the ground state structure. Cation-cation HBs, however,-0.6 occur in the ab-initio simulation of the DAEt-TF tetramer at room temperature, suggesting a stabilisation contribution from entropy. Even the intra-cation HB appears to be significantly more stable than the cation-cation link, although it joins the same

Z / e N type of terminations,-0.8 probably because of the forced1 proximity of the two groups. However, in condensed phases, inter-cation hydrogen bonds might be stabilised by close correlation with anions, hence, estimating the stability of these bonds and quantifying energy barriers for proton transfer becomes a relevant task. -1.0 To this aim, an artificial 1D system-60 has -30 been prepared, 0 consisting 30 of four 60 DAEt-TF ion pairs on a linear arrangement, periodically repeated inτ their[degrees] longitudinal direction to form an extended wire (see Figure 6.7). Because of computational convenience, the system is replicated also in the two transversal directions, but in this case the periodicity is such to prevent sizable interaction among replicas. Because of the topology of cations, able to accept a single HB at its + FIG. S6: Dependence of the atomic charge on the N1 (in -NH2) and N2 (in -NH3) of [DAEt] as NH termination, chains are the most likely type of cation-cation aggregation in these protic − 2 a function of the N1-C-C-N2 dihedral angle. Charge flowing in and out of nitrogen atoms upon 96 rotation is compensated primarily by nearest neighbour hydrogen atoms. For this reason, the e↵ect of the large charge variation might be mitigated, but it remains sizeable. The computation of atomic charges is discussed in the main text.

S8 6.2. Results

(a) N (2) N (2) N (3) N (3)

(b) N (3) N (2) N (2) N (3)

(c) (2) N N (3) N (3) N (3) N (2) N (2)

Figure 6.6 – Chain-like arrangement of [DAEt]+ cations (a), (b), (c), with: (b) bridging by [TF]− and (c) bridging by [TF]− and by water. Possible paths for proton jumps are indicated by dash lines and arrows. Blue dots: N; red dots: O; yellow dots: S. For clarity, the CF moiety of [TF]− − 3 is omitted.

RTILs, analogous but geometrically distinct from those discussed, for instance, in Ref. [126]. The simultaneous acceptance / donation of HBs by each cation provides the crucial degree of cooperativity. Branching of chains in principle is possible, because of the ability of NH + − 3 -NH3+ to donate more than one proton, but in that case cooperativity might act in reverse, weakening multiple HBs from the same NH + group. − 3 The system prepared in this way turns out to be at least metastable, with an optimal N N ··· distance of 2.72 Å . However, to prevent large deformations, or even the collapse of the wire into a compact cluster under the perturbation driving the proton transfer, a weak parabolic restrain has been applied to the carbon atoms in the chain, keeping them close to the position found by the starting local optimisation of the structure. Remarkably, the lowest energy wire configuration we found has all the cations (all the anions), on the same side (on the opposite side) of an ideal line marking the longitudinal direction of the wire. A different geometry, with ions arranged in such a way to cancel the 2D dipole moment in the transversal directions is found to have higher potential energy.

97 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

Figure 6.7 – Linear chain built to investigate the stability and energy profile of hydrogen bonds joining cations.

From this starting point, we carried out the same exploration of the potential energy along the reaction coordinate as it has been done for the other types of HB. In a first stage, a single proton has been displaced along the reaction coordinate. Once again, the results show that the potential energy curve has one minimum only (see the red line in Figure 6.4, panel (b)), but a moderate amount of energy ( 5 kcal/mol) is sufficient to move the proton to within ∼ 1.1 Å from the non-covalently bonded N atom. The absence of a second minimum on the potential energy curve (despite the equivalence of the two N-terminations) is not surprising, since moving a single proton creates a neutral DAEt molecule and a doubly charged [DAEt]++ cation, whose energy would be fairly high even if screened by a corresponding number of neighboring [TF]−.

A double energy minimum is recovered if all the (equivalent) bridging protons in the chain are moved together. The result of this computation is shown by the blue line in Fig. 6.4, panel (b). The curve is not symmetric with respect to the midpoint of the line joining the two nitrogen atoms because the local optimisation routine used to minimise the energy is unable to reach the minimum at the same energy of the original one, which, by symmetry, has to exist. To be precise, the plot reports the variation per moving proton of the potential energy along the reaction coordinate. Hence, the barrier opposing the shift of n protons quickly overcomes the thermal energy with increasing n, even though quantum effects decrease significantly the energy per moving proton. Matching the two pictures, we expect the propagation of protons by a soliton-like excitation, as the one postulated in Ref. [189] for the bi-squaric acid.

These results can be summarised as follows. Density functional computations suggest mech- anisms for the coherent transport of protons along chains of cations, compatible with an accessible energy scale. The precise mechanism and quantitative barrier could be determined

98 6.2. Results by density functional computations at least for rather idealised model geometries, but such a complex undertaking is beyond the scope of our study. The major task left to molecular dynamics simulation, therefore, is to verify the presence of these chains, and to estimate their length and the frequency of their occurrence as a function of temperature.

6.2.3 Molecular dynamics simulations

Simulations based on the classical force field of Section 6.1 have been carried out for samples of DAEt-TF and DABu-TF consisting of 216 neutral ion pairs (4536 atoms for DAEt-TF,5832 atoms for DABu-TF) in a cubic box of 4 nm side with periodic boundary conditions applied. ∼ Most of the effort has been devoted to DAEt-TF while a few simulations on DABu-TF have been carried out for a comparison, aiming to assess the effect of the length of the aliphatic chain joining the two nitrogen terminations. All simulations have been performed at ambient pressure. The experimental melting temperature of DAEt-TF is Tm= 351 K, and its thermal stability extends up to 500 K, as experimentally verified by the absence of weight loss during thermogravimetry [73].

In the DAEt-TF case, simulations started in the liquid range at T 440 K, then the temperature = was progressively decreased in steps of 10 K down to T 200 K, well below the experimental = melting temperature. At each temperature the DAEt-TF sample has been equilibrated during 6 ns, and statistics accumulated over 200 ns. Thus, over the entire sequence of DAEt-TF simulations from T 440 K down to T 200 K, the accumulated statistics covers 5 µs, for = = an average annealing rate of 48 106 K/s, not counting the equilibration runs of 6 ns at × each change of temperature. In the case of DABu-TF, only four temperatures have been considered, i.e., T 440 K, 400 K, 350 K and 300 K. To optimise equilibration, also in this case = we moved from the highest to the lowest temperature, each time collecting 200 ns of statistics. Equilibration, however, has been longer (16 ns) because of the larger temperature variations at each stage.

The average density ρ(T ) of DAEt-TF at T 400K turns out to be ρ 1.44 g/cm3 to be 〈 〉 = = compared with the experimental value ρ 1.6 g/cm3. The 10% difference is the same as the exp = one found in Chapter 3 for TEA-TF,and corresponds to a 3% overestimate of the average side of the cubic simulation box. For molecular species, and for RTILs in particular, an error of this size is not unusual even in DFT computations [190]. Moreover, the discrepancy is comparable to the spread of experimental values in closely related ionic liquid systems. The density of TEA-TF at T 400 K, for instance, is quoted as ρ 1.33 g/cm3 in Ref. [73] and as ρ 1.16 = = = g/cm3 in Ref. [120]. The density of DABu-TF computed at T 400 K is ρ 1.31 g/cm3. To the = = best of our knowledge, no experimental value is available for a comparison.

Despite the hint of a curvature, the ρ (T ) of DAEt-TF is recognizably linear both at low 〈 〉

99 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

-20 1.6 0.006 ] 0.0 -3 -0.5 -40 T [A 0.003 -1.0 T [kJ/mol] 1.6

-1.5 〉 −γ−δ 〈ρ 〉 −α−β -2.0 ] 0.0 E 〈 -60 200 260 320 380 -3 200 260 320 380 440 T [K] 1.5 T [K] [A ρ〉 -80 〈 (T) [kJ/mol] 〉 E 〈 1.5 -100 (a) (b) -120 1.4 200 260 320 380 440 200 260 320 380 440 T [K] T [K]

Figure 6.8 – Average potential energy E and average density ρ as a function of temperature 〈 〉 〈 〉 from MD simulations of DAEt-TF at NPT conditions. In both panels the inset reports the plotted quantity minus its linear interpolation for T 330 K. Data collected on cooling. ≥

(200 T 280 K) and at high T (330 T 440 K) (see Figure 6.8(a)). Over the 280 T 330 ≤ ≤ ≤ ≤ ≤ ≤ K interval, ρ (T ) crosses over these two linear ranges of slightly different slope, with only 〈 〉 a weak anomaly that is highlighted in the inset of Figure 6.8(a) by subtracting from ρ (T ) 〈 〉 the linear fit to the T 380 K data. The transformation has a weak first order component ≥ representing a largely incomplete ordering process, superimposed to what appears to be a predominantly glass transition. No long range order in the ion configuration can be detected by visual inspection of snapshots. This picture is likely to be determined by genuine properties of the material such as the high viscosity, but certainly it is also affected by the small system size and high cooling rate.

The temperature dependence of the density is reflected in an analogous behaviour of the average potential energy, shown in 6.8(b), with the broad dip in the inset of panel (a) becoming an equally broad peak in the inset of panel (b).

More detailed knowledge on the structure and cohesion is revealed by the structure factor

Sαβ(Q), defined as:

1 ­ ® S (Q) ρα(Q)ρ ( Q) , (6.1) αβ = N β −

100 6.2. Results where α, β label atomic species, N is the total number of ions (twice the number of molecules), and:

X iQ rj ρµ(Q) e− · , (6.2) = j µ ∈ rj being the position of ion j belonging to species µ.

Since we aim at highlighting the ionic character of the system, we define the structure factor of a distribution of cations and anions, whose location is identified by the position of the ammonium nitrogen, and by the sulphur atom of [TF]−. The partial structure factors S (Q), ++ S (Q) and S (Q) (see the definition in Ref. [92]) are combined into a density-density Snn(Q) +− −− and a charge-charge SZZ (Q) structure factor (see again Ref. [92]) as:

1 Snn(Q) [S (Q) 2S (Q) S (Q)] and (6.3) = 2 ++ + +− + −−

1 SZZ (Q) [S (Q) 2S (Q) S (Q)]. (6.4) = 2 ++ − +− + −−

The results, displayed in Figure 6.9 (a) and (b) for T 350K, show a prominent peak in the 1 = charge-charge structure factor at Q 1.05 Å− , emphasising the crucial role of Coulomb = interaction driving the strict alternation of cations and anions. In simple ionic liquids, the basic periodicity of charge is roughly twice as long as the periodicity of mass, since charge repeats itself at the next nearest neighbour distance (in a NaCl-type structure). Hence, the 1 major peak in the density-density structure factor is expected at Q 2.1 Å− . This is indeed the = 1 position of the highest peak in Snn(Q), but Figure 6.9 shows clear pre-peaks at Q 1.45 Å− , 1 1 = Q 1 Å− , as well as a sizeable shoulder at Q 0.6 Å− . The last two pre-peaks, in particular, = ∼ point to regularities in the same-ion position of periodicity 6 and 10 Å , beyond the nearest neighbour distance, that might be interpreted as due to the formation of a mesophase. This feature is not unusual in RTILs [191–195], and could be interpreted in terms of the interplay of charged and neutral moieties in both ions. In other terms, to optimise both Coulomb and dispersion interactions, charged moieties cluster in tight configurations surrounded by the non-polar moieties. Depending on the relative size of these charged and neutral moieties, different length scales arise, giving origin to the rich structure of these systems, as discussed, for instance, in Ref. [158]. In protic ionic liquids such as the systems investigated here, hydrogen

101 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

S (k)Q S (k)Q 2 (a) ZZ (b) ZZ (k) (Q) Snn(k)Q Snn(k)Q ZZ ZZ (Q),S (k), S

nn 1 nn S S

T=350 K T=350 K

0 012301234 Qk [A-1] Qk [A-1]

Figure 6.9 – Density-density and charge-charge structure factors at T 350 K of: (a) DAEt-TF, = and (b) DABu-TF.The experimental melting point of DAEt-TF is T 351 K [73]. m = bonding contributes to the nanostructuring of the liquid compound, as apparent from our results, and as already discussed in the literature [126, 196]. Nanostructuring in DAEt-TF might also be enhanced by the low polarity of the fluorinated group in [TF]− [161], although in this case fluorination is reduced to its bare CF minimum. The nanostructuring picture is − 3 confirmed and reinforced by the comparison with the results for DABu-TF,shown in Figure 6.9

(b). The longer saturated chain of [DABu]+ reduces significantly the first peak of SZZ (Q), emphasising the decreasing role of Coulomb interactions. At the same time, the pre-peaks in the density-density Snn(Q) grow in size, and move to slightly lower Q, because of the general expansion of the system caused by the insertion of the additional CH CH segment. Apart − 2− 2− from minor details, the structure factor of DAEt-TF and DABu-TF displays little dependence on T over the interval covered by our simulations, showing only the expected but slow increase in the amplitude of the S (Q), S (Q) oscillations from T 440 K down to T 200 K, while nn ZZ = = the position of peaks and dips remains the same.

The complexity of the relative arrangement of ions at short and medium range is emphasised also by the radial distribution functions, reported in Figure 6.10, showing even more clearly than the structure factor the interplay of different length scales in the local and medium-range structure of the system. Also in this case, we compute and report the radial distribution of cations and anions, identified with the position of nitrogen in NH + and sulphur in − 3 [TF]−. Apparent features are the very prominent first peak of g (r ) at 3 Å , the relatively +− ∼ simple behaviour of g (r ), and the broad, nearly structure-less shape of g (r ), due to the −− ++ complex geometry of the cation. The shape of the second peak of g (r ) at 6 Å is the most +− apparent signature of nanostructuring in the radial distribution function. In simple molten salts such as NaCl close to their triple point, the second peak of g (r ) reaches a value well +− above one [197]. In DAEt-TF,instead, the second peak remains below one (g (r 6) 0.96), +− = = 102 6.2. Results

4

(a) (b) g--(r) g--(r) 3 (r) -- T=350 K g+-(r) T=350 K g+-(r)

(r), g 2 +- g++(r) g++(r) (r), g

++ 1 g

[DAEt][Tf] [DABu][Tf] 0 2 4 6 8 10 2 4 6 8 10 12 r [A] r [A]

Figure 6.10 – Radial distribution functions of ions in (a) DAEt-TF and in (b) DABu-TF. reflecting the depletion of the second cation-anion coordination shell, contradicting the system homogeneity at all length scales. These observations suggests a 12 Å diameter for the average blob made of charged moieties, consistently with the pre-peak in S (Q) at 0.6 1 +− ∼ Å − . In DABu-TF, such a depletion of the second cation-anion shell is more pronounced, with (g (r 6) 0.62), again consistent with the enhanced role of the mesophase in this +− = = compound, as revealed by the structure factor.

The first peak of g (r ) around a central NH + integrates to a coordination number by S +− − 3 atoms of nearly 4, corresponding to a compact coordination of nearly 12 by oxygen atoms.

Needless to say, the alkane chain, the neutral NH termination of [DAEt]+, and the (equally − 2 neutral) CF termination of [TF]− are virtually excluded from this ionic core. − 3

Analysis of trajectories also show that in the [DAEt]+ case, up to T 440 K, the N C C N = − − − backbone remains in the cis configuration, hence the two terminal N atoms of each cation remain within a HB distance (r 3.2 Å ) from each other. The strain of the [DAEt]+ structure, c = however, prevents the alignment of the N H N combination to within 30◦ as required by − ··· ∼ most empirical criteria to identify a HB. Hence, no formal intra-cation HB is found along the trajectory, although these atoms are clearly bound by a sizeable attractive force, as confirmed by the DFT computations for the gas-phase cation. In what follows, the interaction among these atoms on the same cation is loosely referred to as a HB. As expected, the picture is different in DABu-TF,since in that case the gain of entropy made available by the longer chain overcomes the enhanced stability of the HB, and a majority of intra-cation HB opens up, being replaced by further HB to neighbouring ions (see Figure 6.11). Thus, these results from simulation help addressing the question raised in Ref. [73] concerning the intra- or inter-ion chelation of protons, which cannot be unambiguously answered by NMR measurements. Simulation confirms the guess proposed in that same reference, stating that the balance

103 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

1.0

+ 0.8 [DABu]

] +

-1 0.6 [DAEt]

0.4 f(r) [A

0.2

0.0 23456 r [A]

Figure 6.11 – Probability distribution for the N N distance within [DAEt]+ and [DABu]+ ··· cations computed by classical MD at T = 350 K. FIG. S9: Probability distribution for the N N distance within [DAEt]+ and [DABu]+ cations ··· computed by classical MD at T = 350 K. of intra- and inter-ion chelation depends on the length of the spacer chain. In our results, chelation is exclusively intra-cation in DAEt-TF,and predominantly but not exclusively intra- cation in DABu-TF.

The major reason of interest in these materials and in our simulations is the structure, energet- ics and topology of the network of HBs. Each cation forms, on average, more than one HB to neighboring anions, as can be seen in Figure 6.12. Moreover, and perhaps more importantly, the multiple HBs centred on each cation reach out to different anions. Hence, the analysis of the HB network shows that, almost without exceptions, each sample represents a uniquely HB- connected set. This high connectivity of the HB network is certainly one of the reasons of the relatively slow diffusion of ions and high viscosity of these compounds [196]. Here, as before, H-bonding is defined in terms of geometrical parameters only, requesting a distance between the electronegative pairs (N N or N O) of less than r 3.2 Å , and a N H N angle deviating ··· ··· c = − ··· less that 30◦ from linearity. As expected, the average number of cation-anion (N H O) HBs − ··· increases with decreasing temperature, and the relative change over the 200 T 440 K range ≤ ≤ is higher than in the TEA-TF case Chapter 3. Together with strong Coulomb interactions, the network of HB is one of the reasons of the clustering of ionic moieties in the DAEt-TF and

(even more) DABu-TF equilibrium liquid structure, giving origin to the pre-peaks in Snn(Q) already discussed.

As discussed in the ab-initio section (Section 6.2.1), hydrogen bonding could also join amine and ammonium nitrogens on neighbouring cations. According to our simulations, and using the geometric criteria listed above, the number of these HB in DAEt-TF is low, although S11

104 6.2. Results

2.5

2.0 HB n 1.5

1.0 200 240 280 320 360 400 440 T [K]

Figure 6.12 – Average number of N H O HB per cation (or, equivalently, per anion) as a − ··· function of temperature. HBs are defined by N O separation 3.2 Å and N H O angle ··· ≤ − ··· 150◦. The line is a guide to the eye. ≥ not completely negligible. This observation affects the number of paths open for proton conductivity through a Grotthuss-like mechanism. It is important to remark that these results from simulation might also be affected by limitations in the force field model, which treats the amine and ammonium terminations as distinct, while ab-initio computations suggest they are nearly equivalent. Moreover, the polarisability of NH , not included in the force − 2 field, could also stabilise its H-bonding to NH +. The quantitative analysis of paths open for − 3 proton conduction reported in the last part of this section will take these considerations into account.

The long simulation trajectories allow a precise determination of diffusion properties down to low temperature. The diffusion coefficient of cations and anions is computed using Einstein’s relation, i.e., from the slope of the mean-square displacement per ion over the interval 60 ≤ t 100 ns, where the mean square displacement is apparently linear in time. As in TEA-TF ≤ (see Chapter 3) and in agreement with experiments, cations diffuse faster than anions, but the difference is not large, and might simply reflect (the square root of) the mass ratio of cations and anions (p61/149, masses given in amu). As for many RTIL systems, the simulation value for the diffusion coefficient underestimates significantly the experimental value. At 7 2 7 2 T 400K, for instance, our computations give D 3.13 10− cm /s, D 2.74 10− cm /s = + = − = for cations and anions, respectively, while at the same temperature the experimental values 6 2 6 2 [73] are D 1.36 10− cm /s, D 1.18 10− cm /s. Remarkably, the experimental value + = − = for the ammonium proton mobility is higher than the diffusion coefficient of the whole cation, emphasising the presence of Grotthuss mobility. The systematic underestimation of

105 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

-6 10

D- /s] 2 -8 10 D+ [cm - , D +

D -10 10

2.5 3.0 3.5 4.0 4.5 5.0 1000/T [K-1]

Figure 6.13 – Arrhenius plot of the diffusion coefficient of cations and anions in DAEt-TF.Full lines represent the linear interpolation to the low-and high-temperature data for [DAEt]+.

diffusion coefficients is a well know limitations of rigid-ion force fields, and could be corrected by rescaling the charges of cations and anions, for instance, to a total of 0.8e [111]. This ± corrections is not adopted here because it would spoil other properties, such as the average density or the electrical conductivity. A more systematic improvement could be provided by including polarisable force fields, but their usage is computationally much more demanding. More importantly, as already pointed out in Section 6.1, charge polarisation in these systems might have a chemical origin besides the electrostatic one, due to structural isomerisation or to the change of nearest neighbours. Effects of this type can be included in bond-order force fields more naturally than in traditional polarisable force fields.

An Arrhenius plot of the diffusion coefficients as a function of the inverse temperature shows a cross-over between two different linear regimes taking place at T 320K (see 6.13). At high (d) = 1 temperature we estimate an activation energy for diffusion of Ea 4500 K (37.41 kJmol− ). (d) = 1 At low temperature the activation energy turns out to be E 2100 K (17.46 kJmol− ). We a = quote only one value for cations and anions because the difference cannot be resolved.

The approximate Stokes-Einstein relation, already used to analyse dynamical data of ionic liquids [198], provides a way to estimate viscosity. We use the relation in the form:

kB T η , (6.5) = 6πDr where η is the viscosity coefficient, D (D D )/2 is the diffusion coefficient averaged over = + + − 106 6.2. Results species, 6π depends on the choice of boundary conditions (no slip) for the viscous flow, and r measures the hydrodynamic radius of diffusing particles. We estimate r from the position r max of the first peak in g , setting r r max /2. In this way, for DAEt-TF we estimate η 48 +− +− = +− = cP ( mPa s) at T 400 K, η 224 cP at T 350 K, η 24.8 103 cP at T 260 K. Since they are ≡ · = = = = = obtained from the approximate Stokes-Einstein relation, and, moreover, the definition of r is uncertain, these values represent only an order of magnitude estimate. Nevertheless, the value at T 400 K is within a factor of two from the experimental value η 27 cP [73]. More in = exp = general, we observe that the computed values are consistent with the generally high viscosity of these compounds, and, at low temperature, comparable to those of glassy molecular systems as obtained by MD simulation.

Before discussing paths of HBs suitable for Grotthuss proton transport, we collect here our results for a few other dynamical properties, such as the electrical conductivity and the rotational relaxation.

The duration of our simulated trajectories, although long, is not sufficient to provide an estimate of conductivity of quality comparable to that of diffusion. The relatively poor conver- gence of conductivity has simple statistical mechanics motivations, and the problem is well known in simulation, especially for molecular ionic liquids [199]. Nevertheless we plot our best estimate of conductivity, computed using an Einstein-type relation, based on the computation of the time-correlation function (see Equation 3.6). The increased statistical uncertainty forced us to extract the asymptotic linear part of Π(t) on the time interval 40 t 60 ns. ≤ ≤ 4 The value computed for DAEt-TF at T 400 K is 5.25 10− S/m to be compared to the exper- 4 = imental value κ 3.5 10− S/m. The good agreement of computed and measured electrical = conductivities from a simulation reproducing only qualitatively the diffusion dynamics is likely to reflect the compensation of errors.

An Arrhenius plot of κ (see Figure 6.14) shows a nearly linear dependence of log(κ) versus 1/T , with a change of slope possibly corresponding to the one seen in the diffusion coefficient.

A simple estimate of electrical conductivity is provided by the Nernst-Einstein equation, using the ion mobility expressed by their diffusion coefficient, and relying on the assumption that the motion of ions is uncorrelated as in Equation 3.7. Comparison of κNE and κ allows us to estimate the pairing among ions, measured by the parameter ∆ 1 κ/κ . In DAEt-TF pair- = − NE ing reaches up to 0.95 at T 200 K, indicating the expected tight pairing of cations and anions = at low temperature. Up to T 440 K, ∆ does not decrease below ∆ 0.8. As a comparison, the = = same parameter ∆ computed for TEA-TF shows a clear change from tight pairing (∆ 0.8) to ≥ looser pairing (∆ down to less than 0.5) around T 320K. The ∆ value estimated in the same = way from the experimental diffusion and electric conductivity coefficients of DAEt-TF is about 0.7 at T 400 K [73], in semi-quantitative agreement with the computed values. =

107 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

-2 10

-3 10

-4 10

-5

[S/m] 10 κ -6 10

-7 10

2345 1000 / T [K-1]

Figure 6.14 – Arrhenius plot of the electrical conductivity. Full dots: simulation results from Eq. 3.6. Empty squares: Nernst estimate of conductivity, Equation 3.7. The straight lines represent the linear interpolation of the high and low temperature portions of the conductivity data.

The diffusion coefficient of cation and anion is higher in DABu-TF than in DAEt-TF (see

Table 6.4), despite [DABu]+ being slightly heavier than [DAEt]+. This trend is expected, since the melting temperature Tm decreases from DAEt-TF to longer-chain diamine salts. The melting temperature of DABu-TF is not known, but, for instance, Tm decreases by 42 K in going from DAEt-TF to DABu-TF,and by 30 K from DAEt-TF to DADec-TF (H N (CH ) NH -TF) . 2 − 2 10− 3 The enhanced fluidity apparently is the reason also for the increase in electrical conductivity from DAEt-TF to DABu-TF,despite the dilution of the charged moieties in this last compound.

The lifetime of the HBs that join cations to anions in DAEt-TF has been estimated by first identifying all HB in the system at time t0, then following their persistence in time, and averaging over the initial time t0. As before, the definition of an HB is purely geometrical, requesting a N O distance less than 3.2 Å and a N H O angle deviating less than 30◦ from ··· − ··· linearity. Short-time fluctuations in the distance or angle could compromise the integrity of a HB. Similarly to what ha been done in Chapter 3, the broken bond is still counted as intact provided it reforms within 0.4 ps. On the other hand, bonds that break for a time longer than 0.4 ns are no longer counted at later time, even if they do reform. The same bond, however, might contribute again to the time correlation function starting at any later time t 0 . In this way, for DAEt-TF at T 300 K we compute lifetimes of the order of a few ps, 0 ≥ decreasing exponentially with increasing temperature. Slightly longer (by 20 %) lifetimes are ∼ computed in DABu-TF at the same temperature. In many ways, the results are equivalent to those reported in Chapter 3 for TEA-TF,and certainly similar to those found in many other simulation studies [130,131] of non-RTIL hydrogen bonded systems, using classical force field

108 6.2. Results

0 10

Θ -(t)

(t) Θ (t) - +

Θ -1 10 (t), + Θ τ m= 2.75ns τ p= 0.375ns -2 10 0 5 10 15 20 t [ns]

Figure 6.15 – Time autocorrelation function of ion orientation in DAEt-TF at T 350 K. The = full lines give the interpolation of the simulation data with a stretched exponential.

but also ab-initio methods. In the case of RTILs, in particular, comparable lifetimes have been computed both for protic [200] ionic liquids and for water in aprotic ionic liquids [201]. For these reasons, we do not elaborate any further on this property.

Since the two ions in DAEt-TF are anisotropic, rotational diffusion represents an additional type of motion. The orientation of the anion is relatively easy to define, and more difficult for the cation, which is less regular an also less rigid. In what follows, the orientation of the cation is defined by the vector joining the nitrogen atom in NH to the complementary nitrogen in − 2 NH +, while the orientation of the anion is identified by the vector joining the carbon atom − 3 to sulphur in [TF]−, representing a kind of ternary (almost cylindrical) axis for [TF]−. The rotational diffusion is quantified by the average defined in Equation 3.9. At all temperatures covered by our simulation, this time correlation function is well represented by a stretched exponential:

³ ´ Θ (t) A exp (t/τ)β (6.6) α = − as shown in Figure 6.15, reporting both the simulation data and their fit by the expression in Equation 6.6. To be precise, the interpolation does not reproduce a very narrow feature at times of the order of a few ps, that might be due to intra-ion deformations. The exponent β turns out to be almost the same for cations and anions and close to 1/2, being β 0.54 0.01 = ± for [DAEt]+, and β 0.57 0.03 for [TF]−. The quoted values are the average from all the fit = ± 109 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

4 10

τ 2 m 10 τ [ns] p τ

0 10

-2 10 234 1000/T [K-1]

Figure 6.16 – Relaxation time τ for rotations, estimated from the fit of simulation data by a stretched exponential in Equation 6.6. The straight lines represent the linear interpolation of the low- and high-temperature values of the relaxation times of cations and anions.

at different temperatures, since there is no apparent trend in β over the entire temperature range.

Although there is no reason to treat the time τ as the relaxation time of a single exponential relation, we nevertheless report the temperature dependence of τ on an Arrhenius plot (see Figure 6.16). From the dimensional point of view, the slope of logτ vs 1/T is an activation energy, and there is a cross-over at T 324 K (more precisely, T 327K for τ and T 320 c ∼ c = p c = K for τ ). The process taking place with decreasing T at T 324 K is the analog of a glass m c = transition in the rotational motion, since ions rotate fairly easily at T T , while rotations are > c progressively frozen below this temperature, but there is no orientationally ordered phase at low T to mark a genuine plastic transition.

6.2.4 Paths for proton diffusion according to a Grotthuss-type mechanism

The double donor-acceptor functionality of each cation opens the way to proton conductivity through a Grotthuss-type mechanism. In our classical MD simulations based on a force field of fixed topology (i.e., non-reactive) we are unable to follow the process in real time. Ab-initio (DFT) simulation, which is inherently reactive, are too expensive for unbiased simulations, and current DFT approximations, while certainly reliable for systems evolving close to their low energy thermodynamic basin, are less accurate and less tested for systems undergoing chemical reactions that involve the breaking and forming of covalent bonds. For this reason, our study is limited to the investigation of correlation in atomic positions that favour the

110 6.2. Results

10 10

8 7 10 ] 10 -3 m µ

4 10 c(n) [ ] 7 -3 10 m

µ 1 10 2 4 6 8 10 6 n c(n) [ 10

T=440 K 5 10 T=200 K

0 20 40 60 80 n

Figure 6.17 – Logarithm of the concentration c(n) of chains length n, expressed in number of chains per inverse cubic micron. The main panel reports the results considering the possibility of oxygen atoms on [TF]− shuttling protons between two [DAEt]+ cations, see text. Inset: results considering only the HBs linking cations directly, see text. opening of path for proton transfer along chains of cations. Hence, our analysis accounts only for the system geometry, and does not say anything about the kinetics of the proton jump process, even in an approximate way. We focus on DAEt-TF since experiments point to this compound as the most promising candidate for fast proton conductivity.

To account for the limitations in the force field, we select fairly loose criteria to define con- nectivity. First, since the DFT computations show that the ammonium and amine groups in [DAEt]+ are virtually equivalent to each other, in our analysis no distinction is made with respect to the two terminations. Moreover, connectivity is defined through the N N distance ··· of nitrogens on neighbouring cations only, disregarding the orientation of all N H bonds, − assuming that hydrogens can reorient themselves relatively quickly. Then, we define the separation of two cations as the shortest distance between a nitrogen on the first cation and a nitrogen on the second cation, irrespective of their belonging to the -NH2 or NH3+ termination. In other terms, the separation of two cations is the shortest of four N N distances. Then, ··· chains are identified as a sequence of cations related by a nearest-neighbour condition. A schematic view of the chains of interest is shown in Figure 6.6 (a). Chains are terminated when the nearest-neighbour distance is longer than 3.6 Å.

At each temperature, we consider 1000 configurations extracted every 0.2 ns out of the 200 ns production trajectories. For each configuration, we construct chains of cations, starting in turn from each [DAEt]+, and moving to the nearest cation neighbour, with distance measured

111 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids by the shortest separation of N atoms on the two cations. In this progression, the growing chain is self-avoiding, meaning that we exclude re-crossings of the chain identified up to that point. Moreover, chains are mutually non-intersecting, meaning that no cation can belong to more than one chain. The chain is terminated when no cation is within 3.6 Å from the last identified one, or when the following cation is the first of the chain, giving a closed loop. The results of this first restricted analysis is summarised in the inset of Figure 6.17, reporting on a logarithmic scale the n dependence of the concentration c(n) of chains of length n, expressed 3 in µm− . The figure concerns only a few chain sizes (up to n 10), since longer chains are not = found in the simulated samples. Once normalised, the curves in Figure 6.17 can be interpreted as the size probability distribution:

c(n) p(n) P (6.7) = n∞ 1 c(n) = of an equilibrium polymerisation process [202]. In this case, the probability distribution is a decreasing exponential of the size n. Both the concentration of chains of length n and the maximum length of chains in the sample increase slightly with decreasing T , reflecting more a general effect of thermal expansion than a change in the system topology. Although conceptually interesting, the result is not very relevant in view of proton conductivity, since the possibility of moving by 10 15 Å every time a Grotthuss event occurs will not enhance − proton diffusion by much, taking into account that initiating the Grotthuss process requires the formation of a coordination defect, whose concentration is not large even at relatively high T .

The picture changes if we include the possibility of an oxygen from [TF]− shuttling a proton between two successive cations along the chain. Also in this case, the chain is built by a minimum-separation requirement, but this time it includes also protons jumping from N to O and back to a nitrogen on another cation. This bridging mechanism is sketched in Figure 6.6 (b). While constructing the chain, the bridging anion is retained only if the distances N O ··· and O N0 on another cation are both shorter than the separation to the nearest cation, and, ··· in all cases, distances need to be less than 3.6 Å.

The result of this analysis is displayed in the main panel of Figure 6.17. To emphasise the difference, only the results at the two extreme temperatures T 200 K and T 440 K are = = plotted in both panels of Figure 6.17. The results show that chains of up to n 80 cations ∼ (plus a comparable number of bridging anions) can be found, although at relatively low concentration for n 40. For all the chains contributing to Figure 6.17, as already stated, the ≥ longest separation among nitrogen atoms is less than 3.6 Å. Notice that crossing such a gap would require the proton to travel by up to 1.5 Å only, and the jump could also be assisted by quantum mechanical effects. An example of a chain in DAEt-TF at T 350 K, including 12 = cations and 10 bridging anions is shown in Figure 6.18. Because of the self-avoiding constraint,

112 6.2. Results

Figure 6.18 – Chain of 12 cations and 10 bridging anions (see text) forming a connected set in which the longest link is less than 3.6 Å . Two further bridging anions have been omitted for clarity.

the subdivision of the cations into chains depends somewhat on the selection and ordering of the starting points. However, the difference in the size distribution function due to this dependence is limited to quantitative details.

As already stated, the temperature dependence of the restricted analysis (inset of Figure 6.17) is uniform on the entire n range, pointing to a stabilisation of chains with decreasing T . The temperature dependence of the extended analysis is more complex. At n 40, the concentra- > tion of chains increases markedly with decreasing temperature, reproducing the trend of the restricted analysis. However, since the number of ions in the sample is fixed, the trend towards larger clusters at low T has to be compensated by the relative decrease in the concentration of short chains.

With the extended definition of connectivity, including the shuttling by [TF]− oxygens, the probability distribution of chain sizes p(n) is no longer a simple exponential, but it is well reproduced by a stretched exponential. This differs from the results of equilibrium polymeri- sation theory [202], predicting a Zimm-Schultz distribution:

µ ¶ γ 1 n p(n) n − exp γ , (6.8) ∝ − n 〈 〉 where n is the average length of chains. The difference might also be due to the small samples 〈 〉 of our simulations, perhaps distorting the probability distribution at n 40. > On average, one fifth of the chains form closed loops. Moreover, apart from relatively short linear segments, chains tend to be coiled, and perhaps it would be more appropriate to talk about connected clusters instead of chains. The minimum distance condition used to define

113 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids chains prevents the identification of branched structures, that, however, are possible and likely.

Reducing the cut-off distance from 3.6 Å to 3.2 Å reduces the concentration of chains by a factor of two for 2 n 40. Beyond n 40 the relative decrease in concentration is progressively ≤ ≤ = larger, limiting the range of chain sizes to n 60. ≤ All the results in Figure 6.17 refer to self-avoiding, mutually non-intersecting chains. The estimate including all possible chains irrespective of their mutual intersection might also be relevant, since it gives information on the connectivity and multiplicity of the proton transport network. If we count all paths, irrespective of their crossings, the chain concentration curve extends to larger n’s, up to the size of the entire sample. For any given size n, the chain concentration c(n) growth with respect to the self-avoiding case. At n 40, the increase is by = one order of magnitude.

Once again, we emphasise that the relevance of each path has to be assessed a posteriori using a kinetic model. This difficult task is left for further investigations. Nevertheless, a sizeable concentration of paths is an important feature, since the Grotthuss mechanism, in general, requires an initiation step. In water, for instance, the initiation step is represented by the auto- ionization of the H2O molecule, which is a rare event. The initiation step in DAEt-TF could be represented by the neutralisation reaction: DAEt-TF DAEt+HTf, which, in the gas-phase → requires 1.47 eV (see Section 6.2.1). This energy could be reduced by correlations and screening in the condensed phase. For instance, the energy of the same charge defect in the (DAEt TF) − 2 is already reduced to 1.27 eV. Moreover, and more importantly, some other mechanisms of lower free energy could act as the initiation step. For instance, the close approach of an anion to a cation termination could shift the HB balance at the other termination, releasing of accepting a proton. Nevertheless, it is likely that the initiation step still remains a rare event. Hence, every initiation step that naturally occurs by fluctuation has to open a long path for the proton transfer, otherwise the Grotthuss channel is likely to be quantitatively unimportant. Unfortunately, no information on the initiation step is provided by the MD simulation based on a non-reactive force field. Further ab-initio computations on systems larger than nano-clusters are needed to clarify this important point.

6.2.5 Water effect on the structure and dynamics

A preliminary exploration of the effect of water on the structure and dynamics of DAEt-TF has been carried out, paralleling the experimental investigation reported in [73], and following a closely related computational analysis we explained in Chapter 3.

In the present case, we added 25 water molecules to the sample of 216 DAEt-TF neutral ion pairs, corresponding to a 1% weight water contamination. The sample preparation follows the

114 6.2. Results

Table 6.4 – Diffusion constants and electrical conductivity of dry DAEt-TF and DABu-TF samples. Data for DAEt-TF at 1 % weight water contamination are given for a comparison. Diffusion constants in cm2/s; electrical conductivity in S/m.

DAEt-TF Dry samples Type T 250 K T 300 K T 350 K T 400 K T 440 K = = = = = 10 9 8 7 7 [DAEt]+ 3.74 0.5 10− 3.53 0.3 10− 6.57 0.2 10− 3.13 0.05 10− 8.13 0.05 10− ± × 10 ± × 9 ± × 8 ± × 7 ± × 7 [TF]− 2.94 0.4 10− 2.76 0.2 10− 4.42 0.05 10− 2.74 0.05 10− 6.64 0.05 10− ± × 7 ± × 5 ± × 5 ± × 4 ± × 4 κ 6.6 1 10− 1.2 0.1 10− 8.9 0.6 10− 5.25 0.4 10− 14.5 1.2 10− ± × ± × ± × ± × ± × DABu-TF Dry samples Type T 250 K T 300 K T 350 K T 400 K T 440 K = = = = = 9 7 7 6 [DAEt]+ - 8.38 0.9 10− 1.07 0.2 10− 4.96 0.5 10− 1.39 0.1 10− ± × 9 ± × 8 ± × 7 ± × 6 [TF]− - 6.18 0.7 10− 9.24 0.9 10− 5.25 0.5 10− 1.27 0.1 10− ± × 5 ± × 4 ± × 4 ± × 4 κ - 3.7 0.4 10− 6.6 0.5 10− 11.5 1 10− 17.3 1 10− ± × ± × ± × ± × DAEt-TF Wet samples Type T 250 K T 300 K T 350 K T 400 K T 440 K = = = = = 10 9 8 7 6 [DAEt]+ 3.88 0.4 10− 7.00 0.6 10− 8.88 0.7 10− 4.89 0.4 10− 1.21 0.1 10− ± × 10 ± × 9 ± × 8 ± × 7 ± × 7 [TF]− 3.08 0.4 10− 5.43 0.5 10− 7.28 0.6 10− 3.85 0.3 10− 7.34 0.6 10− ± × 9 ± × 7 ± × 6 ± × 6 ± × 6 H2O 7.27 0.8 10− 2.56 0.3 10− 2.02 0.2 10− 5.51 0.4 10− 9.22 0.7 10− ± × 7 ± × 5 ± × 5 ± × 4 ± × 4 κ 6.7 0.3 10− 1.2 0.15 10− 9.4 0.7 10− 7.3 0.1 10− 14.8 1.1 10− ± × ± × ± × ± × ± × same procedure used in Chapter 3, distributing molecules at random over the system volume, quenching to remove short contacts, and equilibrating at the target temperature. Simulations have been carried out at T 440 K, T 400 K, T 350 K. Each production run lasted 200 ns, = = = following 40 ns of equilibration. The longer equilibration time was meant to allow for water diffusion throughout the sample. Additional simulations, following a different schedule, have been carried out at T 300 K and T 250 K, starting from T 350 K, decreasing T in steps of = = = δT 10 K, each time equilibrating during 60 ns, pausing at T 300 K and T 250 K for a 200 = = = ns equilibration and 200 ns statistics.

Comparison of the average density computed for dry and wet samples show that at T 300 K = the volume occupied by water in DAEt-TF is v 26.2 0.4 Å 3 per molecule, to be compared = ± to v 30 Å 3 in bulk water at the same conditions. The 10 % shrinking underlines the good = affinity of water for DAEt-TF,at least at low water concentrations. Over the 300 K T 440 ≤ ≤ K range, the radial distribution function for the water-oxygens (OW-OW) has a clear peak at r 2.72 Å apparently due to water-water hydrogen bonding (see Figure 6.19 (a)). Because of ∼ the low density of water, however, the peak corresponds, on average, to just two hydrogen bonded water dimers, and the distribution of water across the sample is homogeneous. The + OW-nitrogen (in NH ) and OW-oxygen (on [TF]−) radial distributions also clearly show the − 3 signature of hydrogen bonding. In agreement with the experimental results of Ref. [133], the hydrogen bonding of water is particularly strong and geometrically well defined in the case of OW-[TF]−. As expected, the association of water and [TF]− is progressively enhanced with

115 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids

6 3 (a) (b)

2 OW-OW

4 g (r ) 1

0 g(r) 2468 2 r [A]

0 2468 r [A]

Figure 6.19 – (a) Radial distribution function of water in samples of 216 DAEt-TF ion pairs and 25 water molecules at T 350 K. Green line: OW - ammonium N on [DAEt]+; OW - oxygen = on [TF]−; blue line (inset): OW-OW. (b) Typical configuration of a water molecule donating H-bonds to two [TF]− anions and accepting a H-bond from a [DAEt]+.

decreasing T . However, this association is never as strong as in TEA-TF (Chapter 3), in which

[TF]− ions practically sequester water at T 300 K. Figure 6.19 (a) shows a selection of OW- < OW, OW-cation and OW-anions radial distribution functions, documenting these structural features. Moreover, typical water-[TF]− and [DAEt]+-water configurations are illustrated in Figure 6.19 (b).

The effect of water on general chemical physics properties of DAEt-TF turns out to be similar to those found in samples of TEA-TF protic ionic liquid also at 1 % water contamination

(Chapter 3). Both [DAEt]+ and [TF]− diffuse faster in wet samples than in dry samples. Water diffuses faster than either [DAEt]+ and [TF]− at T 300 K. Below this temperature the water ≥ advantage in mobility is progressively reduced, because of its tight association with [TF]−. Quantitative results can be found in Table 6.4. As in the TEA-TF case (Chapter 3), electrical conductivity increases with respect to the dry samples, but the relative variation is fairly small. At variance from the TEA-TF case, the Nernst-Einstein conductivity remains above the direct estimate (Equation 3.6) at all temperatures, showing that even in the presence of water, pairing of cations and anions remains tight.

More interesting, in this case, are the consequences on the statistics of chains of HB that represent paths for the fast proton diffusion. First of all, we observe that the inclusion of water enhances the connectivity of the hydrogen-bonding network, even at temperatures such that water is tightly bound to [TF]−. At all temperatures, in particular, every water molecules that donates more than one proton links to different [TF]− anions. Conversely,

116 6.3. Summary and conclusions

9 10

8 10 Wet sample

] 7 -3 10 µ Dry sample

6 10 c (n ) [m 5 10

4 10 0 20 40 60 80 100 n

Figure 6.20 – Comparison of the concentration of chains in dry and in water contaminated DAEt-TF samples at T 350 K. = the rare times a water molecule accepts two hydrogen bonds, these are donated by different cations. The identification of chains now including also the bridging by water molecules (see Figure 6.6 (c)) shows a widening of the range of sizes present at significant concentration at all simulates temperatures. Moreover, again for n 40, the density of chains c(n) is higher in the > water-contaminated samples, as shown in Figure 6.20. Both observations point to a potential increase of proton conductivity upon water absorption. A similar effect in other hydrogen bonded systems is well documented [203]. Unfortunately, efficiency requirements on electro- chemical devices such as fuel cells force them to operate at temperatures of the order of 400 K, i.e., above the boiling point of water [204]. Nevertheless, computations could provide the way to extrapolate experimental diffusion and conductivity measurements for water contaminated specimens to the limit of ideally dry samples, relevant for power generation applications.

6.3 Summary and conclusions

Half-neutralised diamine cations combined with the triflate anion have been investigated by density functional computations in the generalised gradient approximation (PBE) and by molecular dynamics based on an empirical force field. Three cations have been considered, consisting of a pair of amine-ammonium terminations, separated, or, better, joined by a short alkane segment ( CH ) with n 2, 3 and 4 carbon atoms, whose gas-phase, ground state − 2 n = structure is shown in Figure 6.1. Density functional computations for the isolated cations, for neutral ion pairs and for small neutral clusters with up to eight ions identify low-energy geometrical motifs in these small aggregates, highlighting the primary role of Coulomb forces, as well as the secondary but still important role of hydrogen bonding. In all the aggregates

117 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids we studied, each cation shows a very stable intra-ion hydrogen bond joining its amine and ammonium terminations. Despite strain in the smallest member of the sequence, this intra- cation HB is stable, short, and probably more symmetric than implied by the structural formula, especially taking quantum effects into account.

Strong and stable HBs join each cation to multiple anions (when present), contributing to the determination of the ground state structure. Of particular interest, however, is a different class of HBs, connecting neighbouring cations. Because of electrostatics, these bonds are certainly less stable than cation-anion HBs, and, for this reason, they are not found in the ground state structure of very small aggregates, but they form during 10 ps long ab-initio ∼ simulations at room temperature. Moreover, they could form at sizeable concentration in extended connected phases, stabilised by entropy and by correlation with anions, and in such a case they would support proton transport via the Grotthuss mechanism. To investigate proton displacement by this process, a chain-like geometry made of hydrogen bonded [DAEt]+ cations and neutralising [TF]− anions has been prepared. The potential energy profile upon moving a single proton along the HB has a single minimum, although it is soft enough to allow large amplitude displacements at a modest energy, requiring 5 kcal/mol to bring the proton to 1.1 ∼ Å from the non-covalently bonded nitrogen. The corresponding energy profile for the in-phase displacement of all protons along the HB chain has a double minimum shape. The barrier per proton separating the two minima is low, but, of course, it increases linearly with the number n of protons moving together, hence the barrier becomes high when moving many protons. Although we did not analyse this aspect in detail, it is likely that a semi-localised soliton-like mode combining single proton and collective displacement might provide a mechanism with a barrier compatible with the role of extra-vehicular proton transport measured in experiments on the same ionic liquid compound [73].

Molecular dynamics simulations based on an atomistic empirical force field have been carried out to determine general chemical physics properties of DAEt-TF and DABu-TF,and to explore possible paths for proton conduction through the Grotthuss mechanism. Simulations at ambient pressure for DAEt-TF have been carried out for temperatures from 200 K to 440 K on a thin grid of δT 10 K spacing. Long trajectories covering 200 ns production following = at least 6 ns equilibration have been analysed to compute thermodynamic properties such as density and average potential energy, structural properties such as the structure factors, the radial distribution functions, the number and geometry of the most stable HBs, as well as dynamical properties such as the diffusion constant, the electrical conductivity, the relaxation time for ion rotations, the spatial distribution and the life-time of individual hydrogen bonds.

In the DAEt-TF case, both density and potential energy as a function of T show two linear ranges at high and low temperature, with a crossover interval centred at T 310 K of 20 K = ∼ half-width, identifying what appears to be a glass transition with super-imposed a weakly first

118 6.3. Summary and conclusions order transition, possibly giving origin to a very incomplete degree of ordering that we have been unable to identify. The structure of both high- and low-temperature phases displays periodicity on a few different lengths, hinting to the separation of ionic and neutral domains on the 6 10 Å scale. − The temperature evolution of dynamical properties reflects the two phases and broad transi- tion seen in the thermodynamic functions, as emphasised by the Arrhenius plot of diffusion coefficients, electrical conductivity and rotational relaxation time. The sizeable overestimation of ionic conductivity by the Stokes-Einstein relation, that persists up to the highest tempera- ture in our simulation, points to the long-time association of cations and anions, consistent with the strength of Coulomb interactions, the directionality of hydrogen bonding, and the resulting high viscosity of these compounds.

MD simulations of DABu-TF samples at four temperatures (T 440 K, 400 K, 350 K and 300 K) = and ambient pressure give results similar to those obtained for DAEt-TF,with expected differ- ences due to the relatively lower role of Coulomb forces and to the increased role of dispersion and packing effects with respect to DAEt-TF. In particular, the tendency to a mesophase is enhanced in DABu-TF.The intra-cation HB is somewhat destabilised by the entropy advan- tage of extending the ( CH ) segment and separating the amine-ammonium terminations, − 2 4− resulting in a dynamical equilibrium between the ring and chain configuration for the cations. Remarkably, ions diffuse (slightly) faster in DABu-TF,an its electrical conductivity is higher than for DAEt-TF.The enhanced fluidity of DABu-TF is not unexpected, since it is in line with the role of larger and less symmetric ions in decreasing the melting temperature of RTILs down to room temperature. Possibly because of the lower number density of cations, sequences of [DABu]+ ions separated by less than r 3.6 Å are shorter (by size n) in DABu-TF than in c = DAEt-TF,both including and excluding the possibility of bridging by oxygen atoms.

The exploration of possible paths for proton conduction arguably is the most intriguing part of our study, since the double donor-acceptor capability of cations opens the way to proton transport via the Grotthuss mechanism, breaking the limit on vehicular conductivity set by the relatively high viscosity of these compounds. Unfortunately, size and time scales prevent the usage of ab-initio simulation at this stage, and our analysis has to rely on the equilibrium structure provided by molecular dynamics and the empirical force field. Starting from each cation in turn, we identify self-avoiding sequences moving from one cation to the next ac- cording to a condition of closest proximity, terminating whenever the distance to the nearest neighbour is longer than r 3.6 Å . If we consider only cations, and we define their separation c = as the minimum distance of amine and ammonium terminations (no distinction between the two) on the two ions, only short chains of up to 10 cations can be identified. The ab-initio ∼ investigation of the potential energy landscape for protons moving between a nitrogen atom on DAEt-TF and an oxygen on [TF]−, however, shows that long elongation proton displace-

119 Chapter 6. Equilibrium structure, hydrogen bonding and proton conductivity in half-neutralised diamine ionic liquids ments are possible within an energy threshold of a few kcal/mol. We take this information into account by including the possibility of oxygen atoms from [TF]− shuttling protons across the gap between two cations, following the procedure described in Section 6.2.4. In this way, we find connected sequences of up to 80 cations, consisting of a few short linear segments and a majority of globular domains. Although our approach is silent on the dynamical aspects underlying these observation, we think that the results based on structure might provide a first preliminary explanation of the observed high rate of proton transport in DAEt-TF [73], exceeding the rate implied by the diffusion constant of cations.

In a last stage of our study, we investigated the effect of water contamination at the 1 % in weight on the properties of DAEt-TF. Once again, the results follow expectation but are nevertheless intriguing. At T 300 K water diffuses faster in DAEt-TF that either ions, which, ≥ themselves, diffuse faster than in dry samples. At all temperatures, the water-anion interaction is stronger than water-cation. Below T 300 K, this tight coupling to [TF]− slows down water, = reducing significantly its mobility advantage with respect to both ions. At all temperatures water enhances the electrical conductivity, both because it enhances diffusion and because it decreases (slightly) the strict correlation in the motion of cations and anions.

By donating two HBs to two different [TF]− anions, and accepting, on average, one HB from [DAEt]+, water enhances the connectivity of the hydrogen bond network, and increases the length of cation chains, as defined in Section 6.2.5. In this way, water contamination tends to increase the mobility of protons both by enhancing cation diffusion and, possibly, by allowing longer paths to Grotthuss transfer. Although the cation species in our RTILs include only short (CH ) segments, our results on the effect of water on the HB network and on the relative − 2 n− geometry of water and anions is reminiscent of those presented in Ref. [205] for longer alkyl chain RTILs.

In summary, our extensive computational study provides a comprehensive picture of half- neutralised diamine and triflate salts, outlining a number of quantitative and qualitative details. In many respects, it extends the computational analysis we carried out on TEA-TF (Chapter 3), and is part of a combined experimental and computational investigation of protic ionic liquids focusing, in particular, on their proton conduction capability. The major limitation of our approach is represented by the rigid atomic charges, fixed-topology, classical mechanics picture underlying the force field model used for MD simulations. Full blown DFT simulations for a few hundred RTIL ions, covering 100 ns are still years away, but qualitative ∼ improvements of the force fields, and perhaps the introduction of valence bond (VB) models could greatly extend the scope of simulation in the investigation of proton conductivity in organic ionic systems.

120 7 Methylation impact on the dynamics and structure of imidazolium-based ionic liquids

So far, from Chapters 3 to6 we have shown how hydrogen bonding influences the dynamics of protic ionic liquids (PILs). However, as introduced in Chapter 1, ILs can be classified in two types: protic and aprotic ionic liquids (AILs). This chapter focus on the latter kind and presents a panorama of the hydrogen bonding impact in imidazolium based AILs. The cations of these liquids were selectively methylated at the hydrogen bond most active position C2 (see Figure 7.1), thus, altering the number of possible H-bonds sites in the systems. Our study was inspired by recent infrared and terahertz spectroscopy measurements complemented with computational methods on similar AILs [52,62,206 –216]. Higher viscosities and melting points in addition to lower conductivities where reported for the methylated species, thus revealing the strong effect of H-bonding in the physicochemical properties of ILs. The outcomes of this chapter are preliminary, they will be included in a publication that is in preparation to be submited as: Juan F.Mora Cardozo, Tatsiana Burankova, Daniel Rauber, Rolf Hempelmann and J. P.Embs, Methylation impact on the dynamics and structure of imidazolium-based ionic liquids.

7.1 Materials and methods

7.1.1 Samples

Three AILs samples with the 1-Ethyl-3-methylimidazolium and the methylated 1-Ethyl-2,3- dimethylimidazolium cation analogue (see Figure 7.1 a and Figure 7.1 b respectively) were synthesized and characterized at the Chemistry Department of Saarland University. Table 7.1 summarizes the neutron cross-sections and acronyms of the ionic species and Figures 7.5

121 Chapter 7. Methylation impact on the dynamics and structure of imidazolium-based ionic liquids

2 2

1 3 1 3

5 4 5 4

Figure 7.1 – a) Chemical structure of 1-Ethyl-3-methylimidazolium and b)1-Ethyl-2,3- dimethylimidazolium (methylated) cations. The numbers label the different positions within the imidazolium ring.

Table 7.1 – Neutron cross-sections and chemical formulas of the studied ILs. The cross-sections 24 2 σ are given in barns (1 b 10− cm ) at a wave-length λ 5.75 Å. The abbreviations cat. and = = an. stand for cation and anion, respectively.

Name Molecular Formula Acronym σcat. σan. σcat. σan. σinc [%] coh coh inc inc σtot 1-Ethyl-3-methylimidazolium [C H N ][C N ] EMIM-TCM 74.65 55.23 883.87 1.50 87.21 tricyanomethanide 6 11 2 4 3 1-Ethyl-2,3-dimethylimidazolium [C H N ][C N ]C C C IM-TCM 83.72 55.23 1044.39 1.50 88.27 tricyanomethanide 7 13 2 4 3 2 1 1 1-Ethyl-3-methylimidazolium [C H N ][SCN] EMIM-SCN 74.65 17.58 883.87 0.51 90.56 thiocyanate 6 11 2 1-Ethyl-2,3-dimethylimidazolium [C H N ][SCN] C C C IM-SCN 83.72 17.58 1044.39 0.51 91.16 thiocyanate 7 13 2 2 1 1 1-Ethyl-3-methylimidazolium [C H N ][C N ] EMIM-DCA 74.65 44.13 883.87 1.50 88.17 dicyanoamide 6 11 2 2 3 1-Ethyl-2,3-dimethylimidazolium [C H N ][C N ]C C C IM-DCA 83.72 44.13 1044.39 1.50 89.11 dicyanamide 7 13 2 2 3 2 1 1

to 7.7 show the ground state structures of the AILs. The large neutron incoherent cross section of hydrogen leads to the dominant incoherent signal of the cations for all the AILs, whereas, the anion incoherent contribution to the total scattering can be neglected. Furthermore, the coherent share to the total signal is at most 13% as for EMIM-TCM (see Table 7.1), thus, the neutron signal will mainly reveal the single particle dynamics of the cation.

7.1.2 Differential scanning calorimetry (DSC)

Thermal transitions were measured by DSC, following the procedure introduced in Sec- tion 5.1.2. The results are presented in Figures 7.2 to 7.4 and the phase transition temperatures are summarized in Table 7.2. The figures display the appearance of extra thermodynamic phase transitions for the methylated species. In particular the DSC traces of C2C1C1IM-SCN and C2C1C1IM-DCA are evidently more complex than the ones of the non-methylated coun-

122 7.1. Materials and methods a) b)

1 Figure 7.2 – DSC traces of a) EMIM-SCN, b) C2C1C1IM-SCN at 1 Kmin− scan rate.

1 Table 7.2 – Thermal transitions of the investigated ionic liquids at 1 Kmin− scan rate. Tc: crys- tallization temperature; Tg: glass transition temperature; Tcc: cold crystallization temperature; Tm: melting point; Tss: solid-solid transition. All temperatures are given in K.

cooling heating System Tc Tg Tcc Tm Tss Tss EMIM-DCA 223 – – 269 – –

C2C1C1IM-DCA 302 – – 319 263, 297 271, 311, 315 EMIM-SCN – 117 – – – –

C2C1C1IM-SCN 343 – – 347 265, 334 292, 339 EMIM-TCM 219 186 222 275 – –

C2C1C1IM-TCM 228 – 231 284 – – terpart (see Figures 7.2 and 7.3), the former exhibiting extra solid-solid phase transitions both in the cooling and in the heating cycle. The traces of C2C1C1IM-TCM and EMIM-TCM differ in the manifestation of a glass transition at 186 K in the non-methylated AIL (see Figure 7.4a and b). Our DSC measurements for the EMIM based ILs are comparable to data available in the literature, small discrepancies in the phase transition temperatures are due to different temperature scan rates of each experiment [39,217–220]. In the case of C2C1C1IM based AILs, there are not reported phase transition temperatures to the best of our knowledge.

7.1.3 Quasi-elastic neutron scattering experiments

Neutron experiments were carried out at SINQ at the Paul Scherrer Institute (PSI, Villigen, Switzerland). The cold neutron spectrometer FOCUS was utilized to investigate the dynamics

123 Chapter 7. Methylation impact on the dynamics and structure of imidazolium-based ionic liquids

a) b)

1 Figure 7.3 – DSC traces of a) EMIM-DCA, b) C2C1C1IM-DCA at 1 Kmin− scan rate. in the ps time-window. FOCUS was used with an incident neutron wavelength λ= 5.75 Å, and providing a resolution of 70 µeV (fwhm). The accessible energy-window and momentum 1 transfer were E= 1.4 meV and Q= 0.35–1.9 Å− , respectively. The spectra measured at 40 K ± were used as resolution function R(Q,E).

As done in Section 5.1.3, a vanadium standard was used to calibrate the detectors of the instrument. Background effects were corrected by measuring an empty can at different temperatures. The samples were contained in the gap (0.2 mm wide) of a concentric double- hollow thin Aluminum cylinder. The transmission of the filled sample holder was about 90 %, thus minimizing multiple scattering. The raw neutron data were transformed from time-of- fight (TOF) to I(Q,E) S(Q,E)[78] using DAVE [164] in the standard manner. The sample ∝ signal was normalized to the incoming flux followed by the subtraction of the signal of an empty sample holder, subsequently the energy transfer E was calculated. The detectors were calibrated using a vanadium standard and corrected for their energy dependent efficiency. Finally, the momentum transfer Q was calculated and the data was binned into groups of the same momentum transfer.

7.1.4 Data analysis

Liquid Phase

As proposed in Refs. [214,215] for EMIM- and C2C1C1IM-Br ILs two separable processes could be identified in these cations, thus, we followed the approach of Section 5.1.4; the QENS data was described as the convolution of two dynamically decoupled processes occurring on different time scales; a slower and spatially not restricted motion observed in the time window

124 7.1. Materials and methods a) b)

1 Figure 7.4 – DSC traces of a) EMIM-TCM, b) C2C1C1IM-TCM at 1 Kmin− scan rate. of few picoseconds is connected to the self-diffusion of the cation. A faster dynamical processes characterized by relaxation times in the sub-ps scale, appears to be spatially confined, and is related to the reorientation of the cation’s ethyl group.

The dynamical structure factor of the AILs is presented as :

S (Q,E) I(Q) L(Γ ,E;D ,τ ) SG (Q,E;D ,R ) bg(Q,E), (7.1) AIL = global tr 0 ⊗ alkyl alkyl alkyl +

where I(Q) is an intensity factor containing the Debye-Waller factor, L(Γglobal,E) is a Loren- tizan with half width at half maximum defined by the jump diffusion model with diffusion alkyl coefficient Dtr and residence time τ0 (see Equation 2.21). SG (Q,E;Dalkyl,Ralkyl) describes the ethyl group dynamics using the Gaussian model (see Equation 2.26), with corresponding confinement radius Ralkyl and diffusion coefficient Dalkyl. Finally, bg(Q,E) is the background summarizing all the fast dynamics, which can not be resolved by the used instrumental settings.

7.1.5 Ab-initio simulations

As reported in Section 5.1.5, we performed ab initio computations at the density functional theory (DFT) level to obtain the ground state structure and energy of the ionic pairs. The Perdew-Burke-Ernzerhof [98] approximation for exchange and correlation energy was used, in addition the dispersion interactions were included at empirical level [117]. Simulated annealing was employed to optimize the ground state geometries [116]. The calculations were

125 Chapter 7. Methylation impact on the dynamics and structure of imidazolium-based ionic liquids

a) b)

Figure 7.5 – Ground state geometry of: a) EMIM-SCN, b) C2C1C1IM-SCN. PBE exchange correlation and CPMD calculation. The close contacts represented by doted lines are hydrogen bonds.

performed using the CPMD [113] software package, which is based on soft norm-conserving ab-initio pseudopotentials and plane waves [114]. The calculations included the computation of properties related to the hydrogen-bond such as bond angles and lengths.

7.2 Results and discussion

7.2.1 Density functional computation

The ground state geometries of the different samples are presented in Figures 7.5 to 7.7, where the close contacts represent hydrogen bonds. The figures present an evident difference between the ground state structures of the methylated and non-methylated AILs dimers. The anions SCN and DCA place on top of the plane spanned from the C2C1C1IM cation ring, whereas for the EMIM based ILs, these anions prefer to form hydrogen-bonds (HB) with the hydrogen at C2 (see Figure 7.1), and thus, they locate above C2 coplanar with the cation’s ring. These feature is consistent with published computed structures of similar EMIM and

C2C1C1IM based ILs [212]. In contrast, the two optimized structures for the AILs dimers with the TCM anion find their minimum energy when the anion is above the imidazolium’s ring.

The HB length in the dimers extend from 2.1 Å and below 3.0 Å with corresponding angles in the range of 100° and 170°, which classify the HB strenght between moderate and weak [27,30]. The substitution of the hydrogen at C2 for a methyl group, make the hydrogens of ethyl group

126 7.2. Results and discussion a) b)

Figure 7.6 – Ground state geometry of: a) EMIM-DCA, b) C2C1C1IM-DCA. PBE exchange correlation and CPMD calculation. The close contacts represented by doted lines are hydrogen bonds. and the hydrogens at C4, C5 and the two methyl groups at C2 and N3 to interact more with the different anions, that is evidenced in the formation of HB between the cation and the anion at those sites, which furthermore, impact the conformation of the ground state structures when compared with the EMIM counterparts. In Figures 7.5 to 7.7 is also to be seen, that each HB in EMIM based AILs implies a single hydrogen acceptor (N or S respectively) of the anion, whereas for C2C1C1IM AILs some nitrogens and sulfur accept more than one HB. This reflects the complex interplay between Coulomb and hydrogen bonding interactions in the system.

7.2.2 Dynamics in the liquid phase

On FOCUS we performed QENS experiments on the methylated and non-methylated AILs, the spectra were analyzed using Equation 7.1. The results are presented in Figures 7.8 to 7.10 and Tables 7.4 to 7.6. Overall, the global dynamics of the different ionic pairs are faster for the EMIM based ILs than for the C2C1C1IM based AILs (see Figure 7.8). Nonetheless, for the ILs with the TCM anion, Dtr coincide inside the error bars in the temperature interval from T=300 K to T=360 K, but with slightly longer residence times τ0 for the methylated species (see Table 7.4). This evidence the impact of the structure on the translational dynamics of these sample pair, so as the computed ground state structures of EMIM-TCM and C2C1C1IM-TCM were the ones with lesser changes upon methylation at C2 (see Figure 7.7). Dtr for EMIM-DCA/-

SCN are certainly faster than for C2C1C1IM-DCA/-SCN, however, at 320 K C2C1C1IM-DCA is close to its melting point (see Table 7.2 and Figure 7.3 b), thus, Dtr drops dramatically as

127 Chapter 7. Methylation impact on the dynamics and structure of imidazolium-based ionic liquids a) b)

Figure 7.7 – Ground state geometry of: a) EMIM-TCM, b) C2C1C1IM-TCM. PBE exchange correlation and CPMD calculation. The close contacts represented by doted lines are hydrogen bonds. displayed in the figure. Methylation of EMIM at the C2 site plus its combination with the DCA or SCN anion appear to drastically slow down the unrestricted dynamics of the respective AIL.

The activation energy Ea for the unrestricted dynamics are presented graphically as fits (solid lines) of an Arrhenius behaviour (Equation 5.7) in Figure 7.8 and in Table 7.3. Interestingly, for all AILs the Ea coincide inside the error bars, however, both for the EMIM and the C2C1C1IM cations combined with the lightest anion SCN, result in the slowest the global dynamics of each sample pair. For the methylated species, Dtr increases in an anion increasing mass trend: SCN/DCA/TCM, differently, for the non-methylated we found that Dtr increases as: SC-

Table 7.3 – Activation energy for the global and the alkyl chain dynamics following an Arrhenius behaviour

Global dynamics 1 Ea[kJmol− ] SCN DCA TCM EMIM 13.22 (0.77) 13.39 (0.69) 12.89 (0.78) C2C1C1IM 14.80 (2.99) 13.07 (0.63) 12.57 (1.01) Alkyl dynamics loc 1 Ea [kJmol− ] SCN DCA TCM EMIM 8.63 (0.23) 12.01 (1.40) 11.64 (0.18) C2C1C1IM 9.66 (1.71) 11.48 (0.92) 10.93 (0.33)

128 7.2. Results and discussion

14.0 TCM 12.0 SCN DCA 10.0 ] -1

s 8.0 2 m 6.0 -10 [10 tr

D 4.0

2.4 2.6 2.8 3.0 3.2 3.4 1000/T [K-1]

Figure 7.8 – Temperature dependence of the global diffusion coefficients Dtr. In filled symbols the results for the C2C1C1IM based ILs and in open symbols the results for the EMIM based ILs. The solid lines correspond to the fit of an Arrhenius behaviour, Equation 5.7.

18.0 TCM 16.0 SCN DCA

] 14.0 -1

s 12.0 2

m 10.0 -10 8.0 [10 alkyl

D 6.0

2.4 2.6 2.8 3.0 3.2 3.4 1000/T [K-1]

Figure 7.9 – Temperature dependence of the diffusion coefficients Dalkyl. In filled symbols the results for the C2C1C1IM based ILs and in open symbols the results for the EMIM based ILs. The solid lines correspond to the fit of an Arrhenius behaviour, Equation 5.7.

N/TCM/DCA. Which again, reflects the important role of the ionic structure on the dynamics of the ILs and its consequences in macroscopical properties such as, higher viscosities as Dtr decreases and better electrical conductivities as Dtr increases. This observation is confirmed for our EMIM based ILs and is available in Refs. [218,221–224]. To the best of our knowledge, there is not reported data neither on viscosity nor on conductivity for the C2C1C1IM species, though, we expect they to follow the same behaviour respective to Dtr as for the EMIM ILs.

Figures 7.9 and 7.10 show Dalkyl and Ralkyl, the diffusion coefficient of the ethyl group reorien- tations [214] and its confinement radii for each AIL respectively. As for the global dynamics, the localized motions are also slowed down as response of the cation’s methylation, never- theless, different trends for Dalkyl are to be seen in comparison to the ones of Dtr. First of

129 Chapter 7. Methylation impact on the dynamics and structure of imidazolium-based ionic liquids

0.90

0.81

[Å] 0.73 alkyl R 0.64

TCM 0.55 SCN DCA 300 320 340 360 380 400 420 T [K]

Figure 7.10 – Temperature dependence of the confinement radii for the alkyl chain. In filled symbols the results for the C2C1C1IM based ILs and in open symbols the results for the EMIM based ILs. The dashed lines are a guide to the eyes.

all, although the EMIM-TCM and C2C1C1IM-TCM ground state structure and Dtr were very alike, the TCM anion affects in a different way the localized dynamics of the ethyl group for the different cations. It marks a clear slow-down of the chain dynamics as expressed by the noticeable separation of the black lines in Figure 7.9 in comparison to Figure 7.8. In addition, TCM imposes to the chain a smaller confinement volume (see open an full black symbols in Figure 7.10), thus, making the ethyl group to be overall less mobile. These two facts suggest the higher interaction of the chain with the anion in C2C1C1IM-TCM via HB formation; this is also corroborated by our computations and displayed as extra contacts (sometimes very long H-bondings 3 Å) in Figure 7.7 b when compared to Figure 7.7 a. Eventually, the activation ∼ loc energy of the localized dynamics Ea of all species but for EMIM-SCN coincide inside the error bars (see Figure 7.9 and Table 7.3), however, the spatial confinement experienced by the ethyl group do depend of the ion selection. Given a cation, EMIM or C2C1C1IM, and a one of the anions, the following trend was observed: Independent of the cation selection, the lighter the combined anion is, the lesser the volume of the cation’s ethyl group motions is. This, once more, reflects the determining influence of the anion in the overall AIL dynamics.

Our findings for Ralkyl in all the samples are smaller than for EMIM-Br, as reported in Ref. [214] for QENS experiments. However, the anions utilized in our study are larger than the single bromide anion, and more importantly, they have more than one hydrogen acceptor site.

Thus, when combining SCA, DCA or TCM with the C2C1C1IM cation they form H-bonds (see Figures 7.5 to 7.7) with the cation’s ethyl group, which restrict the chain localized dynamics volume (see Figure 7.10). Differently, when combining the same anions with the EMIM cation, the probability of hydrogen bonding with the ethyl group reduces, due to the preference of HB formation at C2, thus Ralkyl increases with respect to the C2C1C1IM AILs.

130 7.2. Results and discussion

Table 7.4 – Temperature dependence of localized and global diffusion coefficients (D), con- 10 2 1 finement radius (R) and residence time (τ0). Dtr and Dalkyl are given in 10− m s− , R in Å and τ0 in ps.

T [K] System Dtr τ0 Ralkyl Dalkyl EMIM-TCM 4.03 (0.15) 26.54 (3.48) 0.63 (0.02) 5.14 (0.11) 300 C2C1C1IM-TCM 3.30 (0.17) 39.54 (4.84) 0.57 (0.02) 4.52 (0.09) EMIM-TCM 4.94 (0.20) 18.94 (2.95) 0.75 (0.03) 6.86 (0.15) 320 C2C1C1IM-TCM 4.66 (0.15) 21.36 (2.09) 0.64 (0.02) 6.11 (0.11) EMIM-TCM 6.90 (0.23) 11.75 (1.44) 0.79 (0.03) 8.96 (0.18) 340 C2C1C1IM-TCM 6.82 (0.24) 13.91 (1.44) 0.69 (0.02) 7.66 (0.16) EMIM-TCM – – – – 360 C2C1C1IM-TCM 7.84 (0.27) 10.95 (1.34) 0.80 (0.03) 9.66 (0.21) EMIM-TCM 11.16 (0.32) 6.01 (0.72) 0.90 (0.03) 13.56 (0.31) 380 C2C1C1IM-TCM 9.98 (0.33) 8.37 (1.06) 0.87 (0.04) 11.23 (0.27)

7.2.3 Summary and conclusions

The methylation of the EMIM cation at the most active hydrogen bonding site C2 (see Fig- ure 7.1) to create the C2C1C1IM cation, and the subsequent effect on the dynamical behaviour of the cations in the liquid phase was investigated by combining most of the methods used in this thesis: DSC thermal characterization, chemistry computation (ab initio simulations) and QENS. The deactivation of the hydrogen donor site at C2 was investigated in samples of

EMIM and C2C1C1IM mixed with the SCN, DCA and TCM anions, hence, forming a set of three sample pairs. The anion selection varied in structure, thus, they exhibit different number of hydrogen acceptor sites: (at least) 2 for SCN and 3 for DCA and TCM.

The DFT computation of the ground state structure of the different dimers showed that the SCN and DCA anions oriented in the same plane of the imidazolium ring when combined with the EMIM cation, whereas, when combining them with the C2C1C1IM cation, the minimum energy was found when the anions were located above the imidazolium ring. The latter facilitated the interaction of these two anions with the ethyl group and the methyl groups of the C2C1C1IM cation. In contrast, the ground state structure of the two ILs formed with the TCM anion showed more similarities than for the other studied AILs, and located above the imidazolum ring.

The structural features, although just calculated for ion pars, helped to interpreted the dynam- ics of the liquids in a ps time-window. For all the samples, the methylation at C2 slowed down the whole dynamics. The lightest anion SCN combined with the either the two cations were the slowest diffusing system. In addition, the two TCM based ILs had similar self-diffusion

131 Chapter 7. Methylation impact on the dynamics and structure of imidazolium-based ionic liquids

Table 7.5 – Temperature dependence of localized and global diffusion coefficients (D), con- 10 2 1 finement radius (R) and residence time (τ0). Dtr and Dalkyl are given in 10− m s− , R in Å and τ0 in ps.

T [K] System Dtr τ0 Ralkyl Dalkyl EMIM-SCN 3.40 (0.20) 32.40 (3.61) 0.58 (0.01) 5.95 (0.12) 300 C2C1C1IM-SCN – – – – EMIM-SCN 4.36 (0.23) 23.63 (2.73) 0.65 (0.02) 7.32 (0.14) 320 C2C1C1IM-SCN – – – – EMIM-SCN 6.46 (0.28) 14.92 (1.49) 0.69 (0.02) 8.76 (0.16) 340 C2C1C1IM-SCN – – – – EMIM-SCN – – – – 360 C2C1C1IM-SCN 6.26 (0.24) 17.43 (1.40) 0.68 (0.01) 9.38 (0.16) EMIM-SCN 10.09 (0.33) 8.10 (0.81) 0.78 (0.02) 12.37 (0.27) 380 C2C1C1IM-SCN 9.15 (0.30) 11.52 (0.83) 0.69 (0.01) 11.85 (0.22) EMIM-SCN – – – – 410 C2C1C1IM-SCN 11.70 (0.37) 8.34 (0.73) 0.78 (0.02) 13.91 (0.27) rates, which reflected the crucial role of the structure, and hence, of the hydrogen bonding in the unrestricted dynamics. Our measured Dtr for the EMIM ILs followed the same trends as reported viscosity and conductivity measurements. Unfortunately, this properties are still not available in the litterature for the C2C1C1IM based ILs so far we investigated.

The methyl rotation in the EMIM and C2C1C1IM samples are usually faster than the obser- vation time-window of our QENS experiments, thus, the localized part of the spectra was interpreted as the cation’s ethyl group dynamics. The restricted dynamics were also hindered by the methylation of EMIM at C2, however, locally, the anion had a tremendous influence on the chain dynamics as it was clearly evidenced on the TCM sample pair, whose ground state structure and unrestricted dynamics looked alike, but, certainly imposes in the C2C1C1IM a smaller confinement radius for the ethyl group and a lower diffusion rate. The same phenom- ena was also observed for the DCA and SCN sample pairs.

To complete the overview of the dynamics for the selected AILs samples, it would be advanta- geous to perform backscattering measurements, so we can identify the onset of the different cation dynamical modes. Furthermore, calculations of the potential energy surface for the ethyl group dynamics (reorientations) could shed some light on the slow dynamics of the

C2C1C1IM species. Eventually, viscosity, electrical and infrared characterization of the methy- lated samples could also be beneficial to test the validity of our microscopical observations in the physicochemical properties of this liquids.

132 7.2. Results and discussion

Table 7.6 – Temperature dependence of localized and global diffusion coefficients (D), con- 10 2 1 finement radius (R) and residence time (τ0). Dtr and Dalkyl are given in 10− m s− ,Ralkyl in Å and τ0 in ps.

T [K] System Dtr τ0 Ralkyl Dalkyl EMIM-DCA 4.19 (0.29) 24.03 (3.70) 0.64 (0.02) 6.90 (0.18) 300 C2C1C1IM-DCA – – – – EMIM-DCA 5.51 (0.37) 17.22 (3.04) 0.73 (0.03) 8.69 (0.25) 320 C2C1C1IM-DCA 2.90 (0.20) 60.00 (7.00) 0.57 (0.01) 5.34 (0.10) EMIM-DCA 7.84 (0.47) 11.94 (1.99) 0.78 (0.04) 9.99 (0.28) 340 C2C1C1IM-DCA 5.30 (0.20) 18.30 (1.80) 0.66 (0.02) 7.14 (0.10) EMIM-DCA 10.60 (0.53) 8.46 (1.09) 0.83 (0.03) 15.22 (0.35) 360 C2C1C1IM-DCA 7.20 (0.20) 12.40 (1.20) 0.71 (0.02) 9.18 (0.20) EMIM-DCA 12.43 (0.60) 6.05 (0.85) 0.90 (0.03) 18.42 (0.44) 380 C2C1C1IM-DCA 9.10 (0.30) 9.70 (0.90) 0.77 (0.02) 11.60 (0.20) EMIM-DCA – – – – 410 C2C1C1IM-DCA 11.90 (0.30) 6.90 (0.70) 0.86 (0.03) 13.90 (0.30)

133 8 Conclusions and outlook

The major aim of this thesis has been to investigate the influence of hydrogen-bonding on the dynamics, structure and physicochemical properties of ammonium based protic ionic liquids. To investigate this influence, I relied primarily on the combination of computational chemistry simulations, thermal characterization and neutron scattering experiments. The first type of ILs to be examined were PILs based on the TEA cation. This choice was motivated by the QENS results of Ref. [71] for TEA-TF,where fast subdiffusive motions were found and interpreted as possible extra-vehicular proton diffusion.

However, our DFT calculations for TEA-TF show that from a structural and energetic point of view, the proton diffusion through Grotthuss mechanism is rather unlikely for this system. The strength of the hydrogen bond between the TEA cations and the TF anions is relative high, and this strength is reflected in the short distance between the hydrogen donor and acceptor. This short distance, in turn, is insufficient to admit the variety of hydrogen bonding sites

for the acidic hydrogen of [TEA]+ required to form a connected network of hydrogen bonds, suitable for Grotthuss transport. This observation is confirmed by the calculated potential energy surface for this system. Thus, the energy barrier for proton jumps between ions is large at temperatures close to room temperature, at least up to 400 K. As a consequence, the question about the nature of the fast dynamics in TEA-TF was still open when I started my investigations. We addressed this question by performing classical MD simulations. These were based on unpolarisable force fields and covered the temperature range from T=400 K to T=200 K, swept on cooling from the liquid state. The complementary approach of heating the crystal up to and beyond the melting points was unavailable, since the crystal structure of TEA-TF is unknown. The outcomes of this computations identified the PIL melting point at T=310 K and the crystallization point at T=260 K, separated, or one could say connected, through a solid plastic phase. This picture of the phase diagram is in qualitative agreement with experimental calorimetry, showing two distinct transitions in the solid phase. However, the thermal transition temperatures predicted by simulation differed from the experimentally

134 determined ones of Ref. [71]. The mismatch is attributed to the high cooling rate utilized in MD, a well known effect in this type of computations. The solid plastic phase was evidenced in the simulation through to the changes of the radial distribution functions with temperature, and it is characterized by the ions rotating without diffusion. This process accounts for part of the broad component of the TEA-TF spectra reported in Ref. [71]. Thanks to the atomistic resolution of the force field model of our MD simulations, further microscopic information on the thermodynamic functions and the dynamic diffusion coefficients of TEA-TF were obtained. The comparison of the computed electrical conductivity with the estimate of the Nernst-Einstein equation showed that the ion pairing is the main source of correlation in the ion’s diffusion. Here, once more, it was confirmed that the structure and kinetics of the population of HBs in TEA-TF affect measurable properties of this PIL in a significant way.

In Chapter 4, we presented the results of QENS experiments with polarization analysis on TEA-TF, comparing the experimentally obtained diffraction pattern with those computed from our MD trajectories. The comparison between the diffractograms displayed similar features, thus, we decomposed the simulated one into its ionic correlation components, again, due to the atomic resolution of our trajectories. The latter allowed to analyze the collective dynamics of TEA-TF and to identify the dominant correlations at different length scales. The nuclear spin incoherent spectra were analyzed and the obtained diffusion coefficients were compared to those of Ref. [71]. We observed that the standard QENS without polarization analysis underestimates the dynamics of TEA-TF. The broad component of the incoherent spectra in the liquid phase was associated to the localized dynamics of the ion pairs, which corresponded to the HB life-time ( 4 ps) calculated in Chapter 3 and supported the idea of ∼ diffusion of associated ion pairs.

The anion is a further major factor that influences the HB with TEA. The results of this effect were studied with standard QENS and backscattering experiments, and complemented with DFT calculations of the dimers as presented in Chapter 5. Measuring the elastic and the inelastic intensity on fully hydrogenated and selectively deuterated TEA PILs, it was possible to identify the solid plastic phase proposed in Chapter 3. Furthermore, in the ns time-window no extra onset of thermally activated dynamical processes were detected for the acidic hydrogen of the TEA cation. The different anions accompanying TEA affected microscopically both the long range dynamics and the localized dynamics. Macroscopically this was reflected in the different densities, viscosities and conductivities of these PILs. However, once more, due to the strong HB in all of the studied TEA based PILs, proton jumps between ions are not expected in these prototypic ILs, and thus, the vehicular mechanism dominates the ionic conduction.

Eventually, in our search of proton mobility through Grotthuss-like mechanisms in ILs, we performed extensive simulations, see Chapter 3, of ILs based on half-neutralized diamine cations, representing a promising electrolyte for electrochemical devices, for which enhanced

135 Chapter 8. Conclusions and outlook proton mobility was reported in Ref. [73]. The results of our study were presented in Chapter 6. The double functionality of the DAEt cation as donor and acceptor, in addition to the short aliphatic segment joining the amine-ammonium group allowed proton mobility beyond the vehicular mechanism, provided it was assisted by a TF anion. The mechanism highlighted by MD allows the formation of self-avoiding, proton conducting chains of up to 80 cations with a corresponding number of accompanying anions. Diamine based PILs, and in particular DAEt-TF open the door for electrochemical materials with enhanced performance.

However, the experimental confirmation of the presence and size of the conducting aggregates predicted by simulation for this type of material has still to be performed. To this aim, small- angle-X-ray-diffraction (SAXS) and/or small-angle-neutron-scattering (SANS) complemented by MD would be of advantage to quantify the extent of the connected ions, which in addition, is an attractive field for quantitative research in the near future. Such experiments for pure IL are rare, but some approaches to quantify mesoscopic structures in the bulk IL and in solution are already ongoing [225–229]. This combination of novelty and preliminary expertize increases the chances for getting beam time at neutron facilities for such a measurement. In addition, QENS experiments can determine microscopically the enhanced proton dynamics on the diamine based ILs. A further consideration has to be taken into account for diamine based ILs and in general for PILs. It has been observed that PILs tend to be hygroscopic, probably because of the relative facility for water to bind to the HB-network established by the ILs. This contamination by water, in principle could be convenient, since it increases ion mobility, reduces viscosity and enhances conductivity. All these properties are beneficial for energy conversion devices operating at temperatures below 100 ◦C. However, for devices operating at higher temperatures, water contamination is hazardous, since if the water evap- orates the pressure could destroy the device. Thus, knowledge about the thermodynamics of absorption and desorption of water in PILs is a question that has to be further addressed both experimentally and computationally. Computations on this last topic have already been carried out. The results are being analysed and a manuscript is in preparation.

The powerful combination of computations with neutron scattering would be useful to char- acterize diverse types of ionic systems. In this respect, deep eutectic solvents (DES) emerge as an ideal ionic system to undergo future investigations, so as they are direct competitors to conventional ILs for energy conversion applications [230]. DES are usually synthesized by mixing a quaternary ammonium halide with an inorganic metal salt or an organic HB donor like an alcohol or an amide [2]. The easy process for obtaining DES make them cheaper, thus, more attractive, than standard ILs. However, DES posses narrower electrochemical potential windows than ILs and are volatile, a clear drawback. Deeper understanding of DES transport properties is of vital importance to adopt or discard them as a new type of electrolytes.

Last but definitely not least, the Chapter 7 was dedicated to briefly study imidazolium-based

136 ILs. Ionic liquids of this type usually are classified as AILs. However, the acidic proton at posi- tion C2 of the imidazolium ring, able to form HB, partially contradicts the strict definition of apritic compunds. This fact has already been noted and discussed, and the general consensus is that imidazolium IL are a border-line case between PILs and AILs. Although the proper classification of imidazolium-based ILs might still be under debate [29,231,232], we treat here imidazolium-based ILs as primarily aprotic.

The labile proton covalently bonded at C2 can be replaced by a methyl group in a process called methylation. Samples of EMIM were methylated, and the replacement of the proton clearly affects the HB ability of this ion. Moreover it changes the chemical-physics properties of the corresponding ILs. For instance, the emergence of extra phase transitions for the methylated species as revealed by differential scanning calorimetry measurements reflect the impact of HB in the phase-behaviour of the system. DFT calculations of the dimer ground state structure show that for EMIM-based ILs the anions prefer to accept a hydrogen bond from the C2 donor. As a result, the anion preferred location is on the same plane of the imidazolium ring. By contrast, for the methylated species, the anions show close contacts with the ethyl group and with the two methyl groups of the cation, hence, they prefer to sit above/below the imidazolium ring. These close contacts can be understood as weak hydrogen bonds [233]. Microscopically, QENS experiments performed on these liquids, showed that the methylated species overall have slower dynamics. The diffusion coefficient obtained for the non-methylated species follows the same trends as reported macroscopic properties as viscosity and conductivity. Unfortunately, to the best of our knowledge, these very same properties are still not reported for the methylated counterparts, thus, this opens a path for future dielectric spectroscopy, viscosity and voltammetry experiments. The localized component of the spectra for EMIM and the respective methylated ionic liquids has been associated to the reorientation of the cation’s ethyl group, which in addition, are tremendously affected by the accompanying anion. This extends the search for quantification of the different configurational energies of these prototypic ILs. The determination of such energies can be addressed by future ab initio simulations, which subsequently would be used in the optimization of force fields for MD simulations. Then, the trajectories of the bulk ILs will provide a more complex and complete interpretation of the neutron scattering experiments. Furthermore, a proper dissection of the localized modes and the anion influence can be achieved. These are essential parameters to understand the relative high viscosity of this liquids, which simultaneously, is the least appealing characteristic for effective transport materials needed for portable electrochemical devices.

137 A TEA-TF miscellaneous figures

12

9

(r) 6 NO n 3

0 34567 r [A]

Figure A.1 – Running coordination number nNO(r ) at intermediate range. The vertical dash line points to the inflection point in nNO(r ), corresponding to a weak shell closure of 8-fold coordination.

138 3

T = 400 K

2 T = 300 K

T = 200 K (r) NO g 1

0 0 4 8 12 16 r [A]

Figure A.2 – Radial distribution function g (r ) at three different temperatures, P 1 atm. NO =

2

1 (r) NF g T = 400 K

T = 300 K T = 200 K

0 4 8 12 16 r [A]

Figure A.3 – Radial distribution function g (r ) at three different temperatures, P 1 atm. NF =

139 Appendix A. TEA-TF miscellaneous figures

2.0

1.5

1.0 (k) ρρ S 0.5

0.0 0123 k [A-1]

Figure A.4 – Density-density structure factor at T 320 K. See text for the definition. =

1.5

1.0 (k) ZZ

S 0.5

0.0 0123 k [A-1]

Figure A.5 – Charge-charge structure factor at T 320 K. See text for the definition. =

140 30

20

[Tf]- 10

] 2 0

30 MSD(t) [A

[TEA]+ 20

10

0 0 3 6 9 12 t [ns]

Figure A.6 – Mean square displacement of cations and anions as a function of time. Red lines: T 360 K; Blue line: T 300 K; Green line: T 240 K. The vertical scale is the same in the two = = = panels.

141 Appendix A. TEA-TF miscellaneous figures

0.3

T=360 K ] 0.2 2 (t)/e [nm

Π 0.1 T=300 K

T=240 K 0.0 0 3 6 9 12 t [ns]

D¯P ¯2E Figure A.7 – Time dependence of the operator: Π(t) ¯ i qi [ri (t t0) ri (t0)]¯ entering = + − t0 the determination of the electrical conductivity. e is the atomic unit of charge. The sum extends over all atoms in the system.

0.0

[TEA]+

(t)] - - [Tf] Θ

-0.5 (t)] log[ + Θ

log[ T=300

-1.0 02468 t [ns]

Figure A.8 – Logarithm of the angular correlation function of cations (Θ ) and anions (Θ ) as a + − function of time. See main text for the definition of Θ(t). The function has been normalised in such a way that Θ(0) 1. =

142

5

4

3 T=300 ) [%] τ 2 P(

1

0 0 10 20 30 40 t [ps]

Figure A.9 – Probability distribution for the breaking time of individual H-bonds in TEA-TF at T 300 K. =

143 Appendix A. TEA-TF miscellaneous figures

1.5

1.0

] % [Tf]- αα

P [I 0.5

0.0

1.0

] % [TEA]+ αα

P [I 0.5

0.0 0 100 200 300 400 500 2 Ixx, Iyy, Izz [a.m.u. x A ]

Figure A.10 – Probability distribution for the three principal momenta of inertia of [TEA]+ and [TF]− at T 300 K. Masses are measured in atomic mass units (a.m.u.), and coordinates in Å =

144

1.0

0.8 (t) q

F 0.6

0.4

-3.0 0.0 3.0 6.0 log(t)

Figure A.11 – Intermediate scattering function Fq (t) on a semi-logarithmic scale computed at T 280 K. Time is measured in ps. At any time, curves of higher F value correspond to lower = q q.

145 Appendix A. TEA-TF miscellaneous figures

10

30 8

6 [kJ/mol] wet

〉 4 E −〈 2 dry 〉 E 〈 0 0 200 250 300 350 400 T [K] (T) [kJ/mol] 〉

E -30 〈

-60

200 250 300 350 400 T [K]

Figure A.12 – Filled squares and red line: Average potential energy as a function of temperature for a system made of 125 [TEA][Tf] ion pairs and 17 water molecules. The total potential energy is divided by the number of ion pairs. The result for the dry sample (solid dots and green line) is reported for a comparison. The difference of the two sets of data is reported in the inset. All lines are a guide to the eye.

146 8

6 (r) 4 T = 340 K OW-OW g

2 T = 300 K

T = 260 K 0 4 8 12 16 r [A]

Figure A.13 – Radial distribution function of the water oxygens (gOW OW (r )) in samples of − 125 TEA-TF ion pairs and 17 water molecules. The T 300 K and T 400 K curves have been = = shifted along the vertical direction by 2 and 4 units, respectively, for the sake of clarity.

Figure A.14 – Typical configuration of a water molecule donating H-bonds to two TF− anions.

147 Appendix A. TEA-TF miscellaneous figures

Figure A.15 – Lowest energy configuration of a periodic geometry constructed from the ([TEA][TF])4 ground state cluster geometry.

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169 Acknowledgements

At this point, recapitulating my four years stay at PSI, I can draw, for me, the most important conclusion: I have met lots of great people during my PhD. All of them helped me in a way for the success of my project. More specifically, I would like to thank my supervisor Dr. Jan Embs for believing in me and for giving me the chance to be part of this interesting investigation. To Dr. Tatsiana Burankova, for her company during the beam times and subsequent support on the data analysis and interpretation. To Prof. Dr. Christian Rüegg for his time readiness and his very precise and helpful pieces of advice. To Dr. Christof Niedermayer for all his life advices, the consequent chats and for his standing help with administrative formularies. To Dr. Jürg Schefer for his help with ORION. To the team managing the computer cluster and in general the PSI IT team, they always found a way to make everything run smoothly. To our secretary Pamela Knupp for being always so efficient, easy going and for the nice morning small talks. To all my collegues, Nicole Reynolds, Dr. Saumya Mukherjee, Dr. Daniel Mazzone, Alexandra Turrini, Sumit Maity, Stephan Allenspach, Gesara Bimashofer, Jakob Lass, Christian Wessler, Dr. Emmanuel Canevet, Dr. Gregor Tucker, Dr. Flavio Giorgianni, Dr. Julian Munevar and in general all LNS. A special mention goes for my excellent office mates Guratinder Kaur and Roxana Gaina, who more than officemates I consider them my closer friends, I want to thank you two for letting me keep the window open in winter and close in summer, for all the nice conversations embedded in our office and outside of it, I have got a great time with you two.

In Ireland, I would like to thank to Prof. Dr. Antonio Benedetto and more specially to Prof. Dr. Pietro Ballone, who introduced me to the fantastic computer simulation world and who is an example of the always motivated and always curious scientist. In Germany, I want to thank the team of Prof. Dr. Hemplemann for synthesising and characterizing the liquids used in this thesis, in special to Daniel Rauber, who was always very efficient and ready to answer any question.

My daily life in Switzerland would not have been the same without all the nice people form the Box Club Brugg, who kept me fit during my project and who introduced me into the turbulent waters of the Swiss German. I also want to mention the PSI football players for the fun games

170 Acknowledgements and for teaching me to play better. And of course, I can not forget my great flatmates: Simon Schneider, Dr. Giulio Ferraresi and Jan Hess, they made me feel as in home in our flat.

My family was very important in this process, thus, I thank to my aunt Consuelo Cardozo and cousins in Colombia for all their support, love and thoughtfulness during all kind of situations I went through. To Carolina Arboleda for her love, for hearing me and for the great company she is. Finally, to my parents wherever they are for letting me dream and fly.

Thanks to all of you for making this time so special to me! I have learnt a lot, I have fun and I would recommend anybody to come to PSI and moreover to discover by themselves the adventure of knowledge.

Villigen PSI, July 27, 2019 Juan Francisco Mora Cardozo

171 Juan Francisco Mora Cardozo

Date of birth: 14.11.1989 Nationality: Colombian

Education

07.2015-06.2019 University of Geneva, Geneva, Switzerland Laboratory for Neutron Scattering and Imaging (LNS) Doctoral thesis: “Influence of Hydrogen bonding on dynamical properties of Ionic Liquids.”

10.2011-12.2014 Technical University of Munich (TUM), Munich, Germany Department of Physics MSc. Applied and Engineering Physics Master thesis: “Borohydride solutions as electrolyte for a magnesium battery investigated by quasi-elastic neutron scattering.”

01.2007-12.2010 University of los Andes, Bogota, Colombia Department of Physics BSc. Physics Bachelor thesis: “Quantum spin correlations in solid-state nano-systems.”

01.2001-12.2006 Liceo de Cervantes Norte, Bogota, Colombia High school diploma

Work experience

07.2015-06.2019 Research assistant, Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, Villigen, Switzerland − Plan and take part of neutron spectroscopy experiments − Neutron diffraction experiments − Computer simulations (Molecular Dynamics and ab initio) on liquids − Differential scanning calorimetry characterization − Sample preparation − Utilization of glove box

05.2017-06.2019 Instrument responsible for the test diffractometer ORION, Laboratory for Neutron scattering, Paul Scherrer Institute, Villigen, Switzerland − Teach and assist users utilizing the diffractometer − Manage user schedule − Design sample holders for diffraction experiments

07.2012-10.2012 Research assistant, Nuclear Technology, Technical University of Munich, Garching, Germany

172 − Simulate (Density Functional Theory) the nuclear fuel of boiling water reactors

01.2008-11.2010 Teaching assistant, Department of Physics, Universidad de los Andes, Bogota, Colombia − Teach and assist students in several Physics related courses − Plan exams for the lecture − Correct and grade exams

Talks

16.07.2018 H-Bonding influence on the dynamics of imidazolium- based ionic liquids as probed by QENS (contributed) QENS 2018, Hong Kong, China

12.07.2017 Influence of H-bonding on dynamical properties of ionic liquids (contributed) International conference on neutron scattering (ICNS), Daejeon, Korea

Posters

16.07-20.07.2018 Proton diffusion in the protic ionic liquid 2- Aminoethanaminium Triflate: A computational approach QENS 2018, Hong Kong, China

10.07.2017 Influence of H-Bonding on Dynamical Properties of Triethylammonium Triflate International conference on neutron scattering (ICNS), Daejeon, Korea School

03.09-15.09.2017 15th Oxford School on Neutron Scattering St Anne’s college Oxford, Oxford, United Kingdom

Languages

Spanish Mother tongue English Proficient (C2) German Proficient (C2)

Publications i) Tatsiana Burankova, Giovanna Simeoni, Rolf Hempelmann, Juan F. Mora Cardozo, and Jan P. Embs, Dynamic Heterogeneity and Flexibility of the Alkyl Chain in Pyridinium-Based Ionic Liquids, The Journal of Physical Chemistry B 2017, 121 (1), 240-249, DOI: 10.1021/acs.jpcb.6b10235 ii) Juan F. Mora Cardozo, T. Burankova, J. P. Embs, A. Benedetto, and P. Ballone, Density Functional Computations and Molecular Dynamics Simulations of the Triethylammonium Triflate Protic Ionic Liquid, The Journal of Physical Chemistry B 2017 121 (50), 11410-11423, DOI: 10.1021/acs.jpcb.7b10373

173 iii) Tatsiana Burankova, Juan F. Mora Cardozo, Daniel Rauber, Andrew Wildes, and Jan P. Embs, Linking Structure to Dynamics in Protic Ionic Liquids: A Neutron Scattering Study of Correlated and Single-Particle Motions, Scientific Reports 2018 8 (1), 16400, DOI: 10.1038/s41598-018-34481-w iv) Juan F. Mora Cardozo, J. P. Embs, A. Benedetto, and P. Ballone, Equilibrium Structure, Hydrogen Bonding, and Proton Conductivity in Half-Neutralized Diamine Ionic Liquids, The Journal of Physical Chemistry B 2019 (accepted), DOI: 10.1021/acs.jpcb.9b00890

174