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Correlating Intermolecular Cross-Relaxation Rates with Distances and Coordination Numbers in Ionic Liquids Pierre-Alexandre Martin, Fangfang Chen, Maria Forsyth, Michael Deschamps, and Luke A. O'Dell J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b03021 • Publication Date (Web): 05 Nov 2018 Downloaded from http://pubs.acs.org on November 8, 2018

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The Journal of Physical Chemistry Letters

Correlating Intermolecular Cross-Relaxation Rates with Distances and Coordination Numbers in Ionic Liquids

Pierre-Alexandre Martin,1,2 Fangfang Chen,1* Maria Forsyth,1 Michaël Deschamps2 and Luke A. O’Dell1*

1Institute

for Frontier Materials, Deakin University, Geelong, Victoria 3220, Australia

2CEMHTI,

CNRS UPR 3079, Université Orléans, F45071 Orléans, France

Email: [email protected], [email protected]

Abstract The HOESY NMR experiment is commonly used to probe ion associations in ionic liquids and their mixtures. The parameter measured in this experiment is the heteronuclear cross-relaxation rate σ, which has dimensions of s−1. For intramolecular NOEs this scales as r−6 where r is the internuclear distance, but in the intermolecular case (as typically probed in studies of ionic liquids), theory predicts a more complex behaviour including a distance dependence that is affected by the relative frequencies of the nuclei involved. Specifically, for nuclei with similar resonance frequencies such as 1H and 19F, it has been predicted that intermolecular NOEs will be sensitive to longer range distances than for nuclei with very different frequencies such as 1H and 7Li. In this contribution, we test this theory using a combination of quantitative HOESY analysis and molecular dynamics simulations carried out on two different ionic liquid electrolyte systems. In agreement with theoretical predictions, we find excellent correlations between the experimentally measured 1H-7Li NOEs and carbon-lithium distances below 4 Å, while longer distances (> 6 Å) must be considered in order to obtain good correlations between 1H-19F

NOEs and carbon-fluorine coordination numbers.

This

demonstrates the utility of HOESY NMR in understanding structure and interactions in ionic liquids while also illustrating that care must be taken in interpreting the measured cross-relaxation rates.

Keywords: ionic liquids, nuclear Overhauser effect, HOESY, cross-relaxation rates 1 ACS Paragon Plus Environment

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Ionic liquids (ILs) are a versatile class of materials with unique properties that make them useful in a wide variety of applications [1-9]. For example their high intrinsic ionic conductivity, low volatility, high thermal and electrochemical stability and capability to dissolve high concentrations of metal salts makes them potentially suitable as electrolytes for energy storage devices such as lithium ion batteries [10-13]. These properties are highly dependent on the nature of the cation and anion comprising the IL, and as there exists an almost infinite variety of potential combinations of these ions, ILs are potentially highly tailorable for specific applications. Ultimately, their macroscopic properties will be determined by the molecular level structuring and interactions between the constituent ions, and it is well known that ILs can show significant ordering in the liquid phase due to the presence of strong non-covalent interactions such as electrostatic attraction/repulsion and hydrogen bonding [14]. In the case of lithium-containing ionic liquid electrolytes, the local structure around the Li+, including its solvation by anions and interactions with functional groups such as ether oxygens, will determine the mobility of this key electrochemical species and will thereby affect the performance of the device in which it is used. A detailed understanding of molecular-level structure in ILs is therefore highly desirable in order to understand their properties and tailor their performance. Nuclear magnetic resonance (NMR) spectroscopy is widely recognised as a powerful and versatile technique for the molecular-level characterisation of ionic liquids [15,16]. The most common use of NMR in this context is to confirm molecular structure and sample purity, but more advanced methods can provide a wide range of structural and dynamic information. For example, relaxation measurements can be used to extract rotational correlation times over a wide range of frequencies [17,18], pulsed field gradient (PFG) NMR can provide direct measurement of self-diffusion coefficients [19,20], electrophoretic NMR can probe ion clustering [21-23], and dynamic nuclear polarisation (DNP) methods can be used to study both structure and dynamics [24,25]. The HOESY (Heteronuclear Overhauser Effect SpectroscopY) NMR experiment in particular has been used by a number of research groups to probe ionic interactions in ILs and IL electrolytes [2636]. This method involves a transfer of spin polarisation between nuclear isotopes (e.g., from 7Li to 1H)

via a process known as the nuclear Overhauser effect (NOE). This effect is mediated by the dipolar

interactions between the nuclear spins, which are modulated by the rotational and translational dynamics of the ions. The HOESY experiment allows the NOE to be quantified in the form of the crossrelaxation rate σ, which has dimensions of s−1 and, due to the distance dependence of the dipolar coupling strength, is inversely dependent on a power of the internuclear distance r. The majority of HOESY studies of ILs have either discussed 2D HOESY spectra in a qualitative fashion, or have reported 2 ACS Paragon Plus Environment

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the NOEs in a limited, semi-quantitative sense where only relative σ values are reported for each distinct sample. We have recently shown that, with careful analysis, cross-relaxation rates can be determined quantitatively for intermolecular NOEs in ionic liquids, allowing σ values in different ILs (or different temperatures, or salt concentrations) to be compared [37]. However, the interpretation of these intermolecular NOEs in terms of the IL structure, and particularly their conversion into internuclear distances, is not trivial. In the general case of two coupled spins I and S, the crossrelaxation rate is given by: 𝜎 = 0.6𝐽(𝜔𝐼 + 𝜔𝑆) ―0.1𝐽(𝜔𝐼 ― 𝜔𝑆)

(1)

where J(ω) is the spectral density function that describes the modulation frequencies of the dipolar interaction between I and S, and ωI and ωS are the resonance frequencies of the two coupled spins. In the simplest case of an intramolecular NOE where the internuclear distance is fixed, J(ω) is described by a Lorentzian function and σ is found to be proportional to r−6, thus the NOE is only observed between spins close in space (< 5 Å). However, for the case of intermolecular NOEs (as are typically measured from ILs by HOESY), the internuclear distance becomes time-dependent and is affected by both the translational and rotational dynamics of the ions. Weingärtner and co-workers calculated J(ω) for this situation using parameters typical for ILs, and showed that the function is no longer Lorentzian but is instead stretched out to higher frequencies [38,39]. An intriguing consequence of this is that the J(ωI – ωS) term can become dominant for longer internuclear distances, an effect that increases as the frequency difference ωI − ωS becomes smaller. As a result, this theory predicts that intermolecular NOEs measured between spins with similar frequencies, such as 1H and 19F, will be sensitive to longer distances than those measured between spins whose frequencies are further apart, such as 1H and 7Li. To the best of our knowledge, this prediction has yet to be validated experimentally. Herein, we compare experimentally measured 1H-7Li and 1H-19F cross-relaxation rates obtained from two IL electrolyte systems using HOESY, with distance and coordination information obtained from molecular dynamics (MD) simulations. This is the first time, to our knowledge, that intermolecular NOEs have been quantitatively compared between different ionic liquids. The two ionic liquids, N-methyl-N-propyl-pyrrolidinium bis(fluorosulfonyl)imide (C3mpyrFSI) and N-methyl-Nmethoxyethyl-pyrrolidinium bis(fluorosulfonyl)imide (C2O1mpyrFSI), were prepared with LiFSI at 1.0 molal concentration. 1H-7Li and 1H-19F cross-relaxation rates were measured from these samples at various temperatures using HOESY with the same pulse sequence, experimental procedure and data analysis method discussed in detail in our previous publication [37]. Briefly, a 1H-detected HOESY pulse sequence was used with an incremented mixing time τ resulting in build-up curves for each of the distinct 1H signals that were fitted using the following expression: 3 ACS Paragon Plus Environment


M(𝜏) = 𝑀0𝜎

2sinh (Κ𝜏) 𝑒 Κ

― (𝑅𝐼 + 𝑅𝑆)𝜏 2

𝑒

―(

𝐷𝐼 + 𝐷𝑆 2

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𝛿

)𝛾𝐼𝛾𝑆𝑔²𝛿²(∆ ― 3)

(2)

where M(τ) is the observed signal as a function of mixing time, M0 is the thermal equilibrium magnetisation of the source spin (7Li or 19F), σ is the cross-relaxation rate, RI/S are the longitudinal relaxation rates of the two spins, DI/S are the self-diffusion coefficients of the ions in which the spins reside, γI/S are the gyromagnetic ratios of the two spins, g is the gradient pulse strength, δ the gradient pulse length, Δ the delay time between the first and last gradient pulses, and: Κ=

𝑅2𝐼 ― 2𝑅𝐼𝑅𝑆 + 𝑅2𝑆 + 4σ2

(3)

2

The longitudinal relaxation rates and self-diffusion coefficients were measured independently using inversion recovery and stimulated echo pulsed field gradient NMR experiments respectively, while M0 was calculated from the equilibrium 1H signal and the relative concentrations of the spins in each sample. Thus, σ was the sole variable in the curve fitting. The diffusion term in equation 2 is required due to the use of gradient pulses in the HOESY pulse sequence, which cause an additional attenuation of the observed signal [37]. Further experimental details are provided in the Supporting Information. Of the two IL systems studied here, C3mpyrFSI is an archetypal IL whose mixtures with metal salts have been previously investigated as potential electrolytes [40-43], and characterised by NMR including 1H-7Li HOESY [34]. The ether oxygen incorporated on the C2O1mpyr cation is expected to interact with the Li+ and promote its dissociation from the FSI anions, potentially improving the Li+ transport. A comparison of the Li-cation and anion-cation interactions in these two systems is therefore of significant interest. As the theory developed by Weingärtner and co-workers [38,39] predicts the distance dependence of the NOE cross-relaxation rates to depend on the relative frequencies of the spins involved, we will first consider the 1H-7Li cross-relaxation rates in both systems, before subsequently discussing the 1H-19F rates. The experimental 1H-7Li cross-relaxation rates measured at 50 °C are shown for both IL systems in Figure 1. The values (× 10−4 s−1) are shown next to each carbon site on the cation structures. It should be stressed here that these σ values were measured from the 1H nuclei directly bonded to these carbon sites, not from the 13C nuclei, but for simplicity the discussion from hereon will be in terms of the carbon sites. We also note that 1H-7Li cross-relaxation rates for the C3mpyr system at 50 °C have previously been reported [37]. Before comparing the experimental 1H-7Li cross-relaxation rates with the MD results, some observations can be made about the basic trends in their values, noting that larger values are expected to indicate a closer average internuclear distance. In both ILs the 1H-7Li σ values generally increase with increasing distance of the carbon site from the nitrogen (Figure 1). This makes intuitive sense in

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that one would expect the electrostatic repulsion between the lithium cation and the positively charged nitrogen center to result in larger distances of closest approach between the Li+ and the carbon sites closer to that nitrogen. For the carbon sites on the pyrrolidinium ring (C1 and C2), and also for the N-methyl carbon (C3), the 1H-7Li σ values are very similar in both systems, however this is not the case for the aliphatic chain where much larger σ values are observed for the methoxyfunctionalised cation. The largest 1H-7Li cross-relaxation rates were observed for sites C5b and C6b, confirming a strong interaction between the Li+ cation and the electronegative oxygen site as anticipated.

Figure 1 – Experimentally measured 1H-7Li cross-relaxation rates (× 10−4 s−1) obtained from the (a) C3mpyr and (b) C2O1mpyr systems at 50 °C, alongside carbon-lithium radial distribution functions (RDF, solid lines) and coordination numbers (CN, dashed lines) obtained from the MD simulations.

The carbon-lithium radial distribution functions (RDF) and coordination numbers (CN) were calculated from the MD simulations after equilibrating the two IL systems at 353 K, and are shown between 2 and 10 Å in Figure 1 (full details for the MD simulations are provided in the Supporting 5 ACS Paragon Plus Environment


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Information). The RDF bands show relatively broad peaks due to significant variations in the C-Li distances. For the C3mpyr system (Figure 1a), the RDFs show a first coordination shell at a distance of around 4-5 Å, and the CNs in this distance range are in the order C6a > C2a > C3a > C5a > C1a > C4a. As with the experimental 1H-7Li σ values, these results suggest a closer average distance to the carbons that are further away from the nitrogen site. For the C2O1mpyr system (Figure 1b), the RDF plots clearly illustrate the close coordination of the lithium to the C6b and C5b carbon sites either side of the oxygen. Interestingly, for this system the CNs undergo a crossover at a distance of around 4.3 Å. Below this distance, they are ordered C6b > C5b > C4b > C2b > C3b > C1b, which matches the order of the experimental 1H-7Li cross-relaxation rates exactly. At distances of 5 Å and beyond, this order changes significantly, indicating that the experimental 1H-7Li σ values are most sensitive to distances on the order of 4 Å or less (i.e., the first coordination shell of Li+ around the IL cation). The 1H-19F HOESY experiment carried out on the C3mpyrFSI-LiFSI system at a temperature of 50 °C resulted in the observation of 1H signals with both positive and negative intensities, indicating cross-relaxation rates of opposite sign for the different groups of protons. Further measurements at different temperatures showed a crossover in the sign of the σ values occurring at a different temperature in the range 20 to 60 °C for each of the 1H signals (see Supporting Information). No such observation was made in the 1H-7Li HOESY measurements, which all resulted in σ values of identical sign. This can be understood by considering the dependence of these cross-relaxation rates in the simplest case where the correlation function is modelled as a single exponential decay and the spectral density function is therefore represented in a Lorentzian form: τ𝑐

J(ω) = 〈𝐷2〉(1 + 𝜔2𝜏 2)

(4)

𝑐

Here, D represents the dipolar interaction between the two coupled spins. Figure 2 shows calculated cross-relaxation rates for 1H-7Li and 1H-19F spin pairs at 11.7 T as a function of the correlation time. In the case of the 1H-7Li NOEs (Figure 2a), σ is always positive, while for 1H-19F NOEs (Figure 2b), it shows a zero crossing at a correlation time of 2.3 ps. This crossover occurs from negative to positive σ values as the correlation time decreases (or equivalently as the sample temperature increases). On the basis of this model the correct sign of the experimentally measured 1H-19F cross-relaxation rates can be determined by measuring their temperature dependence. We would like to stress that the model used to generate the plots in Figure 2 does not take into account the time dependence of the internuclear distance or the stretched spectral density function discussed by Weingärtner and coworkers [38-39], and we therefore use it only in a qualitative sense to illustrate why the crossrelaxation rate changes sign for the 1H-19F spin pair.


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Figure 2 – Calculated dependence of the cross-relaxation rate σ on the rotational correlation time τc of the internuclear vector for (a) 1H-7Li and (b) 1H-19F NOEs at a magnetic field strength of 11.7 T. The simulations assume a fixed internuclear distance of arbitrary length and a Lorentzian spectral density function.

The fact that the crossover temperature for the experimentally measured 1H-19F NOEs is different for each spin pair suggests that the correlation times associated with the internuclear vectors also differ at any particular temperature. The cross-relaxation rates will therefore be sensitive to these differences in dynamics in addition to the average internuclear distances. In order to compare the experimental 1H-19F cross-relaxation rates with the MD simulation data, we will consider the σ values measured at a temperature of 20 °C (shown in Figure 3) as this was the furthest temperature from the crossover region and also the temperature at which the cross-relaxation rates for the different groups of protons showed the broadest distribution of values. We then make the assumption that the differences in σ values at this temperature are predominantly due to variations in the average 7 ACS Paragon Plus Environment


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internuclear distance rather than the dynamics. We note that this assumption was also implicit in the interpretation of the 1H-7Li NOEs discussed above, which showed good correlation with the MD data. Testing this assumption would require the temperature variation of the cross-relaxation rates to be mapped out and fitted with more accurately modelled spectral densities and/or extraction of the correlation times from the MD trajectories, which is beyond the scope of this work.

Figure 3 – Experimentally measured 1H-19F cross-relaxation rates (× 10−4 s−1) obtained from the (a) C3mpyr and (b) C2O1mpyr systems at 20 °C, alongside carbon-fluorine radial distribution functions (RDF, solid lines) and coordination numbers (CN, dashed lines) obtained from the MD simulations.

Some basic observations can then be made about these 1H-19F cross-relaxation rates (Figure 3). Their magnitudes generally show the opposite trend to that observed for the 1H-7Li values, i.e., the carbon sites closer to the positively charged nitrogen tend to show larger 1H-19F NOEs than those that are more distant. Just as for the 1H-7Li NOEs, this makes intuitive sense if one considers the attraction between the electropositive region of the cation and the FSI anion. Interestingly, the 1H-19F σ magnitudes are larger in the C2O1mpyrFSI system, which superficially would imply an overall closer association of the FSI to this cation. Based on the discussion above, one might expect the opposite to be true given the stronger interaction between the C2O1mpyr cation and the Li+, which would have the effect of displacing the anion. Indeed, the carbon-fluorine RDF and CN plots in Figure 3 show a slightly 8 ACS Paragon Plus Environment

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closer overall coordination between the fluorine and the C3mpyr cation than the C2O1mpyr (this can be seen most clearly where the RDF and CN plots intercept the x-axes). Two potential explanations for this apparent discrepancy are (1) variations in the dynamics within the two ILs, and (2) that the 1H19F

NOEs reflect longer-range distances as proposed by Weingärtner and co-workers [38,39]. The

former explanation would seem unlikely given the close match between the 1H-7Li NOEs for carbon sites C1, C2 and C3 (Figure 1), which would be expected to differ more substantially if the molecular dynamics in the two systems were significantly different. To test the latter explanation, we can consider the distance dependence of the carbon-fluorine RDFs and CNs to see if a better correlation of these quantities with the experimental 1H-19F NOEs is observed at longer distances.

Figure 4 – MD simulation snapshot showing the C2O1mpyr cation and surrounding FSI anions. Fluorine atoms within 4.5 Å of the cation are shown as purple balls, while those between 4.5 and 8.2 Å are shown as green balls.

Both IL systems show a crossover in the order of their carbon-fluorine coordination numbers between 5 and 6 Å (see expansions on the right hand side of Figure 3). This can be understood by considering the structure of the FSI anion, which features two fluorine sites and can be oriented in different ways relative to the cation. Figure 4 shows a snapshot of the MD trajectory for the C2O1mpyr system in which fluorine sites within 4.5 Å of the cation are highlighted as purple balls while those between 4.5 and 8.2 Å are shown in green. Thus the first coordination shell of FSI anions around the 9 ACS Paragon Plus Environment


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IL cations can potentially show multiple peaks at different distances in the RDF plots. Crucially, for these two distance ranges, it is the longer range carbon-fluorine coordination numbers that best correlate with the magnitudes of the 1H-19F cross-relaxation rates in both systems. For example, in the C3mpyr system sites C1a and C4a gave the largest 1H-19F σ values, and in the CN plots these two sites show the highest CNs at 6.5 Å but the lowest at 4.5 Å. Similar results are observed for the C2O1mpyr system. Figure 5 provides a graphical illustration of these correlations. The 1H-19F crossrelaxation rates therefore appear to report on significantly longer distances than the 1H-7Li values, just as predicted by the theory of Weingärtner and co-workers [38,39]. It should be noted that the correlation between the longer range C-F coordination numbers and the 1H-19F σ values is much improved over that for the shorter range CNs but is still not perfect. Both the short and long-range NOEs would be expected to contribute to the measured σ value, but the longer range contributions seem to dominate. Moreover, the negative σ values suggest that the J(ωI − ωS) term from equation 1 dominates, and it is this term that was identified by Weingärtner and co-workers to result in longerrange NOEs for spins with similar resonance frequencies [38,39]. The overall larger magnitudes of the 1H-19F

NOE values observed in the C2O1mpyr system could then potentially be explained by a larger

positive contribution to the σ value from the 19F nuclei in closer proximity to the C3mpyr cation (i.e., the J(ωI + ωS) term in equation 1), though further work will be needed to verify this.

Figure 5 – Graphical illustration of the correlations between the experimentally measured 1H-19F cross-relaxation rates (|σ|) and carbon-fluorine coordination numbers (CN) derived from the MD simulations at different distances for the two IL systems studied (data shown in Figure 3). 10 ACS Paragon Plus Environment

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In summary, 1H-7Li and 1H-19F cross-relaxation rates have been measured from two lithiumcontaining pyrrolidinium-based ionic liquid electrolytes, giving insights into the interactions of the Li+ and FSI species with the IL cation. A comparison of these results with molecular dynamics data shows that the former parameters are sensitive to close-range interactions (< 4 Å) while the latter are affected by both of the fluorine sites on the FSI anions within the first coordination shell of the cation, and are dominated by the more distant fluorine sites (> 6 Å) in agreement with predicted theory [38,39]. This is the first time to our knowledge that intermolecular heteronuclear NOEs have been quantitatively compared between different ionic liquid systems. We believe that this work provides a strong validation of HOESY NMR for studying ionic interactions in this important class of materials, and shows that this technique can give useful, detailed and quantitative information on ionic liquid structure provided that care is taken in interpreting the results.

Acknowledgements The Australian Research Council is acknowledged for research funding through the Australian Centre of Excellence for Electromaterials Science (ACES). Deakin University, CNRS and Université Orléans are also thanked for support.

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Castiglione, F.; Appetecchi, G. B.; Passerini, S.; Panzeri, W.; Indelicato, S.; Mele, A.; Multiple Points of View of Heteronuclear NOE: Long Range vs Short Range Contacts in Pyrrolidinium Based Ionic Liquids in the Presence of Li Salts, J. Mol. Liq. 2015, 210, 215-222.

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Martin, P.-A.; Salager, E.; Forsyth, M.; O’Dell, L. A.; Deschamps, M.; On the Measurement of Intermolecular Heteronuclear Cross Relaxation Rates in Ionic Liquids, Phys. Chem. Chem. Phys. 2018, 20, 13357-13364.

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