Bulk nanostructure of the prototypical ‘good’ and ‘poor’ solvate ionic liquids [Li(G4)][TFSI] and [Li(G4)][NO3]†

The bulk nanostructures of a prototypical ‘good’ solvate ionic liquid (SIL) and ‘poor’ SIL have been examined using neutron diffraction and empirical potential structure refinement (EPSR) simulated fits. The good SIL formed by a 1 : 1 mixture of lithium bis(trifluoromethylsulfonyl)imide (Li[TFSI]) in tetraglyme (G4), denoted [Li(G4)][TFSI], and the poor SIL formed from a 1 : 1 mixture of lithium nitrate (Li[NO3]) in G4, denoted [Li(G4)][NO3], have been studied. In both SILs there are strong Lewis acid–base interactions between Li and ligating O atoms. However, the O atoms coordinated to Li depend strongly on the counter anion present. Li O coordination numbers with G4 are 2–3 times higher for [Li(G4)][TFSI] than [Li(G4)][NO3], and conversely the Li O anion coordination number is 2–3 times higher in [Li(G4)][NO3]. In both solvates the local packing of Li around G4 O atoms are identical but these interactions are less frequent in [Li(G4)][NO3]. In both SILs, Li + has a distribution of coordination numbers and a wide variety of different complex structures are present. For [Li(G4)][NO3], there is a significant proportion uncoordinated G4 in the bulk; B37% of glyme molecules have no Li O contacts and each G4 molecule coordinates to an average of 0.5 Li cations. Conversely, in [Li(G4)][TFSI] only B5% of G4 molecules lack Li O contacts and G4 molecules coordinates to an average of 1.3 Li cations. Li and G4 form polynuclear complexes, of the form [Lix(G4)y] , in both solvates. For [Li(G4)][TFSI] B35% of Li and G4 form 1 polynuclear complexes, while only B10% of Li and G4 form polynuclear complexes in [Li(G4)][NO3].


Introduction
Ionic liquids (ILs) are pure salts with low melting temperatures (o100 1C). 1 ILs have garnered significant research attention for a wide variety of applications, 2-13 but especially as next generation solvents in electrochemical devices. 7,[14][15][16][17][18][19][20] Many studies have investigated IL-lithium salt solutions, with a view to producing high performance electrolytes 17,19,[21][22][23][24][25] with wide electrochemical windows and liquid stability temperature ranges. 15,20 However, low lithium (Li) transference numbers and solubility of electrode materials are recurrent problems in IL-based electrolytes. Solvate ILs (SILs) are an emerging class of ionic liquids with the potential to circumvent these problems. 19 SILs are a sub-class of ILs, consisting of a metal cation bound to a stoichiometric quantity of coordinating ligands via strong Lewis acid-base interactions that yield stable complex cations and counter ions in the bulk. The first known examples of SILs consisted of aqua cations in inorganic hydrate melts. 26 However, perhaps the most widely studied SILs utilise oligoethers (glymes) with metal salts. 22,23,27 Research into glyme-based SILs owes much of its growth to investigations of Li-salt:polyethylene oxide (PEO) rubbery electrolytes. 28 It was found that particular salt:PEO mixtures produced low melting, highly conductive amorphous phases in the ''crystallinity gap'' regions of the phase diagrams. 29 Many stoichiometric mixtures of glymes and lithium salts form crystalline complexes, and a variety of crystal structures have been elucidated. [30][31][32][33] Notably, many of these solvate complexes melt near room temperature. 29 These melts have been identified as SILs, and closely conform to a rigorous set of criteria characteristic of SILs. 34 Interactions between Li + and solvating glyme molecules strongly influence the thermal 22,27,34 and electrochemical 19,24,27,34 stability of lithium-glyme solvates. Moreover, the solvation and coordination environment of Li + controls bulk transport 23,24,27,34,35 of Li + and its behaviour at electrode interfaces. 18,36 Understanding the coordination environment of Li + in the bulk of SILs is critical for practical applications. Li + has a complex coordination chemistry, forming complexes with coordination numbers between 2 to 8 in solution, and crystalline phases. 37 [4][5][6] coordinate structures are much more common while 2 and 3 coordinate structures are rare. 19, 38 Li + has coordination numbers of ca. 4 in both pure molten Li [TFSI] 39 and Li [NO 3 ]. 40 Li + coordination numbers of six are preferred in crystalline structures 37 including glyme-based solvates [30][31][32][33] and crystalline Li[NO 3 ]. 41 Crystalline Li [TFSI], 42 however, is 4 coordinate. In glyme-based solvates, the make-up of the Li + coordination shell is controlled by the relative Lewis basicity of the glyme and the counter anion present. 34 Higher anion basicity leads to fewer LiÁ Á Áglyme contacts and a greater number of LiÁ Á Áanion contacts. In the case of high Lewis basicity anions, strong LiÁ Á Áanion interactions preclude LiÁ Á Áglyme interactions, leading to significant proportions of uncoordinated (''free'') glyme in solution. 25 The presence of 'free' glyme is key consideration for solvate systems. SILs that are comprised of almost purely ionic species are defined as 'good' while SILs that are mixture of ionic and molecular species are categorised as 'poor', with an equilibria of complex cations and dissociated Li + cations and glyme molecules. 34 Strong complexation between Li + and the glyme produces stable [Li(glyme)] + complex cations, producing a good SIL. Conversely, a 'poor' SIL is characterised by stronger interactions between Li + and its counter anion, reducing the prevalence of [Li(glyme)] + complexes and promoting free, uncoordinated glyme in solution.
Here, the bulk structure of two 1 : 1 lithium salt : glyme mixtures have been elucidated using isotopically labelled contrast variation neutron diffraction in conjunction with empirical potential structure refinement (EPSR) fits. EPSR compares simulated and experimental diffraction structure factors, iteratively refining the simulation against the measured data to faithfully reproduce the atom-atom correlations in the system. This means the simulated atomic level structure can be commented on with confidence. Equimolar mixtures of lithium bis(trifluoromethane)sulfonimide ( ]) were selected as prototypical 'good' and 'poor' SILs respectively. These systems are interrogated to determine how the coordination environment of Li + differs in a good SIL compared to a poor SIL. The effect of the anion species on the coordination numbers and coordination geometry around Li + , the geometry of ligandÁ Á ÁLi + interactions, distribution of complexes formed, including both mono and polynuclear complexes and the proportion of free glyme present in solution, is examined.

Synthesis of deuterated tetraglyme isotopomers
Chemicals and reagents of the highest grade were purchased from Sigma-Aldrich and used without further purification. Solvents used in the synthesis of deuterated glymes were purchased from Sigma-Aldrich Chemical Co., Merck and Fronine Laboratory Supplies and were purified by literature methods. When solvent mixtures were used as an eluent, the proportions are given by volume. NMR spectroscopy solvents were purchased from Cambridge Isotope Laboratories Inc. and were used without further purification. Thin-layer chromatography (TLC) was performed on Fluka Analytical silica gel aluminium sheets (25 F254). Davisil s silica gel (LC60Å 40-63 micron) was used for bench-top flash column chromatography and prepacked silica cartridges were used for REVELERISt flash chromatography. Deuterated tetraglyme isotopomers were synthesised via the reaction scheme given in Fig. 1. A full description of the synthesis of the tetraglyme isotopomers and their respective intermediates is given in the (ESI †).
The percentage deuteration of the product tetraglyme isotopologues were characterised using enhanced resolution -mass spectroscopy (ER-MS), 1 H NMR (400 MHz), 13 C NMR (100 MHz), and 2 H NMR (61.4 MHz). The overall percent deuteration of the molecules was calculated by via ER-MS using the isotope distribution analysis of the different isotopologues by analysing the area under each MS peak which corresponds to a defined number of deuterium atoms. The contribution of the carbon-13 (natural abundance) to the value of the area under each [X + 1] MS signal is subtracted based on the relative amount found in the protonated version. In a typical analysis we measure the C-13 natural abundance contribution by running ER-MS of the protonated version (or estimate it by ChemDraw software) and use this value in our calculation using an in-house developed method that subtracts this contribution from each MS signal constituting the isotope distribution. 1 H NMR (400 MHz), 13 C NMR (100 MHz), and 2 H NMR (61.4 MHz) spectra were recorded on a Bruker 400 MHz spectrometer at 298 K. Chemical shifts, in ppm, were referenced to the residual signal of the corresponding solvent. Deuterium NMR spectroscopy was performed using the probe's lock channel for direct observation. Neutron diffraction spectra were collected for all isotopomeric SIL samples (Table 1) using the SANDALS time-of-flight spectrometer at the ISIS pulsed neutron and muon source, Rutherford Appleton Laboratory, UK. The SNADALS instrument has an incident wavelength range of 0.05-4.5 Å, and covers a Q range of 0.05-50 Å À1 . 43 For the measurements, samples were contained in chemically inert, 'null scattering', Ti 0.68 Zr 0.32 flat plate cells with internal geometries of 1 Â 35 Â 35 mm, with a wall thickness of 1 mm sealed with PTFE O-rings. Samples were maintained at a temperature of 298 K using a recirculating heater (Julabo FP50) for the duration of the diffraction experiments. Diffraction measurements were made on each of the empty sample containers, the empty spectrometer, and a 3.1 mm thick vanadium standard sample to enable instrument calibration and data normalisation. The net run time for each measurement was ca. 8 hours. Reduction of raw scattering data was performed using the GUDRUN software package as described in the ATLAS manual. 44 During data reduction, corrections including normalisation to the incident neutron flux, absorption and multiple scattering corrections, Ti-Zr can subtraction and normalisation to absolute units by dividing the measured differential cross section by the scattering of a vanadium standard of known thickness were performed. Fits to the normalised diffraction data were produced using empirical potential structure refinement (EPSR) simulations. 45,46 The simulation used Lennard-Jones 12-6 and electrostatic potentials, truncated at 12 Å.  Previously reported potential values were used for the potential parameters for tetraglyme molecules 47 and lithium, 48 bis(trifluoromethanesulfonyl)imide 49 and nitrate 50 ions. For both systems the spectra for all four isotopomers were fit simultaneously.  3 ]. These peaks indicate the presence of regular repeating structures in the bulk with characteristic lengths of 6.6 Å and 9.7 Å. The smaller of these repeat lengths, characterised by the weak peak in the d 6 contrast, is consistent with the combined packing dimension of the Li + cation 51 and TFSI À anion 52 while the larger repeat length is slightly greater than the packing dimension expected for an [Li(G4)][TFSI] ion pair calculated using the molecular weight and density of the solvate, assuming a cubic packing geometry. 36,53 This suggests the presence of complexes larger than a simple 1 : 1 lithium : glyme complex cation, i.e. polynuclear complexes, which have been previously suggested. 19,39 The primary peak Table 1 Structure and names of isotopomeric contrasts for 1 : 1 lithium salt : tetraglyme (G4) solvates for which neutron diffraction spectra were recorded. Hydrogen atoms are coloured white and deuterium atoms are highlighted green, carbon atoms are grey, oxygen atoms are red, nitrogen atoms are blue, sulphur atoms are yellow, and fluorine atoms are brown , indicating smaller bulk repeat spacings. This can be attributed to two factors. Firstly, the nitrate anion is much smaller than TFSI À and secondly, the local Li + solvation environment is expected to be significantly different in the two liquids. Extracting detailed structural information from the experimentally measured diffraction spectra, S(Q), is difficult without the aid of supporting simulations. This is because the S(Q) is a complex sum of scatting contributions from multiple atomatom correlations, which produce both positive and negative going peaks. [54][55][56][57][58] Accurately modelling S(Q) functions is difficult as there are almost invariably more partial site-site radial distribution functions than independent diffraction data sets. Constraining atom-atom arrangements by defining optimised molecular geometries, preventing unrealistic atom-atom overlap and fixing the bulk atomic density to its known value (calculated from the measured bulk density) ensures only physically plausible structures are produced. Additionally, in the case of neutron diffraction, contrast variation using isotopic substitution of deuterium for hydrogen highlights specific atom-atom correlations contributing to the total S(Q). Simultaneously fitting multiple isotopomeric contrasts with a single model structure affords greater confidence in the simulated structure factors. The EPSR simulated fits produced for   Additionally, the LiÁ Á ÁO correlation with the TFSI À anion has a strong, sharp peak at 2.0 Å. However the LiÁ Á ÁO correlation with TFSI À is weaker than the LiÁ Á ÁO 1 and LiÁ Á ÁO 2 correlations and of comparable intensity to the LiÁ Á ÁO 3 correlation with G4. Caution must be taken when comparing g ij (r) functions peak intensities for atom-atom pairs with different bulk atomic densities because distributions are normalised to this bulk density, giving a value of 1 at wide separations. The calculated coordination numbers (cf.     3 ] the distribution is quite diffuse (Fig. 8B). This is because Li +  LiÁ Á ÁO coordination numbers corresponding to the first g ij (r) peaks are given in Table 2 39 Li + is coordinated by an average of 3.9 G4 O atoms and 1.9 TFSI À O atoms (total coordination number of 5.8).

Results and discussion
All simulations agree that G4 O atoms displace TFSI À O atoms in [Li(G4)][TFSI], such that the Li + coordination shell is dominated by glyme O atoms. Such displacement generally yields systems with a greater total LiÁ Á ÁO coordination numbers: in pure crystalline Li[TFSI], Li + is tetrahedrally coordinated by four oxygen atoms from four different TFSI À anions, 42 whereas in crystalline [Li(glyme)][TFSI] systems, the total LiÁ Á ÁO coordination numbers frequently increase to 5 or 6. 32, 33 The total coordination numbers in the corresponding liquid systems are generally slightly lower (e.g., in liquid Li[TFSI] at 530 K, the LiÁ Á ÁO coordination number is 3.72 39 instead of the above-cited value of 4 for the solid phase).
The different LiÁ Á ÁO coordination numbers from the previous simulations and the EPSR fits to the neutron diffraction data in this work reflect the different types of solvate structures obtained using distinctive models: the torsionally unhindered glyme molecules used in the MC/EPSR simulations are less prone to wrap around a given Li + and coordinate it in a polydentate fashion (cf. Fig. 7 below). This yields Li-G4 solvates that suffer more competition from the anions and are thus coordinated to more TFSI À O atoms. On the other hand, the parameterization of glyme molecules performed by the Tsuzuki et al. 60 39 used torsionallyhindered glyme molecules parameterized by a general forcefield and show a situation where the competition between glyme and TFSI À for the complexation of Li + yields a wide distribution of solvates with distinct coordination numbers. The versatility and dynamics of such a distribution probably accounts for the larger total coordination numbers observed in this last model. The EPSR fits are refined against, and must ultimately fit, the four scattering spectra obtained for different isotopic contrasts. Thus, the EPSR coordination numbers are experimentally validated in ways that the pure simulations are not (or at least not to the same extent 39 62 which is defined as the negative enthalpy value for formation of a 1 : 1 adduct with a standard Lewis acid. A large DN value corresponds to a high Lewis basicity, and therefore Li + coordinating power. DN values have been reported for G4 (69.4 kJ mol À1 ), 63 TFSI À (22.5 kJ mol À1 ) 63 and nitrate (87.9 kJ mol À1 ) 64 showing that their relative coordination power follows the order of TFSI À o G4 o NO 3 À . 65 3 ]. However, the instantaneous coordination environment for any given Li + cation in the two solvates can vary widely. Fig. 9 gives the coordination number probability distributions, p(n), for LiÁ Á ÁO A key consideration for categorising SILs good or poor is the percentage of free glyme in the solvate, i.e. the fraction of glyme molecules which lack coordination interactions with Li + . A good SIL is characterised by strong complexation between the metal cation and the glyme, forming stable [Li(glyme)] + complex cations. 34 The size and distribution of complexes formed is also of interest. The number of ions and G4 molecules in a complex is variable, and both G4 and the counter anions can bridge between Li + cations to produce poly nuclear complexes.
Cluster analysis has been performed for [Li(G4)][TFSI] and [Li(G4)][NO 3 ] to determine the proportion of free glyme and give insight into the distribution of complexes formed in both solvates. A G4 molecule was designated as coordinated to a Li + cation if any of its O atoms were found to be within 3.25 Å of the Li + cation (this distance corresponds to the first local minima in the LiÁ Á ÁO g ij (r) functions involving G4 O atoms in Fig. 5  and 6). The analysis performed considers any two G4 and/or Li + cations to be a part of a single complex if they are joined by an uninterrupted chain of LiÁ Á ÁO linkages between Li + and G4 as defined above. This allows the proportion of [Li(G4) 2 ] + and [Li 2 (G4)] 2+ , and higher, complexes to be determined in addition to the proportion of free glyme present.
In [Li(G4)][TFSI] B5% of G4 molecules lack LiÁ Á ÁO so are 'free' glyme. This agrees remarkably well with the estimation of free glyme concentration in [Li(G4)][TFSI] using Raman spectroscopy, 25 and with the predictions of recent MD simulations for this solvate 39 but is higher than the free glyme concentration determined electrochemically 25  as suggested by ab inito calculations, 35 however the number of LiÁ Á ÁO contacts between Li + and G4 in the complexes determined here are, on average, lower and more variable than predicted. 35 3 ], B37% of glyme molecules lack LiÁ Á ÁO contacts and can be considered as 'free' glyme. This fraction is markedly lower than the fraction determined from Raman spectroscopy 25 and recent MD simulations. 39 However, the degree of LiÁ Á ÁO contacts with G4 in this solvate is low, cf. the coordination number distributions in Fig. 9. The average number of Li + cations coordinated to each G4 molecule is only 0.51 which is a function of the high fraction of free G4 in the bulk and low overall average number of Li + cations coordinated to each G4 molecule. This means the exchange time for G4 complexed to Li + will be markedly shorter in [Li(G4) 22,34 The formation of poly-nuclear clusters could further reduce the Li + self-diffusion coefficient. However, only a relatively small fraction of the Li + is found in poly-nuclear clusters at any time, and these are only weakly associated. This means the diffusion coefficient for Li + in the system is probably not strongly impacted by the presence of poly-nuclear clusters. The apparent measured diffusion coefficient for Li + will be the average for Li + in both 1 : 1 and poly-nuclear complexes, as is seen for example by NMR. 22 SDF plots cannot be produced for packing atoms around Li + as there is no way to define and distinguish a privileged set of axis about the spherical ion. However, atom-triplet angle distributions for OÁ Á ÁLiÁ Á ÁO triplets allow the spatial packing of O atoms around Li + to be deduced. Atom-triplet angle distribu- . This shoulder is due to the TFSI À O atoms bound to the same S atom both falling within the radial limit used to calculate the angle distribution. However, the LiÁ Á ÁO A g ij (r) function (Fig. 4A) and the corresponding SDF plot (Fig. 7C) 3 ] there is no strong preference for any given rotamer. This the consequence of a high proportion  of free glyme and the limited degree of LiÁ Á ÁO glyme connectivity in [Li(G4) 3 ], weaker LiÁ Á ÁO G4 interactions also means that there is 37% free glyme in the bulk and low overall connectivity between Li + and G4; each G4 molecule is coordinated to an average of 0.5 Li + cations. In [Li(G4)][TFSI] only B5% of G4 molecules lack LiÁ Á ÁO contacts with Li + and G4 molecules are coordinated to an average of 1.3 Li + cations.