Reorientation dynamics and ion diffusivity of neat dimethylimidazolium dimethylphosphate probed by NMR spectroscopy

NMR spectroscopy at two magnetic field strengths was employed to investigate the dynamics of dimethylimidazolium dimethylphosphate ([C1C1IM][(CH3)2PO4]). [C1C1IM][(CH3)2PO4] is a low-melting, halogen-free ionic liquid comprising of only methyl groups. 13C spin–lattice relaxation rates as well as self-diffusion coefficients were measured for [C1C1IM][(CH3)2PO4] as a function of temperature. The rotational correlation times, τc, for the cation and the anion were obtained from the 13C spin–lattice relaxation rates. Although from a theoretical point of view cations and anions are similar in size, they show different reorientation mobilities and diffusivities. The self-diffusion coefficients and the rotational correlation times were related to the radii of the diffusing spheres. The analysis reveals that the radii of the cation and the anion, respectively, are different from each other but constant at temperatures ranging from 293 to 353 K. The experimental results are rationalised by a discrete and individual cation and anion diffusion. The [(CH3)2PO4]− anion reorients faster compared to the cation but diffuses significantly slower indicating the formation of anionic aggregates. Relaxation data were acquired with standard liquid and magic-angle-spinning NMR probes to estimate residual dipolar interactions, chemical shift anisotropy or differences in magnetic susceptibility within the sample.


Introduction
Organic salts with a melting point at ambient temperatures (melting points below 373 K) are commonly referred to as ionic liquids (ILs). 1,2 ILs consist almost exclusively of organic cations and in-/organic anions. They are generally characterised by physical and chemical properties different from other molecular or atomic solvents, e.g. negligible vapour pressure, high chemical and thermal stability, high ionic conductivity and non-ammability. Because of their physicochemical characteristics, ILs have attracted wide attention as promising environmental friendly, "green" alternatives for commonly used organic solvents. The possibility of ne-tuning IL properties by an enormous diversity of cation-anion combinations renders ILs as substitute solvents or solvent additives in a wide range of laboratory and industrial applications. 1,[3][4][5][6] In addition to application in chemistry and physics, ILs have attracted considerable attention as solvents or solvent-mixtures in biochemistry. [7][8][9][10][11][12] A deeper understanding of IL properties at a molecular or even atomic level is of vital interest with respect to the rational design of novel ILs or the previous knowledge about the suitability of ILs for a desired process. Facing the plethora of various types and classes of ILs, a comprehensive characterization of the physicochemical properties is, realistically seen, only possible for selected cation-anion combinations. The prediction of the physicochemical characteristics, and, maybe even more importantly, the potential performance for novel task-driven ILs based on structure-function relationships of known cation-anion combinations is a great challenge. Hence, a combined approach integrating spectroscopic, experimental and theoretical/computational methods is required to broaden our understanding of ILs and the cationic-anionic interplay among each other and with solutes as well.
Nuclear magnetic resonance (NMR) is a powerful spectroscopic techniques for studying compounds or molecular systems at an atomic level. Despite some experimental limitations (e.g. high IL viscosity, radio frequency absorption due to high concentration of charged particles resulting in sample heating, detuned frequency channels, or with respect to solutes the suppression of IL solvent signals) it has been frequently shown that ILs can be thoroughly investigated by NMR. [13][14][15][16][17][18] By means of NMR spectroscopy different types of information on IL structure and dynamics are readily accessible by probing chemical shis, nuclear Overhauser effects (NOEs), relaxation times or self-diffusion coefficients. The atomic composition of ILs offers an intrinsic set of NMR active spin-1/2 nuclei, such as 1 H, 13 C, 15 N, 19 F, 31 P, suitable for investigation. In order to understand IL properties as a whole and the single contributions of the IL cation and anion respectively, to the observable IL properties, the characterization of the molecular dynamics is of great interest. The relaxation properties and diffusivity of selected imidazolium-based ILs have been successfully investigated recently using NMR spectroscopy. [19][20][21][22][23][24][25][26][27][28] Here, we examine and analyse 13 C spin-lattice relaxation times (T 1 , relaxation rate: R 1 ¼ 1/T 1 ) as well as self-diffusion coefficients of the ionic liquid dimethylimidazolium dimethylphosphate ([C 1 C 1 IM][(CH 3 ) 2 PO 4 ], Fig. 1) over a wide temperature range. In contrast to other imidazolium-based ILs, [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] is a low-melting (liquid at room temperature), halogen-free IL comprising only methyl groups. The relaxation data were acquired with standard liquid probes at two magnetic eld strengths and compared with data collected with high-resolution magic-angle spinning (HR-MAS) probes.

Samples
[C 1 C 1 IM][(CH 3 ) 2 PO 4 ] was purchased from IoLiTec GmbH (Heilbronn, Germany) in highest available purity ($98%) and used without further purication. The purity was conrmed by 1 H and 13 C NMR spectroscopy. The 1 H and 13

NMR measurements
All NMR experiments were acquired on Bruker AvanceIII systems with different magnetic eld strengths, 9.35 T and 16.45 T, corresponding to a 13 C resonance frequency of 100.6 MHz and 176.2 MHz, respectively. Both systems were equipped with 5 mm room-temperature liquid probes and 4 mm triple resonance HR-MAS probes. Liquid probe samples were tted with a coaxial insert containing D 2 O for eld frequency locking. All HR-MAS NMR experiments were collected without eld frequency locking and the sample spin rate was 6 kHz. The eld dri of both magnets was less than 0.3 Hz per hour without eld frequency locking. The sample temperatures were controlled by variable temperature units. Temperature calibration was carried out with 4% MeOH in CD 3 OD for the low temperature range (278.2-300.2 K) and 80% ethylene glycol in DMSO-d 6 for the high temperature range (300.2-353.2 K).
Inversion recovery experiments (180 -s-90 ) with power gated 1 H decoupling were collected and the 13 C longitudinal relaxation times (T 1 ) were calculated from signal heights by a single exponential t. For all experiments the relaxation delay was at least ve times the longitudinal relaxation time of the slowest relaxing nucleus.
Diffusion coefficients of [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] were measured at several temperatures using the double stimulated echo bipolar pulse-gradient pulse sequence (dstebpgp3s) for convection compensation and longitudinal eddy current delay implemented in the standard Bruker pulse library. The experimental signal amplitudes S were tted to the Stejskal-Tanner . g is the 1 H gyromagnetic ratio, d holds the gradient pulse length, g is the gradient strength, D reects the diffusion time and D t is the diffusion coefficient. d was xed at 3 ms, and D was set appropriately. In order to avoid signal attenuation caused by the 1 H T 1 relaxation timing parameters were kept constant and only the gradient strength g was varied in 32 linear steps from 2 to 95% of the maximum probe gradient strength (4.78 G mm À1 ). The probe gradient system was calibrated by measuring the diffusion coefficient of a water sample at 298.2 K and compared with the literature value (D t ¼ 2.299 Â 10 À9 m 2 s À1 ). 31 Data processing was performed with Topspin 3.5.6 (Bruker Biospin GmbH, Rheinstetten) and the relaxation data were analysed with the soware Dynamics Center 2.4.4 (Bruker Biospin GmbH, Rheinstetten).

Theoretical background
For any given system, the observed longitudinal relaxation rates are in general caused by a combination of different relaxation mechanisms and can be expressed in total according to eqn (1): Typical relaxation mechanisms for nuclear spin systems are magnetic dipole-dipole (DD) interactions, interactions by anisotropy of chemical shis (CSA), spin-rotation (SR), scalar coupling (SC) and electric quadrupoles (Q). The potential contributions from spin-rotations, scalar couplings or electric quadrupole interactions are either absent or negligible for spin-1/2 nuclei. Relaxation studies of heteronuclei, such as 13 C, are long established and generally preferred to 1 H. [32][33][34][35] The relaxation properties for 1 H mainly depend on inter-and intramolecular dipole-dipole interactions with surrounding protons. In contrast, 13 C relaxation in most organic molecules usually results only from intramolecular dipolar coupling to directly attached protons. For proton-attached 13 C nuclei intermolecular and contributions from not directly bonded protons can be safely ignored due to the strong 1 H-13 C distance dependence on r À6 H-C . The Bloembergen-Purcell-Pound (BPP) theory, rst introduced for dipolar 1 H relaxation 36 and later extended to other heteronuclei including 13 C, 37 provides the theoretical basis for describing the observed T 1 temperature dependence in terms of rotational correlation time and resonance frequency. Under broadband 1 H decoupling and neglecting cross-correlation effects between different interactions, the dipolar longitudinal relaxation rate of proton-attached 13 C nuclei is given by eqn (2).
J(u) are the spectral densities with the resonance frequencies, u H and u C , of 1 H and 13 C. The constant A 0 is dened by the number (n) of protons attached to 13 C and given in brackets, the square of the dipole-dipole coupling constant which describes the magnitude of this coupling (eqn (3)). Here, m 0 is the vacuum permeability, g C and g H are the magnetogyric ratios of 13 In summary, A 0 is independent of temperature and frequency and takes the value of 2.15 Â 10 9 s À2 for n ¼ 1 (6.45 Â 10 9 s À2 for n ¼ 3). Another source of 13 C relaxation is CSA. For an axiallysymmetric molecule, the principal components of the chemical shi tensor are parallel (d k ) and perpendicular (d t ) to the symmetry axis and their difference (Dd) is relevant for relaxation. The longitudinal 13 C relaxation due to CSA is given by eqn (4).
For proton-attached 13 C nuclei with only moderately small CSA the contribution of CSA to the overall relaxation rate is one order of magnitude smaller than those for dipole-dipole relaxation and mostly neglected in the discussion of protonattached 13 C relaxation. However, the contribution of CSA to 13 C longitudinal relaxation should be taken into account in particular at high magnetic elds and in situations where the nuclei under investigation exhibits large chemical shi ranges. In such a case, the total longitudinal relaxation rate for a proton-attached 13 C nuclei is the sum of the rate due to dipolar interaction and CSA (eqn (5)). 39 For rigid molecules with isotropic diffusion and a single molecular rotational correlation time (s c ) the spectral density J(u) can be modelled by eqn (6): In situations where the 1 H-13 C dipolar interaction (eqn (2)) is the main source of 13 C relaxation and the contribution of CSA is absent or not considered (second term in eqn (5) vanishes) it is worthwhile to note that eqn (2) by applying the BPP spectral density function (eqn (6)) reaches its maximum point, and hence T 1 a minimum, at u C s c ¼ 0.791. Using the relation u H /u C z 3.98 and rearranging eqn (2) the theoretical 13 C T 1 minimum can be calculated by eqn (7): To account for contributions from additional intramolecular motion to relaxation the generalized order parameter S 2 (0 < S 2 # 1) and an effective internal correlation time (s i ) were introduced in the "simple model-free" approach 40 (eqn (8)).
S 2 gives a measure of the spatial restriction of intramolecular motion. An order parameter of S 2 ¼ 1 implies a complete rigid internuclear vector tumbling with the overall molecular correlation time s c . S 2 would approach 0 for complete unrestricted isotropic internal motion of the bond-vector. 39 For S 2 ¼ 1 or in the slow intramolecular motion regime (s i [ s c ) eqn (8) reduces to eqn (6). In the fast intramolecular motion limit (s i ( s c ) eqn (8) reduces to J(u) ¼ S 2 J(u) BPP . One elegant way to extract information about molecular mobility from 13 C longitudinal relaxation times under the assumption of fast intramolecular motion and neglecting the CSA contribution is given in great detail in recent publications by Matveev et al. [41][42][43] With the knowledge of the precise 13 C T 1 minimum it is possible to independently simplify the determination of the value of S 2 (S 2 ¼ u C /(1.87A 0 T min 1 )) and hence to calculate s c for any given T 1 . Sometimes the relaxation of viscous liquids, even far above the melting point, is insufficiently described by eqn (6) or (8) and a correlation time distribution should be included into J(u). For such systems the molecular motion and relaxation properties can be described more efficiently by a distribution of correlation times rather than a single correlation time and an order parameter. [44][45][46][47][48] Therefore, the empirical Cole-Davidson (CD) approach 49,50 (eqn (9)) is widely used in literature for quantitative analysis of relaxation data with distributed correlation times. In eqn (9) the parameter b (0 < b # 1) describes the width of the distribution and s CD is related to s c by s c ¼ bs CD . For b ¼ 1 eqn (9) simplies to eqn (6).
Eqn (9) can also be extended by S 2 and s i to accomodate additional internal motion. For fast internal motion the spectral density is given by J(u) ¼ S 2 J(u) CD .
In situations where a molecule undergoes anisotropic tumbling or has moieties with fast internal reorientation compared with the overall molecular motion (e.g. fast rotating methyl groups) the order parameter S 2 can be replaced by the expression S i 2 ¼ 1/4(3 cos 2 (4) À 1) 2 . Here, the motion of a 13 C-1 H vector around its rotation axis (symmetry axis) and the azimuthal angle 4 is taken into account. 23,35,[51][52][53][54] For a methyl group with tetrahedral geometry (4 ¼ 109.5 ) S i 2 takes the value 0.11. The motion of the methyl rotation axis itself is considered by setting It is generally accepted that the temperature dependence of s c follows the Arrhenius form (eqn (10)). E A is the activation energy for rotational diffusion and R the universal gas constant.
However, sometimes eqn (10) is only applied for fast internal motion and the overall correlation time is better described by a Vogel-Fulcher-Tammann (VFT) behaviour 2,23 (eqn (11)).
The parameter T 0 is in the order of the glass transition temperature and E VFT is an apparent activation energy. The experimental relaxation data for one 13 C nucleus at both magnetic eld strengths were simultaneously tted with different models and parameter sets. Constrained least-square tting was performed using Python scripts written in-house. Bounds T 0 > 0, 0 < S 2 #1 and 0< b # 1 were imposed. The reduced c 2 value (c red 2 ) was used to assess the validity of the ts.
All mechanisms that contribute to 13 C relaxation mainly arise from intramolecular contributions. Therefore, longitudinal 13 C relaxation times are a reliable probe of molecular mobility and their analysis renders possible the characterization of molecular mobility in detail.

Comparison HR-MAS vs. liquid probe
Most of the 13 C relaxation studies rely on the assumption that aer inversion the recovery of the longitudinal part of the magnetisation follows a single exponential process. However, in situations where 13 C nuclei are directly attached to a proton, heteronuclear cross-relaxation by dipole-dipole interaction can lead to a non-exponential recovery of 13 C longitudinal magnetisation unless the 13 C spectra are collected with broadband 1 H decoupling. 55 The impact of cross-relaxation effects on the 13 C-1 H dipolar relaxation mechanism was estimated by determining the 13 C T 1 values under 1 H broadband decoupling conditions enabling NOE enhancement and under 1 H inverse gated decoupling without NOE enhancement at different magnetic elds and for selected temperatures (Table S1 †). There are no or virtually negligible differences between the 13 C T 1 values measured under broadband and gated 1 H decoupling at selected eld strength and temperature. Based on these data we conclude that there is no impact of cross-relaxation in the 13 C-1 H dipoledipole relaxation mechanism neither for the [C 1 C 1 IM] + cation nor the [(CH 3 ) 2 PO 4 ] À anion within the observed temperature range. The 13 C relaxation by dipole-dipole interaction within [C 1 C 1 IM] [(CH 3 ) 2 PO 4 ] can be considered as a single exponential process. This is in agreement with the result presented by Imanari et al. 19 for the [C 3 To reduce residual dipolar interactions or differences in magnetic susceptibility that might be present in the sample, [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] was also studied by HR-MAS NMR. As already shown for the high-resolution liquid probes even under magic-angle spinning there is nor difference in the 13 C longitudinal relaxation times determined with broadband or gated 1 H decoupling (Table S1 †). The 13 C T 1 values of single carbons obtained by collecting spectra with standard liquid probes and HR-MAS probes are highly comparable at selected eld strength and temperature. On one hand this reects the accuracy of probe temperature calibration. On the other hand the orientational components (3 cos 2 q À 1) of the Hamiltonians for the dipolar interaction, CSA or differences in the magnetic susceptibility due to sample inhomogeneity are averaged to zero by molecular motion without additional sample spinning. Despite the high viscosity of [C 1 C 1 IM][(CH 3 ) 2 PO 4 ], the motional averaging is fast enough to remove the contributions from interactions which would lead to line broadening. This assumption is further conrmed by measuring the 13 C line widths at several temperatures with high-resolution liquid and HR-MAS probes with 6 kHz sample spinning rate (Table S2 †). There are no differences in the 13 C line widths for each carbon at selected temperatures regardless which probe was used.
All 13 are attenuated with decreasing temperature due to increasing line broadening, which indicates a restriction in the molecular motion. However, the methyl groups of the [C 1 C 1 IM] + cation and the [(CH 3 ) 2 PO 4 ] À anion are less attenuated compared with the cation ring carbons. This indicates a less restricted motion of the cationic as well as the anionic methyl groups compared with cation ring carbons.
In conclusion, for [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] a sample spinning at the "magic angle" (q ¼ 54.7 ) is not essential to improve the spectral resolution.

C relaxation studies
were measured at two magnetic eld strengths under broadband proton decoupling within a temperature range from 278.2 K to 353.2 K in the next step. Based on this temperature dependence and the application of different models, characteristic rotational correlation times (s c ) were derived for each 13 C nuclei in the molecule.
The temperature dependence of the 13 C longitudinal relaxation times is shown in Fig. 2. At rst, with increasing temperature the magnitude of the 13 C T 1 values decreases for all cation carbons until reaching a minimum. Aer passing the minimum the magnitude of the 13 C T 1 values increase with increasing temperature. At a eld strength of 9.35 T C2, C4/5 and C1 0 of the imidazolium cation show a T 1 minimum at approx. 298 K. For C2 and C4/5 the observed T 1 minima of 0.231 s and 0.213 s, respectively, are close to the theoretical T 1 minimum of 0.158 s for pure dipole-dipole relaxation of a CH group at that eld strength assuming a BPP spectral density function (eqn (7)). At 16.45 T the T 1 minimum of C2, C4/5 and C1 0 is uniformly shied to 303 K and for C2 and C4/5 the values in the T 1 minimum (0.341 s and 0.305 s) closely match the calculated T 1 minimum of 0.276 s. The fact that all [C 1 C 1 IM] + cation ring carbons for a given magnetic eld strength have a T 1 minimum at nearly the same temperature indicates an isotropic reorientation of the cation. The deviation between the measured and the calculated relaxation times can be explained by a distribution of correlation times or additional internal motion of the H-C bond vector, which corroborates the application of "model-free" approach (eqn (8)).
At all temperatures the product of the T 1 relaxation times of the C1 0 methyl nuclei and the number of attached protons (n ¼ 3) is larger than those of the C2 and C4/5 CH groups (n ¼ 1) by a factor of 9-12. The inverse of this factor is in the order of 0.1 corresponding to the aforementioned expression of S 2 for fast rotating methyl groups with tetrahedral geometry. Furthermore, the measured C1 0 relaxation times indicate an unrestrained rotational motion of the [C 1 C 1 IM] + methyl groups. The theoretical 13 C T 1 values for dipole-dipole relaxation of a methyl group with free internal rotation also depend on the selected X-C-H bond angle 4. For 4 ¼ 109.5 13 C T 1 of a rapidly rotating CH 3 group which is 3-times longer than for a CH moiety under the assumption that both have the same effective rotational correlation time. With an increasing bond angle (4 > 109.5 ) the longitudinal 13 C relaxation time of CH 3 theoretically increases further by a factor of z4, z4.5 and z5 for 4 values of 112 , 113 and 114 , respectively, compared to a CH group. A rough estimation of the 13 C T 1 ratio of C1 0 and C2 or C4/5 of the [C 1 C 1 IM] + cation suggests that the bond angle 4 of the methyl group is slightly greater than 109.5 .
The methyl carbons in the [(CH 3 ) 2 PO 4 ] À anion only reveal a T 1 minimum at 288 K for a eld strength of 16.45 T, indicating a much more active motion compared with the carbons of the cation. Within the selected temperature range no T 1 minimum could be observed at 9.35 T for the methyl carbons of the [(CH 3 ) 2 PO 4 ] À anion. It can be assumed that the methyl carbon of the [(CH 3 ) 2 PO 4 ] À anion would also show a minimum in the 13 C T 1 relaxation time at 9.35 T, which however would appear only at a lower temperature than accessible in this study. For the  Table 2D.
methyl carbons in the [(CH 3 ) 2 PO 4 ] À anion no clear eld strength dependence of the T 1 relaxation could be observed in the high temperature range (>320 K). Also for the carbons of the cation the differences in the T 1 values reduce with increasing temperatures (Fig. 2, Table S3 †).

CSA contribution to 13 C relaxation
Mostly, the relaxation of proton attached 13 C nuclei in the liquid state is solely discussed in terms of dipolar interaction and the contribution of CSA to relaxation is neglected in literature.
Measuring 13 C T 1 relaxation times at different magnetic eld strengths in the fast motion limit (u C s c ( 1) directly allows an estimation of the CSA contribution to relaxation. From the data obtained in this study, we can not completely exclude CSA contributions to relaxation for any carbons of [C 1 C 1 IM] [(CH 3 ) 2 PO 4 ] but the comparable 13 C T 1 times at different magnetic eld strengths in the high temperature range indicate only a minor effect of CSA to relaxation compared to dipoledipole interaction. This is in agreement with the observation of Imanari et al. 19 who stated also a minor impact of CSA for imidazolium based IL cations. However, in situations where CSA additionally contributes to 13 C relaxation eqn (5) should be more suitable to represent the measured 13 C T 1 relaxation times. Therefore, we analysed our data in two ways: without taking account of CSA and in consideration of CSA.

Calculation of s c and E a
Considering the above remarks, at rst we treated the 13 C relaxation times of [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] as a result of the dipole-dipole relaxation mechanism between carbons and directly attached protons which can be described readily by eqn (2) and the modied BPP spectral density function (eqn (8)). We assume that the intramolecular motion is at least one order of magnitude faster than the overall molecular motion (s i (s c ) so that the second term in eqn (8) is negligible. For comparison the CD spectral density (eqn (9)) was also used for tting. The temperature dependence of s c was modelled with the Arrhenius (eqn (10)) and VFT (eqn (11)) approach, respectively. In the Arrhenius approach one activation energy is assumed for the entire temperature range. However, for viscous liquids a decreasing temperature can correlate with an increasing activation energy. Such a behaviour is sometimes better described by the VFT equation. 2,23 For [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] the precise glass transition temperature is not known but it was experimentally shown that for imidazolium based ILs the glass transition temperature is in the range of 180-220 K. [56][57][58][59][60][61] The t parameters are summarized in Table 1.
Regardless of the type of spectral density function or temperature dependence which is applied, all ts provide comparable results with respect to the order parameter, activation energy and rotational correlation time. Even the obtained T 0 parameters are in agreement with values reported in literature. There is no difference in the goodness-of-t between the application of the Arrhenius or the VFT approximation for the temperature dependence of s c . The same applies for the used spectral density functions. However no reliable t could be obtained for the methyl carbon of the anion by applying the VFT approach for the s c temperature dependence. It has to be noted that the application of the Arrhenius approach provides very good ts for the methyl carbon of the anion. The experimental data at 9.35 T are obviously better represented by the t parameters than the relaxation data at 16.45 T potentially indicating a more pronounced CSA contribution at the higher eld strength.
In the next step we treated the 13 C relaxation as a combination of dipole-dipole interaction and CSA (eqn (5)) under the assumption of fast internal motion. Again the experimental data were tted to a BPP (eqn (8)) and CD (eqn (9)) type spectral density function and the Arrhenius (eqn (10)) and VFT (eqn (11)) approach for the temperature dependence of s c , respectively. The obtained t parameters are compiled in Table 2. Taking account of CSA signicantly improves the goodness-of-t and the experimental data at both magnetic eld strengths are well represented by the t parameters. The estimated Dd values for the IL ring carbons are in the range of 112-142 ppm. This is in agreement with Dd for aromatic ring carbons reported by others. 23,62,63 However, the tted Dd values (Table 2)  The calculated s c , for example at 298 K, are nearly equal within the selected spectral density approach for all carbons of the [C 1 C 1 IM] + cation characterizing a uniform reorientation and molecular mobility. Moreover, our 13 C relaxation measurements at two different magnetic eld strengths reveal nearly the same rotational correlation times for all cation carbons (Tables 1 and 2) regardless of the selected type of spectral density function or approach for the temperature dependence of s c . Under this point of view the assumption of isotropic motion for the imidazolium ring is justied at least at room temperature. The activation energies (E A ) of molecular reorientation for the imidazolium ring carbons are in the range of 32-38 kJ mol À1 for BPP type spectral density and 39-42 kJ mol À1 for CD approach, respectively. Using VFT approach to model the temperature dependence of s c results in activation energies (E VFT ) within 2-8 kJ mol À1 . These values are consistent with results obtained by others for imidazolium ring carbons and attached methyl groups. 19,23,41,42,64 The tted E A /E VFT values are nearly unaffected by the inclusion of CSA to the analysis of the relaxation data. Only the combination of BPP spectral density function, including the CSA relaxation mechanism and a VFT type s c temperature dependency results in high E VFT values of 17-23 kJ mol À1 and low T 0 values for the [C 1 C 1 IM] + carbons (Table 2C).
It was shown recently that the behaviour of the anion as a whole can be reasonably described by values obtained for methyl groups in carbon containing IL anions. 43,64 For the methyl carbons of the anion, the calculated activation energies (E A /E VFT ) are considerably lower compared with cation carbons. At 298 K s c is at least three to ve times shorter than the corresponding values of the cation indicating a faster reorientation mobility of the anion. Moreover, this emphasises the hypothesis that cation and anion behave independently as dissociated ions and may form rather short-living ion pairs. We wish to point out that the molecular mobilities of [C 1 C 1 IM] + and [(CH 3 ) 2 PO 4 ] À should be considered as time-weighted averages between the reorientation dynamics of tightly associated [C 1 C 1 IM]-[(CH 3 ) 2 PO 4 ] ion pairs and single dissociated ions.
The S 2 of the ring carbons C2 (z0.6-0.72) and C4/5 (z0.64-0.78) calculated under the assumption of a C-H bond length of 1.09Å and a BPP type spectral density would reveal a moderate degree of additional internal motion. The slightly lower S 2 of C2 compared to C4/5 suggests accordingly that the proton attached to C2 is not preferentially involved in H-bonding in comparison to the other ring protons. The participation of the cationic H2 in hydrogen bonding with anions should result in a more constrained orientation, and hence higher order parameter of the corresponding C-H vector. The prominent role of the C2 position of imidazolium based IL cations in interacting with anions mainly via hydrogen bonding is extensively described in literature. 18,23,[65][66][67][68][69][70][71] It is well known that the length of a C-H bond can vary depending on the hybridization of the carbon atom and the polarity of the bond. 72 In this context, Antony et al. 73 71 The order parameters obtained for the methyl groups in C1 0 and the anion are slightly smaller compared to the ring carbons when the BPP type spectral density is applied for tting. This indicates a slightly higher exibility of the methyl carbons.
With respect to S 2 the results are somewhat different when the CD spectral density function is used. Here, the best ts were obtained when the t parameter S 2 takes rather high values which would correlate with no or only very limited internal motion.

However, the low b values of all carbons in [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] could point to a broad distribution of correlation times.
The consistency between the t parameters and the data derived at two magnetic eld strengths justies the chosen theoretical models and the approach of evaluation. The combination of applying the CD type spectral density function, the VFT approach for the s c temperature dependence and taking CSA into account provides the best t results for our experimental data within the selected temperature range (Fig. 2). Experimental data at lower temperatures or higher magnetic eld strengths than accessible in this study would further improve the reliability of the proposed tting approach mainly Table 1 Fit parameter values for the 13 C relaxation expressed by eqn (2). The spectral density functions given in eqn (8) (A, C) and eqn (9) (B, D) were used for fitting. The temperature dependence of s c was fitted with eqn (10) (A, B) and eqn (11)   for the more mobile IL anion. However, we do not want to conceal that our experimental data are also considerably well represented by the simple assumption of dipolar relaxation and the BPP spectral density function including S 2 only (Table 1A). As already mentioned (see Theoretical background) in situations where the temperature dependence of the 13 C T 1 values reveals a precise minimum the independent calculation of S 2 (S 2 ¼ u C /(1.87A 0 T min 1 )) and thus s c for any given T 1 is possible. For further information we refer to the recent publications by Matveev et al. 41,42,64 Since the 13 C nuclei in [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] reveal T 1 minima, we also calculated S 2 and extracted s c values for each temperature for comparison as proposed by the authors. Finally the s c temperature dependence was tted according the Arrhenius (eqn (10)) and VFT approach (eqn (11)). The motional characteristics of [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] applying this approach are summarized in Table S4 and depicted in Fig. S3 and S4. † Particularly with respect to S 2 , s c and E A the t parameters obtained by applying the BPP spectral density function and neglecting any CSA contributions are in remarkable agreement with the values obtained by simultaneous tting the relaxation data of two magnetic eld strengths (Tables 1 and  2). In conclusion, if a clear temperature dependent 13 C T 1 minimum is observable at one magnetic eld strength, the calculation of S 2 in that point, and thereaer s c and E A , provides a robust and reliable approach for the extraction of information about molecular motion.

Nuclear Overhauser effect
The nuclear Overhauser effect (NOE) is an import consequence of dipolar relaxation. In addition, to validate that the 13 C relaxation proceeds mainly by dipole-dipole interaction with attached protons the NOE enhancement factors h were measured in addition for selected temperatures, eld strengths and probe settings (Table S5 † and Fig. 3). Depending on the selected eld strength comparable enhancement factors were obtained for each temperature using either HR-MAS or liquid probes.
The maximum h observable relies on the rotational correlation time and thus on the molecular motion of the nuclei under investigation. Other relaxation pathways than intramolecular dipole-dipole interaction, which contribute to the longitudinal relaxation rate (e.g. CSA or intermolecular dipole-dipole interaction), can reduce the maximum h (eqn (12)). 39 Here we examine the 13 C NOE enhancement taking CSA into account. In the case that CSA is not considered the term (Dd ¼ d k À d t ) in eqn (12) is set to 0.  13 C relaxation expressed by eqn (5). The spectral density functions given in eqn (8) (A, C) and eqn (9) (B, D) were used for fitting. The temperature dependence of s c was fitted with eqn (10) and (11) On the basis of the best parameters derived from tting the relaxation data (Table 2D, CD type spectral density function and CSA contribution) the dependence of h max on s c was calculated and depicted in Fig. 3. For comparison also the h max dependence on s c was calculated using the t parameter given in Tables 1A and D (see Fig. S5 and S6 †). Because for the selected temperatures (278.2 K, 293.2 K and 323.2 K) the molecular motion of [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] is not in the fast motion limit (u C s c ( 1) and the relaxation by CSA is considered as a leakage term the maximum h observable of 1.98 for pure 1 H-13 C dipolar interaction can not be reached.
However, an increase in temperature resulting in shorter s c correlates with increased h values as shown in Fig. 3. For carbon C2 and C4/5 the observed enhancement factors h match the theoretical ones reasonably well and higher enhancements are obtained in the motion regime of u C s c z 1 at 9.35 T compared with 16.45 T. For the methyl carbons the observed enhancement factors deviate substantially from the expected values. The  Table 2D but a CSA value of 100 ppm. Blue and yellow markers represent data measured at B 0 of 9.35 T and 16.45 T corresponding to a 13 C resonance frequency of 100.6 MHz and 176.2 MHz, respectively.
reason could be that the Dd values for the methyl groups (Dd ¼ 267 and 303 ppm, respectively) are overestimated in the tting procedure. Recalculating the dependence of h max on s c with a Dd value of 100 ppm reveal a nearly perfect agreement between measured and expected NOE enhancement factors (Fig. 3b,  dashed lines). This conrms that the CD spectral density function and tted parameters b, E VFT , T 0 and s 0 at least are suitable to model the molecular mobility of [C 1 C 1 IM] [(CH 3 ) 2 PO 4 ]. From tting the relaxation data and comparing the measured and calculated h values the 13 C relaxation of [C 1 C 1 IM] [(CH 3 ) 2 PO 4 ] partially by CSA can't be excluded. Moreover, for Dd z 100 ppm the maximum relaxation rate due to CSA is 0.4 s À1 (at 9.35 T) and 0.7 s À1 (at 16.45 T). CSA contributes eld strength dependent to the overall 13 C relaxation (6% and 17% at 9.35 T and 16.45 T, respectively) which is nevertheless dominantly driven by dipolar 1 H-13 C relaxation. However, the absolute Dd values, mainly for the methyl groups, needs to be taken with caution and it has to be mentioned that the CSA magnitude can vary with temperature. Additional relaxation data at other magnetic eld strengths or the direct measurement of the CSA is necessary to verify the tted Dd values.

Diffusion study
To gain a deeper understanding of cation-anion association/ dissociation, formation of ion pairs or the aggregation of ions is of vital interest not only in the description of the IL electrical conductance and mass transport but also to rationalise the individual interaction of cation and anion with potential solute molecules.
Each of the four well resolved resonances in the 1 H spectrum of [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] has been used to determine the temperature dependence of the translational self-diffusion coefficients (D t ). Three out of the four resonances were assigned to the [C 1 C 1 IM] + cation and the D values obtained for the cation are averaged (see Table S6 †). The temperature dependence of D is shown in Fig. 4a and tted to an Arrhenius-type equation (eqn (10) [59][60][61][74][75][76] It is interesting that E A for diffusion and rotational correlation give nearly the same values at least for the cation. The activation energy of the anion for diffusion is slightly higher compared to the rotational correlation.
The increase in the diffusion coefficients for both cation and anion with increasing temperature is to be expected. The diffusion coefficients associated with the [C 1 C 1 IM] + cation are higher than the values obtained for the [(CH 3 ) 2 PO 4 ] À for the whole temperature range. The apparent cationic transference number and the predicted molar conductivity derived from the self-diffusion coefficients of [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] are calculated and plotted in Fig. S7. † In contrast to other imidazolium based ILs, 59-61 here, we observe an increase in the apparent cationic transference number with increasing temperature (Fig. S7a †). This can be rationalised by the slightly lower activation energy for the diffusion of the anion compared to the cation. At higher temperatures the diffusion of [(CH 3 ) 2 PO 4 ] À increases relatively less compared to the IL cation. The high cationic transference numbers of [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] also reveal a faster diffusion of the cation than the anion, even though both ions are similar in size, and that the difference in cationic and anionic diffusion increases with temperature.
As already reported in earlier studies on several imidazolium [59][60][61]74,75 or piperidinium 76 based ILs also in our investigation the anion diffuses at a slower rate than the cation. In most of these previous reports the slower diffusing anion was smaller compared to a larger IL cation. The primary aggregation of IL anions resulting in a lower anionic diffusion constant was proposed to rationalise this surprising observation on the one hand. 74,77 On the other hand it was suggested that the diffusion of the IL cation is faster than expected. 75 According to the Stokes-Einstein equation (eqn (13)) the selfdiffusion coefficient is inversely proportional to hydrodynamic radius (r) and, therefore, to the volume (V) of a spherical particle under investigation. 78 For considering the anion and the cation it follow the ratios: 3 OV cation / 3 OV anion ¼ r cation /r anion ¼ D anion / D cation . The calculated van-der-Waals volumes 79  At lower temperatures the experimental D anion /D cation is in total agreement with the theoretical ratio and the lower D anion can be explained by the larger anionic volume. However, at higher temperatures the experimental D anion /D cation deviates clearly from the theoretical ratio.
In order to clarify the disparity the hydrodynamic radii of [C 1 C 1 IM] + and [(CH 3 ) 2 PO 4 ] À were evaluated on the basis of the experimental data. The Stokes-Einstein relationship (eqn (13)), where k B and T correspond to Boltzmann constant and the temperature, models the self-diffusion coefficient (D t ) for a sphere of an effective hydrodynamic radius (r) with the temperature depenent viscosity (h) of a solution. Here, c is a constant that depends on the hydrodynamic particle-uid boundary conditions. Assuming innite dilution of a large diffusing sphere compared to the surrounding solvent the constant c ¼ 1 (stick boundary conditions). In situations where solute and solvent are of similar size (slip boundary conditions) or intermolecular interaction, non-spherical shape or aggregation need to be considered in the adjustment of the constant c was proposed. 18,74,[80][81][82] In our analysis the value 2/3 is applied for the constant c.
In a classical description the rotational correlation time s c of an isotropically diffusing sphere is given by eqn (14). 18,78,81,82 The combination of eqn (13) and (14) by eliminating h, k B and T makes it possible to correlate both NMR accessible values D t and s c to the hydrodynamic radius r of a particle under investigation (eqn (15)). Applying the t parameters from Table  2D allowed the calculation of s c for every temperature.
Based on eqn (15) the hydrodynamic radii of the [C 1 C 1 IM] + cation and [(CH 3 ) 2 PO 4 ] À anion were calculated and presented in Fig. 4b as a function of temperature. The hydrodynamic radius of the anion slightly decrease in the temperature range between 278-293 K and is then nearly constant for the temperature range studied. In contrast the hydrodynamic radius of the cation signicantly reduces with increasing temperature up to 293 K and then reaches a constant value at higher temperatures. The simultaneous decrease in the hydrodynamic radii of both the cation and the anion between 278-293 K suggests the formation of cationic-anion pairs. However, it is reasonable to draw the conclusion that no long existing cation-anion ion pairs are formed in the temperature range above 293 K. Averaged over the temperature range above 293 K the hydrodynamic radii of the  68 Nevertheless, for small and symmetric particles the applied theory is appropriate.
The experimentally acquired r of the cation is slightly smaller than theoretically estimated but in good agreement with other results for imidazolium based IL cations. 68,74,82,83 Within limits, this corroborates the Stokes-Einstein approximation made and shows the applicability of eqn (15) for estimating hydrodynamic radii based on s c and D at least for the imidazolium based IL cation.
However, the experimentally based radius of the anion seems to be unrealistic small and deviates signicantly from the theoretical value. If the aforementioned consideration (r cation / r anion ¼ D anion /D cation ) holds true, one should expect nearly the same value for both ratios. The experimental ratio of the hydrodynamic radii r cation /r anion is in the range of 1.98-2.52 and reveals a clear contradiction to the experimentally obtained ratio of the diffusion coefficients D anion /D cation ¼ 0.76 averaged over the temperature range.
Assuming the radius of the anion derived from rotational correlation times, and hence, the ratio r cation /r anion ¼ 1.98-2.52, is correct, this would imply that the measured diffusion coef-cients of the [(CH 3 ) 2 PO 4 ] À anion are too small by a factor of z2.6-3.3. However, it is more likely that the calculated radius of the anion based on eqn (15) is too small. Under the premise that the calculated s c values of the anion are correct and that the actual hydrodynamic radius of a single and isolated [(CH 3 ) 2 PO 4 ] À particle has nearly the same value as the cation (z2Å, s. above) the measured diffusion coefficients of the anion are too small by a factor of z4 to 6 for this molecular size and s c values. In reverse, if it means that in average 4-6 [(CH 3 ) 2 PO 4 ] À anions cluster, is subject to speculation. The [(CH 3 ) 2 PO 4 ] À anion diffuse substantially slower than expected, in particular in the high temperature range. To explain these phenomena the concept of anion-rich aggregates in ILs was recently suggested and experimentally veried. 74,77 Along this line, the diffusion coefficients and, thus, the derived hydrodynamic radii of [C 1 C 1 IM] + and [(CH 3 ) 2 PO 4 ] À and their interpretation presented in this study render the formation of anionic aggregates a suitable model to explain the comparatively low diffusion coefficients of the anion. One should keep in mind the different NMR time scales at which the diffusion (ms to s) and the reorientation (ns) dynamics are studied. Both time scales are too long for the detection of short-living uncharged IL ion pairs. The lifetime of such ion pairs was estimated to be in $ps time frame. 18 The longitudinal 13 C relaxation of [C 1 C 1 IM] [(CH 3 ) 2 PO 4 ] may reects the rotational reorientation of single/ not aggregated ionic particles in the ns time regime whereas the diffusion represents a "longtime" averaged clustering/ aggregation mainly of the anions. Based on our NMR data presented here no reliable statement about the number of clustering anions is possible. The concept of cooperative hydrogen bonding was introduced to rationalise the cationic aggregates. 84,85 The question needs to be resolved how anionic aggregates can overcome the repulsive Coulomb interaction.

Conclusion
Here, we report about the analysis of reorientation mobility of the room temperature IL [C 1 C 1 IM][(CH 3 ) 2 PO 4 ] on the basis of 13 C longitudinal relaxation times measured at two magnetic eld strengths by means of standard NMR liquid probes and by applying magic angle spinning. In addition, an analysis of the diffusion coefficients measured by PFG-NMR techniques at temperatures ranging from 278 K to 353 K was performed to correlate the rotational correlation times and the diffusion coefficients with the hydrodynamic radii of the [C 1 C 1 IM] + cation and the [(CH 3 ) 2 PO 4 ] À anion.
Despite their high viscosity pure imidazolium based ILs with a melting point at ambient temperatures can be properly studied by standard liquid NMR probe heads. With respect to IL signal line width, and hence resolution no improvement could be obtained by applying HR-MAS probes.
Therefore, the 13 C longitudinal relaxation behaviour of the [C 1 C 1 IM] + cation as well as the [(CH 3 ) 2 PO 4 ] À anion within the tested temperature range is reliably described by the BPP theory, the application of the generalised order parameter and an Arrhenius type s c temperature dependence. However, with regard to the goodness-of-t (c red 2 in Tables 1 and 2) the 13 C longitudinal relaxation behaviour is more precisely represented by the application of the CD type spectral density function, VFT type s c temperature dependence and the consideration of CSA to 13 C relaxation. This agrees with the ndings from others. 23,47 Additional relaxation data at a wider range of magnet eld strengths and/or temperatures would be necessary to corroborate the distinction between different dynamic models and the total amount of CSA contribution. In this respect, it has to be mentioned that eld-cycling NMR relaxometry is a valuable technique to obtain information on molecular dynamics over a broad range of Larmor frequencies (kHz to MHz). 48, 86 We wish to point out that eld-cycling NMR relaxometry is successfully employed to investigate the dynamics of ILs recently. 26,45,47,63,[87][88][89][90][91][92] Although from a theoretical point of view similar in size, the [C 1 C 1 IM] + cation and the [(CH 3 ) 2 PO 4 ] À anion reveal different reorientation mobilities and diffusivities. The [(CH 3 ) 2 PO 4 ] À anion shows a three to ve times faster reorientation at room temperature compared to the cation. This indicates that cation and anion are not tightly associated in their reorientation mobility. The temperature dependence of the self-diffusion coefficients is sufficiently described by the Arrhenius equation in the selected temperature range. In the course of the diffusion measurements we did not observe any indications of phase separation, and hence structural heterogeneity. It can be speculated that at lower temperatures the translational diffusion don't follow an Arrhenius-type but rather a VFT-type thermally activated process, as already observed for ILs. 47,93 Intriguingly, the activation energies derived from relaxation data and diffusion measurements are nearly the same at least for the cation. This suggests that the effective size of the [C 1 C 1 IM] + cation is the same for rotational correlation and diffusion. For the [C 1 C 1 IM] + cation the hydrodynamic radius derived from rotational correlation times and diffusion coefficients ts very well with theoretical considerations and imply the existence of single dissociated cationic particles.
Assuming that the hydrodynamic radius of an isolated [(CH 3 ) 2 PO 4 ] À anion is similar to the [C 1 C 1 IM] + cation the measured diffusion coefficients of the anion are too small to corroborate the model of single diffusing anionic entities. In contrast, the [(CH 3 ) 2 PO 4 ] À anion diffuses slower than expected and reveals a diffusion behaviour that indicates the formation of anionic aggregates.
Mainly with respect to IL ions interacting with solute molecules a better understanding of the ionic aggregation state and the dissociated action of IL cation and anion will help to rationalise the effects observed.
It has to be proven further whether and by which way of action the presence of solute molecules (in addition to carbohydrates e.g. peptides or proteins) in pure ILs has a measurable impact on the IL microstructure.

Conflicts of interest
There are no conicts to declare.