Christoph Wiedemann*^{a},
Günter Hempel^{b} and
Frank Bordusa*^{a}
^{a}Institute of Biochemistry and Biotechnology, Charles Tanford Protein Center, Martin Luther University Halle-Wittenberg, Kurt-Mothes-Str. 3a, D-06120 Halle (Saale), Germany. E-mail: christoph.wiedemann@biochemtech.uni-halle.de; frank.bordusa@biochemtech.uni-halle.de
^{b}Institute of Physics, Martin Luther University Halle-Wittenberg, Betty-Heimann-Str. 7, D-06120 Halle (Saale), Germany
First published on 4th November 2019
NMR spectroscopy at two magnetic field strengths was employed to investigate the dynamics of dimethylimidazolium dimethylphosphate ([C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}]). [C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}] is a low-melting, halogen-free ionic liquid comprising of only methyl groups. ^{13}C spin–lattice relaxation rates as well as self-diffusion coefficients were measured for [C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}] as a function of temperature. The rotational correlation times, τ_{c}, for the cation and the anion were obtained from the ^{13}C 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 [(CH_{3})_{2}PO_{4}]^{−} 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.
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.^{13–18} By means of NMR spectroscopy different types of information on IL structure and dynamics are readily accessible by probing chemical shifts, 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.^{19–28}
Here, we examine and analyse ^{13}C spin–lattice relaxation times (T_{1}, relaxation rate: R_{1} = 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 field strengths and compared with data collected with high-resolution magic-angle spinning (HR-MAS) probes.
Fig. 1 Chemical structure and denotation of dimethylimidazolium dimethylphosphate ([C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}]). |
Inversion recovery experiments (180°–τ–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 fit. For all experiments the relaxation delay was at least five 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 fitted to the Stejskal–Tanner equation^{29,30} S/S_{0} = exp[−γ^{2}δ^{2}g^{2}(Δ − δ/3)D]. γ is the ^{1}H gyromagnetic ratio, δ holds the gradient pulse length, g is the gradient strength, Δ reflects the diffusion time and D_{t} is the diffusion coefficient. δ was fixed at 3 ms, and Δ 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^{−1}). 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} = 2.299 × 10^{−9} m^{2} s^{−1}).^{31}
Data processing was performed with Topspin 3.5.6 (Bruker Biospin GmbH, Rheinstetten) and the relaxation data were analysed with the software Dynamics Center 2.4.4 (Bruker Biospin GmbH, Rheinstetten).
(1) |
The Bloembergen–Purcell–Pound (BPP) theory, first 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).
(2) |
(3) |
Another source of ^{13}C relaxation is CSA. For an axially-symmetric molecule, the principal components of the chemical shift tensor are parallel (δ_{∥}) and perpendicular (δ_{⊥}) to the symmetry axis and their difference (Δδ) is relevant for relaxation. The longitudinal ^{13}C relaxation due to CSA is given by eqn (4).
(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 proton-attached ^{13}C relaxation. However, the contribution of CSA to ^{13}C longitudinal relaxation should be taken into account in particular at high magnetic fields and in situations where the nuclei under investigation exhibits large chemical shift 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}
(5) |
For rigid molecules with isotropic diffusion and a single molecular rotational correlation time (τ_{c}) the spectral density J(ω) can be modelled by eqn (6):
(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 ω_{C}τ_{c} = 0.791. Using the relation ω_{H}/ω_{C} ≈ 3.98 and rearranging eqn (2) the theoretical ^{13}C T_{1} minimum can be calculated by eqn (7):
(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 (τ_{i}) were introduced in the “simple model-free” approach^{40} (eqn (8)).
(8) |
For S^{2} = 1 or in the slow intramolecular motion regime (τ_{i} ≫ τ_{c}) eqn (8) reduces to eqn (6). In the fast intramolecular motion limit (τ_{i} ≪ τ_{c}) eqn (8) reduces to J(ω) = S^{2}J(ω)_{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.^{41–43} 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} = ω_{C}/(1.87A_{0}T^{min}_{1})) and hence to calculate τ_{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(ω). 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.^{44–48} 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 β (0 < β ≤ 1) describes the width of the distribution and τ_{CD} is related to τ_{c} by τ_{c} = βτ_{CD}. For β = 1 eqn (9) simplifies to eqn (6).
(9) |
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} = 1/4(3cos^{2}(φ) − 1)^{2}. Here, the motion of a ^{13}C–^{1}H vector around its rotation axis (symmetry axis) and the azimuthal angle φ is taken into account.^{23,35,51–54} For a methyl group with tetrahedral geometry (φ = 109.5°) S_{i}^{2} takes the value 0.11. The motion of the methyl rotation axis itself is considered by setting S^{2} = 0.11S_{Met}^{2}.
It is generally accepted that the temperature dependence of τ_{c} follows the Arrhenius form (eqn (10)). E_{A} is the activation energy for rotational diffusion and R the universal gas constant.
τ_{c} = τ_{0}e^{EA/RT} | (10) |
τ_{c} = τ_{VFT}e^{EVFT/R(T − T0)} | (11) |
The experimental relaxation data for one ^{13}C nucleus at both magnetic field strengths were simultaneously fitted with different models and parameter sets. Constrained least-square fitting was performed using Python scripts written in-house. Bounds T_{0} > 0, 0 < S^{2} ≤1 and 0< β ≤ 1 were imposed. The reduced χ^{2} value (χ_{red}^{2}) was used to assess the validity of the fits.
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.
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 field strength and temperature. On one hand this reflects the accuracy of probe temperature calibration. On the other hand the orientational components (3cos^{2}θ − 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 confirmed 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}C signals of [C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}] 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}]^{−} 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” (θ = 54.7°) is not essential to improve the spectral resolution.
The temperature dependence of the ^{13}C longitudinal relaxation times is shown in Fig. 2. At first, with increasing temperature the magnitude of the ^{13}C T_{1} values decreases for all cation carbons until reaching a minimum. After passing the minimum the magnitude of the ^{13}C T_{1} values increase with increasing temperature. At a field strength of 9.35 T C2, C4/5 and C1′ 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 field strength assuming a BPP spectral density function (eqn (7)). At 16.45 T the T_{1} minimum of C2, C4/5 and C1′ is uniformly shifted 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 field 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)).
Fig. 2 ^{13}C longitudinal relaxation times (upper panels), the difference between measured and fitted relaxation times (middle panel) and the calculated τ_{c} values (lower panel) for carbons in [C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}] as a function of temperature. (a) carbon C2 (open squares and dotted lines) and C4/5 (filled circles and solid lines), (b) carbon C1′ (open squares and dotted lines) and CH_{3} carbons of the anion (filled circles and solid lines). For denotation see Fig. 1. 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. The lines in the upper panel represent calculated ^{13}C relaxation times according the fit parameters given in Table 2D. |
At all temperatures the product of the T_{1} relaxation times of the C1′ methyl nuclei and the number of attached protons (n = 3) is larger than those of the C2 and C4/5 CH groups (n = 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′ 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 φ. For φ = 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 (φ > 109.5°) the longitudinal ^{13}C relaxation time of CH_{3} theoretically increases further by a factor of ≈4, ≈4.5 and ≈5 for φ values of 112°, 113° and 114°, respectively, compared to a CH group. A rough estimation of the ^{13}C T_{1} ratio of C1′ and C2 or C4/5 of the [C_{1}C_{1}IM]^{+} cation suggests that the bond angle φ of the methyl group is slightly greater than 109.5°.
The methyl carbons in the [(CH_{3})_{2}PO_{4}]^{−} anion only reveal a T_{1} minimum at 288 K for a field 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}]^{−} anion. It can be assumed that the methyl carbon of the [(CH_{3})_{2}PO_{4}]^{−} 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 methyl carbons in the [(CH_{3})_{2}PO_{4}]^{−} anion no clear field 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†).
Measuring ^{13}C T_{1} relaxation times at different magnetic field strengths in the fast motion limit (ω_{C}τ_{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 field strengths in the high temperature range indicate only a minor effect of CSA to relaxation compared to dipole–dipole 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.
S^{2} | E_{A} (kJ mol^{−1}) | τ_{0} (s) | τ_{c} at 298 K (ns) | χ_{red}^{2} | ||
---|---|---|---|---|---|---|
a Fast methyl-group rotation was considered by modifying S^{2} with the factor 0.11 (S^{2} = 0.11S_{Met}^{2}). For methyl carbons S_{Met}^{2} is given.b Reduced χ^{2} values for data at 9.35 T.c Reduced χ^{2} values for data at 16.45 T.d Fitted S^{2} with a C–H bond length of 1.13 Å. | ||||||
(A) | C2 | 0.70 (0.87^{d}) | 38.18 | 1.67 × 10^{−16} | 0.82 | 2.98^{b}/6.78^{c} |
C4/5 | 0.76 | 38.27 | 1.67 × 10^{−16} | 0.85 | 3.60^{b}/8.26^{c} | |
C1′ | 0.56^{a} | 32.22 | 2.09 × 10^{−15} | 0.93 | 4.87^{b}/12.34^{c} | |
CH_{3} anion | 0.64^{a} | 18.97 | 6.58 × 10^{−14} | 0.14 | 1.06^{b}/1.36^{c} |
β | S^{2} | E_{A} (kJ mol^{−1}) | τ_{0} (s) | τ_{CD}/τ_{c} at 298 K (ns) | χ_{red}^{2} | ||
---|---|---|---|---|---|---|---|
(B) | C2 | 0.48 | 0.92 | 41.89 | 7.65 × 10^{−17} | 1.68/0.80 | 2.83^{b}/6.86^{c} |
C4/5 | 0.50 | 0.97 | 41.72 | 8.13 × 10^{−17} | 1.67/0.83 | 3.45^{b}/8.39^{c} | |
C1′ | 0.42 | 0.78^{a} | 36.59 | 8.61 × 10^{−16} | 2.23/0.93 | 4.29^{b}/13.26^{c} | |
CH_{3} anion | 0.44 | 1.00^{a} | 19.06 | 9.39 × 10^{−14} | 0.20/0.09 | 1.33^{b}/1.60^{c} |
S^{2} | E_{VFT} (kJ mol^{−1}) | T_{0} (K) | τ_{0} (s) | τ_{c} at 298 K (ns) | χ_{red}^{2} | ||
---|---|---|---|---|---|---|---|
(C) | C2 | 0.72 (0.89^{d}) | 8.33 | 165.94 | 3.81 × 10^{−13} | 0.76 | 1.93^{b}/7.21^{c} |
C4/5 | 0.78 | 6.89 | 179.09 | 7.24 × 10^{−13} | 0.77 | 2.41^{b}/8.51^{c} | |
C1′ | 0.58^{a} | 3.91 | 203.34 | 5.72 × 10^{−12} | 0.82 | 4.99^{b}/12.53^{c} | |
CH_{3} anion | — | — | — | — | — | — |
β | S^{2} | E_{VFT} (kJ mol^{−1}) | T_{0} (K) | τ_{0} (s) | τ_{CD}/τ _{c} at 298 K (ns) | χ_{red}^{2} | ||
---|---|---|---|---|---|---|---|---|
(D) | C2 | 0.43 | 1.00 | 5.16 | 203.93 | 2.26 × 10^{−12} | 1.66/0.71 | 1.21^{b}/5.47^{c} |
C4/5 | 0.51 | 1.00 | 4.96 | 204.40 | 2.47 × 10^{−12} | 1.46/0.74 | 1.62^{b}/6.82^{c} | |
C1′ | 0.29 | 1.00^{a} | 2.19 | 238.76 | 3.03 × 10^{−11} | 2.64/0.76 | 3.74^{b}/9.89^{c} | |
CH_{3} anion | — | — | — | — | — | — | — |
Regardless of the type of spectral density function or temperature dependence which is applied, all fits 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-fit between the application of the Arrhenius or the VFT approximation for the temperature dependence of τ_{c}. The same applies for the used spectral density functions. However no reliable fit could be obtained for the methyl carbon of the anion by applying the VFT approach for the τ_{c} temperature dependence. It has to be noted that the application of the Arrhenius approach provides very good fits for the methyl carbon of the anion. The experimental data at 9.35 T are obviously better represented by the fit parameters than the relaxation data at 16.45 T potentially indicating a more pronounced CSA contribution at the higher field 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 fitted 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 τ_{c}, respectively. The obtained fit parameters are compiled in Table 2. Taking account of CSA significantly improves the goodness-of-fit and the experimental data at both magnetic field strengths are well represented by the fit parameters. The estimated Δδ values for the IL ring carbons are in the range of 112–142 ppm. This is in agreement with Δδ for aromatic ring carbons reported by others.^{23,62,63} However, the fitted Δδ values (Table 2) for the methyl carbons are unexpectedly high when the motion of the ^{13}C–^{1}H vector around its rotation axis is considered (S^{2} = 0.11S_{Met}^{2}). Excluding the factor 0.11 during fitting would result in Δδ values in the range of 40–60 ppm for the methyl carbons.
S^{2} | E_{A} (kJ mol^{−1}) | τ_{0} (s) | τ_{c} at 298 K (ns) | Δδ (ppm) | χ_{red}^{2} | ||
---|---|---|---|---|---|---|---|
a Fast methyl-group rotation was considered by modifying S^{2} with the factor 0.11 (S^{2} = 0.11S_{Met}^{2}). For methyl carbons S_{Met}^{2} is given.b Reduced χ^{2} values for data at 9.35 T.c Reduced χ^{2} values for data at 16.45 T.d Fitted S^{2} with a C–H bond length of 1.13 Å. | |||||||
(A) | C2 | 0.60 (0.75^{d}) | 38.26 | 1.79 × 10^{−16} | 0.92 | 134.28 | 1.54^{b}/1.39^{c} |
C4/5 | 0.64 | 38.21 | 1.92 × 10^{−16} | 0.96 | 142.58 | 1.69^{b}/1.77^{c} | |
C1′ | 0.45^{a} | 32.09 | 2.57 × 10^{−15} | 1.09 | 280.20 | 1.11^{b}/2.03^{c} | |
CH_{3} anion | 0.44^{a} | 22.99 | 2.14 × 10^{−14} | 0.23 | 207.06 | 0.82^{b}/1.09^{c} |
β | S^{2} | E_{A} (kJ mol^{−1}) | τ_{0} (s) | τ_{CD}/τ_{c} at 298 K (ns) | Δδ (ppm) | χ_{red}^{2} | ||
---|---|---|---|---|---|---|---|---|
(B) | C2 | 0.60 | 0.72 | 40.89 | 1.02 × 10^{−16} | 1.50/0.90 | 112.64 | 1.68^{b}/0.72^{c} |
C4/5 | 0.65 | 0.74 | 40.43 | 1.18 × 10^{−16} | 1.45/0.94 | 121.37 | 1.85^{b}/1.24^{c} | |
C1′ | 0.57 | 0.55^{a} | 34.97 | 1.39 × 10^{−15} | 1.89/1.07 | 280.08 | 0.95^{b}/1.65^{c} | |
CH_{3} anion | 0.27 | 0.64^{a} | 28.91 | 6.99 × 10^{−15} | 0.82/0.22 | 264.62 | 2.04^{b}/1.07^{c} |
S^{2} | E_{VFT} (kJ mol^{−1}) | T_{0} (K) | τ_{0} (s) | τ_{c} at 298 K (ns) | Δδ (ppm) | χ_{red}^{2} | ||
---|---|---|---|---|---|---|---|---|
(C) | C2 | 0.61 (0.75^{d}) | 23.63 | 66.82 | 4.10 × 10^{−15} | 0.89 | 132.84 | 1.22^{b}/1.74^{c} |
C4/5 | 0.65 | 18.78 | 93.24 | 1.49 × 10^{−14} | 0.92 | 140.40 | 1.16^{b}/2.24^{c} | |
C1′ | 0.45^{a} | 17.07 | 84.80 | 6.94 × 10^{−14} | 1.06 | 277.69 | 1.08^{b}/2.35^{c} | |
CH_{3} anion | 0.32^{a} | 4.29 | 191.29 | 3.01 × 10^{−12} | 0.38 | 279.79 | 0.65^{b}/0.99^{c} |
β | S^{2} | E_{VFT} (kJ mol^{−1}) | T_{0} (K) | τ_{0} (s) | τ_{CD}/τ_{c} at 298 K (ns) | Δδ (ppm) | χ_{red}^{2} | ||
---|---|---|---|---|---|---|---|---|---|
(D) | C2 | 0.33 | 1.00 | 5.54 | 203.36 | 2.05 × 10^{−12} | 2.37/0.78 | 125.80 | 0.08^{b}/0.49^{c} |
C4/5 | 0.37 | 1.00 | 5.26 | 205.03 | 2.44 × 10^{−12} | 2.20/0.81 | 134.09 | 0.13^{b}/0.85^{c} | |
C1′ | 0.21 | 1.00^{a} | 2.62 | 236.28 | 2.61 × 10^{−11} | 4.35/0.90 | 267.22 | 0.31^{b}/0.80^{c} | |
CH_{3} anion | 0.12 | 1.00^{a} | 3.52 | 210.58 | 1.12 × 10^{−11} | 1.42/0.17 | 303.64 | 0.22^{b}/1.13^{c} |
The calculated τ_{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 field 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 τ_{c}. Under this point of view the assumption of isotropic motion for the imidazolium ring is justified 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^{−1} for BPP type spectral density and 39–42 kJ mol^{−1} for CD approach, respectively. Using VFT approach to model the temperature dependence of τ_{c} results in activation energies (E_{VFT}) within 2–8 kJ mol^{−1}. These values are consistent with results obtained by others for imidazolium ring carbons and attached methyl groups.^{19,23,41,42,64} The fitted 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 τ_{c} temperature dependency results in high E_{VFT} values of 17–23 kJ mol^{−1} 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 τ_{c} is at least three to five 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}]^{−} 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 (≈0.6–0.72) and C4/5 (≈0.64–0.78) calculated under the assumption of a C–H bond length of 1.09 Å 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.^{18,23,65–71} 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} postulated for the strong hydrogen bonding donor at position C2 of the imidazolium based cation (in this case 1-butyl-3-methylimidazolium) a C–H bond length of 1.13 Å. Reevaluating the C2 data with an elongated C–H bond length results in higher S^{2} values. By applying a C–H bond length of 1.13 Å S^{2} of C2 increases to values up to 0.99. These higher order parameters would corroborate the hypothesis that the proton in C2 position acts in hydrogen bond formation with the anion also for [C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}]. The H-bond formation mainly between the CH group in position 2 of the cation and the [(CH_{3})_{2}PO_{4}]^{−} anion is in agreement with existing hypothesis about the cationic–anionic interaction in imidazolium based ILs and the ability of [(CH_{3})_{2}PO_{4}]^{−} to act as relatively strong H-bond acceptor.^{71} The order parameters obtained for the methyl groups in C1′ and the anion are slightly smaller compared to the ring carbons when the BPP type spectral density is applied for fitting. This indicates a slightly higher flexibility 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 fits were obtained when the fit parameter S^{2} takes rather high values which would correlate with no or only very limited internal motion. However, the low β 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 fit parameters and the data derived at two magnetic field strengths justifies the chosen theoretical models and the approach of evaluation. The combination of applying the CD type spectral density function, the VFT approach for the τ_{c} temperature dependence and taking CSA into account provides the best fit results for our experimental data within the selected temperature range (Fig. 2). Experimental data at lower temperatures or higher magnetic field strengths than accessible in this study would further improve the reliability of the proposed fitting approach mainly 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} = ω_{C}/(1.87A_{0}T^{min}_{1})) and thus τ_{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 τ_{c} values for each temperature for comparison as proposed by the authors. Finally the τ_{c} temperature dependence was fitted 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}, τ_{c} and E_{A} the fit parameters obtained by applying the BPP spectral density function and neglecting any CSA contributions are in remarkable agreement with the values obtained by simultaneous fitting the relaxation data of two magnetic field strengths (Tables 1 and 2). In conclusion, if a clear temperature dependent ^{13}C T_{1} minimum is observable at one magnetic field strength, the calculation of S^{2} in that point, and thereafter τ_{c} and E_{A}, provides a robust and reliable approach for the extraction of information about molecular motion.
Fig. 3 Dependence of maximum {^{1}H}–^{13}C NOE enhancement (η_{max}) on τ_{c} calculated for a CD spectral density function and considering CSA with the fit parameters given in Table 2D (solid lines). (a) carbon C2 (left, open squares) and C4/5 (right, filled circles), (b) carbon C1′ (left, open squares) and CH_{3} carbon of the anion (right, filled circles). Dashed lines in (b) are calculated with the fit parameters given in 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. |
The maximum η 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 η (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 (Δδ = δ_{∥} − δ_{⊥}) in eqn (12) is set to 0.
(12) |
On the basis of the best parameters derived from fitting the relaxation data (Table 2D, CD type spectral density function and CSA contribution) the dependence of η_{max} on τ_{c} was calculated and depicted in Fig. 3. For comparison also the η_{max} dependence on τ_{c} was calculated using the fit 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 (ω_{C}τ_{c} ≪ 1) and the relaxation by CSA is considered as a leakage term the maximum η observable of 1.98 for pure ^{1}H–^{13}C dipolar interaction can not be reached.
However, an increase in temperature resulting in shorter τ_{c} correlates with increased η values as shown in Fig. 3. For carbon C2 and C4/5 the observed enhancement factors η match the theoretical ones reasonably well and higher enhancements are obtained in the motion regime of ω_{C}τ_{c} ≈ 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 reason could be that the Δδ values for the methyl groups (Δδ = 267 and 303 ppm, respectively) are overestimated in the fitting procedure. Recalculating the dependence of η_{max} on τ_{c} with a Δδ value of 100 ppm reveal a nearly perfect agreement between measured and expected NOE enhancement factors (Fig. 3b, dashed lines). This confirms that the CD spectral density function and fitted parameters β, E_{VFT}, T_{0} and τ_{0} at least are suitable to model the molecular mobility of [C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}]. From fitting the relaxation data and comparing the measured and calculated η 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 Δδ ≈ 100 ppm the maximum relaxation rate due to CSA is 0.4 s^{−1} (at 9.35 T) and 0.7 s^{−1} (at 16.45 T). CSA contributes field 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 Δδ 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 field strengths or the direct measurement of the CSA is necessary to verify the fitted Δδ values.
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 fitted to an Arrhenius-type equation (eqn (10)). The activation energies of translational diffusion, E_{A}, for the neat [C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}] are 36.5 ± 1.9 kJ mol^{−1} and 35.8 ± 2.2 kJ mol^{−1} for the [C_{1}C_{1}IM]^{+} cation and the [(CH_{3})_{2}PO_{4}]^{−} anion, respectively. These values are in the same order found for other ILs.^{59–61,74–76} 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}]^{−} 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}]^{−} 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^{59–61,74,75} 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 self-diffusion 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}√V_{cation}/^{3}√V_{anion} = r_{cation}/r_{anion} = D_{anion}/D_{cation}. The calculated van-der-Waals volumes^{79} (and effective radii^{74,80}) of the [C_{1}C_{1}IM]^{+} cation and the [(CH_{3})_{2}PO_{4}]^{−} anion are 89.8 Å^{3} (2.59 Å) and 96.8 Å^{3} (2.82 Å), respectively, and, hence, result in a theoretical ratio of the diffusion coefficients of D_{anion}/D_{cation} = 0.97 and hydrodynamic radii of r_{cation}/r_{anion} = 0.92 for [C_{1}C_{1}IM][(CH_{3})_{2}PO_{4}]. The experimental ratio D_{anion}/D_{cation} continuously decreases from 0.95 at 278.2 K to 0.67 at 353.2 K. 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.
(13) |
In a classical description the rotational correlation time τ_{c} of an isotropically diffusing sphere is given by eqn (14).^{18,78,81,82} The combination of eqn (13) and (14) by eliminating η, k_{B} and T makes it possible to correlate both NMR accessible values D_{t} and τ_{c} to the hydrodynamic radius r of a particle under investigation (eqn (15)). Applying the fit parameters from Table 2D allowed the calculation of τ_{c} for every temperature.
(14) |
(15) |
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 τ_{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 significantly from the theoretical value. If the aforementioned consideration (r_{cation}/r_{anion} = 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} = 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} = 1.98–2.52, is correct, this would imply that the measured diffusion coefficients of the [(CH_{3})_{2}PO_{4}]^{−} anion are too small by a factor of ≈2.6–3.3. 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 τ_{c} values of the anion are correct and that the actual hydrodynamic radius of a single and isolated [(CH_{3})_{2}PO_{4}]^{−} particle has nearly the same value as the cation (≈2 Å, s. above) the measured diffusion coefficients of the anion are too small by a factor of ≈4 to 6 for this molecular size and τ_{c} values. In reverse, if it means that in average 4–6 [(CH_{3})_{2}PO_{4}]^{−} anions cluster, is subject to speculation. The [(CH_{3})_{2}PO_{4}]^{−} 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 verified.^{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}]^{−} 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 reflects 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.
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}]^{−} anion within the tested temperature range is reliably described by the BPP theory, the application of the generalised order parameter and an Arrhenius type τ_{c} temperature dependence. However, with regard to the goodness-of-fit (χ_{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 τ_{c} temperature dependence and the consideration of CSA to ^{13}C relaxation. This agrees with the findings from others.^{23,47} Additional relaxation data at a wider range of magnet field 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 field-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 field-cycling NMR relaxometry is successfully employed to investigate the dynamics of ILs recently.^{26,45,47,63,87–92}
Although from a theoretical point of view similar in size, the [C_{1}C_{1}IM]^{+} cation and the [(CH_{3})_{2}PO_{4}]^{−} anion reveal different reorientation mobilities and diffusivities. The [(CH_{3})_{2}PO_{4}]^{−} anion shows a three to five 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 fits 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}]^{−} 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}]^{−} 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.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9ra07731f |
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