¹⁵N NMR studies provide insights into physico-chemical properties of room-temperature ionic liquids

Abstract

Ionic liquids (ILs) have gained a lot of attention as alternative solvents in many fields of science in the last two decades. It is known that the type of anion has a significant influence on the macroscopic properties of the IL. To gain insights into the molecular mechanisms responsible for these effects it is important to characterize these systems at the microscopic level. Such information can be obtained from nuclear spin-relaxation studies which for compounds with natural isotope abundance are typically performed using direct ¹H or ¹³C measurements. Here we used direct ¹⁵N measurements to characterize spin relaxation of non-protonated nitrogens in imidazolium-based ILs which are liquid at ambient temperature. We report heteronuclear ¹H–¹⁵N scalar coupling constants (nJ_HN) and ¹⁵N relaxation parameters for non-protonated nitrogens in ten 1-ethyl-3-methylimidazolium ([C₂C₁IM]⁺)-based ILs containing a broad range of anions. The ¹⁵N relaxation rates and steady-state heteronuclear ¹⁵N-{¹H} NOEs were measured using direct ¹⁵N detection at 293.2K and two magnetic field strengths, 9.4 T and 16.4 T. The experimental data were analyzed to determine hydrodynamic characteristics of ILs and to assess the contributions to ¹⁵N relaxation from ¹⁵N chemical shift anisotropy and from ¹H– ¹⁵N dipolar interactions with non-bonded protons. We found that the rotational correlation times of the [C₂C₁IM]⁺ cation determined from ¹⁵N relaxation measurements at room temperature correlate linearly with the macroscopic viscosity of the ILs. Depending on the selected anion, the ¹⁵N relaxation characteristics of [C₂C₁IM]⁺ differ considerably reflecting the influence of the anion on the physicochemical properties of the IL.

1. Introduction

Over the past two decades ionic liquids (ILs) have attracted enormous attention as alternative solvents or solvent additives in a wide range of laboratory and industrial applications. ILs represent a diverse class of organic salts with comparatively low melting points (≤ 373 K), high thermal and chemical stability, high ionic conductivity, non-flammability, negligible vapour pressure, and wide liquid and miscibilitiy ranges. These ILs’ properties and their comparatively simple tunability by ion exchange or by introducing desired functionalities raised the concept of ILs as environmentally friendly “designer solvents”, which might replace volatile hazardous organic solvents.^[1–4] ILs are chemical compounds with applications in many fields of chemistry, physics and biochemistry/technology.^[5–8] However, with regard to the synthesis, possible toxicity, and limited biocompatibility, the term “environmentally friendly” is questionable, at least, for some ILs.^[9,10]

In contrast to other types of liquids, ILs consist exclusively of ions. ILs commonly consist of bulky organic cations and in/organic anions. The spectrum of anions ranges from simple inorganic ions (e.g. Cl⁻ , Br⁻) to complex, e.g. fluorinated, organic compounds. The arrangement of cations and anions prevents the formation of solid crystal lattices which in turn leads to the low melting points. ILs with low melting point are highly desirable for many technical and industrial applications dealing with temperature-sensitive compounds or materials. Also, in view of the potential costs of liquefying high-melting-point ILs to make them applicable, ILs with low melting point can be preferred as substitutes. Room-temperature ILs constitute a subset of the large variety of ILs. Their common characteristic is that they exist as liquids at or below ambient temperatures. They are therefore of particular interest.

Although our knowledge of the physicochemical properties of many ILs is growing rapidly, it is still limited compared with conventional solvent systems. Especially the determination of the properties of ILs and, derived from this, the generalisation of observable trends is crucial for our fundamental understanding of ILs and thus also for the selection or design of application-specific ILs. The plethora of available ILs and the numerous possibilities to combine cations and anions make the comprehensive physicochemical description a challenging task. Imidazolium-based ILs are one of the most extensively studied ILs in the literature. In particular, much research has been devoted to 1-alkyl-3-methylimidazolium derived ILs. However, it has to be mentioned that 1-alkyl-3-methylimidazolium derived ILs are not exclusively liquid at ambient temperatures. Frequently, if the anion is a halide, these ILs exhibit melting points well above room temperature. Therefore, imidazolium-based ILs that are liquid at room temperature have the greatest potential for technical or industrial applications.

A comprehensive characterisation of the various structural and dynamic properties is essential for understanding the mode of action of ILs and thus for application-oriented use. Nuclear magnetic resonance (NMR) is one of the most powerful spectroscopic techniques for studying structure and dynamics of compounds or molecular systems at an atomic level. It has been frequently shown that even neat ILs can be thoroughly investigated by NMR with standard equipment.^[11–14] Although there is extensive literature on NMR investigations of ILs, these are mostly limited to nuclei with high natural abundance (¹H, ⁷Li, ¹¹B, ¹⁹F) or with sufficient receptivity at natural abundance (¹³C). However, there are comparatively few ¹⁵N NMR studies of ILs reported in literature.^[15–18] The unfavourable inherent properties of ¹⁵N (low natural abundance of 0.36 %, low receptivity at natural abundance of 3.8×10⁻⁶ relative to ¹H, and the negative magnetogyric ratio which can result in reduction or cancellation of ¹⁵N signal intensity in case of ¹H-¹⁵N cross-relaxation) render ¹⁵N NMR spectroscopic investigations a challenging and time consuming task. However, the high molar concentration when using neat ILs makes these measurements feasible in a reasonable amount of time even with standard NMR equipment. The low number of expected signals in combination with sufficient signal dispersion and narrow line widths make comparably lengthy ¹⁵N NMR measurements useful to provide a substantial contribution to the understanding of ILs. It has been extensively shown in literature that ¹H and ¹³C relaxation contain valuable information about dynamics of ILs.^[19–30] However, the relaxation of any NMR active nucleus in a molecule, when using appropriate models, can provide useful information to describe the dynamics of the whole molecule in more detail. For example, it has been shown that ¹¹B, ¹⁹F and ³¹P relaxation measurements can be very useful for the description of molecular dynamics of ILs.^[31,32]

To investigate the ¹⁵N relaxation times of ILs in general, the impact of the IL anion on the ¹⁵N relaxation times and on medium- to long-range nJ_HN couplings of the imidazolium-based cation we used a set of 10 different ILs. The focus of our investigation is on 1-alkyl-3-methylimidazolium ILs that are actually liquid at room temperature. The cation, 1-ethyl-3-methylimidazolium (see Fig. 1), was the same in all ILs used and only the anions were varied (see Fig. 2).

Fig. 1.

Chemical structure and denotation of the 1-ethyl-3-methylimidazolium ([C₂C₁IM]⁺) cation.

Fig. 2.

Chemical structures of the IL anions used in the study. (a) acetate ([CH₃CO₂]⁻), (b) trifluoroacetate ([CF₃CO₂]⁻), (c) tetrafluoroborate ([BF₄]⁻), (d) tris(pentafluoroethyl)trifluorophosphate ([(C₂F₅)₃PF₃]⁻), (e) diethylphosphate ([(C₂H₅)₂PO₄]⁻), (f) ethylsulfate ([C₂H₅SO₄]⁻), (g) 2-(2-methoxyethoxy)ethyl sulfate ([(C₅H₁₁O₂)SO₄]⁻), (h) hexylsulfate ([C₆H₁₃SO₄]⁻), (i) dicyanamid ([N(CN)₂]⁻), and (j) thiocyanate ([SCN]⁻).

2. Materials and Methods

2.1. Samples

All [C₂C₁IM]⁺-based ionic liquids used for ¹⁵N NMR measurements were purchased from IoLiTec GmbH (Heilbronn, Germany), Merck KGaA (Darmstadt, Germany) or Sigma-Aldrich (St. Louis, Missouri, United States) in highest available purity (≥ 98 %) and used without further purification. The purity was confirmed by ¹H NMR spectroscopy. No signals indicating impurities could be observed in the ¹H spectra except for a very weak water peak. The water peak originated from H₂O traces in the used D₂O. ILs used in this study are: (a) 1-ethyl-3-methylimidazolium acetate ([C₂C₁IM][CH₃CO₂]), (b) 1-ethyl-3-methylimidazolium trifluoroacetate ([C₂C₁IM][CF₃CO₂]), (c) 1-ethyl-3-methylimidazolium tetrafluoroborate ([C₂C₁IM][BF₄]), (d) 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate ([C₂C₁IM][(C₂F₅)₃PF₃]), (e) 1-ethyl-3-methylimidazolium diethylphosphate ([C₂C₁IM][(C₂H₅)₂PO₄]), (f) 1-ethyl-3-methylimidazolium ethylsulfate ([C₂C₁IM][C₂H₅SO₄]), (g) 1-ethyl-3-methylimidazolium 2-(2-methoxyethoxy)ethylsulfate ([C₂C₁IM][(C₅H₁₁O₂)SO₄]), (h) 1-ethyl-3-methylimidazolium hexylsulfate ([C₂C₁IM][C₆H₁₃SO₄]), (i) 1-ethyl-3-methylimidazolium dicyanamid ([C₂C₁IM][N(CN)₂]), and (j) 1-ethyl-3-methylimidazolium thiocyanate ([C₂C₁IM][SCN]). All ILs are listed in Table 2 and the corresponding chemical structures are shown in Figs. 1 and 2, respectively. ¹⁵N signal assignment is in agreement with literature data^[15,17] and was confirmed by ¹H–¹⁵N HMBC spectra with a 100 ms delay for the evolution of long-range couplings. ¹H assignment was confirmed by selective 1D ROESY experiments. As an example, the 1D ¹H, ¹⁵N and the 2D ¹H-¹⁵N-HMBC spectra of [C₂C₁IM][CH₃CO₂] are given in Fig. 3.

Table 2.

Measured ¹⁵N chemical shifts, relaxation times and ¹⁵N-{¹H} heteronuclear NOEs (± standard deviation) of [C₂C₁IM]⁺-based ILs at 293.2 K.

		δ [ppm]	T1 [s]		T2 [s]		NOE
			40.6 MHz	71 MHz	40.6 MHz	71 MHz	40.6 MHz	71 MHz
(a) [C2C1IM][CH3CO2]	N1	186.33	3.01±0.39	1.28±0.02	1.22±0.16	0.89±0.08	0.44±0.05	0.93±0.05
	N3	171.50	2.87±0.31	1.20±0.08	1.43±0.21	0.95±0.21	0.49±0.06	0.94±0.06
(b [C2C1IM][CF3CO2]	N1	185.76	10.50±0.14	4.99±0.35	2.25±0.19	2.25±0.12	−0.47±0.09	0.58±0.14
	N3	170.65	9.65±0.07	4.29±0.20	3.28±0.20	2.56±0.18	−0.50±0.02	0.57±0.09
(c) [C2C1IM][BF4]	N1	185.36	13.25±0.21	7.05±0.06	2.70±0.37	2.67±0.18	−0.47±0.02	0.46±0.13
	N3	170.24	12.65±0.21	6.56±0.26	3.69±0.25	3.05±0.13	−0.52±0.02	0.41±0.08
(d) [C2C1IM][(C2F5)3PF3]	N1	185.75	9.32±0.16	4.33±0.28	1.91±0.41	1.83±0.39	−0.05±0.08	0.56±0.07
	N3	169.91	9.78±0.74	4.81±0.19	2.71±0.24	1.91±0.07	0.00±0.13	0.74±0.08
(e) [C2C1IM][(C2H5)2PO4]	N1	186.28	1.84±0.02	1.13±0.11	0.37±0.05	0.29±0.03	0.80±0.06	1.05±0.08
	N3	171.36	1.77±0.02	1.12±0.08	0.63±0.01	0.36±0.05	0.82±0.08	0.93±0.14
(f) [C2C1IM][C2H5SO4]	N1	185.42	4.63±0.11	1.66±0.28	1.42±0.09	1.11±0.08	0.17±0.01	0.88±0.12
	N3	170.61	4.21±0.31	1.57±0.04	1.69±0.16	1.11±0.39	0.27±0.02	0.76±0.03
(g) [C2C1IM][(C5H11O2)SO4]	N1	185.77	3.06±0.02	1.37±0.14	1.34±0.12	0.87±0.08	0.46±0.05	0.96±0.15
	N3	170.92	2.74±0.01	1.29±0.07	1.56±0.05	0.93±0.08	0.51±0.06	0.93±0.07
(h) [C2C1IM][C6H13SO4]	N1	185.67	2.55±0.04	1.20±0.01	0.86±0.13	0.48±0.05	0.71±0.02	0.90±0.08
	N3	170.75	2.13±0.07	1.24±0.06	0.89±0.06	0.48±0.06	0.78±0.12	0.86±0.11
(i) [C2C1IM][N(CN)2]a	N1	185.69	15.70±2.62	6.65±0.37	4.23±0.26	3.62±0.52	−0.52±0.11	0.46±0.13
	N3	170.79	14.92±1.82	6.55±0.17	5.30±0.18	4.07±0.32	−0.51±0.11	0.48±0.08
(j) [C2C1IM][SCN]b	N1	185.29	9.45±0.08	5.11±0.42	2.12±0.17	2.16±0.29	0.01±0.04	0.48±0.07
	N3	170.47	8.42±0.01	4.58±0.22	2.31±0.24	2.16±0.01	0.04±0.05	0.57±0.06

^aa ¹⁵N NMR signal from the [N(CN)₂]⁻ anion was observed at 165.71 ppm (see Fig. S1)

^bno ¹⁵N NMR signal from the [SCN]⁻ anion was observed in the spectral range between 205 ppm to 155 ppm (see Fig. S1)

Fig. 3.

1D ¹H and ¹⁵N spectra of [C₂C₁IM][CH₃CO₂] are shown in (a) and (b). The ¹H-¹⁵N-HMBC spectrum is shown in (c).

Deuteration of individual [C₂C₁IM]⁺ ring protons was achieved by adding D₂O (4 fold volume excess) and incubating at 60 °C for 24 h under shaking. After drying of the IL at 90 °C for at least 12 h the whole procedure was repeated at least 3 times. Drying was finally performed at 90 °C for at least 24 h. For the ILs (f), (h), (i), and (j) deuteration at ring position 2 was achieved. [C₂C₁IM][CH₃CO₂] (a) was deuterated at positions 2, 4 and 5. The degree of deuteration was at least 70 %, and the deuterated ILs exhibited significantly different ¹⁵N chemical shifts compared to the protonated counterpart (see Tables 2 and 3).

Table 3.

¹⁵N chemical shifts, relaxation times and ¹⁵N-{¹H} NOEs (± standard deviation) of selectively deuterated [C₂C₁IM]⁺-based ILs at 71 MHz.

		δ [ppm]	T1 [s]	T1a[s]	T2 [s]	NOE
(a) [C2C1IM][CH3CO2]-2,4,5-d3	N1	185.78	2.34±0.32	2.69±0.12	1.02±0.18	0.76±0.20
	N3	170.75	2.34±0.22	2.40±0.23	1.34±0.15	0.78±0.10
(f) [C2C1IM][C2H5SO4]-2-d1	N1	185.22	2.56±0.24	2.60±0.26	1.24±0.18	0.81±0.04
	N3	170.35	2.06±0.28	2.07±0.29	1.51±0.01	0.83±0.02
(h) [C2C1IM][C6H13SO4]-2-d1	N1	185.35	1.35±0.27	1.02±0.28	0.48±0.12	0.97±0.29
	N3	170.44	1.44±0.32	1.26±0.16	0.66±0.07	1.08±0.39
(i) [C2C1IM][N(CN)2]-2-d1	N1	185.41	7.29±0.04	7.07±0.36	2.06±0.23	0.63±0.14
	N3	170.51	6.91±0.39	4.51±0.26	3.04±0.17	0.60±0.07
(j) [C2C1IM][SCN]-2-d1	N1	185.02	6.45±0.34	5.79±0.21	2.13±0.22	0.63±0.12
	N3	170.19	6.04±0.18	5.57±0.15	2.74±0.22	0.77±0.08

^ameasured with ¹H broadband decoupling

2.2. NMR measurements

All NMR experiments were carried out at 293.2 K on Bruker Avance III spectrometers with magnetic field strengths of 9.4 T and 16.4 T, corresponding to a ¹⁵N resonance frequency of 40.6 MHz and 71 MHz, respectively. The sample temperature was controlled by variable temperature units. Temperature calibration was carried out with 4 % MeOH in CD₃OD. Both spectrometers were equipped with 5 mm room-temperature liquid NMR probes. ILs were measured as neat liquids using a coaxial insert containing D₂O for field frequency locking and a small amount of 3-(trimethylsilyl)propane-1-sulfonate (DSS) for direct ¹H chemical shift referencing as 0.00 ppm. ¹⁵N chemical shifts were indirectly referenced by the magnetogyric ratio.^[33]

To measure the magnitude of medium- to long-range ¹H-¹⁵N scalar couplings (nJ_HN) a modified spin-state selective in-phase (IP) anti-phase (AP) HSQMBC pulse sequence with zeroquantum filter was utilised.^[34,35] The modified pulse sequence was kindly provided by Dr. Clemens Anklin (Bruker BioSpin, United States) and optimised to nJ_HN=8 Hz. Interleaved IP and AP spectra were acquired at 9.4 T as 16 384 data points in the direct ¹H dimension (F2) and with 16 increments in the indirect ¹⁵N dimension (F1). For each t₁ increment 4 transients were accumulated. The spectral width in F2 and F1 was 13 ppm (5197 Hz) and 30 ppm (1216 Hz), respectively, at 9.4 T. The acquisition time t₂ was 1.58 s resulting in a FID resolution of 0.63 Hz. The recycle delay was set to 1 s. Before processing, data sets were split so that in one data set the anti-phase information was added and in the other data set subtracted from the in-phase information, respecively. Zero-filling to 32 768 points in F2 and 64 points in F1 before Fourier transformation was applied to all data. Data were processed using a 90°-shifted sinesquared (cosine-squared) apodization in both dimensions. The spectral resolution in the ¹H dimension after Fourier transformation was 0.16 Hz/pt. The coupling constants were extracted along the direct dimension by analysing 1D slices from the 2D spectra at the respective ¹⁵N positions. The experimental uncertainties of the obtained coupling constants are on the order of the spectral resolution.

Direct ¹⁵N longitudinal relaxation time (T₁) measurements were performed using an inversion recovery pulse sequence (180°-τ-90°) under ¹H broadband decoupling throughout the measurement or only during acquisition. The ¹⁵N transverse relaxation time (T₂) experiments were acquired using the CarrPurcell-Meiboom-Gill sequence (90°-(τ-180°-τ)_n) with a fixed time τ of 30 ms and ¹H decoupling during acquisition. Longitudinal and transverse relaxation data were collected with eight and seven, respectively, relaxation delays each and adjusted to the respective IL. ¹⁵N-T₁ and T₂ values were extracted from signal heights by a single exponential fit according to I = I₀[1−2exp(−t/T₁)] and I = I₀exp(−t/T₂), respectively.

The ¹⁵N-{¹H} steady-state nuclear Overhauser effect (NOE) measurements were obtained from separate 1D ¹⁵N spectra acquired with and without continuous ¹H saturation during the entire experiment, respectively. Proton saturation in the ¹⁵N-{¹H} NOE experiment was achieved using continuous low power irradiation on ¹H during both relaxation delay (30 s) and acquisition. Values of the ¹⁵N-{¹H} steady-state NOE factors were determined from the ratio of peak intensities according to: NOE = (I_sat /I_eq), where I_sat and I_eq are the ¹⁵N peak intensities with and without ¹H saturation.

For all NMR experiments the recycle delays were at least four times the longitudinal relaxation time of the slowest relaxing nucleus. Data processing was performed with Topspin 3.6.1 (Bruker Biospin GmbH, Rheinstetten, Germany) and the relaxation data were determined with the software Dynamics Center 2.5.6 (Bruker Biospin GmbH, Rheinstetten, Germany).

3. Results

3.1. The anion affects the [C₂C₁IM]+ ring

It has been reported that the choice of the anion has only a minor impact on the ¹⁵N chemical shift values of imidazolium-based IL cations.^[15] Our results show that the same applies also to our selected combinations of [C₂C₁IM]⁺ cation and the various anions. Despite the fact that the anions used in our investigation are partially very different from the selection in previous studies, we obtained comparable results regarding the ¹⁵N chemical shift values of the [C₂C₁IM]⁺ cation and the difference in the ¹⁵N chemical shift values between N1 and N3 (Table 2). The difference in the ¹⁵N chemical shifts between N1 and N3 reflects the asymmetrical charge distribution within the imidazolium cation due to the different alkyl chains attached to the nitrogens. The asymmetry in the charge distribution does not apparently seem to be affected by the choice of the anion. This supports the assumption that the nitrogen atoms of the [C₂C₁IM]⁺ cation do not interact preferentially with their anionic counterparts.^[11,36]

Similarly, the overall molecular geometry, bond strengths, bond angles, and orbital character of the bonds of the cation do not appear to be significantly influenced by the choice of the anion, at first glance. Spin-state selective HSQMBC spectra have been recorded to measure ¹H-¹⁵N scalar coupling constants (nJ_HN) (Fig. 4). The extracted heteronuclear nJ_HN values within the [C₂C₁IM]⁺ cation are generally comparable for all selected cation-anion pairs but require a differentiated assessment (Table 1). Primarily ²J_HN and ³J_HN coupling constants could be measured. Our measurements revealed that the ring proton H2 has a coupling constant ²J_HN of ≈4.5 Hz to both N1 and N3. For both H4 and H5 the same two- and three-bond coupling constants (²J_HN ≈3.3 Hz, ³J_HN ≈4.7 Hz) to N1 and N3 were determined for all selected ILs. The variation of all coupling constants is in the range of 12 %. Only for ²J_HN of H4 to N3 the variation of the coupling constant is 22 % for different anions.

Fig. 4.

(a) Overlaid 2D cross-peaks obtained from spin-state-selective HSQMBC spectra of [C₂C₁IM][CH₃CO₂]: IP+AP in black and IP−AP in red. The insets show zoomed regions of HSQMBC spectra. (b) Corressponding 1D slices taken from (a) at δ¹⁵N 171.5 ppm and 186.3 ppm for proton H2 of [C₂C₁IM][CH₃CO₂].

Table 1.

nJ_HN coupling constants (Hz)

		H2	H4	H5	H1’	H2’	H1
(a) [C2C1IM][CH3CO2]	N1	4.85	4.68	3.43	-	3.34	-
	N3	4.73	3.29	4.75	-	-	2.04
(b) [C2C1IM][CF3CO2]	N1	4.74	4.54	3.25	-	3.13	-
	N3	4.51	3.16	4.65	-	-	1.76
(c) [C2C1IM][BF4]	N1	4.58	4.66	3.30	-	3.50	-
	N3	4.49	3.43	4.79	-	-	2.24
(d) [C2C1IM][(C2F5)3PF3]	N1	4.41	4.45	3.33	-	3.37	-
	N3	4.42	3.31	4.73	-	-	1.82
(e) [C2C1IM][(C2H5)2PO4]	N1	4.88	4.76	3.50	-	3.61	-
	N3	4.76	3.67	4.89	-	-	2.05
(f) [C2C1IM][C2H5SO4]	N1	4.61	4.74	3.19	-	3.36	-
	N3	4.73	3.45	4.70	-	-	1.99
(g) [C2C1IM][(C5H11O2)SO4]	N1	4.61	4.45	3.21	-	3.42	-
	N3	4.62	3.46	4.78	-	-	2.11
(h) [C2C1IM][C6H13SO4]	N1	4.34	4.57	3.42	-	3.40	-
	N3	4.29	3.36	4.74	-	-	2.06
(i) [C2C1IM][N(CN)2]	N1	4.33	4.35	3.13	-	3.66	-
	N3	4.21	3.22	4.64	-	-	2.39
(j) [C2C1IM][SCN]	N1	4.88	4.89	3.50	-	3.04	-
	N3	4.74	3.87	4.89	-	-	2.49

With respect to the alkyl groups, only coupling constants of H2’ to N1 (³J_HN ≈3.3 Hz) and H1” to N3 (²J_HN ≈2 Hz) were observable. The coupling constants of H2’ to N1 and of H1” to N3 vary within 20 % and 40 %, respectively, for different anions. Although the difference in Hz is small because these couplings are medium range and weak, the fractional differences are certainly significant and may suggest that the electronic structure of the cation is affected by the nature of the anion. It is subject to speculation whether the interaction with the anion takes place via the methyl or ethyl groups of the cation, but it is these ¹H-¹⁵N couplings in particular that vary the most.

The experiments were repeated optimised for smaller nJ_HN values (1 Hz to 3 Hz), but we could not observe any additional cross-peaks. The sign of the coupling constants cannot be determined with definite certainty. We have recorded selective HSQMBC-TOCSY (mixing time 45 ms) spectra to determine the sign of the nJ_HN.^[37] However, for the imidazolium-based compounds we see hardly any ¹H–¹H-TOCSY transfer and there is no transfer in the spin system when selectively excited. Thus, we were unable to determine the sign of the coupling constant, because we do not have ¹J_HN or ³J_HN as a reference for relative sign determination in the 1D slices corresponding to the nitrogens. From the signal displacement of the IP+AP and the IP−AP selective HSQMBC-TOCSY spectra we can conclude that ²J_HN and ³J_HN have the same sign.

The observed variation of at least some coupling constants within the [C₂C₁IM]⁺ cation throughout all selected anions contradicts the observations made above for the ¹⁵N chemical shifts. At least as far as the nitrogens are concerned, the choice of the anion has apperently little or no influence on the ¹⁵N chemical shift. By contrast, the significant variation of at least some two- and three-bond coupling constants suggests that the anion affects the electronic structure of the cation.

3.2. ¹⁵N relaxation times of [C₂C₁IM]+-based ILs

The ¹⁵N longitudinal and transverse relaxation times (T₁, T₂) were measured at two magnetic field strengths in the next step (Table 2). Figure 5 shows the NMR signal relaxation curves of [C₂C₁IM][CH₃CO₂] as an example. For the same IL and magnetic field strength, N1 and N3 show generally similar relaxation times. However, it is noticeable that N1 has slightly longer T₁ relaxation times than N3 for almost all ILs used. The opposite is true for T₂. Here N3 exhibits slightly longer relaxation times than N1. [C₂C₁IM][N(CN)₂] has the longest ¹⁵N T₁ and T₂ values and [C₂C₁IM][(C₂H₅)₂PO₄] the shortest, respectively. The order of the ¹⁵N [C₂C₁IM]⁺ T₁ relaxation times with respect to the anions is: [N(CN)₂]⁻, [BF₄]⁻ > [CF₃CO₂]⁻ > [(C₂F₅)₃PF₃]⁻ , [SCN]⁻ > [C₂H₅SO₄]⁻ > [CH₃CO₂]⁻ > [C₅H₁₁O₂)SO₄]⁻ > [C₆H₁₃SO₄]⁻ > [(C₂H₅)₂PO₄]⁻ . The ¹⁵N T₁ values differ between the slowest and the fastest relaxing IL by a factor of 6 to 9 depending on the magnetic field strength. For ¹⁵N T₂ values the ratio between [C₂C₁IM][N(CN)₂] and [C₂C₁IM][(C₂H₅)₂PO₄] is nearly 12 at both field strengths. To assess the potential impact of cross-correlation between ¹H-¹⁵N dipolar interaction and ¹⁵N CSA the ¹⁵N T₁ values were also measured under ¹H broadband decoupling applied throughout the entire experiment. The experimental results are listed in Supplementary Material (Table S1). The differences in the T₁ relaxation times between the conditions with and without ¹H decoupling during the recycle delay and the pulse sequence are not particularly pronounced. This result indicates that the effect of cross-correlation between ¹H-¹⁵N dipolar interaction and ¹⁵N CSA on ¹⁵N T₁ is minimal, therefore, it will not be considered in the subsequent analysis of relaxation data.

Fig. 5.

As an example, ¹⁵N longitudinal ((a, c, d, f) and transverse (b, e) relaxation curves (upper panels) of [C₂C₁IM][CH₃CO₂] at 40.6 MHz ((a-c)) and 71 MHz ((d-f)). Sample temperature was 293.2 K. (a, b, d, e) Spectra were collected with ¹H decoupling during acquisition. (c, f) Broadband ¹H decoupling was applied during the entire experiment. Experimental data for N1 and N3 are shown as black squares and red dots, respectively. The fitted curves are shown as black dashed and red dotted lines for N1 and N3, respectively. The lower panels show the residuals of fit, i.e. the difference between measured and back-calculated signal intensities.

It is evident from our data that ILs without proton-bearing anions have longer ¹⁵N T₁ and T₂ relaxation times than the ILs with proton-bearing anions. Thus, the presence of protons in the anion has an impact on the ¹⁵N relaxation time of the cation.

To explore the influence of the [C₂C₁IM]⁺ ring protons, at least qualitatively, the ring hydrogens were exchanged for deuterium. The relaxation data of the deuterated ILs at 71 MHz are summarized in Table 3. It can be seen that deuteration at the [C₂C₁IM]⁺ ring leads to slightly longer ¹⁵N T₁ and T₂ relaxation times. This indicates contribution to ¹⁵N relaxation from ¹H-¹⁵N dipolar interactions of the exchanged protons. The longer relaxation times could also be an indication that the quadrupole moment of the deuterons has no major effect on the relaxation of the [C₂C₁IM]⁺ ring ¹⁵N nuclei. However, we wish to point out that it is not clear if the observed increase in the relaxation times is due to solely removal of dipolar interaction or if it reflects the difference in the contributions from dipolar and quadrupolar interactions. It should also be noted here that deuteration generally increases IL viscosity due to the increase of the molar mass of the deuterated ILs.^[38] An increase in molecular mass by 1 % leads to a 3 % increase in viscosity. With the molecular weight of [C₂C₁IM]⁺ (111.17 g mol⁻¹) and deuteration at a maximum of 3 positions, an increase in viscosity up to about 10 % can be expected. Increased viscosity will cause slower rotational diffusion of cation molecules, and the resulting increase in the overall rotational correlation time will affect the spin relaxation rates in the cation. In particular, one would expect shorter ¹⁵N relaxation times T₁ and T₂ at 71 MHz and the temperature used in these studies. The observed general increase in the ¹⁵N relaxation time upon cation deuteration suggests that this effect is compensated by the stronger effect of reduced contribution from the ¹H-¹⁵N dipolar interactions.

Our results clearly show that at room temperature the ¹⁵N relaxation times of the cation are significantly influenced by the selection of the anion. The question that arises is whether the ¹⁵N relaxation times are affected by the choice of the anion alone or whether other physical parameters are responsible for the observation made. For this reason, we have summarised the viscosities of the individual ILs, where available, from the Ionic Liquids Database - ILThermo (Table 4).^[39,40] Not surprisingly, ILs with weakly coordinating anions, such as [N(CN)₂]⁻, [SCN]⁻ or [BF₄]⁻, have a lower viscosity compared to ILs with sulfate, phosphate or acetate-containing anions.^[41–45] The effect is particularly impressive for [CH₃CO₂]⁻ and [CF₃CO₂]⁻ where the substitution of the protons with fluorines drops the viscosity by a factor of 5 at 293.2 K. The viscosities of the ILs in our study follow the order: [N(CN)₂]⁻ < [SCN]⁻ < [CF₃CO₂]⁻, [BF₄]⁻ < [(C₂F₅)₃PF₃]⁻ ≪ [C₂H₅SO₄]⁻ < [CH₃CO₂]⁻ ≪ [C₆H₁₃SO₄]⁻ < [(C₂H₅)₂PO₄]⁻ which reflects to some degree the coordinating capability of the selected anions. We would like to emphasize at this point that we are referring here to the macroscopic viscosity of the ILs.

Table 4.

Dynamic viscosities (η) and theoretical rotational correlation time (τ_c) of the cation in selected [C₂C₁IM]-based ILs at 293.2 K. Viscosity values are taken from the Ionic Liquids Database - ILThermo.^[39,40]

	η [Pa s]	τc [ns]a	τc [ns]b
(a) [C2C1IM][CH3CO2]	0.202	0.95	0.72
(b) [C2C1IM][CF3CO2]	0.040	0.19	0.14
(c) [C2C1IM][BF4]	0.047	0.22	0.17
(d) [C2C1IM][(C2F5)3PF3]	0.076	0.36	0.27
(e) [C2C1IM][(C2H5)2PO4]	0.665	3.12	2.37
(f) [C2C1IM][C2H5SO4]	0.127	0.59	0.45
(g) [C2C1IM][(C5H11O2)SO4]c	0.288d	-	-
(h) [C2C1IM][C6H13SO4]	0.438	2.05	1.56
(i) [C2C1IM][N(CN)2]	0.017	0.08	0.06
(j) [C2C1IM][SCN]	0.029	0.13	0.10

^aEq. (7) and r =0.303 nm was assumed for calculation

^bEq. (7) and r =0.278 nm was assumed for calculation

^cno dynamic viscosity is available in the Ionic Liquids Database

^dthe viscosity was calculated using the factor 3.74 nsPa⁻¹ s⁻¹ (see text and Eq. (7)) and τ_c=1.08 ns obtained from relaxation data

3.3. Analysis of ¹⁵N relaxation rates and ¹⁵N-{¹H} NOE

In general, the ¹⁵N relaxation rates (R_1,2=1/T_1,2,) contain contributions from different relaxation mechanisms and can be expressed as:

$$R_{1,2}^{\text{total }}=\frac{1}{T_{1,2}^{\text{total }}}=\frac{1}{T_{1,2}^{\text{DD}}}+\frac{1}{T_{1,2}^{\text{CSA}}}$$ (1)

For the description of the ¹⁵N relaxation of imidazolium-based ILs only magnetic ¹H-¹⁵N dipole–dipole (DD) interactions and interactions caused by anisotropy of ¹⁵N chemical shifts (CSA) are relevant relaxation mechanisms. Contributions from spin-rotational interaction, scalar couplings or electric quadrupole interactions are either absent or negligible. In this study the effect of cross-correlation between ¹H-¹⁵N dipolar interaction and ¹⁵N CSA is not considered explictly. The ILs are isotopically ¹³C and ¹⁵N labelled only at natural abundance, therefore contributions from ¹⁵N-¹³C dipolar interaction and from cross-correlation between ¹⁵N CSA and ¹⁵N-¹³C dipolar relaxation mechanisms are negligible. Here we assume that the different sources of relaxation (¹H-¹⁵N dipolar interaction and ¹⁵N CSA) can be described by the same correlation function. For a rigid molecule undergoing isotropic rotational diffusion with a single molecular rotational correlation time (τ_c) the normalized spectral density J(ω) (real part of the Fourier transform of the auto-correlation function) can be modelled by Eq. (2)^[46]:

$$J(\omega )=\frac{2}{5}\left(\frac{{\tau }_{\text{C}}}{1+{\left(\omega {\tau }_{\text{C}}\right)}^2}\right)$$ (2)

The experimentally directly accessible relaxation parameters (longitudinal (R₁) and transverse (R₂) ¹⁵N relaxation rates and the steady-state heteronuclear ¹⁵N-{¹H} NOE) can be described by Eqs. (3) to (5), respectively. Eqs. (3) and (4) consider the contribution of the ¹H-¹⁵N dipolar interaction and ¹⁵N CSA to the longitudinal and transverse ¹⁵N relaxation rates as follows:^[47]

$$R_1=\frac{1}{T_1}=3\left(d^2+c^2\right)J\left({\omega }_{\text{N}}\right)+d^2\left[J\left({\omega }_{\text{H}}-{\omega }_{\text{N}}\right)+6J\left({\omega }_{\text{H}}+{\omega }_{\text{N}}\right)\right]$$ (3)

$$R_2=\frac{1}{T_2}=\frac{1}{2}\left(d^2+c^2\right)\left[4J(0)+3J\left({\omega }_{\text{N}}\right)\right]+\frac{1}{2}{d}^2\left[J\left({\omega }_{\text{H}}-{\omega }_{\text{N}}\right)+6J\left({\omega }_{\text{H}}\right)+6J\left({\omega }_{\text{H}}+{\omega }_{\text{N}}\right)\right]$$ (4)

$$NOE=1+\frac{{\gamma }_{\text{H}}}{{\gamma }_{\text{N}}}{d}^2\frac{\left[6J\left({\omega }_{\text{H}}+{\omega }_{\text{N}}\right)-J\left({\omega }_{\text{H}}-{\omega }_{\text{N}}\right)\right]}{R_1}$$ (5)

The strength of the ¹H-¹⁵N dipolar interaction is given by $d=-\left({\mu }_0\hslash {\gamma }_{\text{N}}{\gamma }_{\text{H}}\right)/\left(8\pi r_{\text{NH}}^3\right)$, where μ₀ is the permeability of vacuum, ħ is Planck’s constant divided by 2π, γ_H and γ_N are the magnetogyric ratios and ω_H and ω_N are the resonance frequencies of ¹H and ¹⁵N, respectively. The distance between the interacting spins is r_NH. The contribution of the ¹⁵N CSA to relaxation for an axially-symmetric chemical shift tensor is determined by c = −ω_N(δ_‖ − δ_⊥)/3, where (δ_‖ − δ_⊥) is the difference between the principal components of the chemical shift tensor parallel (δ_‖) and perpendicular (δ_⊥) to the symmetry axis of the tensor. Because the nitrogens in [C₂C₁IM]⁺ are not protonated, it can be assumed that relaxation via CSA is dominant, at least in situations where the anion does not bear any proton or fluorine and at high magnetic field strengths.

Since we are not dealing with an isolated spin pair, such as an amide NH pair of a peptide bond, when considering the contribution to ¹⁵N relaxation from ¹H-¹⁵N dipolar couplings with the non-bonded protons we follow the approach of Allard and Härd^[48] proposed for the interpretation of carbonyls’ relaxation and replace those protons with a “virtual ¹H” interacting via dipolar coupling with the nitrogens. Thus, we replace r_NH in the d²-containing terms in Eqs. (3) to (5) with the effective distance between a given nitrogen atom and the virtual proton, calculated as $r_{\text{NH},\text{ eff }}={\left(\sum _i{r}_{\text{NH},i}^{-6}\right)}^{-1/6}$, where r_NH,i is the distance between the nitrogen and the i^th proton and the summation is over all protons in the cation. This treatment accounts for contributions to ¹⁵N relaxation rates and heteronuclear NOE from dipolar interactions with every proton in the cation, assuming the same correlation function for all ¹⁵N-¹H pairs and neglecting any possible cross-correlation effects. The distances between N1 and N3, respectively, and the surrounding protons in the [C₂C₁IM]⁺ cation are depicted in Fig. 6. Based on this, the calculated effective distance between the virtual ¹H and N1 is 1.66 Å and 1.62 Å for N3. This slight difference in the distance for N1 and N3 is reflected in the small difference in the T₂ and T₁ relaxation times for these nitrogens as described above. With this approach it should be noted that possible dipolar interactions between the N1 and N3 of the [C₂C₁IM]⁺ cation and nuclei of the anions are not explicitly considered. However, taking into account the strong distance dependence of the dipolar interaction, this approach allows estimation of the magnitude of the ¹H-¹⁵N dipolar interaction relative to ¹⁵N CSA. If we assume a value of −180 ppm for (δ_‖ − δ_⊥) of ¹⁵N, which seems realistic for nitrogens in imidazolium rings^[49], and consider the effective distance from ¹⁵N to the virtual ¹H we obtain c > d at the magnetic fields used in this study: c²/d² = 3.3 at 40.6 MHz and 10.2 at 71 MHz. Although the contribution of CSA to relaxation is larger at the selected field strengths than the contribution due to dipolar interaction, the total relaxation can be adequately described only by including both sources of ¹⁵N relaxation.

Fig. 6.

Distances of ¹H to the respective N1 (red) and N3 (blue) in the [C₂C₁IM]⁺ ring. The distances were determined from an energy and geometry optimised [C₂C₁IM]⁺ structure using the Avogardo software.^[50] The effective distances r_NH,eff between the virtual ¹H (see text) and nitrogens N1 and N3 are 1.66 Å and 1.62 Å, respectively.

The ¹⁵N-{¹H} steady-state NOE value provides information to assess the contribution of neighbouring non-bonded protons to ¹H-¹⁵N cross-relaxation. At 40.6 MHz a negative or zero ¹⁵N-{¹H} NOE value is observed for all ILs with non-protonbearing anions used in this study, which indicates the presence of relevant dipolar interactions in the cation (Table 2). The reduced signal intensity due to the negative heteronuclear ¹⁵N-{¹H} NOE effect does not allow reliable data evaluation for [C₂C₁IM][(C₂F₅)₃PF₃] and [C₂C₁IM][SCN] at 40.6 MHz. Interestingly, the heteronuclear NOE value is the lowest for ILs with non-proton-bearing anions. By contrast, ILs with anions that contain the most protons ([C₂C₁IM][C₆H₁₃SO₄], [C₂C₁IM][(C₂H₅)₂PO₄]) exhibit the highest NOE values. A similar tendency is observed at the ¹⁵N resonance frequency of 71 MHz, where the observed heteronuclear NOE values are close to 1 for [C₂C₁IM][CH₃CO₂], [C₂C₁IM][(C₂H₅)₂PO₄] and [C₂C₁IM][(C₅H₁₁O₂)SO₄]. This could suggests that dipolar interactions with the proton-bearing anion may have an effect on the heteronuclear NOEs measured in the cation.

3.4. Analysis of T₁, T₂ and NOE in terms of the overall rotational correlation time and CSA

One question we want to address here is whether the respective contributions of the two relevant ¹⁵N relaxation mechanisms (¹H-¹⁵N dipolar interaction and ¹⁵N CSA) can be quantified. A common approach to extract information about dynamics from relaxation data is the analysis of a physically reasonable set of parameters in terms of the spectral density function.^[51] To obtain the overall rotational correlation time τ_c and the difference in principal components of the chemical shift tensor (δ_‖ − δ_⊥) a global parameter optimization was performed by minimizing the target function:

$$\begin{gathered} {\chi }^2={\left(\frac{R_1^{\text{exp}}(40.6\text{MHz})-R_1^{\text{cal}}(40.6\text{MHz})}{R_1^{\text{error}}(40.6\text{MHz})}\right)}^2 \\ +{\left(\frac{R_2^{\text{exp}}(40.6\text{MHz})-R_2^{\text{cal}}(40.6\text{MHz})}{R_2^{\text{error}}(40.6\text{MHz})}\right)}^2 \\ +{\left(\frac{NO{E}^{\text{exp}}(40.6\text{MHz})-NO{E}^{\text{cal}}(40.6\text{MHz})}{NO{E}^{\text{error}}(40.6\text{MHz})}\right)}^2 \\ +{\left(\frac{R_1^{\text{exp}}(71\text{MHz})-R_1^{\text{cal}}(71\text{MHz})}{R_1^{\text{error}}(71\text{MHz})}\right)}^2 \\ +{\left(\frac{R_2^{\text{exp}}(71\text{MHz})-R_2^{\text{cal}}(71\text{MHz})}{R_2^{\text{error}}(71\text{MHz})}\right)}^2 \\ +{\left(\frac{NO{E}^{\text{exp}}(71\text{MHz})-NO{E}^{\text{cal}}(71\text{MHz})}{{\mathit{\text{NOE}}}^{\text{error}}(71\text{MHz})}\right)}^2 \end{gathered}$$ (6)

in which the superscripts “exp” and “cal” denote the experimental and calculated parameters, respectively, at the corresponding ¹⁵N resonance frequency. The “error” denotes the standard deviations of the experimental R₁, R₂ and NOE values. To account for a possible variation in the effective ¹H-¹⁵N distance r_NH,eff we introduced a correction factor A in the calculation of the ¹H-¹⁵N dipolar interaction strength d (see Eq. S1). The possible field strength-dependent contribution of chemical exchange or other factors not considered here to transverse relaxation are accounted for by the separate terms B and C, respectively (see Eq. S5 and S6). The rigidity of the [C₂C₁IM]⁺ ring will hardly contribute to conformational changes as a cause for chemical exchange. However, it is conceivable that fluctuating charges within the cationic ring, cationic cluster formation or cation-anion association/dissociation could contribute to transverse relaxation in addition to contributions from the chemical shift anisotropy (c) and the dipolar interaction (d). The minimization of Eq. (6) was performed with an in-house Python script utilizing global optimization algorithms implemented in the SciPy package.^[52] Bounds −250 ppm< (δ_‖ − δ_⊥) ≤ −140 ppm, 0.1 < A ≤ 1.5, 0 ≤ B ≤ 3, and 0 ≤ C ≤ 3 were imposed. The best-fit values with lowest χ² are summarized in the Supplementary Material. To estimate the uncertainty in these best-fit values we applied the Monte-Carlo method with 500 simulated synthetic sets of R₁, R₂ and NOE values per IL. We would like to clarify here that from the relaxation data and the limits imposed for the fitting, it is not possible to make a definitive statement about the sign of the ¹⁵N CSA. Therefore we present the absolute value of |(δ_‖ − δ_⊥)| in the following. The globallyoptimized results are summarized in Table 5.

Table 5.

Globally optimized parameters (± estimated uncertainty) of [C₂C₁IM]⁺-based ILs at 293.2 K.

		τc [ns]	|(δ‖ - δ⊥)| [ppm]	A	B	C	D
(a) [C2C1IM][CH3CO2]	N1	0.86±0.03	191.68±3.21	1.06±0.01	0.43±0.04	0.14±0.09	-
	N3	0.81±0.09	204.89±12.69	1.10±0.01	0.29±0.03	0.05±0.06	-
(b) [C2C1IM][CF3CO2]	N1	0.23±0.09	177.56±35.91	1.12±0.04	0.36±0.01	0.23±0.01	0.01±0.02
	N3	0.22±0.06	192.80±23.87	1.11±0.03	0.20±0.00	0.13±0.01	0.00±0.01
(c) [C2C1IM][BF4]	N1	0.10±0.04	205.44±41.88	1.11±0.07	0.32±0.00	0.24±0.00	0.03±0.00
	N3	0.08±0.02	233.71±25.55	1.07±0.04	0.21±0.00	0.18±0.00	0.03±0.00
(d) [C2C1IM][(C2F5)3PF3]	N1	0.20±0.10	200.20±32.19	1.16±0.03	0.43±0.02	0.31±0.02	0.03±0.01
	N3	0.12±0.02	222.01±15.77	1.19±0.02	0.30±0.00	0.31±0.00	0.04±0.00
(e) [C2C1IM][(C2H5)2PO4]	N1	2.39±0.32	164.63±4.36	1.03±0.03	1.67±0.85	1.06±1.01	-
	N3	2.49±0.31	164.63±3.97	1.04±0.04	0.78±0.05	0.90±1.04	-
(f) [C2C1IM][C2H5SO4]	N1	0.39±0.07	229.54±20.73	1.10±0.00	0.46±0.01	0.25±0.03	-
	N3	0.37±0.00	249.95±0.06	1.12±0.00	0.32±0.01	0.20±0.17	-
(g) [C2C1IM][(C5H11O2)SO4]	N1	1.01±0.08	173.77±7.87	1.06±0.01	0.36±0.02	0.21±0.08	-
	N3	1.17±0.06	169.61±4.03	1.06±0.01	0.20±0.01	0.05±0.05	-
(h) [C2C1IM][C6H13SO4]	N1	1.41±0.02	170.10±0.87	1.09±0.01	0.69±0.14	1.09±0.70	-
	N3	2.07±0.18	156.38±2.41	1.06±0.04	0.50±0.06	0.99±1.01	-
(i) [C2C1IM][N(CN)2]	N1	0.13±0.05	204.12±37.60	1.09±0.06	0.17±0.00	0.10±0.00	-
	N3	0.14±0.04	195.04±30.43	1.13±0.04	0.12±0.00	0.07±0.00	-
(j) [C2C1IM][SCN]	N1	0.10±0.02	222.69±16.09	1.16±0.02	0.41±0.01	0.30±0.01	0.05±0.01
	N3	0.11±0.02	236.22±11.73	1.17±0.02	0.36±0.01	0.27±0.02	0.06±0.00

The back-calculated relaxation data are shown in Table 6. Our analysis shows that realistic τ_c and |(δ_‖ − δ_⊥)| values are obtained with the selected set of parameters for ILs with ¹H-bearing anions and [N(CN)₂]⁻ . That the measured and back-calculated T₁, T₂ and NOE values at both magnetic fields agree very well is illustrated by the low χ² values. Also for ILs with ¹⁹F-bearing anion ([CF₃CO₂]⁻, [BF₄]⁻, [(C₂F₅)₃PF₃]⁻) and for [SCN]⁻ reliable optimized results for τ_c and |(δ_‖ − δ_⊥)| can be obtained using the same set of adjustable parameters (see Table S1). However, in these cases the χ² values are significantly higher, indicating a larger discrepancy between the back-calculated and measured values. To overcome this limitation and to account for a possible contribution, so far not considered, of the ¹⁹F nuclei of the anions or the anion in general to the ¹⁵N R₁ relaxation rate of the cation, an additional term D (0 ≤ D ≤ 3) was introduced in Eq. (3) (see Eq. S11). Then Eq. (6) was minimized again with the extended parameter set (see Table 5). The introduction of term D to the equation for R₁ relaxation rate improved the χ² values most significantly for the [C₂C₁IM]⁺-based ILs with [CF₃CO₂]⁻, [BF₄]⁻, [(C₂F₅)₃PF₃]⁻) and [SCN]⁻ as anionic counterparts. Only for N3 of [C₂C₁IM][C₂H₅SO₄], which shows the highest deviation between measured and calculated values, no relevant reduction of χ² could be achieved even by introducing the additional adjustable term D. In general, we conclude that this approach leads to reliable results regarding τ_c and |(δ_‖ − δ_⊥)| for all ILs used here. The derived |(δ_‖ − δ_⊥)| values are in a range of 160 ppm to 250 ppm with an average value of approx. 200 ppm. As already mentioned, these are realistic CSA values for ¹⁵N in imidazolium-based rings.^[49] The correction factor A values are generally similar for all selected ILs (1.03 to 1.17), suggesting that the effective distance r_NH,eff between the virtual ¹H and the nitrogen, responsible for the the dipolar interaction, is slightly larger than initially assumed. This in turn results in a lower significance of relaxation by ¹H-¹⁵N dipolar interaction compared to relaxation by ¹⁵N CSA. It is interesting that the ILs with proton-bearing anions have the smallest A factors. It is worth mentioning that in our analysis of the relaxation data we did not introduce an order parameter (S) to account for the modulation/averaging of the ¹H-¹⁵N dipolar interaction by fast internal motions, as is often done in the model-free approach to characterize local dynamics in macromolecules.^[53,54] For a completely rigid internuclear vector S = 1 and would approach 0 for fully unrestricted internal motion. Thus, alternatively, the correction factor 1/A, which is in the range of 0.85 to 0.97, might also be seen as a kind of order parameter that accounts for the flexibility of the virtual N-H bond.

Table 6.

Calculated ¹⁵N relaxation times and ¹⁵N-{¹H} NOEs of [C₂C₁IM]⁺-based ILs at 293.2 K based on the parameters in Table 5 applied in Eqs. (S4) to (S7) or (S11) to (S14), respectively. χ² is the target function value (Eq. (6)) when using the measured (Table 2) and calculated (this table) relaxation times. ± represents the estimated uncertainty.

		T1 [s]		T2 [s]		NOE		χ2
		40 MHz	70 MHz	40 MHz	70 MHz	40 MHz	70 MHz
(a) [C2C1IM][CH3CO2]	N1	3.01±0.02	1.28±0.01	1.22±0.06	0.89±0.07	0.44±0.03	0.93±0.00	0.32±0.31
	N3	2.90±0.05	1.20±0.03	1.43±0.06	0.92±0.05	0.49±0.03	0.94±0.00	0.47±0.38
(b) [C2C1IM][CF3CO2]	N1	10.50±0.00	4.99±0.01	2.25±0.02	2.25±0.01	−0.47±0.05	0.58±0.08	0.00±0.01
	N3	9.65±0.00	4.29±0.01	3.28±0.01	2.56±0.02	−0.50±0.01	0.57±0.05	0.00±0.00
(c) [C2C1IM][BF4]	N1	13.25±0.00	7.05±0.00	2.70±0.03	2.67±0.02	−0.46±0.01	0.47±0.05	0.09±0.13
	N3	12.65±0.00	6.56±0.01	3.69±0.01	3.05±0.01	−0.54±0.00	0.41±0.02	0.17±0.20
(d) [C2C1IM][(C2F5)3PF3]	N1	9.32±0.01	4.32±0.06	1.92±0.07	1.83±0.07	−0.10±0.04	0.69±0.05	4.00±2.51
	N3	9.82±0.04	4.80±0.01	2.71±0.02	1.97±0.01	0.02±0.05	0.69±0.01	0.54±0.74
(e) [C2C1IM][(C2H5)2PO4]	N1	1.84±0.00	1.13±0.06	0.47±0.16	0.41±0.13	0.81±0.04	0.97±0.01	1.93±2.13
	N3	1.77±0.00	1.13±0.04	0.63±0.01	0.43±0.14	0.81±0.05	0.97±0.01	0.86±1.29
(f) [C2C1IM][C2H5SO4]	N1	4.62±0.00	1.81±0.03	1.42±0.03	1.11±0.04	0.17±0.01	0.85±0.01	0.57±0.45
	N3	4.15±0.03	1.59±0.01	1.69±0.03	1.09±0.18	0.26±0.01	0.87±0.00	14.82±4.41
(g) [C2C1IM][(C5H11O2)SO4]	N1	3.06±0.00	1.37±0.04	1.33±0.04	0.87±0.06	0.47±0.03	0.93±0.00	0.40±0.36
	N3	2.74±0.00	1.29±0.02	1.56±0.01	0.92±0.04	0.51±0.03	0.94±0.00	0.39±0.35
(h) [C2C1IM][C6H13SO4]	N1	2.55±0.00	1.20±0.01	0.86±0.10	0.48±0.14	0.71±0.01	0.96±0.00	1.07±1.03
	N3	2.13±0.01	1.24±0.02	0.89±0.05	0.48±0.16	0.76±0.06	0.96±0.01	1.27±1.18
(i) [C2C1IM][N(CN)2]	N1	15.81±0.21	6.65±0.01	4.23±0.01	3.62±0.02	−0.52±0.03	0.48±0.06	0.05±0.10
	N3	15.51±0.28	6.54±0.01	5.30±0.00	4.07±0.01	−0.52±0.06	0.49±0.04	0.14±0.12
(j) [C2C1IM][SCN]	N1	9.45±0.00	5.14±0.17	2.12±0.02	2.16±0.04	−0.00±0.02	0.66±0.01	5.42±2.28
	N3	8.42±0.00	4.52±0.17	2.31±0.03	2.16±0.01	0.01±0.03	0.67±0.02	3.77±2.66

The optimization parameters B and C reveal no obvious field strength dependence, as would have been expected for the contribution of chemical exchange to transverse relaxation. However, it has to be mentioned here that the derived values of B and C are of the same order of magnitude as the R₂ relaxation rates. One can only conclude that the contribution B to transverse relaxation rate R₂ at 40.6 MHz is larger for almost all ILs than the contribution C to R₂ at 71 MHz. A detailed explanation of the physico-chemical reasons for this observation is not available at this point, but it can also not be excluded that other contributions than just chemical exchange may play a role here.

An essential physical parameter that can be derived from this analysis is the overall rotational correlation time τ_c of the [C₂C₁IM]⁺ cation (see Table 6). The τ_c values at 293.2 K obtained from ¹⁵N relaxation rates in this study are comparable to those obtained in previous studies from the investigation of ¹H or ¹³C relaxation data for other imidazolium-based ILs in the same temperature range.^{[21,28,29,55,56]}

When evaluating τ_c values of the cations derived from ¹⁵N relaxation measurements, it is necessary to consider the viscosity of the IL, since the rotational correlation time of a diffusing particle is determined by its shape and size/molecular weight and the viscosity of the surrounding medium. Not surprisingly, the ILs with the highest macroscopic viscosity (see Table 4) show the longest derived rotational correlation times. The order of the τ_c values of the [C₂C₁IM]⁺ cation for various anions reads as follows: [SCN]⁻ , [N(CN)₂]⁻, [BF₄]⁻ < [(C₂F₅)₃PF₃]⁻, [CF₃CO₂]⁻, [C₂H₅SO₄]⁻ < [CH₃CO₂]⁻, [(C₅H₁₁O₂)SO₄]⁻ < [C₆H₁₃SO₄]⁻ < [(C₂H₅)₂PO₄]⁻. The experimentally obtained τ_c values thus reflect the order of the ILs according to their viscosity, which in turn underlines the reliability of the chosen approach to data analysis. To verify the correctness of the experimentally determined τ_c values, the theoretical τ_c of [C₂C₁IM]⁺ in the different ILs were calculated based on the Stokes-Einstein-Debye equation (see Eq. (7)) taking into account their macroscopic viscosity. In Eq. (7) η is the dynamic viscosity, r is the hydrodynamic radius of [C₂C₁IM]⁺, k_B is the Boltzmann constant and T is the temperature. The factor f_rot (Gierer-Wirtz-factor) compensates for the effect of rotational microfriction and is given by f_rot = (6r_L/r + 1/(1 + r_L/r)³)⁻¹, where r_L and r are radii of solvent and the solute molecules, respectively.^[24,57,58] For pure liquids (r_L = r) the factor f_rot takes the value of 8/49 (=0.163).

$${\tau }_{\text{C}}=\frac{4\pi \eta r^3}{3k_{\text{B}}T}{f}_{\text{rot}}$$ (7)

To calculate the theoretical τ_c values, an r of 0.303 nm was used for the [C₂C₁IM]⁺ cation.^[41] The theoretical τ_c values for r=0.303 nm are summarized in Table 4. Conversely, the hydrodynamic radius of [C₂C₁IM]⁺ can also be estimated from the τ_c value determined from experimental data by rearranging Eq. (7) and assuming f_rot is 0.163. The hydrodynamic radius of [C₂C₁IM]⁺ averaged over experimental τ_c values for all used ILs is 0.278 nm ± 0.040 nm. This averaged r value is slightly smaller than stated in Tokuda et al.^[41], but in absolute agreement with the hydrodynamic radius for the [C₂C₁IM]⁺ cation obtained by Green et al.^[56]. The theoretical τ_c values calculated with r =0.278 nm are also listed in Table 4. The comparison of the theoretical (Table 4) and the experimental/fitted (Table 6) τ_c values indicates that the application of the simple hydrodynamic model including the Gierer-Wirtz correction factor is very suitable to describe physico-chemical parameters of imidazolium based ILs over a broad range of viscosities.

Figure 7 illustrates the relationship between the τ_c values and the macroscopic viscosity. The experimentally determined τ_c values of all ILs correlate linearly with the viscosity (square of the correlation coefficient: R²=0.98 and 0.97 for N1 and N3, respectively) in excellent agreement with the Debye-Einstein-Stokes equation (Eq. (7)). The slope of the regression line for N1 and N3 is 3.46 ns Pa⁻¹ s⁻¹ ± 0.16 ns Pa⁻¹ s⁻¹ and 4.02 ns Pa⁻¹ s⁻¹ ± 0.25 ns Pa⁻¹ s⁻¹, respectively, and the molecular average is 3.74 ns Pa⁻¹ s⁻¹ ± 0.21 ns Pa⁻¹ s⁻¹. Basically this agreement indicates that the viscosity for imidazolium-based ILs at room temperature (more precisely at 293.2 K) can be determined if τ_c is known or vice versa.

Fig. 7.

Experimentally (red N1 and blue N3) and theoretically (gray and black) determined rotational correlation times (τ_c) of the [C₂C₁IM]⁺ cation versus macroscopic IL viscosity (η). [C₂C₁IM][CH₃CO₂] (◯) [C₂C₁IM][(C₂F₅)₃PF₃] (▽), [C₂C₁IM][(C₂H₅)₂PO₄] (△), [C₂C₁IM][C₂H₅SO₄] (◁), [C₂C₁IM][C₆H₁₃SO₄] (▷), [C₂C₁IM][N(CN)₂] (□), [C₂C₁IM][SCN] (◊), [C₂C₁IM][BF₄] (+), [C₂C₁IM][CF₃CO₂] (x). The gray solid and the black dashed line were calculated using Eq. (7), the η values in Table 4 and r of 0.303 nm and 0.278 nm. The blue dotted and the red dashdotted line are the regression curve. The inset shows a zoomed region of the correlation plot.

3.5. Contributions from dipolar interaction and CSA

When looking at the globally optimized parameters, it also becomes clear that the individual values of the fitted parameters for N1 and N3 are consistent within an IL. With the fitted parameters at hand we can assess the relative contributions of the various relaxation mechanisms to the overall relaxation (s. Tables S9–S10). At 40.6 MHz the ¹H-¹⁵N dipolar interaction contributes 20 % to 30 % and ¹⁵N CSA 70 % to 80 % to ¹⁵N longitudinal relaxation for ILs with proton-bearing anions and [N(CN)₂]⁻. If an additional contribution besides dipolar interaction and CSA to R₁ has to be considered, as for the ILs with ¹⁹F in the anion and [SCN]⁻, the proportion of the additional contribution is about 40 % and the contribution of ¹⁵N CSA for these ILs is only about 40 % to 50 %. At 71 MHz ¹⁵N CSA is obviously the main relaxation mechanism with the relative contribution of 70 % to 90 %. Dipolar interaction accounts for only 5 % to 10 %, and for those ILs where an additional contribution is considered, this contribution is in the range of 10 % to 25 % of the overall ¹⁵N R₁. For transverse relaxation, the contributions from ¹H-¹⁵N dipolar interaction are 2 % to 10 % at both magnetic field strengths. The contribution of ¹⁵N CSA is somewhat more heterogeneous. For the ILs with proton-bearing anions and [N(CN)₂]⁻ the contributions due to ¹⁵N CSA are 25 % to 50 % at 40.6 MHz and increase to 60 % to 90 % at 71 MHz. For the other ILs the contribution originating from ¹⁵N CSA is lower. However, for the ¹⁹F bearing ILs and [C₂C₁IM][SCN] the relative contribution to R₂ from the parameters B and C, respectively, is comparatively large (70 % to 90 % at 40.6 MHz and 50 % to 60 % at 71 MHz). This could be due to contributions to ¹⁵N relaxation from interactions with anions, which are not explicitly accounted for in our analysis.

It should be mentioned that the minimization of Eq. (6) was repeated also with reduced parameter sets (omitting B or C), but resulted in significantly worse χ² values (s. Supplementary Material).

4. Conclusions

In this study we determined and analyzed short- to medium-range ¹H-¹⁵N scalar coupling constants (^2–3J_HN) and ¹⁵N relaxation data for a number of [C₂C₁IM]⁺-based ILs with a wide range of different anions. All ILs used in our study are liquid at ambient temperature. Our results indicate that the choice of the anion has some impact on the coupling constants in the [C₂C₁IM]⁺-cation. The anionic impact on the overall molecular geometry, bond strengths, angles, and orbital character of the bonds at least for [C₂C₁IM]⁺ appears not to be completely negligible or independent from the nature of the anion. The significant variation of at least some of the ¹H-¹⁵N scalar couplings indicates a certain degree of sensitivity of the [C₂C₁IM]⁺-cation to different anions.

With the here chosen, admittedly very simplified approach and the assumptions we made (with respect to CSA and dipolar cross-correlation, axial symmetry of the ¹⁵N CSA tensor, isotropic rotational diffusion and the virtual single ¹H approximation for the dipolar coupling) the analysis of ¹⁵N relaxation data at two magnetic field strengths allowed us to determine reliably dynamic parameters of the cation from spin-relaxation measurements of the non-protonated ¹⁵N nuclei of the [C₂C₁IM]⁺ ring.

We assessed the contributions of different relaxation mechanisms to the total ¹⁵N relaxation rates. Not surprisingly, both the longitudinal and transverse relaxation are significantly determined by the ¹⁵N CSA contribution, and this influence increases with the magnetic field strength. Furthermore, the obtained τ_c values closely reflect the viscosities of the imidazolium-based ILs, which are one to two orders of magnitude higher than that of water. Taken together, our results demonstrate that the relaxation behavior of non-protonated ¹⁵N nuclei in [C₂C₁IM]⁺-based ILs, which are liquid at ambient temperature, can be adequately described and interpreted by simple and well-established models. Given the enormous range of viscosities of the ILs used (0.029 Pa s to 0.665 Pa s), it is remarkable that our simplified approach gives such reasonable values with respect to ¹⁵N CSA, rotational correlation time, and the hydrodynamic radius of the cation.

The nice linear correlation between the derived τ_c values and the viscosity of the ILs suggests that the measured ¹⁵N relaxation of the [C₂C₁IM]⁺ cation is determined by physico-chemical properties of the overall system. The choice of the anion and thus the coordinating capability determine these physico-chemical properties (e.g. viscosity).

We show here with imidazolium-based ILs, using the example of ¹⁵N, that a meaningful analysis is possible when using NMR of non-protonated hetero-nuclei. It is quite conceivable that this approach could also be applicable for the direct analysis of other non-protonated hetero-nuclei, ideally with spin 1/2. Thus, at least theoretically, ILs with non-protonated quaternary carbons, silicon^[59], rhodium^[60] or selenium^[61,62] could also be studied.

Furthermore, this approach should be applicable not only to ILs themselves but also to molecules dissolved in ILs. The direct ¹⁵N detection of molecules, enriched with ¹⁵N, dissolved in ILs, could overcome the challenges (e.g. massive solvent peaks, signal overlap, low receiver gain) posed by the high molecular concentration of ILs when studying solutes by ¹H or ¹³C NMR spectroscopy. For example, with appropriate ¹⁵N isotopic enrichment, it should be possible to study very specifically the nitrogen chemical shifts, relaxation behaviour, and finally the dynamics, of prolines in Xaa-Proline peptide bonds. This would open the possibility of a direct investigation of the cis/trans equilibrium with appropriate model peptides to further understand the alteration of cis/trans equilibrium in Xaa-Proline bonds observed in imidazolium-based ILs.^[63]