Anion dynamics and motional decoupling in a glycerol–choline chloride deep eutectic solvent studied by one- and two-dimensional ³⁵Cl NMR

Abstract

Chlorine-35 is among the few nuclides that provide an experimental handle on the anion dynamics in choline based deep eutectic solvents. By combining several nuclear magnetic resonance (NMR) techniques, the present work examines the Cl⁻ motions within glyceline, a glycerol : choline chloride 2 : 1 solution, in a large temperature range down to the glass transition temperature T_g. The applied methods include spin relaxometry, second-order line shape analysis, as well as two-dimensional central-transition exchange and stimulated-echo spectroscopy. The finding of unstructured central-transition NMR spectra characterized by a relatively small average quadrupolar coupling attests to a highly disordered, essentially nondirectional anionic coordination in glyceline. For temperatures larger than about 1.3T_g the chlorine motions are well coupled to those of the glycerol and the choline moieties. At lower temperatures the local translational anion dynamics become Arrhenian and increasingly faster than the motion of glyceline's matrix molecules. Upon further cooling, the overall ionic conductivity continues to display a super-Arrhenius behavior, implying that the choline cations rather than the Cl anions dominate the long-range charge transport also near T_g.

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1. Introduction

Deep eutectic solvents (DESs) represent an important class of materials¹ because of the many applications for which they are discussed^2–4 as well as for the scientific challenges they provide. Typical DESs are produced by mixing a hydrogen bond acceptor (HBA) with a hydrogen bond donor (HBD). Knowledge regarding the properties of the components within a given DES and the mutual interplay of all of the components forming liquids such as glyceline (a mixture of glycerol and choline chloride) is essential to achieve further progress in the field. Yet, most studies focus either on the response of the DES as a whole or on the dynamics of the HBD and/or the choline ion, while the mobility of the anion was barely addressed, so far. In fact, heretofore in DESs the Cl⁻ dynamics were probably investigated explicitly only using computer simulations.^5,6 Chlorine as a probe in nuclear magnetic resonance (NMR) experiments should definitively be useful in this context as well. However, its full potential to monitor dynamic processes in DESs remains to be explored.

As a prerequisite for an understanding of the anionic motion in DESs, knowledge regarding the local structures in which the Cl⁻ ions reside is vital. To unravel these structures, neutron diffraction, most profitably in combination with numerical simulations, has been exploited and optimized structural motifs centered about the Cl⁻ ions have been presented: examples include 1 : 2 mixtures of the HBA choline chloride with glycerol (forming glyceline),^7–9 with ethylene glycol (forming ethaline),^7,10 and urea (forming reline).^10,11

For glyceline, which is in the focus of the present study, it was reported that the Cl⁻ ions are predominantly solvated by the glycerol molecules, more precisely by the protons (H_G) of their hydroxyl groups, and to a much lesser extent by the OH_C group of the choline cations:¹² In the first correlation shell, the coordination number of the Cl⋯H_G hydrogen bonds was found to be about 2.4 and that of the Cl⋯H_C bond roughly ten times smaller. With respect to the choline moiety, in glyceline the Cl⁻ ion is obviously located in a region between the –OH_C and the –N(CH₃)₃ groups, a finding that is consistent with results from density-functional modeling¹³ and molecular dynamics simulation.¹⁴

Based not the least on neutron spin-echo experiments on glyceline which, like most of the simulations, also focus on the rather fluid and only moderately viscous regime of the DESs, it was suggested that glycerol's hydrogen-bonding network is barely disrupted by the addition of the choline moieties which rather reside in voids of the HBD network.^7,15 The function of the glycerol-solvated anions was described as mediating a bridge between choline-rich and glycerol-rich clusters.¹² Furthermore, it was suggested that the “Cl anions have a greatest correlation through ion–ion attraction with the charged choline cation N-centre rather than through hydrogen bonding to the hydroxyl moiety”.¹² This kind of chlorine coordination appears special among choline based DESs: for instance in mixtures of choline chloride and urea, the HBD⋯Cl interactions are much more prominent.^16–18

Apart from scattering techniques, also vibrational¹¹ and NMR spectroscopies allow for a selective access to the dynamics of the HBD and HBA components in DESs. To study the mobilities of these components ¹H,^19–232H,²⁴¹³C²⁵ and other nuclides²⁶ were exploited as probes. Even the ³⁵Cl nuclide (which is three times more abundant than ³⁷Cl) was already used, however, barely to unravel dynamical properties of DESs,²⁷ but mostly to monitor hydration-induced chemical shifts.^28–31 The rare exploitation of the ³⁵Cl resonance is probably due to the fact that for halide ions spin relaxation times can become fairly short (down to the μs regime).^32,33 Nevertheless, the ³⁵Cl probe was utilized³⁴ to explore static material properties for ordered crystals,^35–37 glassy crystals,³⁸ and glasses,³⁹ and for liquids as well.^40–42

For glyceline, strongly quadrupolarly perturbed spin I = 3/2 nuclei such as ³⁵Cl should be well suited to study the dynamics of the anion itself or that in its local environment. Since glyceline is glass forming, with a calorimetric glass transition at T_g = 175 K,⁴³ for its detailed study a combination of techniques is required that cover a wide range of ionic correlation times. Therefore, apart from applying spin-relaxometry and wideline spectroscopy,^44–46 that are particularly sensitive to faster motions in the nano- to microsecond range, one goal of the present study is to adapt two-dimensional central-transition slow-motion techniques for use also with the ³⁵Cl probe. Here, we have in mind the stimulated-echo methods that were developed for (other) quadrupolar nuclei in order to examine the dynamics in the milliseconds regime.^47–49

The present results regarding the dynamics of the Cl⁻ ions will be compared with the time constants reported^24,25 for the choline cations as well as for glycerol in glyceline and of course also with its overall response that has been studied over a wide dynamic range by means of dielectric spectroscopy^15,43,50 and shear rheology.⁵¹

2. Experimental details

All ³⁵Cl NMR experiments were carried using a Bruker Avance III spectrometer working at 39.2 MHz with an estimated dead time of about 15 μs. The ³⁵Cl frequencies are referenced with respect to a 0.1 M solution of NaCl in D₂O. The π/2 pulse length for the central-transition excitation was 6.3 to 7.0 μs. Proton decoupling usually showed no discernible effect on the spectra and therefore was not applied, unless noted otherwise. We study 33 mol% methyl deuterated choline chloride (ChCl-d₉) in protonated glycerol, here simply called glyceline (or glyceline-d₉ in previous work).²⁴

For T > 300 K, the spectra were directly obtained from the free-induction decay, otherwise a π/2 − π sequence was used. For the processing of the ³⁵Cl spectra we applied a Gaussian apodization with a spectral width of 0.1 kHz for T > 302 K, of 1 kHz for 202 and 196 K, and otherwise of 0.5 kHz. Details regarding the two-dimensional ³⁵Cl NMR carried out in the frequency and in the time domains will be given in Section 3.C, below.

Additionally, deuteron stimulated-echo experiments were performed using a home-built spectrometer operated at 45.6 MHz on glyceline-d₄ (featuring alkyl deuterated choline chloride, ChCl-d₄) and glyceline-d₅ (featuring glycerol-d₅) for which ²H spin relaxation times were reported in ref. 24.

3. Results and analyses

A. Temperature dependent ³⁵Cl spectra

In Fig. 1 we present ³⁵Cl spectra recorded for glyceline. Near 330 K where, e.g., from dielectric measurements,⁴³ the glyceline dynamics is expected to be much faster than the present ³⁵Cl Larmor frequency, the narrow absorption line is centered at 0.87 kHz (22 ppm). The motionally fully narrowed line, which comprises the magnetization of the central +1/2 ↔ −1/2 transition and of the satellite ±1/2 ↔ ±3/2 transitions, broadens significantly as the sample is cooled closer to room temperature. Then, below about 280 K, the appearance of very short spin relaxation times (see Section 3.B) hampers the data acquisition.

Fig. 1 ³⁵Cl spectra of glyceline as measured for a range of temperatures are shown as solid lines. The vertical lines and the arrows mark a line shift of about 10.6 ± 0.3 kHz. The dashed line represents the Czjzek model, see eqn (1), and is calculated using σ_Cz = 0.85 MHz and a 2 kHz Gaussian apodization.

Only near 240 K it became possible again to record spectra. The arrows in Fig. 1 indicate that these have undergone a pronounced shift with respect to their high-temperature position. Below ≈240 K the spectra, now reflecting only the central +1/2 ↔ −1/2 transition of the ³⁵Cl nucleus, eventually broaden significantly and develop an asymmetric shape. At the lowest temperature reached in the present work the spectrum exhibits a central second moment M₂ of about (2π × 12.5 kHz)².

Broad, essentially featureless asymmetric lines of the type seen in Fig. 1 are characteristic for quadrupolar nuclei in strongly disordered environments.⁵² In this situation, the components |V_ZZ| ≥ |V_YY| ≥ |V_XX| of the electrical field gradient (EFG) tensor at the nuclear site are typically subject to considerable disorder. Thus, a large variation of the quadrupolar coupling constant C_Q = eQV_ZZ/h and of the asymmetry parameter η = (V_XX − V_YY)/V_ZZ arises.^53–56 For I = 3/2 nuclei such as chlorine-35, C_Q is related to the quadrupolar frequency via ν_Q = C_Q/2. In the limit of so called Gaussian disorder where all tensor elements are characterized by the same variance, the Czjzek model can be derived which involves a bivariate frequency distribution^57–61

Here, the standard deviation σ_Cz is related to the mean squared quadrupolar product via⁵⁹

〈C_Qη²〉 = 〈C_Q²(1 + η²/3)〉 = 20σ_Cz² (2)

Thus, the quadrupolar product can be estimated by comparing the low-temperature line shape with numerical simulations. The latter were generated on the basis of eqn (1) by performing powder averages over all available second-order quadrupolar frequencies and asymmetry parameters, as described previously.⁴⁸ In Fig. 1 we add the result for σ_Cz = 0.85 MHz as dashed line. Further calculations are shown in Fig. S1 of the ESI.† Obviously, the computed spectra included in Fig. 1 capture the overall features of the experimentally determined low-temperature line shape, but a close inspection reveals deviations in particular on the left hand side of the spectra. Nevertheless, the calculations may serve as a rough estimate for the root mean square quadrupolar product for which eqn (2) yields 3.8 MHz.

From the spectra measured on both sides of the 240 to 280 K interval, in which spectra could not be recorded, one recognizes that that their center of gravity has shifted considerably. This so-called dynamic frequency shift or quadrupolar induced shift, which can be related to the imaginary part of the spectral density function,⁶² is well-known for halfinteger quadrupolar nuclei.^63–69 Towards low temperatures the NMR line seemingly returns back to its high-temperature position (in fact only the peak absorption does). This observation is similar to that reported for other strongly quadrupolarly perturbed nuclei in disordered materials.⁴⁸ There, this phenomenon was rationalized by noting that for the asymmetric Czjzek line shape the peak frequency does not agree with its center of gravity. Further analyses of the second-order central-transition ³⁵Cl line shapes, in particular of their widths are provided in the following.

B. Spin relaxation

To be sensitive to the fluctuations of the anionic resonance frequencies, we measured the decay of the ³⁵Cl longitudinal magnetization M_z using inversion recovery. The transversal dephasing M_xy was recorded by employing a π/2 − t − π sequence as a function of the pulse separation t. The resulting magnetization curves were fitted by stretched exponential functions or, for very short transversal dephasing, by an exponential function to obtain spin–lattice relaxation times T₁ and spin–spin relaxation times T₂.

The temperature dependence of glyceline's ³⁵Cl spin-relaxation times is presented in Fig. 2. At temperatures larger than corresponding to the (unobserved) minima of the spin relaxation times we find T₁ ≈ T₂, demonstrating that the motional correlation times are shorter than the inverse Larmor frequency, i.e., short on the nanosecond scale. With the spin relaxation times turning comparable to or even shorter than the spectrometer dead time, measurements could not be carried out in the regime near the expected T₁ and T₂ (global) minima. Below this gap, T₁ increases in a monotonic fashion, while T₂ displays a maximum near 225 K and a minimum near 210 K before it tends to saturate towards a low-temperature value near about 470 μs. This value can be compared to the inverse of the largest heteronuclear dipolar coupling of ³⁵Cl. Taking the shortest Cl–H distance, r_Cl–H ≈ 2.1 Å, reported for glyceline,¹² from one has v_D ≈ 1.3 kHz as a measure of the dipolar frequency scale.

Fig. 2 Chlorine-35 spin–lattice relaxation times T₁ (red triangles) and spin–spin relaxation times T₂ (green dots) of glyceline measured at 39.2 MHz. The red solid line for T₁ is calculated using eqn (3) and the green dashed line for T₂ is calculated using eqn (8). The green plusses (+) refer to the effective transversal dephasing time as obtained from the ³⁵Cl spectral width Δν_1/2. For comparison as blue dash-dotted line we added the fit to the deuteron T₁ times, measured at a 45.6 MHz, that relate to alkyl chain deuterated glyceline-d₄.²⁴ This fit is based on eqn (7) in conjunction with the timescale parameters given in ref. 24 for T > 220 K, i.e., τ_∞ = 2 × 10⁻¹³ s, D = 7.75, and T₀ = 153 K. To achieve an approximate overlap of the spin relaxation times at high temperatures, the values relating to the ²H fit curve were divided by a factor of 280. This number reflects primarily the different ²H and ³⁵Cl quadrupolar couplings.

Fig. 2 also includes the temperature dependent full line widths at half maximum, Δν_1/2(T), in the form of the effective transversal dephasing times . Interestingly, below about 200 K, continues to be somewhat T dependent. Thus, although barely visible from Fig. 1, the line width broadens slightly upon cooling in this range, obviously reflecting the freeze-out of librational motions on the μs scale. Eventually, at sufficiently low temperatures is governed by a broad, essentially static distribution of (quadrupolar) precession frequencies. Using the π/2 − t − π sequence a refocusing is achieved for the T₂ measurements and thus one has in the low-temperature regime.

As soon as motional processes come into play, the fluctuations of the large quadrupolar interactions govern the spin relaxation at the chlorine site. Hence, in good approximation the spin–lattice relaxation time can be described by⁷⁰

Analogously, the spin–spin relaxation time, describing the transversal dephasing after exciting the central +1/2 ↔ −1/2 transition, can be written as⁷⁵

1/T₂ = K_Q²[J(ω_L) + J(2ω_L)]. (4)

Here, relates to the fluctuating part of the quadrupolar product. Furthermore, J(ω) denotes the spectral density which is a measure for the fluctuation probability of the quadrupolar frequency at the chlorine site on the scale of the Larmor frequency. In the presence of a unique correlation time τ_c, the spectral density⁷¹

J(ω) = τ_c/[1 + (ωτ_c)₂], (5)

given by Bloembergen, Purcell, and Pound (BPP) results. If a distribution of correlation times is present, a Cole–Davidson spectral density⁷²is often useful. Here, the parameter β_CD < 1 governs the width of the τ_c distribution. Note that for ωτ_c ≪ 1, eqn (6) yields J_CD(0) = β_CDτ_c.

In glassforming materials the temperature dependent correlation times τ_c often obey the Vogel–Fulcher law

τ_c = τ_∞ exp[DT₀/(T − T₀)] (7)

and this also applies to glyceline.^24,43Eqn (7) involves the divergence temperature T₀, Angell's strength parameter D,⁷³ and a pre-exponential factor τ_∞. Thus, combining eqn (7) with eqn (4) and (5), which accounts for the time dependent fluctuations of the first-order quadrupolar interaction, (global) minima in T₁ and T₂ are expected to arise at roughly the same temperature, see the solid and dashed lines, respectively, in Fig. 2. Due to the large quadrupolar product estimated in Section 3.A for ³⁵Cl in glyceline, the minima of the very short spin relaxation times are obviously too small for us to be observable.

Note that in Fig. 2 the lines for the description of the ³⁵Cl spin relaxation times are calculated using K_Q = 6.5 × 10⁶ s⁻¹ (corresponding to ) and an exponent β_CD = 0.38 (close to the exponent reported on the basis of the ²H spin relaxation times²⁴). Furthermore, also the timescale parameters, for convenience reproduced in the caption of Fig. 2, are those used in ref. 24. One notes that the (fluctuating part of the) root mean square quadrupolar product given here differs somewhat from extracted on the basis of the spectra shown in Fig. 1. Part of this discrepancy certainly stems from the fact, that the spectral shape implied by eqn (1) does not fully match the measured one.

To obtain the dashed (T₂) line shown in Fig. 2, another effect was taken into account: When the correlation times τ_c are shorter than 1/ω_L (≈ 1 ns) fluctuations of the second-order quadrupolar interaction can become relevant. Thus, down to timescales of 1/(2πM₂^1/2) ≈ 6.4 μs rather than eqn (4), the central-transition spin–spin relaxation time has to be written as^74–76

instead. For β_CD = 1 this expression predicts a local maximum in T₂ to occur when⁴⁵. Similar to ref. 77, for β_CD = 0.38 the value numerically obtained (see Fig. S2 of the ESI†) from eqn (8) is τ_c ≈ 2.5 μs. For I = 3/2 nuclei it has been pointed out that at somewhat lower temperatures a local T₂ minimum appears near the onset of motional narrowing. At this point the corresponding motional correlation time can be estimated from⁴⁵

τ_c ≈ 1/(2.56M₂^1/2). (9)

Using the square root of the experimentally determined low-temperature second moment, cf.Fig. 1, one arrives at τ_c ≈ 5 μs. These time scales as well as those inferred froma relation which in the extreme narrowing regime results from eqn (3) and (5), will be compiled in Section 4, below.

C. Stimulated ³⁵Cl echoes and 2D exchange spectra

Ultraslow anionic motions referring to correlation times in the milliseconds regime are accessible using two-dimensional spectroscopy. Corresponding measurements can be carried out in the time domain using stimulated echoes or in the frequency domain using exchange spectroscopy. Since presently we exploit quadrupolar central-transition frequencies, in both cases it is essential to utilize appropriately phase cycled three- (or more) pulse sequences, to generate central-transition signals of the form⁷⁸andIf signal maximizing radio-frequency pulses are employed, for I = 3/2 nuclei the amplitude prefactors are s_3/2 = c_3/2 = 1/5.⁴⁷ Suitably Fourier transforming the signals that appear in eqn (11) with respect to the evolution time t₁ and the detection time t₂ one can produce purely absorptive 2D exchange spectra for fixed mixing times t_m. This technique has been demonstrated for a range of halfinteger quadrupolar nuclei including ¹¹B, ¹⁷O, and ⁸⁷Rb.^49,79,80 For ³⁵Cl, obviously only 2D spectroscopy in the absence of an external static magnetic field has been performed, so far.^81–83

To acquire two-dimensional ³⁵Cl central-transition NMR spectra for glyceline we employed a five-pulse sequence,⁸⁴ thereby generating the signals summarized in eqn (11). The echo delays between the first and the second and the fourth and the fifth pulse were fixed to 10 and 35 μs, respectively. For the spectra shown in Fig. 3 we collected (a) 160 × 512 data points and co-added 240 scans (25 W continuous-wave proton decoupling, Rabi frequency 10.5 kHz), (b) 128 × 8192 points (16384 scans, no decoupling), and (c) 208 × 8192 points (32768 scans, no decoupling). The t₁ increment was 1 μs and the t₂ increment was 4 μs. After symmetrization and zero filling to 2048 × 8192 points a Gaussian apodization of 2 kHz was applied. Due to the short ³⁵Cl T₁ times relative to the correlation times τ_c and the constraints imposed also by T₂ we were unable to record an initial-state (=diagonal) and a final-state (t_m ≫ τ_c) two-dimensional spectrum at the same temperature.

Fig. 3 Two-dimensional ³⁵Cl central-transition exchange spectra recorded for (a) a mixing time t_m = 10 ms at 151 K, (b) t_m = 10 μs at 186 K, and (c) t_m = 5 ms at 186 K.

Therefore, as Fig. 3(a) we show a diagonal low-temperature spectrum which documents the absence of any translational ionic hops. The spectrum recorded at the higher temperature, see Fig. 3(b), reveals the presence of some exchange processes, although it is collected for a very short mixing time t_m = 10 μs. From the two-dimensional spectrum measured at 186 K for a much longer mixing times of 5 ms, one recognizes that the spectral intensity has spread out much more into the exchange plane, cf.Fig. 3(c). These somewhat time consuming experiments are helpful in order to demonstrate that at the higher temperature the Cl⁻ ions are mobile on the millisecond time scale. However, these spectra are less suited to retrieve quantitative information.

Alternatively, rather than recording two-dimensional spectra in the frequency domain, in the time domain one can monitor the decay of the F₂ signals as a function of t_m for fixed t_p = t₁ = t₂. This way, eqn (11) yields correlation functions that characterize the motionally induced changes of the local ³⁵Cl precession frequencies ω(t) directly.

For glyceline corresponding stimulated ³⁵Cl echo measurements, with the evolution time set to 25 μs, are presented in Fig. 4. For lower temperatures more slowly decaying anionic correlation functions are observed. To extract the correlation times τ_c and other parameters, the measured signals S₂(t_m) are written as F₂(t_m)M_z(t_m). For the analysis, the parameters entering the longitudinal magnetization M_z(t_m) are taken from independent T₁ measurements, cf. the arrows in Fig. 4. This accounts for the fact that also spin–lattice relaxation takes place during t_m. The F₂(t_m) part which reflects the motion-induced correlation decay, in practical terms, is written here as a normalized Kohlrausch function

From least-square fits the motional time constant τ_c, the stretching parameter β_2,Cl, and the final-state amplitude Z can be obtained. In the first round of fitting, the Kohlrausch exponent β_2,Cl displayed some scatter and in the second round we fixed it to 0.39, its average value. This parameter indicates a wide distribution of Cl⁻ hopping times which in turn reflect the heterogeneity in the anionic environments within glyceline. While the hopping of the ³⁵Cl ions governs the decay of the Kohlrausch term in eqn (12), the final-state amplitude Z can be viewed as a measure for the fraction of anions which have not jumped during t_m. This immobile (on the scale set by τ* ≈ t_p) fraction of anions increases from zero near 195 K to about 0.5 at 175 K, see Fig. S3 of the ESI.† In Section 4, below, the temperature dependence of the resulting time constants τ_c will be discussed together with those determined using the other NMR techniques applied in the present work.

Fig. 4 Temperature dependent ³⁵Cl stimulated-echo amplitudes measured for glyceline. Based on eqn (12), the solid and dashed lines are fits to the normalized cos-cos and sin-sin amplitudes, respectively. The arrows indicate the 1/e decay times of the normalized longitudinal magnetization recoveries M_z(t_m).

For comparison of the ³⁵Cl based time scales with those on which the HBA and HBD components move, we performed deuteron stimulated-echo experiments for glyceline-d₄ and for glyceline-d₅. Such experiments yield signals of the form given by eqn (11), however, with s₁ = 3/4 and c₁ = 1.⁸⁵ Since the main focus of the present work is on the ³⁵Cl resonance, we provide the ²H stimulated-echo decay data (recorded for t_p = 20 μs) as Fig. S4 of the ESI.† The results from the analysis of these data, again carried out in terms of eqn (12), are compiled together with the ³⁵Cl based time scales in Section 4, below.

4. Discussion

The Arrhenius plot shown as Fig. 5 compiles the anionic correlation times that we detected using ³⁵Cl spin relaxometry and stimulated-echo spectroscopy and compares these time scales with results from dielectric relaxation spectroscopy,⁴³ shear rheology,⁵¹ and ²H NMR.²⁴ For temperatures larger than about 280 K it is seen that by and large all time scales follow the same overall Vogel–Fulcher type of behavior. However, starting from the high-T regime, the Cl⁻ motion appears to be slightly faster as compared to that of the HBD molecules (as measured for glycerol in glyceline-d₅) and of the HBA cations (as measured for choline in glyceline-d₄).²⁴

Fig. 5 Time constants for glyceline from measurements of the dielectric constant ε⁴³ and the shear compliance J⁵¹ as well as from ²H-T₁²⁴ experiments are compared with the data from the present work: These include the ³⁵Cl based correlation times from eqn (10) and (12), from the measured T₂ minimum, see eqn (9), and maximum, see below eqn (8), as well as those obtained after rescaling (see text) from stimulated deuteron echo spectroscopy, see Fig. S4 of the ESI.† The dash-dotted line represents eqn (7) using the parameters listed in the caption of Fig. 2. As a guide to the eye, the dashed line connects data obtained from the ³⁵Cl spin relaxation times. The solid line reflects an Arrhenius law, eqn (13), with τ_∞,Cl = 3 × 10⁻¹⁸ s and E_Cl = 5150 K. The yellow dotted line marks an effective low-temperature energy barrier E_eff,Ch = 14 900 K that is introduced here for later analyses.

At first glance, the temperature dependence of the ³⁵Cl spin-relaxation times, see Fig. 2, is reminiscent of that previously measured using ²H NMR.²⁴ Despite the similar temperature dependence of ²H and ³⁵Cl based correlation times for T > 280 K, it has to be emphasized that the two nuclei are sensitive to rather different dynamical processes. The deuteron frequencies probe the reorientational motion of the C–D bonds in the glycerol molecules or in the choline cations.

Conversely, judged from their relatively small ³⁵Cl quadrupolar coupling constant (on the 67.6 MHz scale set by the covalently bonded HCl molecules),^86,87 in glyceline the Cl⁻ anions with their almost 100% ionicity cannot directly be sensitive to reorientational motions. Rather they can sense the motions of the (partially) charged moieties in their immediate environments. Here, for the mobile anions two limiting scenarios can be envisioned: (1) Assuming that the Cl⁻ ions hop (translationally and “actively”) from site to site, each time into a completely different charge environment, their field gradient tensor and thus their local precession frequencies are expected⁸⁸ to display significant, i.e., relatively large jumps. The other scenario assumes that (2) at a spatially fixed Cl⁻ ion site the motion of the (partial) charges δq in its vicinity changes the EFG experienced by that nuclear probe. The magnitude of the EFG is ∝|δq|/r³, so that for scenario (2) the motions of glycerol's hydroxyl groups (with the H_G protons carrying a partial charge |δq| = 0.39e at a distance of r_Cl–H ≈ 2.1 Å),¹² govern the (“passive”) fluctuations of the quadrupolar frequency at the Cl⁻ site. It is highly improbable that all of the 2 to 3 Cl⋯H_G hydrogen bonds which coordinate each Cl⁻ ion move simultaneously. Therefore, within scenario (2) the frequency jumps experienced by the mobile Cl⁻ ions should be smaller than for scenario (1).

The approximate coupling of the anionic and the other time scales that we observe in the fluid and the moderately viscous regimes of glyceline favor a mixture of scenarios (1) and (2). Thus, like for many other weakly supercooled liquids,^89–92 the rotational and translational motions appear to be intimately coupled at high temperatures. Also, force field based calculations carried out near room temperature for glyceline (and ethaline),^5,6 show that for all three components (HBA, HBD, and chlorine) the self-diffusion coefficients agree within a factor of about 2 (with the cation diffusing slightly faster than the anion which in turn displays a diffusion coefficient similar to that of the HBD).

However, below about 230 K which corresponds to about 1.3T_g (also like for other glass formers),^89,90 from Fig. 5 the situation is seen to change qualitatively. While the motion of the glycerol and the choline components continue their Vogel–Fulcher type of slowdown, the temperature dependence of the Cl⁻ ion dynamics turns over to a less steep behavior. Here, the time constants follows an Arrhenius law

τ_c = τ_∞,Cl exp(E_Cl/T). (13)

involving the energy barrier E_Cl (in temperature units) and the pre-exponential factor τ_∞,Cl. Consequently, in the deeply supercooled regime the glyceline matrix is practically rigid on the time on which the Cl⁻ ions move through it.

Thus clearly, in the low-temperature range scenario (1) is applicable: Here, at the Cl⁻ sites, the local precession frequencies are “actively” modulated in large steps by translational hops of the mobile anions. In this scenario and in harmony with findings regarding the ionic hops in a molten salt,⁴⁸ the stimulated-echo functions should barely depend on the evolution time.⁹³ This situation is to be distinguished from that known for the reorientational molecular motion near the glass transition temperature of low-molecular weight glass formers:⁹⁴ Here, the deuteron F₂ functions typically display a strong t_p dependence so that the rotational correlation functions (i.e., the t_p → 0 limit of Legendre polynomial rank l = 2 functions) can be a factor of 5 to 10 faster than for t_p = 20 μs. For comparison of the dielectric (rank l = 1) with the time scales detected by NMR, and depending on the motional model, an additional factor of 1 to 3 can be required to achieve overlap of the deuteron echo time scales with the dielectric ones.⁹⁵ In harmony with these expectations, from Fig. 5 one recognizes that an overall factor of 8, applied to the deuteron stimulated-echo times, aligns all of the matrix correlation times.

At first, the finding of a decoupled ³⁵Cl motion may appear unexpected because the temperature dependence of the overall electrical conductivity (to which obviously also the choline ions contribute) parallels the correlation times determined for the matrix moieties.⁵¹ However, one has to realize that the ³⁵Cl stimulated-echo functions probe the elementary step of the translational dynamics. And with scenario (1) being prevalent, a single step is sufficient to lead to a complete decay of the ³⁵Cl F₂ function. Hence, it appears likely that the translational motion of the mobile Cl ions is of a spatially localized nature (e.g., taking place within a clustered structure) or is highly obstructed.

In addition, as signified by the final-state amplitude Z, the fraction of immobile anions increases upon cooling. From the temperature T_1/2 ≈ 175 K at which Z is about 0.5, see Fig. S3 (ESI†), the (mean) energy barrier against Cl⁻ hopping can be assessed. Following the analysis applied for other ion conducting materials,^96–98E_mean can be inferred from the Arrhenius law written as E_mean = T_1/2ln(τ*/τ_∞,Cl). Using τ* = 25 μs and τ_∞,Cl, see the caption of Fig. 5 we find E_mean = 5200 ± 450 K. This barrier is close to E_Cl = 5150 K as determined directly from the correlation times shown in Fig. 5. Yet, another independent estimate for the energy barrier is possible: Within the framework of the coupling model, based on the (energy barrier E_p of the) so called primitive or elementary relaxation, the (energy barrier E_c of the) coupled process is obtained.⁹⁹ This approach predicts that E_p/E_c = β₂. Identifying E_p with E_Cl and E_c with E_eff,Ch, the ratio of the corresponding energy barriers (for their values and how they are determined, see the caption of Fig. 5) yields β₂ = 0.35 ± 0.04. This exponent compares favorably with the stretching parameter describing the stimulated-echo decays measured for the cations (β_2,Ch = 0.34, see Fig. S4, ESI†) and for the anions (β_2,Cl = 0.39, see Section 3.C). Thus, consistent values for the activation energy describing the anionic hopping in the low-temperature regime are arrived at by pursuing several independent routes.

The decoupling of the anionic dynamics from that of the glyceline matrix may appear somewhat surprising. However, one has to realize that similar dynamic decoupling phenomena are in fact well known for a wide range of highly concentrated ion conducting materials.^100–103 To conclude this section, we wish to emphasize that the two-dimensional and two-time ³⁵Cl NMR methodology applied and refined in the present work should be useful for future studies of motional processes. This includes not only further DESs, but systems such as ZnCl₂ or other chlorides either in molten salts, in ionic liquids, and in aqueous solutions as well.^104–106

5. Conclusions

With the goal to unravel the anion dynamics in glyceline, the present work exploits ³⁵Cl NMR, an approach which has barely been applied to DESs and other liquids in their highly viscous states. First, we examined the thermal evolution of the absorption spectra. Their widths, like those of the spin–spin relaxation times display the non-monotonous temperature dependence expected for nuclei that are predominantly subjected to second-order quadrupolar interactions. Furthermore, the line shape analysis revealed the nondirectional bonding character at the site of the anions. By combining the results from the spin relaxation times with those from two-dimensional exchange spectra and stimulated-echo decays, the chlorine mobility could be explored over wide dynamic and temperature ranges. We found that above about 230 K, the dynamics of the chlorine ions basically trace those of glyceline's matrix components, i.e., of glycerol and choline. Then, below about 1.3T_g, a motional decoupling is observed. Here, the local ³⁵Cl precession frequencies are modulated by translational jumps of the mobile chlorine ions, which become increasingly slower than those of the matrix species. Nevertheless, the comparison of the vastly different anionic and cationic mobilities, in the low-temperature range following an Arrhenius and a super-Arrhenius behavior, respectively, demonstrates that the choline molecular ions continue to dominate the overall electrical conductivity. The finding that the much larger cationic rather than the smaller anionic species governs the charge transport, can be rationalized in a scenario in which the chlorine ions perform a localized or otherwise highly obstructed type of motion. Taken together, with the previous and current results from deuteron NMR and based on the component-selective detection that we have exploited, the present work provides important insights regarding the motional interplay of all of the three species forming the deep eutectic glyceline solvent.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was financially supported by the Deutsche Forschungsgemeinschaft under project no. 444797029.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp03668e

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