Combining results from impedance spectroscopy and oscillatory shear rheology, the present work focuses on the relation between the mass and charge flows and on how these are affected by the H-bonding in viscous ionic liquids (ILs). In particular, we compare the relaxational behaviors of the paradigmatic IL 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM-TFSI) and its OH-functionalized counterpart 1-(2-hydroxyethyl)-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (OHEMIM-TFSI). Our results and their analysis demonstrate that the presence of cationic OH-groups bears a strong impact on the overall dynamics of OHEMIM-TFSI, although no signatures of suprastructural relaxation modes could be identified in their dielectric and mechanical responses. To check whether at the origin of this strong variation is the H-bonding or merely the difference between the corresponding cation sizes (controlling both the hydrodynamic volume and the inter-charge distance), the present study includes 1-propyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (PMIM-TFSI), mixtures of EMIM-TFSI and PMIM-TFSI with lithium bis(trifluoromethylsulfonyl)imide (Li-TFSI), and mixtures of OHEMIM-TFSI with PMIM-TFSI. Their investigation clearly reveals that the dynamical changes induced by H-bonding are significantly larger than those that can be attributed to the change in the ion size. Moreover, in the mixtures of OHEMIM-TFSI with PMIM-TFSI, a dilution of the OH-groups leads to strong deviations from ideal mixing behavior, thus highlighting the common phenomenological ground of hydroxy-functionalized ILs and other H-bonded liquids.
Ionic liquids (ILs) contain anions and cations only and, therefore, can be regarded as molten salts.1,2 At ambient conditions, their high charge carrier density combined with fast liquid-like structural rearrangements enables one of the most efficient charge transport mechanisms among the different classes of ion conductors.3,4 The combination of high electric conductivity, large chemical variability, negligible vapor pressure, low melting point, ability of glass formation, and high thermal stability renders ILs highly attractive for both fundamental and applied research.5–8
The macroscopic behavior of these liquids has been thoroughly investigated using a wide range of techniques with the main focus on their room-temperature characteristics such as their solubility in other fluids,9 electrical10,11 and thermal conductivities,12 density,13,14 diffusivity,15 and viscosity.13,16 Their ability to circumvent crystallization provides experimental access also to their viscous regime, making these liquids model systems for the study of the glass transition. Such low-temperature studies recently led to the identification of the dielectric and mechanical signatures of supramolecular aggregates in several ILs and their mixtures17 and to the development of new concepts regarding their charge transport mechanism18–20 and the relationship between their translational and orientational degrees of freedom.21
Despite all these experimental efforts, the connection of various observables and transport phenomena with the microscopic structure and the local rearrangement of the molecular constituents of ILs remains highly controversial. In particular, disentangling the different contributions to their complex energy landscape is essential for their physical understanding. The subtle mélange of Coulombic and dispersion forces complicates this situation already.22 However, from analyses of melting points, enthalpies of vaporization,23 and the ability to form supramolecular networks when mixed with other associating liquids,24–26 the notion emerged that hydrogen bonding must additionally be taken into consideration.27,28 In this respect, a plethora of recent experimental investigations, based on infrared (IR) and THz spectroscopies, computer simulations, x-ray diffraction, and nuclear magnetic resonance (NMR),29 provide clear evidence for the existence of H-bonds in many ILs and their crystalline counterparts.30–33
In these studies, mostly performed at room temperature, considerable efforts have been undertaken to investigate H-bonding in imidazolium-based ionic liquids.34,35 Several experimental observations obtained from structural studies of this particular class of ILs have been attributed to the prevalence of H-bonding interactions. Their fingerprints include unusually close proximities of the anions to the C–H groups of the cations, the red shift of the IR-active C–H stretching modes, and the reduction in the NMR chemical shift of the carboxyl protons.36,37 Consequently, pure imidazolium ILs have been regarded as supramolecular polymers38 with a self-organized structure similar to that of other H-bonded (non-ionic) materials.
With respect to the Coulombic and dispersion interactions controlled by interionic distances and molecular configurations, the degree of H-bonding is sensitive to the type and number density of the atoms that are able to form H-bonds.39 Since the latter affects the ion pairing propensity and, thus, the structure of ILs, it is natural to consider that it also impacts on the local and global dynamics of these liquids and on the rates of the chemical reactions in which they might get involved. Therefore, a rationalization of these effects could significantly expand the applicability range of ILs. A two-step strategy can be devised in this direction: First, one may enhance the influence of H-bonding in these materials by functionalizing their molecular constituents with associating groups such as the hydroxyl moieties.40 In a second step, one may vary the magnitude of the newly introduced effects using several different physical variables: According to previous studies of “classical” H-bonded liquids such as monohydroxy alcohols,41 the variation of temperature,42,43 pressure,44,45 and concentration46,47 is very effective in modifying the fabric of the existing H-bonded networks.
The present work takes the first steps in this direction and reports on the change in the dielectric and rheological responses triggered by the OH-functionalization of an imidazolium-based IL. We note that the structural properties of OH-functionalized piperidinium- and pyridinium-based ILs have recently attracted particular attention. Several works demonstrated (somehow counterintuitively) that not only the cation–anion- but also the cation–cation-clustering induced by H-bonding plays a major role for the structural organization and the crystallization tendency of these liquids.48–53 Striving for a maximum impact of H-bonding, the liquids chosen here are EMIM-TFSI, exhibiting the smallest cationic alkyl chain (hence, the smallest cation size) among the asymmetrical imidazolium-based aprotic ILs, and its structurally modified counterpart OHEMIM. Moreover, the present investigation focuses on the deeply supercooled regimes of these liquids since, at low temperatures, the fraction of H-bonding species is certainly higher than in the highly fluid regime.54
The current results of EMIM-TFSI nicely complement those previously reported for other imidazolium-based ILs,19 while we find significant differences regarding the properties of OHEMIM. To enable a clear-cut interpretation of the experimental observations, we also studied the viscoelastic response of PMIM-TFSI, the dielectric response of the OHEMIM-TFSI mixed with PMIM-TFSI, and the dielectric and mechanical responses of EMIM-TFSI and PMIM-TFSI mixed with Li-TFSI. All experimental results have been analyzed using recently introduced procedures, which provide access to important hydrodynamic parameters and to the relationship between the structural and the charge rearrangements in these materials. Most importantly, our results clearly demonstrate that H-bonding plays a major role for the dynamics of OH-functionalized ILs and can be technologically exploited to significantly tune the viscoelastic and conductivity behaviors of viscous ionic liquids.
II. EXPERIMENTAL DETAILS
The chemical structures of the cations and the anion entering the composition of the presently studied ILs are shown in Fig. 1.
PMIM-TFSI (purity 98%+) has been purchased from Merck KGaA and Li-TFSI (purity 99%+) from 3M GmbH. EMIM-TFSI and OHEMIM-TFSI were synthesized at QUILL (Queen’s University Ionic Liquid Laboratories, Belfast UK) by following a two-step methodology mimicking those reported in the literature55,56 and exemplified therein for the case of OHEMIM-TFSI. First, for the preparation of 1-(2-hydroxyethyl)-3-methylimidazolium chloride, a mixture of N-methylimidazole (12.32 g, 0.15 mol) and 2-chloroethanol (12.08 g, 0.15 mol) was placed in a Parr autoclave sealed reaction vessel along with 50 cm3 of HPLC grade acetonitrile. The reaction mixture was heated up to 70 °C and then held at this temperature for 24 h while stirring at 500 rpm. After cooling of the reaction mixture, acetonitrile was removed under vacuum. Then, a solution of Li-TFSI (28.71 g, 0.1 mol) in ultrapure water (100 cm3) was added dropwise to a rapidly stirred solution of 1-(2-hydroxyethyl)-3-methylimidazolium chloride (15.44 g, 0.095 mol) in dichloromethane (50 cm3) and stirred overnight under ambient conditions. The organic layer was then extracted and washed with ultrapure water (100 cm3) five times. The organic layer was then dried under vacuum.
All the anhydrous solvents used for the synthesis of EMIM-TFSI and OHEMIM-TFSI, such as N-methylimidazole (purity 99%+), bromoethane (99%+), 2-chloroethanol (99%+), dimethyl sulfoxide-d6 (99%+, with 99.96 at. % D), acetonitrile (99.9%+), ethyl acetate (99.8%), and dichloromethane (99.8%+), have been supplied by Sigma-Aldrich and used as received. The ultrapure water (18.2 MΩ cm) was freshly obtained from a Milli-QTM water purification system.
The purities of EMIM-TFSI and OHEMIM-TFSI were estimated based on microanalysis as well as by NMR. The lithium content was determined by inductively coupled plasma optical emission spectroscopy (ICP-OES) on an Agilent 5100 ICP-OES, along with microanalysis performed by Analytical Services at Queen’s University, Belfast. The 1H and 13C NMR spectra were recorded at 293 K on a Bruker Avance DPX spectrometer at 300 MHz and 75 MHz, respectively, and the chemical shifts are given in the ppm downfield in Appendix A. The water content in the dried ILs was determined by Karl Fischer titration using an 899 Coulometer from Metrohm. The water level after drying in each IL was below 50 ppm. The Li content was close to 4 ppm and 15 ppm in EMIM-TFSI and OHEMIM-TFSI, respectively. In each case, the halide content, such as Br (EMIM-TFSI) and Cl (OHEMIM-TFSI), was below the detectable limit by AgNO3 testing and thus lower than 10 ppm.
Prior to preparing the mixtures and to performing the experiments, the neat liquids were dried in a vacuum oven for at least 12 h at 80 °C. Thereafter, PMIM-TFSI, EOHMIM-TFSI, and their mixtures with Li-TFSI could be supercooled using moderate cooling rates (of typically 10 K/min). However, even after extensive vacuum drying, EMIM-TFSI still exhibited a strong tendency of crystallization. This may explain why the viscous regime of this liquid has not been investigated so far. To further lower the amount of its impurities and, thus, of potential nucleation centers, this liquid was degassed via a freeze–thaw–pump procedure: The sample, placed in a glass tube, is solidified under liquid nitrogen. The tube is then vacuum-pumped so that after removing it from the Dewar flask, the thawing sample releases gas bubbles. The quenching and warming up cycle is repeated until no (visible) gas bubbles are longer released. The degassed EMIM-TFSI material did not crystallize and, therefore, could be investigated dielectrically.
The glass transition temperature Tg of OHEMIM-TFSI has been estimated to be 191 ± 2 K based on measurements performed with a Q2000 differential scanning calorimeter from TA Instruments. This value has been determined from the onset of the endothermic step on heating with 10 K/min, and the corresponding thermogram is presented in Appendix B.
The dielectric experiments were conducted via an Alpha Analyzer and a Quattro temperature controller from Novocontrol. The samples were placed in spacer-free cells consisting of two parallel plates, 18 mm in diameter and separated by 0.1 mm or by 2.3 mm. The larger spacing, providing a larger impedance of the sample cell, was used to investigate the OHEMIM-TFSI and EMIM-TFSI liquids that are highly conductive at high temperatures. During the acquisition of the spectra, the temperature varied less than 0.1 K. All dielectric investigations were performed with voltage amplitudes of 0.1 Vrms.
The mechanical shear spectra were acquired by means of a MCR502 rheometer in combination with an EVU20 temperature module from Anton-Paar. The samples were placed between two parallel plates separated by 1 mm. The lower plate is fixed, and the upper one, chosen to be 4 mm in diameter, can oscillate and, thus, apply shear strains in a frequency range up to 102 Hz. All the mechanical spectra were probed in the linear-response regime, i.e., using strain amplitudes that bear no impact on the material parameters. The temperature variation during each frequency scan was kept below 0.2 K.
III. RESULTS AND ANALYSES
A. Dielectric investigations
The dielectric spectra of EMIM-TFSI, (EMIM0.85Li0.15)-TFSI (the indices indicating the molar fractions), and OHEMIM-TFSI are presented in Fig. 2 in terms of the real part (σ′) of the complex conductivity σ* and the real part (ε′) of the complex permittivity ε*. The high-T conductivity data for EMIM-TFSI are in good agreement with previous investigations.57 Since σ′ is directly related to the dielectric loss ε″ (according to σ′ = 2πνε0ε″ with ν the frequency and ε0 the vacuum permittivity), the two parameters included in Fig. 2 define the complete electrical compliance response of the investigated materials.
The salient spectral features of the presently considered ILs are similar to those reported for other ionic conductors:5,10,58 According to Figs. 2(a), 2(c), and 2(e), at low frequencies σ′(ν) exhibits a plateau with an amplitude defining the steady-state conductivity σ0. This so-called “DC” regime reflects the long-time diffusive motion of the charge carriers. Above a certain characteristic frequency ν0, in the so-called “AC” conductivity regime, σ′ becomes ν-dependent as it reflects the contributions of local ion hopping.59 Upon lowering the temperature, both σ0 and ν0 strongly decrease and the DC and AC regimes progressively shift through the frequency window covered in Fig. 2.
In the frequency range marking the crossover in the conductivity spectra, ε′(ν) exhibits the signature of a relaxation process, see Figs. 2(b), 2(d), and 2(f). This spectral feature has been observed also for ion conductors devoid of permanent dipole moments,60 its relaxation step refers to motions that can be faster than the structural relaxation in non-crystalline conductors,61,62 and it is usually referred to as the conductivity (or σ-) process.5,63 As can be observed in Figs. 2(b) and 2(d), an increase in ε′(ν) at lower frequencies due to the electrode polarization effects64,65 hampers the identification of the static permittivity εs of this relaxation. However, the relaxation strength Δε = εs − ε∞ (where ε∞ designates the high-frequency permittivity) can be determined by subtracting from the overall ε′(ν) response a power-law that mimics the contribution of the electrode polarization. As seen in Fig. 2(f), a large electrode spacing, as used for the study of OHEMIM-TFSI, can shift the relative contribution of this undesired phenomenon to lower frequencies, thus providing direct access to Δε.
The current literature provides several options for the parametrization of the dielectric response of ion conducting materials.5,10,58,66 Following recent works,62,67–69 here we apply the numerical solution of the Random Barrier Model (RBM) connecting the normalized quantities and according to59,70,71
This model generates a σ′(ν) curve with an unique (material and temperature invariant) shape. It relies on two parameters only, σ0 and ν0,72 determined as the vertical and horizontal factors superimposing the solution of Eq. (1) on top of the experimental data,73 see Figs. 2(a), 2(c), and 2(e). Here, we observe that the model predictions deviate from the experimental data at high frequencies, most prominently for the σ′ spectra measured at low temperatures. As shown in Appendix C, these deviations are caused by the interference of secondary processes, unaccounted by the RBM and previously identified in other imidazolium-based ILs as well.5,74,75 The physical interpretation of these secondary relaxation processes is beyond the scope of the present study.
For each set of parameters σ0 and ν0 one can convert the RBM predictions for σ′ and σ″ to any other type of response function, for example to the dielectric storage according to ε′(ν) = [σ″(ν)/2πνε0] + ε∞. As ε∞ is a non-relaxational quantity, it must be considered in addition to the RBM term for a complete description of the experimental ε′(ν) results.67–69 As observed in Fig. 2, the RBM solution, despite its lack of flexibility, provides a good description of both the spectral shape and the relaxation strength Δε of the σ-process.
B. Rheological investigations
As one may note from Fig. 2(a), due to crystallization effects, the dielectric investigations of EMIM-TFSI cover only the high T and the low T regimes. The latter is accessed only after the sample was dried, degassed, and fast quenched (by submersing the sample cell in liquid nitrogen before transferring it into the cryostat). Because our rheological setup does not allow for large cooling rates, we were unable to probe the mechanical response of this viscous liquid. This is why, in Figs. 3(a) and 3(b), we show the mechanical response of PMIM-TFSI instead of that of EMIM-TFSI [shown in Figs. 2(a) and 2(b)].
For a direct comparison with the dielectric results, the rheological responses of PMIM-TFSI, (EMIM0.85Li0.15)-TFSI, and OHEMIM-TFSI are presented in Fig. 3 using the real part (F′) of the complex shear fluidity F* and the real part (J′) of the complex shear compliance J*. Their frequency dependences resemble those of σ′ and ε′, respectively (see Fig. 2).67–69 Based on this similarity, we previously proposed to employ the RBM solution also for the description of the molecular rearrangements that give rise to the viscoelastic α-relaxation of viscous liquids.76,77
As demonstrated by the solid lines in Fig. 3, a rheological RBM expression
(here and with the index “r” referring to “rheology”), indeed, describes well the structural relaxation of the presently investigated materials.
Like in the dielectric case, the RBM analysis has been performed at temperatures at which both the DC and AC fluidity regimes are present in the accessible frequency range. Analogous to the dielectric results, the instantaneous (non-relaxational) compliance J∞ has to be added to the model predictions for J′(ν).67–69 At low frequencies, the so-called recoverable compliance Js = J′ν→0 plateau is superimposed by experimental artifacts. Nevertheless, where visible, the amplitude of this plateau is well reproduced by the RBM predictions, which is based on the two parameters F0 and ν0,r obtained from the interpolation of the F′(ν) curves. Significant contributions from secondary processes have not been noticed in the frequency range corresponding to the rheological investigations.
As best recognized for viscous OHEMIM-TFSI, the mechanical relaxation strength ΔJ = Js − J∞ increases slightly with T, therefore exhibiting an anti-Curie-like behavior. This observation is similar to that made for its dielectric counterpart Δε, see Fig. 2(f).
A. The relation between the relaxation parameters of the - and -processes
Using the parameters provided by the RBM analyses, let us first seek for generic relaxational features of different ILs as investigated using dielectric spectroscopy on the one hand and shear rheology on the other. Then, we can examine whether a more general relation exists among the main dielectric and mechanical processes exhibited by these materials.
According to the arrows included in Fig. 2, the dielectric strength of the different ILs appears to be fairly insensitive to their composition. Considering that all ions except Li+ are characterized by permanent dipole moments and that the presence of OH groups should further enhance the polarity of OHEMIM, this observation is quite remarkable: It implies that the dipolar fluctuations either are very slow, hence masked by the electrode polarization, or have relatively low dielectric strength, e.g., akin to the kinetic depolarization phenomena in aqueous ionic solutions, they are somehow screened.78–80 As discussed in Sec. III B, the absence of rheological modes slower than the main relaxation process precludes the former possibility.
The good RBM estimates of Δε based on the values of the steady-state conductivity and of the characteristic rate of charge rearrangements (included in Fig. 2) suggest that the origin of this dielectric process is purely ionic. For such a conductivity relaxation feature, Barton, Nakajima, and Namikawa proposed that these parameters are connected according to what is known as the “BNN” relation,81
Here, p is a material constant and ω0 = 2πν0 is the characteristic angular frequency of the σ-process. To check whether this relation holds for the presently investigated systems, Fig. 4 displays σ0 as a function of ω0 as accessed via the RBM analysis for the presently studied ILs. Here, the dashed line with a slope of 1 demonstrates that the BNN relation, indeed, holds well for all the presently investigated ILs. This phenomenological approach is also valid for other ILs, as is demonstrated by the brown stars representing σ0(ω0) data for the 17 additional systems compiled in Ref. 19. Inspected more closely, the σ0(ω0) curves display some variation among the different materials. However, these are hardly noticeable on the large σ0- and ω0-scales used in Fig. 4. In this respect, the following estimates are not intended as being system specific.
From the intercept of the “BNN” line in Fig. 4, one estimates that on average the product pΔε is about 10. Since, for the presently studied materials, Δε is also very close to 10 (see Fig. 2), Eq. (3) returns a p value of about 1 if in the BNN analysis one chooses the ω0 parameter provided by the RBM expression, Eq. (1). In the recent literature, one finds several alternatives to estimate the ionic characteristic rate, e.g., from the position of the inflection point in ε′(ν),62 as provided by the interpolation of σ′(ν) with the Jonscher expression,66,82 or from the position of the maxima in the corresponding modulus loss spectra.5,58,83 The different estimations of the compliance relaxation times deviate by a factor of about 2, and the difference between the compliance and modulus-related responses depends on the corresponding relaxation strengths.84 Important in the present context is that with respect to the RBM, the alternative analyses provide larger ω0 values and, consequently, p values lower than 1.
Independent of the validity of the approaches that are used to describe the spectral form, the relation between global and local dynamical quantities can provide access to static parameters that are highly relevant for a deeper understanding of the transport phenomena. This will be demonstrated next for the conductivity. According to previous considerations,62,85 the σ-process reflects the reorientation dynamics of ion pairs (regarded as local dipoles) so that its dielectric strength is given by
Here, n is the total number density of ions, q is the elementary charge, λ is the average interionic distance that can be considered as large as the ion diameter,20 and gi is a factor that accounts for the degree of charge correlations, similar to the dipolar Kirkwood factor for molecular reorientations.10,87 For uncorrelated ion motions, gi equals to 1 and the macroscopic conductivity can be estimated using the Nernst–Einstein (NE) relation,
where D0 designates the self-diffusion coefficient of the ions. Considering the often-employed relation between the interionic distance, the diffusivity, and the ionic relaxation rate λ2 ≈ 6D0/ω088 in the absence of correlations (gi = 1) Eqs. (4) and (5) leads to the BNN relation with p ∼ 1.
However, it is well known that in concentrated ionic systems, correlations lead to corrections of the expected NE conductivity. These can be expressed using the so-called ionicity or the inverse Haven ratio H−1, according to σ0 = σNE H−1.59 In this case, gi can also not be neglected in Eq. (4) and the BNN relation implies
While p can be directly accessed from the experimental data (as shown in this work for the considered ILs), the factor gi can be estimated as the ratio between the experimentally probed Δε and the “ideal” relaxation strength, as provided by Eq. (4) for gi = 1 (which can be calculated knowing the structural details of the material). In other words, the experimentally determined Δε can provide access to H−1, i.e., the ratio between the charge and the ion diffusivities,89,90 access which typically involves a combination of NMR and dielectric data.18 In this way, one can rationalize the anti-Curie temperature dependence of Δε (which seems to be a salient feature of the conductivity relaxation processes,68,69,89) as reflecting the increase in the degree of charge correlations (reducing H−1) as the temperature is decreased.
To test directly whether these considerations are applicable, one needs to independently determine p⋅gi (from the dielectric data) and H−1 (from a combination of NMR and dielectric data) under the same experimental conditions. To address this issue, further investigations are necessary to access the low-viscosity regime of the presently studied systems.91
Turning our focus on the mechanical investigations, we point out that in several previous studies (of ionic67–69 and nonionic liquids76), we demonstrated that an equivalent to the BNN relation can be used to connect the rheological parameters of the α-process according to
Figure 4, which includes the F0(ω0,r) results, confirms that this relation holds well for the presently investigated materials. The BNN analysis of mechanical results returns pr values that are close to 1 as well, in good agreement with previous shear studies.67–69,76 Figure 4 also suggests that, as long as the characteristic frequencies of the main dielectric and mechanical processes are similar, in other words, if the two relaxations are coupled,20 the ratio between σ0 and F0 is fairly insensitive to temperature and chemical composition. As demonstrated in Sec. IV C, the characteristic rates assessed for the two processes from the compliance quantities, indeed, agree well with each other. Combining Eq. (5) with the Stokes–Einstein relation,
and using for σ0/F0 a value of about 0.03 (S Pa s/m), as implicit in Fig. 4, one obtains a ratio between H−1 and the hydrodynamic ion radius RH of about 0.3 nm.92 Unless H−1 is significantly lower than 1, the value obtained here for the translational hydrodynamic radius is in harmony with those previously reported for similar ionic liquids.5,20,62 However, these radii are smaller than the geometrical ones of the molecular constituents, as similarly observed in studies of molecular liquids.93
B. The spectral shapes of the dielectric and mechanical responses
As suggested by Figs. 2 and 3, the spectral signatures of the conductivity and the structural relaxations are similar, at least in the compliance representation of the experimental data. To check the extent of this similarity in more detail, the dielectrically probed conductivity spectra and the mechanically probed fluidity spectra of OHEMIM-TFSI are directly compared in Fig. 5(a). As observed there, a temperature-independent vertical shift factor (i.e., the σ0/F0 ratio discussed above) provides a good overlap of the rheological and dielectric spectra in their common frequency range.
As shown in Appendix D, similar spectral shapes of F′(ν) and σ′(ν) are also observed for the ILs with molecular constituents devoid of OH groups. These results are in harmony with previous findings68 and simply reflect that charge and structural rearrangements are well coupled in ILs not only in their diffusive (DC), but also in their deeply sub-diffusive (AC) regime.
How can one understand this rheo-dielectric equivalence on a microscopic level? Here of fundamental importance is the mean square displacement ⟨r2(t)⟩ of the ions, which is directly related to the real part D′(ω) of the complex diffusivity D*(ω) via94
Taking into account ionic correlations through the inverse Haven ratio, H−1, the generalized Nernst–Einstein relation [i.e., Eq. (5) with σ0 replaced by σ*(ω) and D0 by D*(ω)] bridges the mean square displacement of the ions and the experimentally accessed conductivity according to94
A seemingly more general expression connecting these two quantities is95
In the above argument, replacing the relation for the charge flow with the generalized Stokes–Einstein relation for the molecular flow [thereby connecting D*(ω) to F*(ω)], we propose that the real part of the complex fluidity can also be exploited to assess the single-particle mean square displacement according to
or, the other way round,
Accordingly, the common frequency dependence of F′ and σ′ demonstrated in Fig. 5(a) implies that the same ⟨r2(t)⟩ is at the origin of both the rheological and the dielectric main processes. Consequently, the dielectric response of ILs can be described by any theoretical approach, which is able to capture the salient features of their (more fundamental) mechanical α-responses. This brings us to the following questions: How different are the mechanical responses of various ILs, and how different are these when comparing ILs with other (non-ionic) glass forming liquids?
In this context, an important observation is that the shear compliances of all presently considered liquids can be well interpolated by the unique solution of the RBM. One should recall that this approach is based on rough assumptions and that it was initially designed for describing the dynamics of particles in frozen energy landscapes,70,71 thus not in liquids.96 Therefore, it could be merely coincidental that the generic outcome of this approach interpolates well not only the conductivity spectra of ionic materials but also the viscoelastic structural relaxation of liquids. However, one can still employ it as a vehicle that helps in connecting seemingly different relaxational aspects of different materials. For example, if for a given material the spectra probed at different temperatures can be interpolated by the same spectral-shape-invariant function (it does not matter which one), one may conclude that frequency–temperature superposition holds in this case. If the same function applies for different materials, then these share a common spectral shape. These conclusions hold independently of the physical validity of the employed approach and can be checked using simple scaling procedures.
For example, for each system studied in this work, the F′(ν) spectra probed at different temperatures can be overlapped to a master curve using appropriate horizontal (ν0) and vertical (F0) shift factors. The corresponding results obtained for OHEMIM-TFSI and PMIM-TFSI are included in Fig. 6(a). The two master curves nicely agree with each other and both are well interpolated by the RBM function. Since the same function applies for many other (ionic and non-ionic) systems as well,67–69,77 one concludes that these two ILs share a rheological behavior that was previously proposed to be generic to the liquid state.76
It is important to note that the “degree” of this rheological simplicity depends on how the data are presented. To emphasize this point, in Fig. 6(b), we include the master curves obtained for the shear modulus loss G″ of the two ILs. In this representation, the mechanical responses appear to be material specific. There are two ways to rationalize this situation, which has been encountered before in relation to the σ-process:58,85,97 (i) the compliance (retardation) responses J′(ν) and σ′(ν) are generic and the deviations in the corresponding moduli are caused by the material-specific parameters J∞ and ε∞,97 and (ii) the G″(ν) and M″(ν) responses reveal a genuinely non-generic response98 and the agreement in J′(ν) and σ′(ν) for different materials and among each other is coincidental.
Considered separately, the individual dielectric and mechanical datasets cannot provide clear-cut arguments for the validity of one or the other specific scenario. However, in view of the present case of ionic liquids and the above rationale relating F′(ν) and σ′(ν) to the same ⟨r2(t)⟩, it is difficult to envision that the dielectric and mechanical responses (each with their underlying distributions of time scales) of a given IL can differ as strongly as suggested by the comparison of the two modulus responses included in Fig. 5(b). Note that in the modulus representation not only the spectral shapes but also the time scales of the main processes are different, suggesting a decoupling between the mass and the charge transport, at variance with what one concludes from the compliance data shown in Fig. 5(a).
C. Impact of H-bonding and of variable cation size
According to the discussion so far, significant differences among the presently considered systems with respect to the spectral shapes of their dielectric and mechanical compliances do not exist. As observed in Figs. 3 and 6, the rheological response of OHEMIM-TFSI is similar to that of “regular” liquids. The OH groups, clearly identified in the infrared absorption spectrum of this liquid,91 do not generate discernable viscoelastic modes that are slower than the structural relaxation. This situation is at variance with that encountered for other H-bonded liquids, with monohydroxy alcohols as a prominent example.99,100 Based solely on its viscoelastic signature, one cannot draw any conclusions regarding the presence of H-bonding in OHEMIM-TFSI.
However, a direct comparison of the conductivity responses of EMIM-TFSI and OHEMIM-TFSI probed at the same temperature (190 K), cf. Fig. 7, reveals that the charge dynamics is strongly affected by the presence of the cationic OH groups. For comparison, the same plot includes the dielectric response of PMIM-TFSI, which unequivocally demonstrates that a change in the cation size (equivalent to the one induced by the inclusion of an OH group) cannot be held responsible for the large dynamical contrast between EMIM-TFSI and its OH-functionalized counterpart. Clearly, H-bonding strongly affects the time scale of the structural fluctuations leading to an increase of the glass transition temperature Tg and, implicitly, of the time scale of the (coupled) charge rearrangements in OHEMIM-TFSI.
To a certain extent, the present situation resembles the one previously encountered for polyalcohols, systems that also lack the mechanical suprastructural complexity that characterizes monohydroxy alcohols. In polyalcohols changing the terminal group from OH to CH3 causes a drastic increase of the overall molecular mobility (reflected by a significant change in Tg) but does not lead to significant differences with respect to their spectral signature.101 The absence of supramolecular shear modes in OHEMIM-TFSI suggests that either the aggregates are small (e.g., that mostly dimers are formed) or the H-bonded networks are short-lived with respect to the time scale of the structural rearrangements.
Figure 7 includes the conductivity results obtained at 190 K also for the other investigated systems. Here, one observes that the replacement of EMIM and PMIM cations by relatively small amounts of Li also leads to a decrease in the characteristic frequency of the σ-process. This observation can be rationalized by considering that the inclusion of Li ions, albeit reducing the overall hydrodynamic cationic volume, also decreases the effective interionic distances and, consequently, increases the strength of the Coulombic interactions. Another interesting observation is that the change in the characteristic frequency induced by the structural composition of different ILs is closely followed by a change in the amplitude of the DC conductivity plateau. In fact, the dashed line in Fig. 7, obtained isothermally for different materials, corresponds to that obtained upon changing the temperature in Fig. 4. Their equivalence demonstrates the generic relationship between the characteristic frequency of the microscopic charge rearrangements and the DC conductivity characterizing the macroscopic charge flow in ILs.
To further reveal the impact of a change in the cation size and H-bonding on the dynamics of the investigated materials, Fig. 8 includes Arrhenius plots obtained for the characteristic compliance times accessed in this work via dielectric spectroscopy and shear rheology. For PMIM-TFSI one recognizes here that the time constants reported in the present work agree well with those from NMR characterizing the reorientational dynamics of the cations in this material.75
All time scales exhibit supra-Arrhenius behaviors, and the individual datasets probed with the two techniques agree well in their common temperature range. At least in the highly viscous regime, the strong influence of H-bonding is obvious from Fig. 8(a), as the time scales of local rearrangements in OHEMIM-TFSI are significantly larger than those of PMIM-TFSI. In Figs. 8(b) and 8(c), one also recognizes that the replacement of PMIM and EMIM cations with the Li ones slows down the overall dynamics, this slowing-down becoming more pronounced as the Li content increases.
To put the dielectric results of the newly investigated materials EMIM-TFSI and OHEMIM-TFSI in a broader perspective, in Fig. 9 we present the characteristic temperature T* at which their DC conductivity is 10−12 S/cm as a function of the molecular weight Mw of their constituent anion–cation pairs. Here we also included the T* values corresponding to 1-butyl-, 1-hexyl-, and 1-octyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide known in the literature as BMIM-TFSI, HMIM-TFSI, and OMIM-TFSI, respectively.19 These systems, together with EMIM-TFSI and PMIM-TFSI, constitute a homologous series of imidazolium-based ILs with different sizes of their cationic alkyl chains.102
For the presently considered ILs, the variation of T* with Mw should closely reflect that corresponding to their glass transition temperature (which for charge transport fully coupled to structural relaxation corresponds to σ0 ∼ 10−14 S/cm − 10−15 S/cm).103,104 As observed in Fig. 9, for EMIM-TFSI T* fits well in the smooth variation exhibited by its structural homologs, while T* of OHEMIM-TFSI differs significantly. Note that both the decrease and the increase in the effective size of the cations, induced by the inclusion of Li and by the increase in the length of the cationic alkyl chain, respectively, lead to an increase of T*. According to recent investigations, smaller ions promote stronger electrostatic interactions, while larger ions increase the strength of the van der Waals attractions.105 Corroborated by the apparent saturation of T* observed for the ILs devoid of OH-groups at large Mw, the peculiar behavior of OHEMIM-TFSI demonstrates that H-bonding hinders the charge transport much more effectively than a variation of the ion size.
Let us finally consider how the charge dynamics evolves with the number density of groups involved in H-bonding. To address this issue, we “diluted” the OH-functionalized cations of OHEMIM-TFSI by mixing this liquid with PMIM-TFSI. For the present study, three mixtures with OHEMIM-TFSI molar ratios x of 0.25, 0.5, and 0.75 were prepared. Since the mixing partners have similar Mw, the observations to be presented next stem primarily from the scissoring of H-bonds.
The temperature dependence of the DC conductivities characterizing the deeply supercooled state of the two neat ILs and of their mixtures is shown in Fig. 10. As observed here, preserving the population of anions and systematically replacing the OH-containing cations with those devoid of OH groups lead to a progressive cancellation of the anomalous slowing down depicted in Fig. 9. This clearly demonstrates that the peculiar behavior of neat OHEMIM-TFSI should be related to its ability of sustaining cation–cation clustering.
For each system, T* has been determined as the temperature at which σ0 = 10−12 S/cm. The corresponding results, normalized to the value corresponding to OHEMIM-TFSI, are shown as a function of x in the inset of Fig. 10. Overall, the “iso-conductivity” T* parameter increases with an increasing fraction of OH groups; however, it does it in a non-smooth fashion. A strong variation in T*(x) occurs for x ≥ 0.75, indicating that here relatively small amounts of PMIM cations trigger a significant increase in the overall charge flow.
Similar deviations from an ideal mixing behavior (represented by the dashed line in the inset of Fig. 10) were previously reported for a large variety of monohydroxy alcohols mixed with liquids devoid of H-bonding.106–109 In such binary systems, relatively small mixing-induced “perturbations” of the H-bonded networks can generate strong changes in the dielectric and rheological responses of highly concentrated alcohol solutions. The emergence of a critical concentration in the alcohol mixtures has been interpreted as marking a crossover between a regime in which the H-bonding cooperativity effects prevail and another one in which such effects play only a minor role.110 Cooperativity effects are essential for the stability of supramolecular aggregates also in other H-bonded liquids such as water,111 as their strength increases with the number of molecules in the cluster.112,113
Adopting this knowledge to the presently investigated materials, it is suggested that similar cooperativity effects are present in the highly concentrated OHEMIM-TFSI mixtures as well. Below a certain concentration threshold (i.e., for x ≤ 0.75), the size of the aggregates becomes small enough, so these effects lose their efficiency. Infrared spectroscopy which may provide information on the H-bond strengths and their evolution with concentration could be useful to test this scenario in detail.
The present work analyzes the impact of H-bonding and changing cation sizes on the local and global dynamics of imidazolium-based ILs. To this end, we employed oscillatory shear rheology and dielectric spectroscopy to gain access to the structural and the charge fluctuations in EMIM-TFSI, in its OH-functionalized counterpart OHEMIM-TFSI, in PMIM-TFSI, and in the mixtures of OHEMIM-TFSI with PMIM-TFSI and of EMIM-TFSI and PMIM-TFSI with Li-TFSI. Despite the large variation in their structural composition, all these ILs exhibit similar spectral signatures of their dielectric and mechanical responses. The same fitting function, with an invariant spectral shape, is able to capture most relaxational features of the main dielectric and mechanical processes of these materials. Since their characteristic compliance times are also method-independent, this demonstrates that the charge fluctuations are well coupled to the structural rearrangements in the entire dynamical range characterizing their rheological α- and dielectric σ-relaxations.
Exploiting the equivalence between the Nernst–Einstein and Stokes–Einstein relations, we were able (i) to express the conductivity and fluidity responses of these materials through a common mean square displacement of the structural constituents and (ii) to relate the steady-state values of these response functions to microscopic quantities such as hydrodynamic ionic radii and Haven ratios. The employed dielectric and mechanical BNN analyses reveal that the long-range viscous and charge flows are intimately related to the local molecular rearrangements. Their characteristic time scales are highly sensitive to the material composition, reflecting both the ion size and, most prominently, the H-bonding ability provided by the hydroxyl groups.
As clearly demonstrated in this work, the OH-functionalization of an ionic liquid can change its local dynamics by several orders of magnitude, despite the fact that the Coulombic interaction is usually considered to be the dominant one in these liquids. As this large variation is proportionally reflected in the macroscopic mass, charge, and, presumably, also heat transport coefficients of these materials, it becomes clear that controlling the H-bonding ability of ILs can be technologically much more relevant than the classical alternative of simply varying their molecular composition.
The German team acknowledges the financial support from Deutsche Forschungsgemeinschaft under Project No. GA2680/1-1. We thank Ali Mansuri and Professor Markus Thommes from the Department of Biochemical and Chemical Engineering of TU Dortmund University for the help with the calorimetric investigations. A.P.S. thanks the NSF Chemistry program (Grant No. CHE-1764409 award) for financial support of the data analysis.
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
APPENDIX A: NMR AND CHNS PARAMETERS
1H NMR (300 MHz, d6-DMSO) δ/ppm: 8.48 (s, 1H), 7.42 (s, 1H), 7.34 (s, 1H), 4.17 (q, 2H, J = 7.3 Hz), 3.84 (s, 3H), 1.44 (t, 3H, J = 7.4 Hz); 13C NMR (75 MHz, d6-DMSO) δ/ppm: 135.60, 123.36, 121.65, 119.70 (q, 2C, J = 320.5 Hz), 45.65, 35.37, 14.02. CHNS calc. C, 24.55%; H, 2.83%; N, 10.74%; S, 16.39%; found: C, 24.60%; H, 2.67%; N, 10.49%; S, 16.42%. Off-white liquid in < 97% yield.
1H NMR (300 MHz, d6-DMSO) δ/ppm: 9.09 (s, 1H), 7.70 (t, 1H, J = 1.8 Hz), 7.66 (t, 1H, J = 1.8 Hz), 5.16 (s, 1H), 4.22 (t, 2H), 3.87 (s, 3H), 3.74 (t, 2H); 13C NMR (75 MHz, d6-DMSO) δ/ppm: 136.78, 123.23, 122.56, 120.51, 118.38, 59.25, 51.59, 35.54. CHNS calc. C, 23.59%; H, 2.72%; N, 10.32%; S, 15.74%; found: C, 23.56%; H, 2.95%; N, 10.01%; S, 14.66%. Off-white liquid in < 95% yield.
APPENDIX B: CALORIMETRIC RESULTS FOR OHEMIM-TFSI
Figure 11 shows the thermogram recorded for OHEMIM-TFSI.
APPENDIX C: SPECTRAL CONTRIBUTION OF THE SECONDARY RELAXATIONS
As mentioned in Sec. III A, the RBM function alone is not able to capture all the dielectric spectral features of the presently considered liquids at low temperatures and high frequencies. This is demonstrated in Fig. 12 for the dielectric loss and conductivity spectra of EMIM-TFSI and OHEMIM-TFSI probed close to the glass transition temperatures of these two liquids. As shown here, an approach employing a Cole–Cole (CC) function accounting for the contribution of a secondary β-process, added to the RBM function, is able to describe the full dielectric response of these materials.
APPENDIX D: OVERLAP OF FLUIDITY AND CONDUCTIVITY SPECTRA FOR NON-FUNCTIONALIZED ILs
Figure 13 demonstrates that the conductivity and fluidity spectra of two ILs devoid of OH groups can be scaled on top of each other using a vertical T-independent factor, similar to the situation for the OHEMIM-TFSI data presented in Fig. 5(a).
The equivalence between the relations
is demonstrated here for the condition ⟨r2(t = 0)⟩ = 0, which is trivially fulfilled by Eq. (E2).
which proves the equivalence of the two expressions.
In the above derivation, we used the identities
Note that this characteristic frequency has been interpreted as reflecting the average rate ωc (via ω* = 2πν0) of an elementary diffusion step in the conduction process, see Ref. 19.
The presently employed solution of the Random Barrier Model is provided as supplemental material in Ref. 71.
For this estimation we used an average man density of 1.4 g/cm3 and an average molecular weight of the ions of 200 g/mol.