Dielectric relaxation of nitromethane and its mixtures with ethylammonium nitrate: Evidence for strong ion association induced by hydrogen bonding

    Dielectric Relaxation of Nitromethane and its Mixtures with Ethylammonium Nitrate: Evidence for Strong Ion Association Induced by Hydrogen Bonding Andreas Nazet, Lisa Weiß, Richard Buchner PII: DOI: Reference:

S0167-7322(16)31946-8 doi: 10.1016/j.molliq.2016.09.008 MOLLIQ 6285

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

18 July 2016 30 August 2016 2 September 2016

Please cite this article as: Andreas Nazet, Lisa Weiß, Richard Buchner, Dielectric Relaxation of Nitromethane and its Mixtures with Ethylammonium Nitrate: Evidence for Strong Ion Association Induced by Hydrogen Bonding, Journal of Molecular Liquids (2016), doi: 10.1016/j.molliq.2016.09.008

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Dielectric Relaxation of Nitromethane and its Mixtures with Ethylammonium Nitrate: Evidence for Strong Ion Association Induced by Hydrogen Bonding Andreas Nazeta , Lisa Weißa , Richard Buchnera,∗

für Physikalische and Theoretische Chemie, Universität Regensburg, D-93040 Regensburg, Germany

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Abstract

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Binary mixtures of the aprotic protophobic solvent nitromethane (NM) and the protic room-temperature ionic liquid ethylammonium nitrate (EAN) were studied with dielectric relaxation spectroscopy in the two single-phase regions, 0 < xEAN ≤ 0.013 and 0.4 ≤ xEAN < 1, of the binary mixtures at 25 ℃. All spectra were well described by a superposition of two relaxation processes whose origins were of composite nature. At low xEAN the solutions behave as a strongly associated electrolyte, displaying moderate ion solvation by nitromethane at the infinite-dilution limit. At high xEAN far from the miscibility gap, the observed dynamics represents the typically observed behaviour of a lubricated ionic liquid smoothly reaching the properties of pure EAN. Additionally, neat NM was investigated in the temperature range of (5 to 65) ℃ to explore its potential as a calibration standard in dielectric spectroscopy. The obtained (0.05 to 89) GHz spectra were well fitted by a single Debye equation. The dynamics of this medium-permittivity dipolar liquid is governed by rotational diffusion of NM dipoles close to slip boundary conditions with only weak dipole-dipole correlations. Unfortunately, difficulties in obtaining samples of reproducible purity discredit NM as a calibration standard for dielectric measurements. Keywords: Dielectric relaxation, Dipolar Liquids, Protic Ionic Liquids, Ion Solvation, Hydrogen Bonding, Ion Association

∗ Corresponding

author Email address: [email protected] (Richard Buchner)

Preprint submitted to Journal of Molecular Liquids

September 2, 2016

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1. Introduction

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During the recent three decades research on room temperature ionic liquids (RTILs) has grown into a mature field with many promises. Accordingly, an enormous effort has been undertaken to understand and utilize this lowmelting (Tm < 100 °C) class of mostly organic salts exhibiting interesting and unique properties, like low vapour pressure or high decomposition temperatures [1, 2, 3, 4]. Although often claims on their “greenness” and environmentally benign nature are far fetched and not tenable, the possibility to create a seemingly endless number of different RTILs by varying the structure and/or nature of cations and anions, as well as the possibility to tune properties further by blending them with each other or mixing them with molecular solvents [5] still leaves room for numerous potential applications. An interesting subgroup of RTILs are protic ionic liquids (PILs) which exhibit strong hydrogen bonding in addition to van-der-Waals and Coulomb interactions [6]. The best investigated representative is ethylammonium nitrate (EAN), which has gained much attention due to its ability to form a three dimensional hydrogen-bond (HB) network and its possible use for organic synthesis, protein crystallization or as a medium for self-assembling supramolecular materials [7, 8, 9, 10, 11, 12]. Investigations of the physicochemical properties of RTIL-containing systems have mainly focused on structure [2], thermodynamic and transport properties [13, 4]. Dynamics was much less investigated so far and in particular mixtures of RTILs with molecular solvents are not well studied yet [14, 15, 16, 17]. A convenient technique probing the cooperative dynamics of liquids, including RTILs and electrolyte solutions, is dielectric relaxation spectroscopy (DRS) [18]. The thus detected sample polarization, recorded as complex permittivity spectrum, εˆ(ν) = ε′ (ν) − iε′′ (ν) (ε′ (ν) is the relative permittivity, ε′′ (ν) the dielectric loss at frequency ν), is sensitive to all dipolar species, including ion pairs, in the sample and therefore grants access to both their rotational dynamics and concentration [19]. For RTILs generally also interionic vibrations —formally a frequency-dependent conductivity— contribute to a significant extent [20]. In an earlier DRS study binary mixtures of the PIL ethylammonium nitrate and the aprotic protophobic solvent acetonitrile (AN) were investigated [17]. There, the exceptionally large solute relaxation at low PIL concentrations could be traced back to the formation of abundant amounts of EAN contact ion pairs (CIPs). The prevalence of CIPs in this medium-permittivity solvent (static relative permittivity ε = 35.96 [21]) could only be explained by the formation of strong hydrogen bonds between anions and cations as aprotic RTILs, like usual 1:1 electrolytes, exhibited only moderate ion-pairing in AN [17, 22, 23, 24, 25, 26]. With the present investigation we extend our studies to a further dipolar aprotic protophobic solvent and report on the properties of binary mixtures of EAN with nitromethane (NM) at 25 ℃. We complement this work by a discussion of the dielectric relaxation of pure NM in the temperature range of (5 to 65) °C as a literature search for this potential alternative to acetonitrile as a calibration standard in DRS revealed only a single study so far [27], suffering from insufficient frequency coverage and limited accuracy. 2

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2. Experimental

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2.1. Materials and chemicals

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Two different batches of nitromethane (both Carl Roth, ∼ 97%) were used for the investigation of the pure compound and the mixture studies, respectively. Both were purified as recommended in literature [28] and dried over freshly activated 3 Å molecular sieves yielding a final water contents w < 2·10−4 (m/m) and ∼99% GC purity. Ethylammonium nitrate (IoLiTec, >97%) was dried in high vacuum (p < 10−8 mbar) for 5 days at 40 ℃. The final water content was also < 2 · 10−4 (m/m) as measured by coulometric Karl Fischer titration. No further purifications were performed. The materials were stored in a glovebox filled with dry nitrogen and in all following steps of sample preparation, handling and measurement samples were kept under dry N 2 . Compared to the starting material, the water content of samples recollected after measurements had increased by less than 10%. Mixtures were prepared on an analytical balance without buoyancy correction, resulting in a combined relative uncertainty of their concentrations of ∼0.2 %. 2.2. Measurements and data processing

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Density. Solution densities, ρ, necessary for the calculation of molar concentrations, c, were determined with a vibrating-tube density meter (DMA 5000 M, Anton Paar, Graz, Austria), yielding an estimated uncertainty of 1 · 10−5 kg L−1 for ρ. For instrument calibration the procedure recommended by the manufacturer was followed, using deionized water and air as standards. Viscosity. Dynamics Viscosities, η, were measured with a rolling ball microviscometer (AMVn, Anton Paar, Graz, Austria). The instrument was calibrated with deionized water and N14 calibration oil (Cannon Instruments, Pennsylvania). The nominal relative uncertainty of the instrument is ∼0.5% but considering all possible sources of error the combined relative uncertainty of η is estimated to be 2%. Conductivity. Electrical conductivities, κ, of the samples were determined with a combined uncertainty of 0.5% employing the setup described previously [29]. For the present work the then used three-electrode flow cell was replaced by a set of five two-electrode capillary cells connected via an electronic switching device to the LCR Bridge (HM8118, HAMEG Instruments GmbH, Germany). The cells were calibrated with (0.01 and 0.1) molal aqueous KCl solutions using recommended reference data [30]. The densities and viscosities of neat NM as a function of temperature, T , are summarized in Table S1 of the Supplementary Content; (ρ, η, κ) data for the mixtures are given in Table S2. Dielectric Spectroscopy. Dielectric spectra were determined in the frequency range 0.05 ≤ ν /GHz ≤ 89 with a temperature uncertainty of 0.05 K. For ν ≤ 50 GHz reflection measurements were performed with a vector network analyzer (VNA, Agilent E8364B) with electronic calibration module (ECal, Agilent N4693A). Two commercial open-ended coaxial-line probes (Agilent 85070E020 / -050) were employed, using air, mercury, and N,N-dimethylacetamide as

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open, short, and load standards for calibration [20]. Raw VNA data was corrected for spurious calibration errors with a complex Padé approximation [31], using as secondary standards (all spectroscopical grade) benzonitrile and 1butanol for NM-poor samples, whereas benzonitrile and acetonitrile were taken for NM-rich samples and pure NM. For 60 ≤ ν /GHz ≤ 89 a waveguide interferometer with variable path-length transmission cell was employed, which does not require calibration [32]. To crosscheck the VNA results, additional measurements were made for selected samples with three variable path-length waveguide transmission cells hooked to the VNA and covering (8.5-12.4, 13-18 and 26-40) GHz. The quantities directly assessed by DRS are relative permittivity, ε′ (ν), and the total loss, η ′′ (ν) = ε′′ (ν) + κ/(2πνε0 ), where ε0 is the vacuum permittivity [33, 19]. For further processing, the total loss was corrected for its Ohmic contribution, κ/(2πνε0 ), with the separately determined dc conductivity, κ, so that the remaining complex permittivity spectra, εˆ(ν) = ε′ (ν) − iε′′ (ν), summarized all contributions depending explicitly on frequency and thus reflected the cooperative dynamics of the samples. For a formal description εˆ(ν) was then fitted to relaxation models of the kind n  Sj . (1) εˆ(ν) = ε∞ + 1−αj ]βj j=1 [1 + (i2πντj )

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based on sums of n independent relaxations, j, with specific amplitudes, Sj , relaxation times, τj , and shape parameters, αj & βj ; ε∞ is the high-frequency limit of ε′ (ν), its ν → 0 plateau defines the static relative permittivity, ε = Sj +ε∞ , of the sample [33, 18]. Fitting was performed using a home-built procedure implemented in the commercial IGOR software (Wavemetrics, V.6.22A) [35]. All reasonably conceivable fitting models were tested and scrutinized according to the criteria discussed in detail in Ref. [21]. For dipole mixtures exhibiting n relaxations the amplitudes, Sj , associated with the various species, j, of permanent (gas-phase) dipole moment, µj , can be evaluated individually [34]. Taking into account ellipsoidal cavity fields, the present amplitudes were analyzed with the equation 3(ε + Aj (1 − ε)) NA × Sj = × cj × µ2eff,j kB T ǫ 0 ε

(2)

where cj is the molar concentration and µeff,j the effective dipole moment [36]. In Eq. (2) Aj is the cavity field factor, determined by the geometry of the dipole, NA and kB are the Avogadro and the Boltzmann constant, respectively. The effective dipole moment can be written as √ (3) µeff,j = µap,j gj where µap,j = µj /(1 − fj αj ) Here the empirical factor gj is a measure for possible dipole-dipole correlations and the apparent dipole moment, µap,j , accounts for the effect of molecular polarizability, αj , on the permanent (gas-phase) moment, µj ; fj is the geometrydependent reaction-field factor [36, 37]. In this work all required values of µap,j were directly calculated with semiempirical methods using MOPAC [38]. 4

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Figure 1: (a) Relative permittivity, ε′ (ν), and (b) dielectric loss, ε′′ (ν), spectra of neat NM as a function of temperature, T (= 278.15; 288.15; 298.15; 308.15; 318.15; 328.15 and 338.15 K). Symbols represent experimental data (partly omitted for visual clarity); solid lines indicate fits with Eq. (1) assuming a single Debye equation.

3. Results

3.1. Nitromethane Nitromethane was investigated from 5 to 65 ℃ in steps of 10 ℃, yielding the dielectric spectra of Fig. 1. A single Debye-type (D) equation (Eq. (1) with n = 1, α1 = 0 & β1 = 1) was sufficient to describe those in the investigated frequency range. The obtained fit parameters are summarized in Table 1. Static, ε, and high-frequency permittivity, ε∞ , decrease linearly with temperature, T , following the equation Y = a + b × (T − T0 )

where

Y = ε, ε∞ ; T0 = 273.15 K

(4)

with a = (40.33±0.15) and b = −(0.149±0.004) K−1 for ε, and a = (3.69±0.06) and b = −(0.0101±0.0015) K−1 for ε∞ . The relaxation time, τ1 , is well described 5

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ε

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278.15 288.15 298.15 308.15 318.15 328.15 338.15

39.85 38.00 36.37 34.97 33.61 32.35 30.60

36.17 34.59 32.92 31.57 30.29 29.27 27.60

5.35 4.66 4.29 3.92 3.54 3.20 2.94

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by the Eyring equation [33]

ε∞

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3.68 3.42 3.44 3.40 3.32 3.09 3.00

1.93 1.92 1.90 1.89 1.88 1.87 1.85

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Table 1: Parameters (static permittivity, ε = S1 + ε∞ , amplitude, S1 , relaxation time, τ1 , and high-frequency permittivity, ε∞ ) of the D model fitting εˆ(ν) of NM in the frequency range 0.05 ≤ ν/GHz ≤ 89 at temperature T . Also included is the squared refractive index, n2∞ , interpolated from literature data [39].

" ! h ∆H #= − T ∆S #= τ1 = exp kB T RT

(5)

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with activation enthalpy, ∆H #= = (5.11 ± 0.17) kJ mol−1 (corresponding to an Arrhenius activation energy of Ea = (7.7 ± 0.2) kJ mol−1 ), and activation entropy, ∆S #= = −(10.1 ± 0.6) J K−1 mol−1 ; h and R have their usual meaning. To the best of our knowledge, the only other DRS study of NM was performed by Chandra and Nath [27]. For their measurements at (3, 15, 30, 45, and 60) ℃ the authors used a Cole-Cole (CC) equation (Eq. (1) with n = 1, 0 < α1 < 1 & β1 = 1) to evaluate five εˆ(ν) values covering 1.9-31.7 GHz plus the additionally determined static permittivity. Directly comparable with the data of Table 1 are the static permittivities, ε = 37.79 & 33.35, and relaxation times, τ1 = 4.3 ps & 3.3 ps, at 15 and 45 ℃. Whilst ε values are in rather good agreement (deviation < 1 %) τ1 differs considerably, reflecting the lack of high-frequency data for Chandra and Nath. A fair number of ε values determined with standard capacitance methods could be found. In Fig. S1 of the Supplementary Content these are compared to the present data from Table 1. Generally, the agreement is reasonable to good but compared to other dipolar aprotic liquids the literature data for ε scatter considerably. Although other sources of error cannot be excluded, sample purity seems to be a major problem here. The —compared to the corresponding values of Table 1— rather different values for amplitude, S1 = 33.36, relaxation time, τ1 = 4.24 ps, and high-frequency permittivity, ε∞ = 3.01, of the NM sample used for the 25 ℃ mixture studies, seem to support this hypothesis. In any case, the present data base cannot be reasonably used to define a set of dielectric reference parameters for instrument calibration in a manner similar to what was done previously for acetonitrile [21].

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Figure 2: Fits to (a) relative permittivity, ε′ (ν), and (b) dielectric loss, ε′′ (ν), spectra of binary EAN+NM mixtures (sold lines) and the neat compounds (dashed lines) at 25 ℃ with EAN mole fractions of (1) xEAN = 0; 0.00341; 0.00621; 0.00836; 0.0112; 0.0129, and (2) xEAN = 0.4004; 0.5017; 0.6126; 0.6993; 0.7968; 0.8952; 0.9502; 1, increasing in arrow direction.

Figure 3: Dielectric loss spectra, ε′′ (ν) (), of EAN+NM mixtures for (a) a NM-rich solution (xEAN = 0.0084) and (b) a NM-poor solution (xEAN = 0.699) and corresponding fits with Eq. (1) (lines). The shaded areas represent the resolved modes, a Cole-Cole (CC) and a Debye (D) relaxation for (a), and a Havriliak-Negami (HN) and a Debye (D) relaxation for (b).

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cEAN /M

ε

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α1

β1

0a 0.00341 0.00621 0.00836 0.0112 0.0129 0.4004 0.5017 0.6126 0.6993 0.7968 0.8952 0.9502 1

0 0.0636 0.115 0.154 0.207 0.237 5.961 7.088 8.173 8.956 9.750 10.475 10.864 11.194

36.37 37.00 37.61 38.23 38.82 39.20 35.72 30.02 28.03 27.50 27.48 27.54 28.24 28.73

1.92 2.82 3.70 4.72 5.26 29.27 25.24 24.34 23.70 23.12 23.33 23.76 24.26

0.33 0.40 0.41 0.43 0.41 0.37 0.32 0.30 0.24 0.16 0.04 0.00 0.00

1.00 1.00 1.00 1.00 1.00 0.87 0.92 0.8F 0.66 0.60 0.50 0.50 0.50

τ2 /ps

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10.5 20.3 32.4 37.7 43.1 35.0 26.6 43.6 79.5 120 171 189 209

33.36 32.03 31.74 31.48 31.05 30.89 3.60 1.20 0.55 1.13 1.24 1.99 2.23 0.43

4.24 4.28 4.31 4.33 4.34 4.32 6.77 6.59 0.5F 0.28 0.68 0.29 0.38 1.30

3.01 3.05F 3.05F 3.05F 3.05F 3.05F 2.85 3.57 3.14 2.67 3.12 2.22 2.26 4.04

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Table 2: Parameters (static permittivity, ε , amplitudes, Sj , and relaxation times, τj (j = 1, 2), symmetrical, α1 , and asymmetrical, β1 , width parameters, and high-frequency permittivity, ε∞ ), as a function of EAN mole fraction, xEAN , and molar concentration, cEAN . Parameters marked F were not adjusted during the fitting procedure.

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3.2. NM+EAN mixtures Whilst the dielectric spectrum of neat NM is well described by a single Debye equation, fitting εˆ(ν) of EAN in the present frequency range of 0.189 GHz requires the the superposition of a lower-frequency Cole-Davidson (CD) equation (parameters S1 , τ1 , α1 = 0, 0 < β1 < 1), peaking at ∼1 GHz, and a higher-frequency Debye mode (S2 , τ2 , α2 = 0, β2 = 1) centered at ∼130 GHz. It must be noted that this formal description of the EAN spectrum is approximate as only the α relaxation due to cation reorientation (j = 1) is fully covered, whereas the second mode resolved in this fit (plus the rather large values of ε∞ ) maps the low-frequency wing of the rather complex terahertz part of the full spectrum [17, 40] that extends into in the present frequency range. The fit parameters are given in Table 2. At room temperature the system NM+EAN exhibits a rather broad miscibility gap. Homogeneous mixtures were found for very low, 0 ≤ xEAN ≤ 0.013, and moderate to high EAN mole fractions, 0.4 ≤ xEAN ≤ 1. Accordingly, the recorded εˆ(ν), Figs. 2 & 3, could be divided into two groups. The spectra of EAN-poor mixtures resembled electrolyte spectra, i.e. were dominated by the higher-frequency (j = 2) solvent mode of Debye type at ∼36 GHz. The amplitude of this relaxation decreased weakly with increasing xEAN . Simultaneously, a solute-related mode (j = 1) grew rapidly at ∼ 3 GHz. As a consequence, 8

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Figure 4: Static permittivity, ε (), of EAN+NM mixtures as a function of xEAN . Solid lines as a guide to the eye only.

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the static permittivity, ε, increased considerably (Fig. 4). In this region the solute relaxation was best described by a rather broad CC relaxation-time distribution (α1 ≈ 0.4, β1 = 1) and its relaxation time, τ1 , increased considerably with xEAN (Fig. S3). On the other hand, the spectra of the EAN-rich mixtures smoothly evolved from that of the pure PIL. Two modes were required to fit εˆ(ν), with j = 2 being of D type as for pure EAN, albeit with a distinct jump in τ2 at xEAN ≈ 0.55 (Fig. S3). However, with decreasing xEAN the lower-frequency mode (j = 1) dominating the spectra in this mixture region broadened considerably (Fig. S4) compared to pure EAN and was best described by a Havriliak-Negami (HN) equation (0 < α1 < 1, 0 < β1 < 1). Its relaxation times, τ1 , decreased markedly on NM addition (Fig. S3). Also ε decreased on initial dilution of EAN with a flat minimum at xEAN ≈ 0.75 but raised again considerably on approaching the miscibility gap (Fig. 4). The fit parameters for the mixture spectra are summarized in Table 2. Attempts to split the broad lower-frequency (j = 1) contribution further into several individual relaxations were not successful. 4. Discussion 4.1. Nitromethane The finding of only one mode in the microwave region is not surprising for NM as the dipole vector of this symmetrical top is oriented along one of the principal axes of inertia. The observed Debye-type relaxation monitors the reorientation of this dipole at long times. The presence of fast molecular

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librations and cage rattling [41] is obvious from the significant difference between the ν → ∞ limit of ε′ (ν) from the present spectra, ε∞ , and the squared refractive index at optical frequencies, n2∞ (Table 1). However, proper discussion of this fast dynamics would require measurements in the far-infrared region and is thus outside the scope of this contribution. As expected for a compound with a rather large permanent (gas-phase) dipole moment (µ = 3.46 D [42]) but no specific intermolecular interactions, like hydrogen bonding, NM possesses a medium-size relative permittivity (Table 1), comparable to that of acetonitrile [21]. Information on possible static dipole-dipole correlations can be inferred from the Kirkwood factor, gK , of the Kirkwood-Fröhlich equation [43],

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(6)

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Here ε∞,FIR is the value of ε′ (ν) at far-infrared frequencies where all intermolecular dynamics has ceased to contribute but all intra-molecular dynamics is still operative. Unfortunately, no ε∞,FIR data is available for NM. Since n2∞ ε∞,FIR < ε∞ , Kirkwood factors calculated from ε∞ should be definitely too small. Those obtained with n2∞ from Ref. [39] will be somewhat too large but are probably a fair indicator. As can be seen from Fig. S2 the latter gK values are close to unity, suggesting —if at all— only weak antiparallel (gK < 1) dipole-dipole correlations and thus no pronounced liquid structure. This is in line with inference of Sassi et al. from Rayleigh-Brillouin scattering experiments [44]. The obtained dielectric relaxation time, τ1 (Table 1) is a collective property [33]. To compare with single-molecule rotational correlation times of rank l from other methods (for DRS l = 1) and infer on the possible relaxation mechanism, the corresponding rotational correlation time $ # g˙ 2ε + ε∞ τ (l = 1; DR) = τ1 · (7) gK 3ε

is required [45]. Since no independent information on the factor g, ˙ accounting for correlated molecular motions, was available and because of the uncertainty for gK , the approximations τ1′ = τ (l = 1; DR) × gK /g˙ and τ1′′ = τ (l = 1; DR) × gK were compared with literature data for the rotational correlation time in Fig. 5. Where necessary, the latter were converted to their rank l = 1 equivalent via the equation τ (l = 1; X) = l′ (l′ + 1)τ (l′ ; X)/2. (8) where X designates the method naturally probing a direction-specific property associated with a Legendre polynomial of rank l′ [33]. Equation (8) is valid for rotational diffusion, i.e. molecular reorientation through random small-angle jumps. The DR data of Ref. [27] were not included in Fig. 5 for reasons discussed in Section 3.1.

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Giorgini et al. determined correlation times of NM from time-resolved optical Kerr effect (OKE) measurements, Rayleigh scattering and the Raman bandwidth of NM’s ν5 vibration [46]. All three methods probe l′ = 2 but only the latter directly yields the rotational correlation time. Rayleigh and OKE experiments probe collective dynamics and experimental relaxation times thus require corrections similar to dielectric relaxation times, with dynamic correlations generally assumed to be negligible [46]. Since Raman and Rayleigh data almost coincided, Fig. 5, the authors concluded that also static orientational correlations were essentially negligible. This is in line with the present findings for gK . However, the correlation times reported by Giorgini et al. [46] yielded τ (l = 1; Rayleigh) and τ (l = 1; Raman) values significantly exceeding the present data (Fig. 5). Similar results were obtained by Ombelli et al. from their analysis of ν5 Raman band shapes [47]. However, their results for ν3 match the present values very well. Possible reasons for the significantly larger OKE values were already discussed in Ref. [46]. On the other hand the converted 14 N NMR relaxation time, τ (l′ = 2; NMR) = 1.03 ps, published by Suchanski and Canepa [48] for 25 ℃ as well as the temperature dependence of this quantity, reconstructed from the also given Arrhenius activation energy (Ea = 8.0 kJ mol−1 ), fall exactly between the present data for τ1′ and τ1′′ . Since NMR directly yields molecular rotational correlation times, this suggests that the ratio gK /g˙ for DRS and thus also g˙ is close to unity. We may therefore conclude that not only the molecular alignment of NM molecules is negligible but also cross-correlations in their reorientational motions. The relaxation mechanism is through rotational diffusion. As expected for rotational diffusion τ1′ and τ1′′ scale linearly with η/T , Fig. 5, i.e. follow the extended Stokes-Einstein-Debye (SED) equation [49]

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τ (l = 1; X) =

3Vm f C η · + τ0 kB T

(9)

where Vm is the volume of the molecule (approximated as a prolate ellipsoid), f a geometric factor determined by the aspect ratio of the ellipsoid and C the empirical friction coefficient experienced by the rotating molecule; τ0 is the empirically found intercept which is occasionally associated with the freerotor correlation time [46]. Within the framework of hydrodynamic continuum theory the limiting values for stick, Cstick = 1, and slip boundary conditions, Cslip = 1 − f −2/3 , can be given. For a nitromethane molecule MOPAC [38] yielded semi-principal axes of a = 3.0 Å and b = c = 2.1 Å, thus Vm = 55.4 Å3 , f = 1.170 and Cslip = 0.099. Since τ1′ and τ1′′ almost agree within error limits it suffices to discuss the average values of their slopes and intercepts obtained with Eq. (9), yielding an average value for effective friction coefficient of C = 0.077 and τ0 = 0.81 ps. The latter value is somewhat larger than the free-rotor correlation time of τFR ≈ 0.5 ps estimated from the MOPAC moments of inertia but in view of the disputed equivalence of τ0 and τFR this should not be over-interpreted. More relevant is that within the given uncertainties C ≈ Cslip . This means that the friction experienced by the rotating NM dipoles is essentially that exerted 11

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Figure 5: Comparison of the quantities τ1′ () and τ1′′ (!) from the present DRS data for neat NM, plotted as a function of η/T , with rotational correlation times, τ (l = 1; X), of Giorgini et al. [46] obtained from Raman bandwidths (ν5 ; △), OKE (⊲) and Rayleigh (▽) experiments; of Ombelli et al. [47] obtained from the widths of the ν3 (#) and ν5 (⋄) Raman bands; of Suchanski and Canepa [48] from NMR ("). The broken line was calculated from the activation energy given by the latter authors; the solid lines are fits with Eq. (9).

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by an unstructured medium of viscosity η, corroborating the inference from the Kirkwood factor. Thus, with regard to liquid-state structure and collective dynamics nitromethane closely resembles acetonitrile [21]. 4.2. NM+EAN mixtures To the best of our knowledge there is no data on the dielectric behaviour of mixtures of NM with ionic liquids or any other electrolyte so far. However, given the similarities of NM and acetonitrile (AN) regarding dipole moment, static permittivity and dynamics of the pure compounds [21] it is reasonable to assume that our previous investigations of AN+RTIL mixtures [23, 50] and in particular that on AN+EAN [17] provide a guideline for the interpretation of the present data. Nevertheless, some differences have to be expected with regard to ion-solvent interactions as both solvents have similar donor numbers (NM: 20.5; AN: 18.9), thus comparably poor solvating power toward anions, but the acceptor number of NM (2.7) is considerably smaller than that of AN (14.1), so that cation solvation in nitromethane is considerably weaker [51]. As discussed in Section 3.2, on both sides of the miscibility gap of EAN+NM (0.013 < xEAN < 0.4) the dielectric spectra of the mixtures were best described by the superposition of a lower-frequency (j = 1 in Eq. 1) relaxation-time distribution and a higher-frequency (j = 2) Debye mode. The first relaxation is clearly associated with the presence of EAN as it is not present for neat NM. 12

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Figure 6: (a) Experimental amplitude of the lower-frequency mode, S1 (), of EAN+NM mixtures at room temperature and values, S+ (solid line), predicted under the assumption that only EtNH+ 3 cations contribute. (b) Corresponding effective dipole moment, µeff,EAN , calculated with Eq. (2) under the assumption that only EAN participates. The solid line corresponds to an exponential fit of all data except for the bracketed and the open points (see text). Error bars correspond to 2σfit (S1 ) = 0.6 of a polynomial fit to S1 (broken line in (a)).

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Its amplitude, S1 , rises rapidly with EAN concentration in the EAN-poor region (Fig. 6a). Beyond the miscibility gap S1 initially decreases, before passing through a flat minimum at xEAN ≈ 0.8 and then rising slightly again to the value of pure EAN. This behaviour is reminiscent of EAN+acetonitrile mixtures [17]. Most unusually, already at the lowest PIL content, xEAN = 0.00341 corresponding to cEAN = 0.0636 mol L−1 , the CC width parameter of the EAN-related mode jumped to the rather large value of α1 = 0.33. Almost certainly, this is in part due to experimental noise affecting the separation of two rather close relaxations (τ1 /τ2 = 2.45; Table 2) of very different amplitudes and explains why this point turned out to be an outlier in the amplitude analysis, see bracketed points in Figs. 6 & 7. At higher concentrations this separation is much less problematic and accordingly, smoothly varying values for S1 and S2 were obtained. Note that interpolated values of both amplitudes at xEAN = 0.00341, obtained from polynomial fits with intercepts clamped to zero for S1 and to 33.36 for S2 yielded well matching results (open symbols in Figs. 7 & 6). However, these were not considered in the further analysis as they do not represent directly determined data. Higher-frequency mode. At xEAN ≤ 0.013 the second relaxation can be safely assigned to NM but at xEAN ≥ 0.4 EAN cage rattling and libration also contribute and —as seen from the drop of τ2 (Fig. S3)— dominate at xEAN ≥ 0.6. This becomes also obvious from the corresponding amplitude, S2 , which exhibits a clear minimum at xEAN ≈ 0.55 before linearly rising to the value found for pure EAN (Fig. 7a). Similar to EAN+AN mixtures [17], up 13

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Figure 7: (a) Observed amplitude of the higher-frequency D mode, S2 (•; dashed lines as NM (solid line). (b) Effective solvation a guide to the eye), and expected NM amplitude, Scalc numbers, Zeff , as a function of EAN concentration, cEAN . The solid line represents a straightline fit to the data except for the bracketed and the open points (see text).

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to the minimum S2 is considerably smaller than the NM amplitude predicted from the analytical solvent concentration, cNM (Fig. 7a). This indicates strong interactions of a notable fraction of NM molecules with the ions so that at xEAN ≈ 0.55 practically no free solvent remains and the detected contribution is entirely due to fast EAN dynamics. Confirmation for the predominance of NM reorientation for the higherfrequency mode in the electrolyte-like region comes from τ2 . Figure 8a shows the corresponding time constant, τ2′ , calculated with Eq. 7, as a function of solution viscosity. Given that the dynamics of pure NM is governed by rotational diffusion and g/g ˙ K ≈ 1 (see Section 4.1), τ2′ should be a good approximation for the rotational correlation time and accordingly follow the SED equation, Eq. (9). Indeed, except for the value at the phase boundary but including pure NM, a straight line was found, yielding an effective friction coefficient of C = 0.038 ± 0.004. This value is much smaller than that obtained from temperature dependence of neat NM (C = 0.077). However, such differences between friction coefficients determined for pure dipolar aprotic solvents via variation of η through temperature and C values of their electrolyte solutions, where the increase of η is due to salt addition at constant T , seem to be common [23, 22, 17, 52], suggesting that in these systems solute-solvent interactions are essentially limited to the first solvation shell [19]. Also for the electrolyte-like mixture regime, comparison of cNM with the apparent NM concentration, capp NM , calculated from S2 with Eq. (2) assuming slip boundary conditions for kinetic depolarization [53], yielded effective solvation

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Figure 8: (a) Rotational correlation time, τ2′ , and (b) dielectric relaxation time, τ1 , as a function of solution viscosity, η, of the binary mixtures of EAN+NM. The insert in (b) expands the electrolyte-like region, xEAN ≤ 0.013.

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cNM − capp NM (10) cEAN given in Fig. 7(b). Except for the outlier at the lowest concentration (see above), Zeff decreases linearly from a value of 7.3 ± 0.5 at infinite dilution to ∼4.3 at the lower phase boundary (xEAN = 0.013). Beyond the miscibility gap Zeff decreases smoothly from ∼1.1 at xEAN = 0.4 to zero in pure EAN. Similar trends for Zeff were found for EAN [17] and various imidazolium RTILs in AN [23, 50] and with values of ∼6-7 even the magnitudes for Zeff (0) are comparable with the present data. Almost certainly, this reflects the lack of specific ion-solvent interactions in these systems. The DRS-detected effective solvation numbers appear to arise essentially from the alignment of NM, respectively AN, molecules in the electric field of the ions in such a way that effectively Zeff solvent dipoles cancel. However, there is one significant difference between the mixtures of EAN with NM and AN and those of imidazolium ILs with AN: For the latter it could be shown that the “missing” free AN quantitatively contributes to the lower-frequency relaxation [23, 50], meaning that these solvating AN molecules and the solvated RTIL ions had similar dynamics. As for EAN+AN [17] the present analysis of the EAN-related amplitude, S1 , is not compatible with such a conclusion, see below. Apparently, in the case of EAN the reorientation of the solvating NM, respectively AN, molecules is practically frozen. Lower-frequency mode. Close inspection of Fig. 8(b) reveals two different regions where the relaxation time of mode 1, τ1 , is proportional to viscosity. One of them comprises the entire electrolyte-like region, xEAN ≤ 0.13. The second is for 0.6 xEAN ≤ 1, i.e. EAN-rich mixtures where no free NM is detectable anymore (Fig. 7). Since nitrate has no dipole moment it is thus reasonable to assume that in this second region mode 1 is dominated by the reorientation of [EtNH+ 3 ] cations similar to the situation for pure EAN [40]. Application of Eq. 9 for the second region results in an empirical friction coefficient of C = 0.159 which is grossly similar to the value (0.127) found for the corresponding region in EAN+AN mixtures [17] but significantly larger than that for pure EAN (0.091). Apparently NM and AN have similar effects on cation reorientation which in the pure PIL occurs through large-angle jumps [54, 12]. Both dipolar aprotic solvents speed up dynamics at these small solvent-to-EAN ratios but simultaneously couple their reorientation to that of the cation as no free solvent is detectable. Simultaneously, the effective dipole moment, µeff,EAN , of EAN calculated with Eq. 2 from S1 increases with decreasing xEAN (Fig. 6b). In view of the high ion concentration at xEAN ≥ 0.6 the other possible explanation for rising µeff,EAN , the formation of sufficiently long-lived (life time $ τ1 ) EAN ion pairs seems unlikely. Interestingly, in the electrolyte region, xEAN ≤ 0.13, viscosity changes only weakly whereas τ1 exhibits a four-fold increase. Application of Eq. (9) results in an effective volume Veff = Vm f C of ∼1060 Å3 , which is far too large to be compatible with reorientation of free [EtNH + 3 ] cations under stick boundary conditions, corresponding to Veff = 65.2 Å3 . On the other hand, the experimental

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Figure 9: Associations constants, KA () as a function of nominal ionic strength, I, at 298.15 K for EAN+NM mixtures. The dashed line is a fit to Eq. (13) without the bracketed and the open points (see text).

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value is too small to be due to EAN contact ion pairs (CIPs) alone. It is thus reasonable to assume that —similar to EAN and various imidazolium ILs in AN [17, 23, 50]— an equilibrium between CIPs and free cations is probed where the relaxations of both components are too close to be resolved but manifest by large width parameters, α1 ≈ 0.4. A significant presence of CIPs at xEAN ≤ 0.13 is also suggested by the effective dipole moment calculated from S1 assuming a spherical cavity field (A = 1/3) as the obtained values extrapolate to 16.6 D at infinite dilution (Fig. 6b). This value is comparable to the CIP dipole moment of µeff,CIP = 18 D estimated by Weingärtner et al. [55] and the value of 19.3 D obtained in our investigation of EAN+AN mixtures [17]. In order to disentangle the contributions of CIPs and [EtNH + 3 ] to S1 in the electrolyte-like region the approach of Ref. [17] was followed, i.e. Eq. (2) was rewritten as & % ε NA × (11) S1 = × (cEAN − cCIP )µ2eff,+ + cCIP µ2eff,CIP 2ε + 1 kB T ǫ0 where cEAN = cEA+ + cCIP is the analytical EAN concentration, cEA+ ) and cCIP are the concentrations of free cations and CIPs, and µeff,+ = 4.9 D and µeff,CIP = 19.3 D the corresponding dipole moments [17]). Attempts to analyze the present S1 data by assuming the formation of solvent-shared ion pairs instead of CIPs or a contribution of bound solvent, as was the case for imidazolium RTILs+AN [23, 50], yielded unphysical results. From species concentrations obtained with Eq. (11) association constants KA =

cCIP (cEAN − cCIP )2 17

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were calculated (Fig. 9) and the corresponding standard-state association con◦ stant, KA , determined by extrapolation with the Guggenheim-type equation [56] √ 2ADH I ◦ √ + AK I + BK I 3/2 (13) log KA = log KA − 1 + Rij BDH I

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where I (≡ cEAN ) is the stoichiometric (nominal) ionic strength; ADH = 1.616 L1/2 mol−1/2 and BDH = 4.829 L1/2 mol1/2 are the Debye-Hückel constants for NM at 298.15 K [57]. For the distance of closest approach of the ions Rij = 0.322 nm was chosen, which corresponds to the contact distance obtained with MOPAC [38]. The factors AK = −3.937 L mol−1 and BK = 1.196 L3/2 mol−3/2 are empirical fit parameters. ◦ = (965 ± 27) The thus obtained standard-state association constant, KA −1 L mol , is comparable to the values found for EAN in AN (1094 L mol −1 [8]; 970 L mol−1 [17]) and indicates pronounced CIP formation of this PIL also ◦ in NM. The present KA is an order of magnitude smaller than ([EtNH 3 ][Cl]: −1 36806 L mol , [EtNH3 ][Br]: 10086 L mol−1 , all Ref. [58]; [Quinuclidinium][Cl]: 43326 L mol−1 [59] & 28800 L mol−1 [60]) or comparable to ([2,6-Lutidinium][Cl]: 5800 L mol−1 , [EtNH3 ][I]: 603.7 L mol−1 [58]) association constants reported for protic salts in NM. On the other hand, similar to AN solutions [17, 23, 50], apro◦ tic salts exhibit only small to moderate KA values ([Et4 N][NO3 ]: 15.87 L mol−1 , −1 −1 KSCN: 107.6 L mol , KI: 40.38 L mol , tetraalkylammonium halides: ∼1020 L mol−1 [58]) in NM. The above comparison provides clear evidence that hydrogen bonding among the ions is the main driving force for the strong association of EAN to contact ion pairs in nitromethane, as it is in AN [17]. The reason why NM exhibits a miscibility gap with EAN but AN does not is probably the considerably smaller acceptor number of the first, namely 2.7 for NM vs. 14.1 for AN [51]. Due to the significantly weaker cation solvation in NM self-aggregation and subsequent segregation of EAN should be promoted. 5. Concluding Remarks

According to the present findings the dielectric spectrum, εˆ(ν), of nitromethane in the microwave region (0.05 ν/GHz 100) is well described by a single Debye relaxation. The obtained relaxation parameters show a smooth change with temperature and the obtained static relative permittivities are in good agreement with some literature data from capacitance measurements. Nevertheless, NM cannot be recommended as a dielectric reference because samples of well-defined purity are difficult to obtain. In particular, the content of organic impurities seems to be problematic. For the mixtures of nitromethane with ethylammonium nitrate a behaviour similar to mixtures of this PIL with AN has been observed. At low concentrations EAN is strongly associated to contact ion pairs and the absence of strong solute-solvent interactions gives way to phase separation in the region

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0.013 < xEAN < 0.4. At infinite dilution EAN effectively freezes the reorientation of ∼7 NM molecules, with Zeff linearly decreasing in the electrolyte-like region. The observed effective solvation number of the ionic liquid could not be unequivocally assigned to a specific ion. Keeping in mind the rather small acceptor and donor numbers of AN it is likely that Zeff arises solely from electrostatic ion-solvent interactions. Dynamics of the PIL-rich phase is dominated by EAN, most likely through jump-reorientation of the cation. For xEAN $ 0.6 no free NM is detectable anymore. The here observed increase of µeff,EAN on dilution with NM suggests that in this range PIL and added solvent share the same dynamics which speeds up with increasing NM concentration.

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Ethylammonium nitrate is strongly associated in mixtures with nitromethane at xEAN 0.013. At xEAN " 0.4 EAN+nitromethane mixtures behave as “lubricated” ionic liquid. Cooperative dynamics of mixtures and ion association dominated by hydrogen bonding among ions. Ion solvation by nitromethane is weak.