We have measured the complex dielectric function of the protic ionic liquid ethylammonium nitrate in the frequency range between 0.15 and 1.8 THz with a terahertz time domain spectrometer. The experiments reveal a terahertz mode which can be described as a damped harmonic oscillator with a central frequency of 1.3 THz. The terahertz mode is assigned to an intermolecular vibration, presumably associated with hydrogen-bond dynamics. The data are combined with microwave data to represent the dielectric spectrum from quasistatic conditions up to 1.8 THz.

There is much effort for characterizing the intermolecular dynamics of liquids as a prerequisite for understanding solvation dynamics and solvent-controlled chemical reactions. Among the experimental methods, dielectric spectroscopy is widely applied.1 Dielectric spectroscopy probes polarity fluctuations due to the collective rotational dynamics of dipolar species. In electrically conductive systems, as considered here, there are additional translational contributions due to charge transport.2 

The dielectric response of low-viscosity liquids is distributed over several decades in time from subpicosecond intermolecular vibrations to diffusive processes on the picosecond-to-nanosecond scale. Due to limitations of conventional microwave dielectric techniques to frequencies up to about 50 GHz,2 dielectric spectroscopy has mainly focused on the slower diffusive regime. To understand the elementary steps of solvation dynamics and solvent-controlled chemical reactions, the fast, subpicosecond portion of the dielectric response is of prime interest.3 In principle, these processes can be probed by FTIR spectroscopy. In the last few years, the experimental capabilities have, however, greatly benefited from advances in femtosecond laser pulse technology, which allow to probe the complex index of refraction with femtosecond resolution by terahertz time domain spectroscopy.4–6 

There is an increasing interest in terahertz spectroscopy in diverse fields of physics, chemistry, biology, or materials science,4 including applications to study intermolecular dynamics of liquids.5 Because terahertz spectroscopy covers the typical time scale of the collective fluctuations of water’s three-dimensional (3D) hydrogen-bonded network, terahertz spectroscopy allows to address fundamental questions concerning H-bond dynamics and its coupling to solvation and to chemical and biological processes.5,6

Therefore, terahertz spectroscopy is an obvious tool to probe 3D H-bonded network formation. One intriguing candidate is ethylammonium nitrate (EAN), which is a representative of a class of low-melting salts, denoted as “ionic liquids.” Owing to their unusual materials and solvent properties ionic liquids are attracting much interest as innovative solvents.7 Specifically, EAN belongs to the subgroup of “protic ionic liquids” formed by combination of a Brønsted acid and a Brønsted base.8 The ethylammonium cation and nitrate anion act as donor and acceptor sites for H-bonding. On the macroscopic level, EAN possesses a number of waterlike properties,9 for example driving the self-assembly of amphiphilic solutes to micelles.10 On the other hand, it lacks the typical anomalies of water. Its hydrophilicity and H-bonding ability prospect intriguing applications in biotechnology, e.g., in driving protein crystallization11 and refolding.12 

Previously, we have used microwave spectroscopy to study the dielectric spectrum of EAN up to 40 GHz (1.3cm1).13 This spectrum reveals a strong mode centered near 2 GHz, but also indicates processes beyond the frequency window up to 40 GHz. The intensity of the fast portion was estimated to come close to the strong terahertz absorption of water.13 Fumino et al.14 have reported on FTIR data for EAN between 30cm1 (0.9 THz) and 600cm1 (18 THz), observing several intra- and intermolecular vibrations.

The present paper aims at characterizing the “complete” dielectric spectrum of EAN from quasistatic conditions up to the infrared regime by combining microwave data with terahertz data. Special attention is given to the regime below 2 THz, where one expects contributions caused by H-bond dynamics. Calculations by DFT in comparison to FTIR spectra14 suggest deformation bands of asymmetric and symmetric stretching modes of hydrogen bonds like NH…O in the spectral range 6078cm1. Attempts to characterize the dielectric response of ionic liquids have dealt with “aprotic” dialkylimidazolium salts,15 which are not capable of forming extended H-bonded structures.

The high-frequency part of the dielectric spectrum of EAN is of particular interest with regard to photophysical studies of the solvation dynamics.16 These experiments use the time-dependent fluorescence emission of solvatochromic dyes to probe the solvent reorganization following a sudden change of the dye’s dipole moment by photon excitation. There are theoretical approaches which link the solvation spectra to the dielectric spectra.3 For molecular liquids, these approaches work fairly well,3 but there is a current debate about their utility for systems involving charged particles.3,16,17 EAN has been suggested to form an ideal test case for such models.16 

For recording the terahertz spectra of EAN (water content <1000ppm),18 we used two experimental setups. The FTIR vacuum spectrometer (Bruker, Vertex 80v) with a bandwidth from 10 to 600cm1 (0.3–18 THz) is equipped with a Si bolometer operated at liquid helium temperature. Our terahertz time domain spectrometer, sketched in Fig. 1, has a maximum band width from 5 to 115cm1 (0.15–3.5 THz).19 The measured sets of terahertz transients E(t) for each sample thickness are Fourier-transformed to obtain the complex frequency response T(ω) of the sample and the reference, respectively.

FIG. 1.

Terahertz time-domain spectrometer. For simplicity, only the terahertz radiation path is displayed. The pump pulse train from a mode-locked femtosecond laser generates subpicosecond terahertz pulses in a large-area semiconductor antenna. The pulses are focused via off-axis parabolic mirrors onto the sample cell. The electric field of the terahertz pulses induces a change in polarization which is probed by the Ti:Sa pump laser. The time-dependent electric field amplitude is detected via electro-optic sampling. The measurement cell is kept at a constant temperature of (20±0.5)°C and consists of two 4 mm thick quartz windows with Teflon spacers of 53, 107, 122, and 161μm (uncertainty ±1μm).

FIG. 1.

Terahertz time-domain spectrometer. For simplicity, only the terahertz radiation path is displayed. The pump pulse train from a mode-locked femtosecond laser generates subpicosecond terahertz pulses in a large-area semiconductor antenna. The pulses are focused via off-axis parabolic mirrors onto the sample cell. The electric field of the terahertz pulses induces a change in polarization which is probed by the Ti:Sa pump laser. The time-dependent electric field amplitude is detected via electro-optic sampling. The measurement cell is kept at a constant temperature of (20±0.5)°C and consists of two 4 mm thick quartz windows with Teflon spacers of 53, 107, 122, and 161μm (uncertainty ±1μm).

Close modal

Dielectric processes in charged systems can be described by representations in terms of the frequency-dependent complex dielectric constant, the frequency-dependent complex electrical conductance, or the complex dielectric modulus.2 While the different representations accentuate different aspects of the data, they are equivalent and can be converted into one another.2 As in recent experimental studies15,20–22 and molecular dynamics simulations of dielectric spectra of ionic liquids,17,23 we describe here dielectric relaxation in terms of the complex dielectric permittivity ε̃=ñ2, where ñ=nik is the complex refractive index. The real part, n, of the complex refractive index describes the deceleration (dispersion) of the traveling electromagnetic wave. The imaginary part, k, exhibits damping (absorption) of this wave. The real and imaginary parts of the frequency-dependent dielectric constant are then given by

Re(ε̃)=n2k2;Im(ε̃)=2nk.
(1)

In order to determine ε̃ from the terahertz absorption we adapted an iterative procedure for analyzing the pulse propagation in the sample cell.24 The measured complex ratio of the frequency-dependent electric fields of the reference and the sample was fit to a theoretical model which accounted for reflection and transmission in the sample cell and at each optical interface. Air and quartz were treated as transparent media with refractive indices of n=1.0 and 2.1, respectively.25 For each frequency, the error was estimated assuming Gaussian error propagation of the Fourier transformation.26 The real and imaginary parts of ε̃ were determined from n and k using Eq. (1).

Figure 2 displays the real and imaginary parts of the complex dielectric constant deduced from the joint analysis of the terahertz and microwave spectra of EAN. The terahertz data were recorded at (20±0.5)°C. The temperature-dependent microwave data13 were interpolated to this temperature. There is a gap between 40 and 150 GHz which is covered by the terahertz time-domain experiment but with low signal-to-noise ratios. It is therefore not shown and excluded from the analysis to prevent the introduction of systematic errors. The terahertz and microwave segments of the spectra can, however, be smoothly connected. The spectral increase in the real part of the dielectric constant, mainly determined by the refractive index, could hint to further processes,13,22 but our model predicts the data in the imaginary part very well. The majority of data points for the real part with their respective error are traversed by the model with good agreement so that the statistical evidence for an additional mode in EAN is low.

FIG. 2.

Shown are the real (top) and imaginary (bottom) parts of the frequency-dependent complex dielectric constants and the model according to Eq. (3). The simulated microwave extracted from microwave data measured (down to 3 MHz, not shown here, see Ref. 13) and measured terahertz time-domain spectra are shown as a solid line, whereas the overall fit is shown as a dot-dashed line. The dashed and dotted lines correspond to the deconvolution of the spectrum into the microwave and terahertz contributions, respectively. The insets focus on the terahertz data and display the fitted model (dot-dashed) and the measured terahertz spectra (solid) with error bars. Here, the negative imaginary part Im(ε) is shown in the same scale as the real part Re(ε).

FIG. 2.

Shown are the real (top) and imaginary (bottom) parts of the frequency-dependent complex dielectric constants and the model according to Eq. (3). The simulated microwave extracted from microwave data measured (down to 3 MHz, not shown here, see Ref. 13) and measured terahertz time-domain spectra are shown as a solid line, whereas the overall fit is shown as a dot-dashed line. The dashed and dotted lines correspond to the deconvolution of the spectrum into the microwave and terahertz contributions, respectively. The insets focus on the terahertz data and display the fitted model (dot-dashed) and the measured terahertz spectra (solid) with error bars. Here, the negative imaginary part Im(ε) is shown in the same scale as the real part Re(ε).

Close modal

As noted, the complex dielectric permittivity of a charged system involves a translational contribution due to charge transport,2 which is particularly pronounced for highly conductive ionic liquids. In particular, there is a 1/ν-dependent component of the dielectric absorption (the so-called “Ohmic loss”), which diverges as the frequency ν approaches zero.2 To avoid the divergence, this 1/ν-dependent component is usually subtracted from the measured absorption spectrum23 by considering the quantity

Im(Δε̃)=Im(ε̃)+κ2πνε0,
(2)

where κ is the static (dc) conductivity of the sample (here, κ=25mScm1) and ε0 is the dielectric permittivity of the vacuum. The real part (dielectric dispersion) does not involve the 1/ν-dependent term. The correction given by Eq. (2) is confirmed by rigorous theory of the dielectric response of ionic liquids.17,23 It should, however, be noted that the corrected absorption still encapsulates those contributions due to translational motions which depend on frequency.

The joint microwave and terahertz data could be fitted to the bimodal expression

ε̃=ε+W1(1+i2πντ)β+W2ν02ν02ν2+iγν.
(3)

Following the earlier work, the microwave process is described by an asymmetrical Cole–Davidson (CD) distribution of relaxation times,13 involving the amplitude W1, relaxation time τ, and shape parameter β of the distribution as fit parameters. The fast process is best described by a damped harmonic oscillator (DHO).15 W2 is the amplitude, γ the damping constant in units of frequency, and ν0 the central frequency. The adjusted parameters are given in Table I.

Table I.

Parameterization of the dielectric spectrum of EAN including the terahertz data (T=293K).

ParameterFitted valueUncertaintya(%)
εS 26 
ε 3.2 
τ/ps 158 
β 0.52 
W1 21.9 
ν0/THz 1.3 
γ/THz 2.4 
W2 1.3 
ParameterFitted valueUncertaintya(%)
εS 26 
ε 3.2 
τ/ps 158 
β 0.52 
W1 21.9 
ν0/THz 1.3 
γ/THz 2.4 
W2 1.3 
a

Calculated by error propagation of the fit.

It was noted in Ref. 13 that the CD representation was superior over other distributions of relaxation times such as the symmetrical Cole–Cole (CC) distribution. The CD function is well known to describe stretched dynamics in systems revealing structural heterogeneity, for example near the glass transition. Small angle neutron scattering experiments of Atkin and Warr27 point toward nanoscale segregation of EAN, which may indeed impose the typical conditions for asymmetrical CD-type stretched dynamics. On the other hand, we cannot exclude that the quality of the symmetrical CC representation becomes similar to that of the CD representation, if it is supplemented by a further term at the high-frequency edge of the microwave regime, near 50 GHz say. In this sense, the tail of the CD function may mask the presence of higher-frequency modes. Any such conclusion would, however, be highly speculative.

The static dielectric constant, defined as the zero-frequency limit of Re(ε̃), is given by εS=W1+W2+ε, where ε accounts for contributions to Re(ε̃) beyond the upper cut-off frequency of the experiments. In the ideal case ε reflects the electronic displacement polarization is ε=nopt22.1, where nopt=1.45 is the optical refractive index of EAN.13 Although we have now extended the spectrum more into the terahertz range, the fitted value ε=3.2 is still markedly above this limiting value. Note that the parameters for the microwave mode obtained from the fit of the entire spectrum agree well with those determined earlier from the microwave segment.13 The effective high-frequency limit, ε, in Table I is, however, lower than the value deduced from the microwave spectrum because in the latter case the effective value of ε includes the amplitude W2 accounting for a 1.3 reduction of ε. Individually, the IR modes contribute less than the terahertz mode to the refractive index change because the change in the real part scales with ν02 for a DHO. The sum of all IR modes gives a value of 1.1.

For comparison, we have performed FTIR measurements of the same sample. In order to increase the sensitivity compared to previous measurements14 we have used a sample cell with diamond windows and a sensitive liquid helium cooled bolometer. This improved the signal-to-noise ratio significantly, revealing additional infrared modes, and allowed the smooth connection of the terahertz data to the infrared spectrum. By measuring the absolute thickness of the Teflon spacer, (28±1)μm, we were able to determine the absorption coefficient α. Figure 3 shows the complete absorption spectrum ranging from the microwave via the terahertz range up to the infrared regime. The FTIR data smoothly join the data obtained by terahertz spectroscopy.

FIG. 3.

Comparison of the absorption coefficient simulated in the microwave range (solid black), extrapolated from the pure microwave model (dashed black), as measured with the terahertz time-domain spectrometer (solid black) and taken from our FTIR measurements (solid blue). The absorption coefficient calculated from the combined microwave and terahertz model is shown in dot-dashed red. The inset shows a magnification of the measured terahertz absorption coefficient with error bars. The combined model, valid for the microwave and terahertz part, reflects the data very well and predicts up to approximately 1.5 THz the contribution to modes measured by FTIR.

FIG. 3.

Comparison of the absorption coefficient simulated in the microwave range (solid black), extrapolated from the pure microwave model (dashed black), as measured with the terahertz time-domain spectrometer (solid black) and taken from our FTIR measurements (solid blue). The absorption coefficient calculated from the combined microwave and terahertz model is shown in dot-dashed red. The inset shows a magnification of the measured terahertz absorption coefficient with error bars. The combined model, valid for the microwave and terahertz part, reflects the data very well and predicts up to approximately 1.5 THz the contribution to modes measured by FTIR.

Close modal

The present study clearly reveals the existence of a distinct dielectric dispersion/absorption regime near 1.3 THz (40cm1). The assignment of modes obtained by FTIR spectroscopy are discussed in Ref. 14. The observed band near 1.3 THz is tentatively assigned to an intermolecular band reflecting the reformation of H-bonds. We suspect some similarity to a process near 60cm1 in the Raman spectrum of water.28 The corresponding process in the direct absorption spectrum of water is very weak,29 as H-bond bending in a highly symmetric environment imposed by the tetrahedral network of water implies a low molar absorption coefficient. One may speculate that the lower symmetry of the H-bonded network of EAN may enhance the infrared activity of such a bending mode relative to a similar process in water.

In summary, terahertz spectroscopy of EAN indicates a fast process described by a slightly underdamped harmonic oscillator with a damping time constant of 2/γ=830fs, corresponding to the typical time scale expected for an intermolecular mode due to H-bond reformation. It is worthwhile to note that the spectrum of EAN turns out to be simpler than those of imidazolium-based ionic liquids in the same frequency regime, which are yet little understood.15 The existence of a pronounced mode due to H-bond dynamics in EAN is expected to play a major role in solvation dynamics and solvent-controlled chemical reactions in EAN.

M.K. thanks the Foundation of German Economics (SDW) and the Ruhr-University Bochum Research School for funding. The FTIR was funded by the German Federal Ministry of Education and Research (BMBF) under Grant No. BMBF 05KS7PC2 and the terahertz system under the HBFG program of DFG. H.W. thanks the DFG for financial support within the priority program SPP 1191 (ionic liquids). Mian-Mian Huang is acknowledged for help with the sample preparation.

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