# Dielectric Study of Tetraalkylammonium and Tetraalkylphosphonium Levulinate Ionic Liquids

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}anion studied in literature. In order to analyze dielectric data, different fitting approaches were employed. The original random barrier model cannot well describe the conductivity especially at the higher frequencies region. In electric modulus representation, two overlapping mechanisms contribute to the broad low frequencies peak. The slower process is related to the conduction mechanism and the faster to the main polarization process of the complex dielectric permittivity representation. The correlation of the characteristic time scales of the previous relaxation processes was discussed in terms of ionic interactions.

## 1. Introduction

_{2}absorption processes [11,12], or in the dissolution and modification of cellulose [13,14,15,16].

## 2. Results and Discussion

#### 2.1. Dielectric Data

_{8881}]Lev and [P

_{8881}]Lev, respectively, are presented. Although quantities in different representations of dielectric data are interrelated and contain equivalent information, dielectrically active processes of ILs are differently emphasized in each representation, giving complementary information, making their separate discussions helpful.

_{8881}]Lev where M″ reveals a two-contribution structure. In M″ representation, the low-frequency steady increase in ε″ caused by conductivity and discussed above is converted into a peak. The peak frequency, f

_{M}, which depends on the value of dc conductivity, σ

_{0}, and the dielectric constant ε

_{s}, ${\mathsf{\sigma}}_{0}={\mathsf{\epsilon}}_{\mathrm{o}}{\mathsf{\epsilon}}_{\mathrm{s}}2{\mathsf{\pi}\mathrm{f}}_{\mathsf{{\rm M}}}$ [40], is often used as the characteristic frequency of conductivity relaxation in ILs. The peak observed in M″ arising from conductivity usually occurs close to the crossover frequency between the frequency independent (dc) and the frequency dependent (ac) part of σ′. However, the polarization processes (dielectric relaxations) also lead to peaks in M″, which are shifted to higher frequencies compared to the peaks observed in ε″ [39]. So, the broad peak in M″, especially its double structure observed for the systems under investigation (Figure 1c and Figure 2c), indicates the contribution of a dielectric relaxation except the conductivity relaxation in the dielectric response of these IL systems. Moreover, the linear increase of M″ values at lower temperatures and at the higher frequency region in logM″–logf plots (Figure 1c and Figure 2c), indicates the contribution of a faster additional dielectric relaxation. The influence on the frequencies window of a high frequency dielectric relaxation can also be verified if the slope of diagrams logM″–logf is not constant at the higher frequencies region.

^{−}

^{1}dependence, while in ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$, there is a power law increase at low frequencies, which leads to the formation of a peak at even lower frequencies (Figure 1b and Figure 2b). In the modulus representation, EP effects are eliminated.

#### 2.2. Dielectric Data Evaluation

#### 2.2.1. Ionic Conductivity

_{0}, where D is the so-called strength parameter, which is used to distinguish between strong and fragile glass formers [45]. A small value of D leads to a significant deviation from the Arrhenius-type behavior and vice versa. Alternatively, the fragility index m is also used for the classification of glass formers. Both parameters are connected via the relation $\mathrm{m}\approx 16+590/\mathrm{D}$ [46]. Fits of the VFT equation on the data are shown as solid lines in Figure 3. Slightly higher values of D and correspondingly lower values of m were found for [N

_{8881}]Lev compared to [P

_{8881}]Lev (D = 13.2, m = 61 and D = 11.7, m = 66, respectively). As pointed out [47], except for the influence of the glass transition temperature, T

_{g}, on the room temperature conductivity of ILs, an important role, ‘plays’ the fragility (m or D). A higher value of m found for [P

_{8881}]Lev compared to [N

_{8881}]Lev is consistent with the higher conductivity at room temperature found for it (Figure 3). Table 1 shows the VFT parameters obtained from fitting of conductivity for [N

_{8881}]Lev and [P

_{8881}]Lev.

_{8881}]Lev compared to [N

_{8881}]Lev can be understood in terms of lower viscosity and T

_{g}values found for the former [48]. In the inset of Figure 3 the logarithm of molar conductivity was plotted as a function of the logarithm of inverse viscosity, known as a Walden plot [35,49]. Molar conductivity was calculated as $\mathsf{\Lambda}={\mathsf{\sigma}}_{0}\mathsf{{\rm M}}/\mathsf{\rho}$, where M is the molecular weight and ρ the density. For the calculations, ρ values obtained for the same systems reported in [48] were used. The Walden plot was used for the determination of the relationship between ionic conductivity and viscosity as well as for a qualitative description of ILs regarding their ion association. The data for both ILs studied here fall in a straight line of slope close to unity (1.0 for [P

_{8881}]Lev and 0.97 for [N

_{8881}]Lev), indicating that the charge transport in both systems is controlled by viscosity, as has been reported for many aprotic ILs [2,49,50,51]. The charge and mass transport in the investigated ILs are well coupled to each other, pointing to a vehicular charge transport, dominating its conductivity response at least at high temperatures where measurements of both techniques are available.

_{8881}]NTf

_{2}IL reported in the literature [25] are plotted as crosses in Figure 3, along with current results. Considerably lower ion conductivity values were obtained for [N

_{8881}]Lev compared to [N

_{8881}]NTf

_{2}in accordance with the higher viscosity measured for the former (at 298 K 1019 mPas [48] and 620 mPas [4], respectively). Interestingly, the same values for ionic conductivity were found for [N

_{8881}]NTf

_{2}and [P

_{8881}]Lev although lower viscosity values were measured for the latter (at 298 K 620 mPas [4] and 366 mPas [48], respectively). The lower conductivity values from that expected according to its viscosity obtained for [P

_{8881}]Lev, could be understood in terms of enhanced ion association in this IL compared to [N

_{8881}]NTf

_{2}. Datum for [N

_{8881}]NTf

_{2}at 298 K, using a value of ρ equal to 1.1 g/cm

^{3}, reported in [25], is included as red star in the Walden plot (inset of Figure 3). The positions of the data obtained for [N

_{8881}]NTf

_{2}relative to those obtained for the ILs under investigation indicate a stronger ion association in the latter.

#### 2.2.2. Dynamics

_{0}is the dc conductivity value and τ

_{RBM}is a time constant at which the transition from ac to dc conductivity takes place. The time constant τ

_{RBM}corresponds to the attempt rate f

_{RBM}(f

_{RBM}= 1/2πτ

_{RBM}) to overcome the highest energy barrier. For f = f

_{RBM}Equation (2) gives σ′ = 1.17σ

_{0}. The real part of Equation (2) was used to fit σ′(f) data in the frequency region of dc–ac transition. The RBM model describes relatively well the experimental data of both ILs in the selected region, while it lacks describing the data at higher frequencies, as can be seen in Figure 4 and Figure 5. When the fit is performed in the whole frequency range (not shown here) a negative divergence of the fitting curves from experimental data are observed even in the region of the ac–dc transition. However, it should be noted here that the use of the RBM model is questionable, and is obviously not expected to describe the dielectric response of materials when the basic assumptions of this model are not met. The ILs studied here do not satisfy the assumptions and considerations of the RBM model, because in addition to the existence of mobile ions that create a polarization mechanism at low frequencies, and at even lower frequencies contribute to the dc conductivity, there is also the contribution of a faster dielectric relaxation at higher frequencies, as mentioned above. As will be seen below, the effect of this faster dielectric mechanism is significant in the frequency window of the present study. Thus, it would be expected that the discrepancy of the RBM model at high frequencies would be due to the fact that the contribution of this fast mechanism was not taken into account in Equation (2). In the case where the extension of the best fit of Equation (2) resulted in lower values compared to the experimental data in the high frequency range, the lack of the faster mechanism contribution to Equation (2) could explain the inability of this relation to describe the conductivity response at higher frequencies. However, the extensions of the best fit of Equation (2), in both ionic liquids, lead to higher values than the corresponding experimental data in the high frequencies region, as shown in Figure 4 and Figure 5. Thus, it becomes clear that the RBM model is not able to describe satisfactorily the overall conductivity response of ILs studied in the present work. The application of the original RBM in ionic liquids describes the conductivity spectra σ′(f) reasonably well but is not able to describe the data in the ε*(f) representation [33]. Similar behavior was reported in [N

_{8881}][NTf

_{2}] ionic liquid where the RBM describes the data in σ′(f) very well, but underestimates the data in σ″(f) at lower frequencies and, as a consequence, lacks describing the ε′(f) [27]. In the present study, the original RBM describes reasonably well the dc–ac region but overestimates the data in σ′(f) at higher frequencies. In the framework of RBM, noninteracting charge carriers were considered to perform hopping on a simple cubic lattice. The charge transport process was governed by a broad distribution of energy barriers while the charges have to overcome a certain percolation barrier in order for random diffusion to take place. So, the inability of RBM to describe the overall conductivity response of some ionic liquid systems is possibly due to the fact that some of the basic assumptions of this model cannot satisfactorily describe the charge transport mechanisms in these materials. It is also possible that the transport of ions is accompanied by dipolar contribution, as a result of their structures, which is not taken into account by RBM.

^{-s}). Figure 6c and Figure 7c show a representative fitting of ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$ data at 218 K for [N

_{8881}]Lev and [P

_{8881}]Lev, respectively. Individual contributions of relaxation processes are shown as dashed and dotted lines in these plots.

_{8881}]Lev and [P

_{8881}]Lev, respectively. The contribution, observed as a kink at high frequencies, was modeled by a Cole–Cole (C–C) function with a α

_{CC}parameter close to 0.3. The latter process is ascribed to secondary relaxations observed in ILs [26,54,55] and will not be discussed further here. However, from Figure 6c and Figure 7c, it is obvious that the secondary dielectric relaxation significantly influences the dielectric response up to 0.5 KHz, and 5 KHz for the [N

_{8881}]Lev and [P

_{8881}]Lev ILs, respectively. Dielectric data in all the formalisms can be reproduced assuming the contributions of the relaxation processes obtained by fitting of the ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$ and the dc conductivity. So, dielectric data in different representations (ε′, ε″, ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$, M″) at 218 K for [N

_{8881}]Lev and [P

_{8881}]Lev are shown in Figure 6 and Figure 7, respectively. The parameters obtained from the fitting of ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$ data were used to reproduce data in all other representations. For the reproduction of data in different formalisms, additional terms were used. For the reproduction of ε′ (f) (Figure 6a and Figure 7a), the instantaneous permittivity, ε

_{∞}, for ε″ (f) (Figure 6b and Figure 7b), conductivity term ($\frac{{\mathsf{\sigma}}_{0}}{{\mathsf{\epsilon}}_{0}2\mathsf{\pi}\mathrm{f}}$), and for M″(f) (Figure 6d and Figure 7d), both ε

_{∞}and the conductivity term were added. The values used are those obtained directly from dielectric data. For both ILs under investigation, the dielectric data are perfectly described in all the representations assuming the contributions of two relaxation processes and of dc conductivity as shown in Figure 6 and Figure 7.

_{M}is the lower frequencies peak in the M″ representation.

_{ε}of the main dielectric relaxation in the ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$ representation and the characteristic frequency f

_{M}of the conductivity relaxation in M″ are presented in Figure 8 and Figure 9. In the same figures, the characteristic frequencies of the RBM model, f

_{RBM}, at which σ′ = 1.17σ

_{0}(from the experimental data) and the fitting processes, are also included. The unsatisfactory applicability of the RBM model to ionic liquids studied in the present work, even in the dc–ac transition region, is shown by the difference in f

_{RBM}frequency values as calculated from the experimental data (σ′ = 1.17σ

_{0}) and the fitting processes (Figure 8 and Figure 9). The characteristic frequency, f

_{RBM}, as graphically estimated from σ′–f plots, always takes values between the characteristic frequencies f

_{ε}and f

_{M}of both ILs. According to the Arrhenius plots of Figure 8 and Figure 9, the relative difference of the characteristic frequencies f

_{ε}and f

_{M}is higher for [N

_{8881}]Lev, at each temperature. Moreover, the characteristic frequencies f

_{ε}and f

_{M}of [P

_{8881}]Lev are higher than the respective ones of [N

_{8881}]Lev, which means faster mechanisms.

_{M}is related to the dc conductivity via the relation ${\mathsf{\sigma}}_{0}={\mathsf{\epsilon}}_{\mathrm{o}}{\mathsf{\epsilon}}_{\mathrm{s}}2{\mathsf{\pi}\mathrm{f}}_{\mathsf{{\rm M}}}$, the frequency f

_{ε}of the main dielectric relaxation related also to the dc conductivity via the well-known BNN relation ${\mathsf{\sigma}}_{0}={\mathrm{p}\mathsf{\epsilon}}_{\mathrm{o}}\mathsf{\Delta}\mathsf{\epsilon}2{\mathsf{\pi}\mathrm{f}}_{\mathsf{\epsilon}}$, where Δε is the contribution of the main dielectric relaxation in ε’ [56]. The coefficient p usually takes values close and around unity, $\mathrm{p}\approx 1$ [57]. Therefore, ${\mathrm{f}}_{\mathrm{M}}/{\mathrm{f}}_{\mathsf{\epsilon}}\approx \mathsf{\Delta}\mathsf{\epsilon}/\left(\mathsf{\Delta}\mathsf{\epsilon}+{\mathsf{\epsilon}}_{\infty}\right)$ and, hence, f

_{M}< f

_{ε}. So, the distances of the characteristic frequencies f

_{ε}and f

_{M}depend macroscopically on the parameters $\mathsf{\Delta}\mathsf{\epsilon}$ and the unrelated to ionic motion instantaneous permittivity ${\mathsf{\epsilon}}_{\infty}$. Microscopically, in the framework of IC structures [58], a possible scenario that could explain the dielectric response of both ionic liquids in Arrhenius plots of Figure 8 and Figure 9 are as follows. Because the stimulus in dielectric relaxation spectroscopy is the alternating electric field, E, the concept of signals period T = 1/f is useful to better perceive the overall dielectric response. The main dielectric relaxation, as detected in ε″ representation, could be a result of the dipolar moments induced by the relative displacements of ions in IC structures by the application of the ac electric field E. Stronger ionic interactions in IC imply more difficult displacements of ions, so a longer duration of E (higher period or lower frequency) is required to complete the polarization mechanism and reach the peak f

_{ε}. Therefore, stronger ionic interaction means a lower value of f

_{ε}and as a consequence, a lower value of f

_{M}(${\mathrm{f}}_{\mathrm{M}}<{\mathrm{f}}_{\mathsf{\epsilon}}$) and, hence, lower dc conductivity, a behavior that characterizes the experimental data of [N

_{8881}]Lev IL. This is in accordance with a recent work [48]. The viscosity values and the related activation energy of both ILs [48], suggest that [N

_{8881}]Lev has stronger interactions between anion–cation pairs than [P

_{8881}]Lev. The higher the viscosity and the activation energy, the stronger the ionic interactions.

_{M}, which appears below f

_{ε}, as shown previously. The relative distance of these two characteristic frequencies depends on how strong the ionic interactions are in the IC structures. Stronger interactions imply that a longer duration of E (higher period or lower frequency) is required to assist the ions to escape from the coulombic cage in IC structures, and then move at a longer distance, giving rise to the conductivity relaxation mechanism as detected in the M″ representation. Therefore, a larger relative difference between the characteristic frequencies f

_{ε}and f

_{M}indicates stronger ionic interactions, and this behavior characterizes [N

_{8881}]Lev, as discussed previously. Both characteristic frequencies f

_{RBM}and f

_{M}are related to the conduction mechanism. According to the Arrhenius diagrams in Figure 8 and Figure 9, f

_{RBM}(from σ′ = 1.17σ

_{0}) is systematically higher than f

_{M}and lower than f

_{ε}, ${\mathrm{f}}_{\mathrm{M}}<{\mathrm{f}}_{\mathrm{RBM}}<{\mathrm{f}}_{\mathsf{\epsilon}}$. While f

_{RBM}is related microscopically to the ion hopping rate of the largest energy barrier according to the RBM model, f

_{M}is directly connected to the macroscopic parameters σ

_{0}and ε

_{s}, which are measurable quantities.

## 3. Materials and Methods

#### 3.1. Materials

#### Synthesis of [N_{8881}]Lev and [P_{8881}]Lev

_{8881}]Lev and trioctylmethylphosphonium levulinate [P

_{8881}]Lev were synthetized from methylcarbonate precursors following a previously reported procedure [15].

^{1}H and

^{13}C NMR, and FTIR spectra, were in agreement with those reported.

#### 3.2. Methods

^{−1}–10

^{6}Hz and temperature 173–333 K range was used to study the ILs. Measurements were performed using an Alpha-A analyzer combined with a Novocool temperature controller, both provided by Novocontrol. The capacitor was prepared by placing ionic liquids between two parallel gold-plated flat electrodes, 20 mm in diameter. The distance between the electrodes was kept constant at 50 μm using silica spacers. Since the transport properties of ILs have been found to be significantly affected even by low water contamination [59], prior to the measurements, the samples were kept at 353 K for 24 h in a vacuum oven. The two ILs analyzed in this work belonged to the same batch of samples studied in the previous work on levulinate-based ILs [48] where the results of Karl Fischer titrations for [N

_{8881}]Lev and [P

_{8881}]Lev were 88 and 92 ppm, respectively. The samples were dried at 333 K for 12 h in vacuum before the analysis. Considering that [N

_{8881}]Lev and [P

_{8881}]Lev are hydrophobic ILs and that our drying procedure is similar, similar values of water contents can possibly be assumed. A voltage amplitude equal to 0.1 V was used.

## 4. Conclusions

_{2}as anion, revealed that the levulinate anion used in the present study results in stronger interactions and ion association, and as a consequence to lower values of room temperature conductivity. The analysis presented here demonstrates that the original random barrier model does not describe well the conductivity response, especially in the higher frequency range. The broad low frequency peak in electric modulus representation consists of two overlapping contributions. The slower process is related to the conduction mechanism while the faster process corresponds to the polarization mechanism of the main dielectric relaxation in the complex dielectric permittivity representation. Stronger ionic interactions were found to lead to a slower conductivity relaxation mechanism, which means a lower dc conductivity value and vice versa.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Different representations of dielectric data obtained for [N

_{8881}]Lev at the temperatures indicated on the plot. Real part of dielectric permittivity ε′(f) (

**a**), imaginary part of dielectric permittivity, ε″(f) (

**b**), derivative of ε′, ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}\left(\mathrm{f}\right)$ discussed in the text (at two selected temperatures, red symbols in (

**b**), imaginary part of electric modulus, M″(f) (

**c**), and real part of conductivity, σ′(f) (

**d**).

**Figure 2.**Different representations of dielectric data obtained for [P

_{8881}]Lev at the temperatures indicated on the plot. Real part of dielectric permittivity ε′(f) (

**a**), imaginary part of dielectric permittivity, ε″(f) (

**b**), derivative of ε′, ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}\left(\mathrm{f}\right)$ discussed in the text (at two selected temperatures, red symbols in (

**b**), imaginary part of electric modulus, M″(f) (

**c**) and real part of conductivity, σ′(f) (

**d**).

**Figure 3.**Arrhenius diagram of conductivity σ

_{0}[S/cm] for [P

_{8881}]Lev (squares) and [N

_{8881}]Lev (circles) IL systems. The solid lines are VFT fits to the data. The red crosses are reproduced data from [25] for conductivity of [N

_{8881}]NTf

_{2}IL system. The inset shows a Walden plot for the systems under investigation and the [N

_{8881}]NTf

_{2}IL system (red star) along with the “ideal” Walden line (KCl aqueous solution).

**Figure 4.**Real part of conductivity σ′ as a function of frequency f at different temperatures, indicated on the plot, for [N

_{8881}]Lev. The lines are best fits of the expressions of the original RBM performed in the frequency region of the dc–ac transition and extrapolated to the whole frequency range.

**Figure 5.**Real part of conductivity σ′ as a function of frequency f at different temperatures, indicated on the plot, for [P

_{8881}]Lev. The lines are best fits of the expressions of the original RBM performed in the frequency region of the dc–ac transition and extrapolated to the whole frequency range.

**Figure 6.**Dielectric data for [N

_{8881}]Lev at 218 K. ε′(f) in (

**a**), ε″(f) in (

**b**), ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$(f) in (

**c**), and M″(f) in (

**d**). Solid lines are fitting curves. In (

**c**,

**d**) individual relaxations are shown as dashed and dotted lines. The solid line in (

**d**) is conductivity relaxation (see text for details). The arrows in (

**c**,

**d**) indicate the main peak position.

**Figure 7.**Dielectric data for [P

_{8881}]Lev at 218 K. ε′(f) in (

**a**), ε″(f) in (

**b**), ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$(f) in (

**c**), and M″(f) in (

**d**). Solid lines are fitting curves. In (

**c**,

**d**), individual relaxations are shown as dashed and dotted lines. The solid line in (

**d**) is conductivity relaxation (see text for details). The arrows in (

**c**,

**d**) indicate the main peak position.

**Figure 8.**Arrhenius diagram of the characteristic frequencies of the main peak in ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$ and of the low frequency peak in M″, as well as of the frequency at which σ′ = 1.17σ

_{0}and of the characteristic frequency fRBM obtained by fitting the expression of the original RBM to σ′(f) data for [N8881]Lev presented in Figure 4.

**Figure 9.**Arrhenius diagram of the characteristic frequencies of the main peak in ${\mathsf{\epsilon}}_{\mathrm{deriv}}^{\u2033}$ and of the low frequency peak in M″, as well as of the frequency at which σ′ = 1.17σ

_{0}and of the characteristic frequency f

_{RBM}obtained by fitting the expression of the original RBM to σ′(f) data for [P

_{8881}]Lev presented in Figure 5.

VTF σ _{0} (T) | [P_{8881}]Lev | [N_{8881}]Lev |
---|---|---|

σ_{∞} [S/cm] | 1.11 | 1.92 |

B | 1608 | 1845 |

D | 11.7 | 13.2 |

T_{0} [K] | 138 | 140 |

m | 66 | 61 |

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## Share and Cite

**MDPI and ACS Style**

Kripotou, S.; Tsonos, G.; Mezzetta, A.; Mero, A.; Guazzelli, L.; Moutzouris, K.; Stavrakas, I.; Tsonos, C.
Dielectric Study of Tetraalkylammonium and Tetraalkylphosphonium Levulinate Ionic Liquids. *Int. J. Mol. Sci.* **2022**, *23*, 5642.
https://doi.org/10.3390/ijms23105642

**AMA Style**

Kripotou S, Tsonos G, Mezzetta A, Mero A, Guazzelli L, Moutzouris K, Stavrakas I, Tsonos C.
Dielectric Study of Tetraalkylammonium and Tetraalkylphosphonium Levulinate Ionic Liquids. *International Journal of Molecular Sciences*. 2022; 23(10):5642.
https://doi.org/10.3390/ijms23105642

**Chicago/Turabian Style**

Kripotou, Sotiria, Georgios Tsonos, Andrea Mezzetta, Angelica Mero, Lorenzo Guazzelli, Konstantinos Moutzouris, Ilias Stavrakas, and Christos Tsonos.
2022. "Dielectric Study of Tetraalkylammonium and Tetraalkylphosphonium Levulinate Ionic Liquids" *International Journal of Molecular Sciences* 23, no. 10: 5642.
https://doi.org/10.3390/ijms23105642