Electrical Conductivities and Interactions in Binary Mixtures of Imidazolium-Based Ionic Liquids with Acetonitrile and Dimethyl Sulfoxide

This paper reports experimental electrical conductivities data of eight binary systems of four ionic liquids: 1butyl-3-methylimidazolium tetrafluoroborate, [Bmim][BF4], 1-hexyl-3-methylimidazolium tetrafluoroborate, [Hmim][BF4], 1-butyl-3-methylimidazolium hexafluorophosphate, [Bmim][PF6] and 1-butyl-2,3-dimethylimidazolium tetrafluoroborate, [Bmmim][BF4] with the organic solvents dimethyl sulfoxide (DMSO) and acetonitrile (ACN) at atmospheric pressure and temperatures from 298.15 to 328.15 K. It was found that conductivities in the investigated ionic liquids follow the order: [Bmim][BF4] > [Bmim][PF6] >[Bmmim][BF4] > [Hmim][BF4]. Experimental results demonstrate that the binary mixtures possess higher electrical conductivity compared with pure components. Electrical conductivity data were correlated using Casteel–Amis and Arrhenius equations. The molar conductivity was derived from experimental data and fitted to Walden rule. The influence of the cation structure and anion type on the conductivity was discussed, which help understanding the intermolecular interactions in the binary systems. A deeper understanding of the transport behavior of ILs is given by means of density functional theory calculations (DFT) .

Ionic liquids (ILs), also known as molten salts, represent a new class of solvents with potential to replace volatile organic solvents within the chemical and related industries. Their strengths come from their negligible volatility, nonflammability, excellent thermal and chemical stability, high solubility, high ionic conductivity, and wide electrochemical potential window. These properties recommend them as electrolytic materials in electrochemical devices [1], solvents/adsorbents for capture of greenhouse gases like CO2 [2], solvents in catalysis [3] or in synthesis of metallic oxides [4], etc.
To explore these numerous applications, one needs to know their most important physico-chemical properties. Among them, transport properties such as electrical conductivity and dynamic viscosity are important in chemical and engineering processes, especially electrochemical field. The drawbacks of ILs are the high viscosities and moderate conductivities, that can be adjusted by mixing with molecular liquids. This was found to cause a significant decrease of viscosity and a significant enhancement in the electrical conductivity, especially at some composition of the mixtures [5][6][7][8][9][10][11][12][13][14].
The organic solvents used in this study are polar substances which belong to the class 2 (ACN) and 3 (DMSO) of solvents, according to the classification used in pharmaceutical industry; ACN was chosen due to its wide applicability in electrochemistry and physical chemistry of electrolyte solutions [6][7][8][9] and DMSO, for its extensive use in many chemical processes, biology and medicine [14,15]. In this study we selected the commonly investigated ILs with tetrafluoroborate (BF4 − ) and hexafluorophosphate (PF6 − ) anions and imidazolium cation, due to the relatively lower viscosities, higher ionic conductivities and large potential windows associated with these ions.
During our systematic research on the thermodynamic and transport properties of the binary and ternary systems [16,17] we also studied mixtures with ionic liquids [18][19][20][21][22] Rev. Chim. ♦ 71 ♦ no. 2 ♦ 2020 ♦ https://revistadechimie.ro conductivity by the Arrhenius equation. The concentration dependence of the electrical conductivity of the mixtures was fitted by the empirical Casteel−Amis equation. Conductivity data, coupled with information on viscosity, are discussed in terms of Walden's rule. The main goals of the study are to report new electrical conductivity data for eight binary systems, and to discuss the influence of different parameters on the conductivity. Thus, we consider the structure, size and shape of constitutive ions of ionic liquids, but also the interactions between ILs and organic solvents.
In order to obtain a deeper inside molecular view of ionic pairs, a series of quantum chemical descriptors and structural features were obtained with DFT calculations and used to characterize the ionic liquids in terms of kinetic stability and chemical reactivity, trying to correlate them with special properties of ILslow ionic conductivity and high viscosity. There are studies with DFT calculations in the literature [23] which are conducted in order to predict ILs ion volumes, masses, moments of inertia and interaction energies, used to construct models for computing conductivity.
Apparatus and Procedure. The binary mixtures were prepared gravimetrically with a HR-120 (A&D Japan) electronic balance with a precision of ± 10 -4 g. The experimental uncertainty in mole fractions was estimated to be less than ± 0.0002.
Measurement of electrical conductivity (). The conductivity measurements were carried out with a Cobra 3 Chem-Unit (PHYWE) conductivity meter, using a specially designed cell (electrode LTG 1/24) suitable for low conductivity measurement. Before any measurement the conductivity cell was calibrated with a standard KCl solution (=1.4 mS·cm -1 ). The conductivity cells were filled with samples and sealed with parafilm, then transferred to the thermostat bath. The temperature was kept constant within ±0.05 K with an external oil bath. All measurements were done by means of a static isothermal method, thus we waited for about 20 min with the sample at constant temperature before any single measurement was performed. The uncertainty of the conductivity measurements was estimated to be ± 2%.

Computational details
Density functional theory (DFT) calculations were carried out on the optimized geometries, as lowest energy structures of ionic pairs, using Becke's Three Parameter Hybrid Functional using the Lee-Yang-Parr correlation functional theory (B3LYP) [24] and basis set 6-31+G* [25,26], with Spartan'18 Parallel Suite software package from Wavefunction, Inc., Irvine, CA, U.S.A. [26]. The quantum chemical calculations were performed in vacuum, for equilibrium geometry at ground state.
Ion-pair formation and movement of ions influence the electrical (ionic) conductivity of the IL. For ILs with the same cation the conductivity is a function of mobility and size of the anion. Indeed, for the ionic liquid [Bmim][BF4], which has smaller anion than [Bmim][PF6], a higher conductivity (higher mobility) was observed at all investigated temperatures. Decrease of the electrical conductivity for ILs with longer alkyl chain length is in accordance with the fact that electrical conductivity largely depends on the viscosity of the system [31]. Moreover, the conductivity of [Bmim][BF4] is higher than of [Bmmim][BF4], coupled with higher viscosity of last one because of the poorer mobility of the tri-substituted cation. This can be explained by the restriction of the butyl chain free rotation due to the steric bulk caused by the methyl group at the 2-position of the cation and also to the energetic preference of the anion to lie above or below the imidazolium ring rather than in front of it [32].
The temperature dependence of the conductivity of the neat ionic liquids was observed to follow the behavior predicted by the Arrhenius equation where  is the electrical conductivity, Ea is the activation energy for ion transportation by migration, A is the preexponential factor (or frequency factor), R is the universal gas constant. Figure 1 shows this behavior and Table 2 presents the values of parameters, including correlation coefficient R 2 and standard deviation. The standard deviation of the fit was found in the range of 0.015-0.127 mS·cm -1 . The obtained activation energies ( [BF4], reflecting the above statements. In general, a more precise equation like Vogel-Fulcher-Tamman equation is used for temperature behavior of transport properties, especially on larger temperature intervals, including lower temperatures [7,33,34]. Molecular dynamics studies [35][36][37] have indicated that there is significant ionic association in neat ILs which leads to high viscosity, limited conductivity and other peculiar properties of these organic salts. Mixing ionic liquids with molecular solvents will reduce coulombic interactions and release free ions from their associations, leading to decreased viscosity and increased conductivity [13,38]. A fluid with a large dielectric constant (as is DMSO or ACN) can interact more effectively with both ions of the ionic liquid, disrupting its polar network and causing a decrease in the viscosity of the mixture. As a result, it increases the conductivity, thus facilitating mass transport [14,38].
The dependence of electrical conductivity on IL mole fraction (XIL) follows the typical pattern of concentrated electrolyte solutions: after a rapid initial rise at low XIL due to the increasing number of charge carriers, conductivity exhibits a pronounced maximum at around XIL ≈ 0.1 to 0.2 (depending on the mixture) due to the counterbalancing effect of the rapidly rising viscosity on ion mobility [9,10,39]. In fact, the studies from literature demonstrate that ionic conductivity maximum occurs at compositions where the number of ion pairs, the so called "contact ion pairs" starts to exceed the number of free ions, or when ions come into contact, leading to a rapid growth of viscosity [6,9].
To reproduce such concentration dependence, the empirical Casteel-Amis equation is widely used [40]. Generally, data fitting is done on the molality scale, and the obtained parameters are the maximum conductivity, max, the corresponding where Xmax is the IL mole fraction at max.
The fitted parameters are summarized in Table 3, together with the corresponding standard deviations,  defined as follows: where n is the number of experimental data and m is the number of parameters. The solid lines represent the fit of these data to eq. Casteel-Amis To understand the influence of cation and anion on extreme conductivity in the binary mixtures we present the dependence of maximum conductivity, max, on temperature (Figures 3a and 4a) and the dependence of conductivity on mole fraction (Figures 3b and 4b). As it can be seen from Fig. 3a, the values for max follow the same regularity as in the  . 4a), while at higher compositions (XIL> 0.5) the order of variation of conductivity is almost similar as in neat ILs. One reason for this observed inversion of the expected order could be the lack of enough experimental data in the diluted region (0<XIL<0.15). https://doi.org/10.37358/RC.20.2.7942 Fig. 3 Dependences of (a) maximum electrical conductivity, max, on temperature and of (b) electrical conductivity at 298. According to Canongia Lopes et al. [34], most small dipolar solvents dissolve the polar network of ILs' and will be able to interact directly with the ions that compose it. The difference between the systems with DMSO and ACN, both solvents having high dipole moments, can be explained by their specific structural features. On one hand, these solvents have different molar volumes (73,3 cm 3 •mol -1 for DMSO and 52.9 cm 3 •mol -1 for ACN at 298.15 K), on the other hand, the DMSO molecule has a larger nonpolar moiety (weakly polar group S=O anchored by two methyl groups). Therefore, the DMSO molecule will be only partially dissolved into the nonpolar regions of the ionic liquid [38]; molecules of acetonitrile could accommodate better in the interstitial space of ionic liquids, having a larger distribution in the nanosegregated parts of the ionic liquid. In conclusion, ACN molecules can better "solubilize" ionic liquids than DMSO. This trend of variation of electrical conductivities in the systems of imidazolium-based ionic liquids with ACN was observed by other authors, too [9,12].
An useful tool is the relation between transport properties, i.e. the Walden rule [41], which connects ionic conductivity with dynamic viscosity. From the conductivity data and densities and viscosities data previously reported by us [19][20][21]42] we calculated the molar conductivities, Λ, with the usual equations: for neat ILs: / M     (4) for mixtures: / c   (5) where M is the molar mass (kg•mol -1 ) of the ILs, c is the molar concentration of the mixtures.
In literature the reciprocal poise (P -1 ) is used as a unit for fluidity, while S•cm 2 •mol -1 is used for molar conductivity. This Walden plot serves as a reliable means for quantification of ion association in neat ILs and includes the "ideal" Walden line, which represents the Walden plot for 0.01 mol•dm -3 KCl aqueous solution, known to be fully dissociated and having ions of equal mobility [34,43]. For such ideal dilute aqueous KCl solution no interaction occurs among the constituent ions. This implies that molar conductivity and viscosity exhibit a perfectly inverse temperature dependence [44]. The deviation from ideal KCl line is indicative of the existence of ion pairs or ionic aggregates with less conductivity https://doi.org/10.37358/RC. 20.2.7942 than that predicted by the Walden rule. Deviation from the ideal line is commonly observed for most ILs and their mixture [39]. Figure 5 shows the Walden plots for the studied systems with ILs at temperatures varying from 298.15 to 328.15 K. According to Angell et al. [43], for ionic liquids the most favorable systems will have their ambient-temperature values located in the top right-hand corner of the diagram (they include data for systems with fluidities that vary by more than 8 orders of magnitude). Our data are below the "ideal" KCl line, similar to what other authors have reported [45,46]. In view of the studies reported by Angell et al. [39], we can conclude that since the neat based-imidazolium ionic liquids lie within an order of magnitude below the ideal line, they should be classified as "good" ionic liquids (Fig. 5a). From the Fig. 5 b) we can see that Walden plots for the mixtures of [Bmim][BF4] with DMSO and ACN, respectively, are both below the ideal line and, in particular, the data calculated for IL mole fraction corresponding to a maximum of electrical conductivity are placed further to the right in the diagram. This indicates that the binary systems can be considered "better" ionic systems than the pure ones at those "special compositions". Therefore, we could remark the superiority of ILs−ACN/DMSO binary systems for practical purposes.

Computed quantum chemical parameters
Johansson et al. [23] confirmed that electrical conductivity is inversely proportional to the ion volumes and affected by the reduced masses of the ion pairs. To elucidate the influence of microscopic structure on macroscopic transport properties of the imidazolium-  Figure 6, together with their 2D representations. Selectivity parameters involved in chemical reactivity such as HOMO (the highest occupied molecular orbital) and LUMO (the lowest unoccupied molecular orbital) atomic distribution and their energy diagram were predicted and used to calculate other related properties such as: HOMO -LUMO energy gap (E), electron affinity (E), ionization potential (I), electronegativity (χ), chemical hardness (η), global softness (σ), chemical potential (µ), global electrophilicity index (ω), according to Koopmans' theorem [47,48]. Their values are listed in Table 4, along with molecular volume, dipole moment and polarizability.  The results from Table 4 suggest that among the ionic liquids studied, [Bmim][BF4] is the most stable, having the greatest energy gap between frontier molecular orbitals (the biggest ∆E values). The introduction of a second methyl group in the imidazolium ring leads to an increase in reactivity (the smallest HOMO -LUMO energy gap). The molecular volumes increase with the increase in alkyl side chain length on the aromatic imidazolium ring:   . 7), it appears that the highly localized negative charge on the anions can explain relatively strong cation−anion coulombic interactions in the IL ion pairs and can predict interactions with the polar molecules like DMSO or ACN.

Conclusions
We  15 K. An universal property of binary ionic liquid-organic solvent mixtures is the presence of maximum on the electrical conductivity dependence on ionic liquid mole fraction. Notably, all binary systems exhibit conductivity maximum between XIL = 0.1 and 0.2 and these values for max are smaller for binary systems with DMSO than with ACN. We have discussed the factors affecting the interactions between ILs and organic solvents such as the structure and molecular volume of the molecular solutes. The Walden plots obtained for the neat ILs/mixtures indicate that these systems can be classified as "good" ionic systems, especially the mixtures with maximum in electrical conductivity.