1 Introduction

Ionic liquids (ILs) in recent years have been attracting a considerable attention from the scientific and industrial community in general and electrochemists in particular [1–4]. On account of their unique and tunable inherent physicochemical characteristics, ILs are now increasingly being used as reaction media, novel solvents for separation and analysis and as electrolytes in electrically, photochemically or chemically driven electrochemical setups [1–3, 5]. A comprehensive understanding of ion−ion and ion−solvent interactions in ILs and IL+ co-solvent mixtures is a must to achieve the as desired characteristics of ILs in such systems. Among the large variety of ILs known until now, those based on imidazolium cations are probably the most intensively investigated and used, perhaps on account of their high air, moisture, thermal, electrochemical and chemical stability [3, 6]. The imidazolium based ILs are very complex innovative systems which are capable of interacting simultaneously with other molecules via dispersive, ionic, π−π, dipolar and hydrogen bonding interactions. These interactions when understood completely can be intelligently made use of in changing the course of chemical or electrochemical reactions through a proper use of ILs as solvents or electrolytes [4, 7–11].

In view of the recent developments related to theory of conductance of electrolyte solutions [12, 13], conductometry is increasingly being used as a reliable, affordable and convenient bench level technique that provides valuable information about the ion−ion and ion−solvent interactions in electrolyte solutions. In view of the fact that mixed solvents enable the variation of properties such as dielectric constant and viscosity over a wide range, conductometric investigations of ILs in mixed solvent systems seems very interesting. Such studies are expected to shed new light on the mechanism and extent of ion−ion and ion−solvent interactions and solvation of ILs in solutions, wherein nonelectrostatic forces contribute significantly to the equilibrium and dynamic characteristics of constituent ions. In view of the above mentioned facts, we carried out detailed conductometric investigations of 1-butyl-3-methylimidazolium chloride ([BMIM][Cl]) and 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) in binary acetonitrile (MeCN) + methanol (MeOH) mixed solvent systems. The studies were aimed at exploring the solvent and ion specific transport and ionic association characteristics of imidazolium based IL electrolyte solutions. Such studies are of considerable interest for the optimal and desired use of IL+ mixed organic solvent systems in high energy batteries [14] and other electrochemical systems, and for understanding the ion pair effect and organic reaction mechanisms in such systems [7, 8, 15].

2 Experimental

MeCN (GR grade, 99.9 %) and MeOH (GR grade, 99.9 %) were purchased from Merck, India and purified following reported standard methods [16]. Electrochemical purity grade ILs used were synthesized following a two step procedure [17] as reported earlier [7, 8]. Briefly, in the first step 1-methylimidazole was refluxed with n-butyl chloride for 90 h under argon atmosphere for the synthesis of 1-butyl-3-methylimidazolium chloride as a white crystalline solid. In the next step the halide anion was exchanged with PF −6 by treatment with HPF6. The ILs were vacuum dried and stored in desiccators under an inert atmosphere and were characterized through 1H-NMR, mass spectrometry and 13C-NMR spectroscopy. The water content of dried ILs was less than 50 ppm, as analyzed by Karl Fischer titration. Binary solvent mixtures were prepared by mixing the required volumes of MeCN and MeOH. The value of relative dielectric constant (ε r ) and coefficient of viscosity (η) of the solvent mixtures were obtained by interpolation of literature [18, 19] values for MeCN + MeOH mixtures at 298.15 K. The physical properties of the used mixture composition are listed in Table 1.

Table 1 Dielectric constant\((\epsilon_{r})\) and viscosity (η) of methanol (MeOH) + acetonitrile (MeCN) mixtures at 298.15 K; the values were calculated by interpolation of the literature reported [18, 19] values for these parameters for MeCN + MeOH mixed solvent systems
Full size table

Stock solutions of ILs were prepared by adding their required mass into the mixed solvent system to be investigated. Conductivity was recorded by a digital microprocessor based conductivity meter (CYBERSCAN CON 500) from Eutech instruments having a sensitivity of 0.1 μS·cm−1; details are reported elsewhere [20]. During data processing the conductivity of the solvent system was subtracted from the recorded values to obtain IL only conductivity in the solution. Numerical calculations and data fitting was performed through codes written in Origin 6.0 (Microcal Software Inc.)

3 Results and Discussions

The concentration dependent molar conductance values \((\Uplambda_{m})\) for [BMIM][Cl] and [BMIM][PF6] in MeCN + MeOH mixtures with changing volume fractions of MeOH (WMeOH%) are presented as Fig. 1. The conductance results were analyzed by following the framework of Barthel’s low-concentration chemical model (lcCM) [13]. According to this framework:

Fig. 1
figure 1

Molar conductivities \((\Uplambda_{m})\) of (a) [BMIM][Cl] and (b) [BMIM][PF6] in methanol + acetonitrile mixtures in the composition range 10–100 % methanol (by volume) in steps of 10 %. Lines show the results of the lcCM calculations

Full size image
$$ \Uplambda_{m}= \alpha\left( \Uplambda_{m}^{0}-S(\alpha C)^{1/2} + E\alpha C \rm ln(\alpha c)+ J_{1}\alpha C- J_{2}(\alpha C)^{3/2}\right) $$
(1)

where

$$ K^{0}_{a}= \frac{1-\alpha}{\alpha^2C(y_{\pm})^2} $$
(2)
$$ y_{\pm}= {\text exp}\left(\frac{-k_{\rm{D}}q}{1+k_{\rm{D}}R}\right) $$
(3)
$$ k_{D}= (16\pi N_{\rm{A}} q\alpha C)^{1/2} $$
(4)
$$ q= \frac{e^{2}}{8\pi \epsilon_{0}\epsilon_{r}k_{\rm{B}}T} $$
(5)

where \(\Uplambda_{m}^{0}\) is the molar conductivity at infinite dilution, (1 − α) is the fraction of charged ions bound as ion pairs, and K 0 a is the standard state association constant. The activity coefficient of the free cation (y +) and free anion (y −) are defined as

$$ (y_{\pm})^{2}= y_{+}y_{-} $$
(6)

where k D is the Debye parameter, e is the proton charge, \(\epsilon_{0}\) the dielectric constant of the vacuum and \(\epsilon_{r}\) the dielectric constant of the solvent system. T is the Kelvin temperature and N A and k B are the Avogadro’s and Boltzmann’s constants, respectively.

According to the lcCM model two oppositely charged ions are counted as ion pairs if the inter-ionic distance, r, is within the limits of a < r < R, where a is the lower limit for distance of closest approach and taken as the sum of their crystallographic radii (a = a + + a −) and R, the upper limit of distance of closest approach for ion pair formation taken as \(R= a+n \cdot s\). Expressions for the coefficients S, E, J 1 and J 2 are given by Barthel et al. [13]. The limiting slope S and the parameter E are fully defined by the known values of \(\epsilon_{r}\) and η (Table 1) of the solvent system. The coefficients J 1 and J 2 are both functions of the distance parameter R, representing the distance up to which oppositely charged ions can move as freely moving particles in solution. In the present study, the data analysis was carried out by a non-linear least square fitting procedure with the coefficients S, E and J 1 preset to their calculated values and with \(\Uplambda_{m}^{0}, K_{a}^{0}\) and J 2 as adjustable parameters. For these calculations a + = 0.330 nm [21], \(\it{a}_{\text{Cl}^{-}}\) = 0.181 nm [13] and \(\it{a}_{\text{PF}_6^-}\) = 0.256 nm [22] were used. In calculations for R, n was taken as 1 and in view of the literature reports [23], s = 0.47 nm for MeOH and s = 0.58 nm for MeCN; s for the mixed solvent systems employed in present study was calculated through the equation;

$$ s= X_{\rm{MeOH}}\cdot0.47 + (1-X_{\rm{MeOH}})\cdot0.58 $$
(7)

where X MeOH is the mole fraction of MeOH in the mixed solvent system.

Fig. 2
figure 2

(a) Limiting ion conductance \((\Uplambda_{m}^{0})\) and (b) ion association constant (K 0 a ) of [BMIM][Cl] and (b) [BMIM][PF6] in methanol + acetonitrile mixtures in the composition range 0–100 % methanol (by volume) in steps of 10 %

Full size image

.

Figure 1 compares the experimental \(\Uplambda_{m}\) values for [BMIM][Cl] (Fig. 1a) and for [BMIM][PF6] (Fig. 1b) solutions in the mixed solvent systems of changing compositions with the results of the lcCM calculations, Eqs. 1–5. The estimated values for \(\Uplambda_{m}^{0}\) together with the K 0 a and distance parameter R ij calculated from the last term of Eq. 1 are presented in Table 2.

Table 2 Association constants(K 0 a ), limiting molar conductivities (\(\Uplambda_{m}^{0}\)), input radii (R) and parameter (R ij ) for [BMIM][Cl] and [BMIM][PF6] in MeCN+MeOH mixed solvent systems at 298.15 K
Full size table

The value of R ij can be used as a compatibility control of the fit as it should be similar to the input radius \(R= a + n\cdot s\) chosen for calculation of J 2 and y ± . As evident from the Table 2, R and R ij are in good agreement for both the ILs. The vaules of \(\Uplambda_{m}^{0}\) estimated for the investigated ILs in the present work seem a bit higher than those reported in MeOH and MeCN in earlier reports [24–26]. However the data presented in earlier reports related to conductance of ILs in molecular solvents [24–27] indicates a significant variation in the values of \(\Uplambda_{m}^{0}\), reported for the same ILs in the same solvents. Such discrepancies in the reported values of \(\Uplambda_{m}^{0}\) are being attributed to (a) estimation of \(\Uplambda_{m}^{0}\) through use of different conductivity equations and (b) the use of concentration data in different ranges for the estimation of said values. As can be clearly seen from the entries in Table 2, the values for \(\Uplambda_{m}^{0}\) for [BMIM][PF6] and [BMIM][Cl] fall with the increase in MeOH fraction in the mixed solvent system. This is in line with the decrease in the dielectric constant of the solvent and increase in its viscosity with decrease of MeCN fraction in the solvent system. Nevertheless, it was observed that the Walden product (\(\Uplambda_{m}^{0} \cdot \eta\)) does not remain constant as expected in cases where ion−solvent interactions do not vary with changing composition of solvent [12]. This implies that the changing mole fractions of MeCN and MeOH lead to changes in ion−solvent interactions in the present case. Similar observations have been made for RTILs in earlier studies [28].

Interestingly, for all solvent compositions (except at wMeCN = 0) investigated, the \(\Uplambda_{m}^{0}\) values for [BMIM][Cl] were found to be higher than the corresponding values for [BMIM][PF6]. As depicted in Fig. 2a the relative difference between the \(\Uplambda_{m}^{0}\) values for the investigated ILs decreases with increase in W MeOH of the mixed solvent system. Since the the investigated ILs have a common cation, the observed variations in \(\Uplambda_{m}^{0}\) can be attributed to differences in solvation and mobility characteristics of Cl− and PF −6 in the mixed solvent systems. As has been reported in the literature [29], while MeOH interacts strongly with anions in such systems, MeCN on the contrary interacts preferentially with the imidazolium cation suggesting that the observed variations in \(\Uplambda_{m}^{0}\) are anion driven. In the light of our observations, it can be safely argued that while in MeCN the mobility of Cl− is more than that for PF −6 , in MeOH solutions the reverse is true. This trend suggests that the greater is the size of anion the smaller is its mobility in MeCN, while in MeOH the reverse is true, which we attribute to differing ion solvating abilities of the two solvents. In view of its smaller size, Cl− has a higher charge density than that of PF −6 ; thus the former species interacts with MeOH more than the later which is more solvated by MeCN on account of its higher polarizibility.

More interesting findings of the present investigations are the relative magnitudes of the K 0 a and its variations in the mixed solvent systems for the two ILs with a common cation. As seen from Table 2 and Fig. 2b, at lower fractions of MeOH in the mixed solvent system the K 0 a of [BMIM][Cl] was higher than that observed for [BMIM][PF6], whereas in MeOH rich solvent systems the reverse was observed. In addition while for [BMIM][Cl] the K 0 a value decreases with increase of MeOH fraction in the mixed solvent system, for [BMIM][PF6] an increasing trend was observed. While the trend observed for variation of K 0 a of [BMIM][Cl] with the change in content of MeOH fraction in the solvent system is quite expected in light of the resulting variations in \(\epsilon_{r}, \) the trend observed in the case of [BMIM][PF6] is quite unexpected. We observed a similar trend for the IL [BMIM][BF4]. From molecular dynamic studies [29] it has been established that hydrogen bonding solutes like MeOH strongly solvate halide ions by forming hydrogen bonds, while non hydrogen bonding solvents like MeCN interact more strongly with easily polarizable solutes through ion−dipole interactions. In light of these reports, on account of its smaller size and higher charge density, Cl− is expected to show weaker ion−solvent and stronger ion−ion interactions with its imidazolium counterpart and hence larger K 0 a values in solvents like MeCN. However, in solvents like MeOH where Cl− is expected to be strongly solvated due to its ability to engage in strong hydrogen bonding interactions with the solvent molecules, an opposite trend is expected. For the IL [BMIM][PF6], where the anion is more polarizible, the ion−solvent interactions are expected to be stronger and hence K 0 a values lower than for the [BMIM][Cl] homologue in solvents like MeCN. However, in solvents like MeOH the ion−ion interactions for [BMIM][PF6] are expected to be stronger and hence expected to show K 0 a values larger than its chloride counterpart (Fig. 2).

In light of these facts we propose that for an IL with smaller anions, like [BMIM][Cl], the stronger ion−ion plus weak ion−solvent interactions are replaced by weaker ion−ion and stronger ion−solvent interactions with increase of the MeOH fraction in the MeCN + MeOH mixed solvent systems, which is responsible for the resulting decrease in K 0 a . On the contrary, in ILs with larger anions like [BMIM][PF6], the weaker ion−ion plus strong ion−solvent interactions are replaced by stronger ion−ion and weaker ion−solvent interactions with increase of MeOH fraction in the MeCN + MeOH mixed solvent systems resulting in the observed variations in K 0 a with changing fraction of MeOH. This is in agreement with the report by Mohammed et al. [30] wherein it has been proved that, while the interaction energy for the [BMIM][PF6]+ MeCN system is negative, for [BMIM][PF6]+ MeOH the same quantity is positive. The present studies are an excellent example of tuning the physicochemical characteristics of closely related IL electrolytes through alterations in solvophobicity achieved through similar variations in the composition of the mixed solvent systems.

4 Conclusions

Conductometric investigations of imidazolium based ILs, viz 1-butyl-3-methylimidazolium chloride ([BMIM][Cl]) and 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) were performed in binary acetonitrile + methanol. The data were analyzed with Barthel’s low-concentration chemical model, establishing that the conducting behavior and ion association is highly specific to the nature of IL and composition of the mixed solvent system. Thus, while in MeOH ion-association and \(\Uplambda_{m}^{0}\) were found to be larger for [BMIM][PF6] than for [BMIM][Cl], in MeCN the opposite was observed. Also, with an increase in MeOH fraction in MeCN + MeOH mixed solvent systems, while \(\Uplambda_{m}^{0}\) was observed to decrease for both the ILs investigated, opposing trends were observed in the variation of K 0 a . For [BMIM][PF6] there was an increase in K 0 a while for [BMIM][Cl] a decrease in the corresponding value was observed.