Introduction

Creating sets of data on physical and chemical properties of ionic liquids (ILs) are of essential significance for both pure scientific and industrial purposes. The transport properties of the mixtures of ionic liquids (conductance, viscosity, and transference numbers) are important because the values provide useful and sensitive information about ion–solvent interaction, ionic association, and solvent structure. A survey of literature indicates that most studies report only the specific conductivity data for pure ionic liquids or binary and ternary mixtures of ILs with various solvents at 298.15 K. The conductance studies of dilute solutions of ionic liquids in a wide temperature range allow the determination of the values of association constants and thermodynamic functions of association, which consequently allows the better understanding of the behavior of ILs in various solvents [1–3]. This paper is both a continuation and an extension of our and other authors’ works on association of imidazolium-based ionic liquids, i.e., [emim][BF4] and [bmim][BF4] in water [4], 1-propanol [5], N,N-dimethylformamide [6], acetonitrile [7, 8], dimethylsulfoxide [9], and methanol [9, 10]. Moderate ionic association of ILs occurs in N,N-dimethylformamide, acetonitrile, and methanol, slight in dimethylsulfoxide, whereas it becomes significant in 1-propanol. Water promotes significantly dissociation of the ionic liquids.

According to our knowledge, conductometric data for solutions of [emim][BF4] and [bmim][BF4] in dichloromethane (DCM) at various temperatures have not yet been reported. The only paper is by Katsuda et al. [11], who investigated the conductance of [bmim][BF4] in DCM exclusively at 298.15 K. Aiming to cover this topic, the present work deals with the precise conductivity measurements, which have been carried out in the concentration range c = 0.4 to 4 · 10−4 mol · dm−3 of [emim][BF4] and [bmim][BF4] in DCM at temperatures range 278.15–303.15 K at atmospheric pressure. Imidazolium-based ionic liquids were chosen because of their thermal and chemical stability and the insignificant degree of susceptibility to air and moisture. The obtained data were used to calculate the values of the limiting molar conductivities, Λo, and the association constants, K A on the basis of lcCM model. The Eyring activation enthalpy of charge transport, ΔH ‡λ , as well as the Gibbs energy, ΔG oA , enthalpy, ΔH oA , and entropy, ΔS oA , of ion pair formation, for the electrolytes have been evaluated.

It should be stressed that measuring the conductance in the selected systems is a difficult task, since the experiments require high accuracy. It results from the fact that the relative permittivity of dichloromethane is low, its ionization properties are relatively weak, and electrolytes dissolved in DCM are strongly associated [11–15]. Therefore, it is necessary to use the extremely low concentrations of the electrolyte. For concentrations below the limit given by Fuoss [16], c max = 3.2 · 10−7 · ε r 3 mol · dm−3 (in DCM c max = 2.3 · 10−4 mol · dm−3), it can be expected that only the free ions and ion pairs are present in the solution [17].

Experimental

Materials

[Emim][BF4] of 99 % purity and [bmim][BF4] of 98.5 % purity were purchased from Fluka and were used as received. The water content of the studied chemicals was determined by Karl–Fischer titration. The final water mass fraction was less than 0.015 % in [emim][BF4] and 0.05 % in [bmim][BF4], respectively. Dichloromethane (minimum 99.8 %, water content <0.02 %) was received from POCH Gliwice (Poland) and was used without further purification. The actual purity of DCM was estimated to be 99.97 % by gas chromatography. The specific conductance, к, of the solvent was in the range of 2–2.5 · 10−9 S · cm−1 at 278.15–303.15 K, which is in good agreement with available data [11, 15].

Methods

All the solutions were prepared by mass using an analytical balance (Sartorius RC 210D) with a precision of ±1 · 10−5 g.

The measurement procedure was based on the method described by Bešter-Rogač et al. [13, 18] and used by us in our previous works [4–6, 19, 20]. Conductivity measurements were performed with a three-electrode cell with the use of a Precision Component Analyzer 6430B (Wayne-Kerr, UK) under argon atmosphere and at the different frequencies, ν, (0.2, 0.5, 1, 2, 3, 5, 10, and 20) kHz. The temperature was kept constant within 0.003 K (Calibration Thermostat UB 20F with Through-flow cooler DLK 25, Lauda, Germany). The details of the experimental procedure for conductometric measurements were described in our previous paper [6]. The estimated uncertainty of the measured values of conductivity was 0.20 %. The estimation of this uncertainty takes into account the high degree of difficulty associated with the conductivity measurements of electrolyte solutions in DCM. These difficulties, among others, are related to the use of very low concentrations of electrolytes and high ionic association.

Densities were measured with an Anton Paar DMA 5000M oscillating U-tube densimeter equipped with a thermostat with a temperature stability within ±0.001 K. The densimeter was calibrated with extra pure water, previously degassed ultrasonically. The estimated uncertainty of the density is ±2· 10−4 g · cm−3.

Results and discussion

The physical properties of dichloromethane are given in Table 1.

Table 1 Densities, ρ o, viscosities, η, and relative permittivities, ε r, of dichloromethane at different temperatures
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The measured density of DCM agreed well with those values published in the literature [13, 21, 22].

To convert molonity, \( \tilde{m} \) (moles of electrolyte per kilogram of solution) into molarity, c, the values of density gradients, b, have been determined independently and used in the equation

$$ c/\tilde{m}=\rho ={\rho}_{\mathrm{o}}+b\tilde{m} $$
(1a)

where ρ o is the density of the solvent. Molar concentrations, c, were necessary to use the conductivity equation. The density gradients and the molar conductivities of the ILs in solution, Λ, as a function of IL molality, m (moles of electrolyte per kilogram of solvent) and temperature are presented in Table 2. The relationship among m, m̃, and c is the following

$$ \tilde{m}=c/\rho = m/\left(1+mM\right) $$
(1b)

where M is the molar mass of electrolyte.

Table 2 Molar conductivities, Λ, corresponding molalities, m, and density gradients, b, for solutions of [emim][BF4] and [bmim][BF4] in DCM over the temperature range from 278.15 to 303.15 K
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The plot of molar conductivity, Λ, versus the square root of the molar concentration, c 1/2, for the investigated systems monotonically decreases as shown in Figs. 1 and 2, respectively, over the temperature range from 273.15 to 303.15 K. The values of Λ for ionic liquids in DCM are smaller than in DMF [6], water [4], and 1-propanol [5]. With a change of temperature, they change very slightly, in contrast to the above-mentioned solvents.

Fig. 1
figure 1

Molar conductivity, Λ, of [emim][BF4] solutions in DCM versus c 1/2 at experimental temperatures; 278.15 K, 283.15 K, 288.15 K, 293.15 K, 298.15 K, 303.15 K

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Fig. 2
figure 2

Molar conductivity, Λ, of [bmim][BF4] solutions in DCM versus c 1/2 at experimental temperatures; 278.15 K, 283.15 K, 288.15 K, 293.15 K, 298.15 K, 303.15 K

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The conductivity data were analyzed in the framework of the low concentration Chemical Model (lcCM) [23]. This approach uses the following set of equations

$$ \varLambda =\alpha \left[{\varLambda}_{\mathrm{o}}-S{\left(\alpha c\right)}^{1/2}+E\left(\alpha c\right) \ln \left(\alpha c\right)+{J}_1\left(\alpha c\right)+{J}_2{\left(\alpha c\right)}^{3/2}\right] $$
(2)
$$ {K}_{\mathrm{A}}=\left(1\hbox{--} \alpha \right)/\left({\alpha}^2c{y_{\pm}}^2\right) $$
(3)

and

$$ \ln {y}_{\pm }=-\left(A{\alpha}^{1/2}{c}^{1/2}\right)/\left(1+BR{\alpha}^{1/2}{c}^{1/2}\right) $$
(4)

In these equations, Λo is the limiting molar conductivity, α is the dissociation degree of an electrolyte, K A is the ionic association constant, R is the distance parameter of ions, y ± is the activity coefficient of ions on the molar scale, and A and B are the Debye–Hückel equation coefficients. The analytical form of the parameters S, E, J 1, and J 2 was presented previously [23].

In all previous papers [4–6, 19, 20], the values of Λo, K A, and R were obtained using the well-known procedure given by Fuoss [24]. However, in this case, we were unable to optimize the values of R in a sufficiently reliable manner. Therefore, we calculated the values of R independently, assuming the possible existence of contact (CIP) and solvent-separated (SSIP) ion pairs in the solution. For this purpose, the distance of closest approach (contact distance) of cation and anion, R = a = a + + a −, we calculated from the ionic radius of BF4 −, a − = 0.227 and a + = 0.331 nm for [bmim]+ and a + = 0.310 nm for [emim]+ [11]. The latest value was extrapolated by us from the radii of ions [bmim]+, [hmim]+, and [omim]+[11]. In the case of solvent-separated ion pair, R = a + s, where s is the length of an orientated solvent molecule, we assumed according to [13, 25] s = 0.177 nm. The results obtained by a two-parameter fit (Λo and K A) are collected in Table 3. For the last three concentrations from Table 2, the calculated values of Λ were lower than the experimental ones. Moreover, the differences between calculated and experimental values of Λ increase with an increase of concentration. This suggests that in solution form higher aggregates such as triple ion formation. Therefore, we did not use the last three concentrations for calculations, and we used a range of concentrations (c = 0.4 to 4 · 10−4 mol · dm−3) consistent with the Fuoss condition [16].

Table 3 Limiting molar conductivities, Λo, association constants, K A, and standard deviations, σ(Λ), for the investigated electrolytes in DCM at different temperature
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As seen from Table 3, the limiting molar conductivities increase as the temperature increases since the mobility of free ions is higher. The values of Λo for [emim][BF4] are higher compared to those values for [bmim][BF4] because the Λo values increase with decreasing alkyl chain length of the ILs. Furthermore, the differences between the Λo values for both ionic liquids increase with increasing temperature. The limiting molar conductivities for [emim][BF4] and [bmim][BF4] presented in Table 3 are much higher than corresponding values determined in 1-propanol, DMF, and water [4–6]. However, one should pay attention to the fact that the determining factor that affects the Λo value, a macroscopic viscosity of the solvent, in the case of dichloromethane, is very small (see Table 1). The value of Λo for [bmim][BF4] at 298.15 K is in good agreement with this reported by Katsuta et al. [11] (Λo = 162.5 S cm2 mol−1). Obtained values of standard deviations, σ(Λ), may be considered to be high, but should be noted that the conductometric measurements of analyzed systems are very difficult to be performed.

From data collected in Table 4 for investigated ILs in various solvents results that the values of limiting molar conductivities, Λo, follow the order: acetonitrile > dichloromethane > methanol > water > N,N-dimethylformamide > dimethyl sulfoxide > 1-propanol. As mentioned above, the conductivity increase is related to the decrease in solvent viscosity. However, for the series given above, this relationship is not entirely fulfilled. But if we consider the protic and aprotic character of solvents, the conductivity decreases in the order: MeOH > Water > 1-PrOH, and for aprotic: ACN > DCM > DMF > DMSO, which correlates very well with viscosity increase.

Table 4 Comparison of limiting molar conductivities, Λo, association constants, K A, and Gibbs-free energy ΔG oA , for solutions of [emim][BF4] and [bmim][BF4] in various molecular solvents of viscosity, η, and relative permittivity, ε r, at 298.15 K
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It is observed from Table 3 that both ionic liquids are very highly associated in DCM. This observation stays in agreement with literature data for various imidazolium ILs in DCM (KA ≈ 1 · 104–38 · 104 dm3 mol−1) [11, 13]. The value of K A = 384300 dm3 mol−1 for [bmim][BF4] in DCM at 298.15 K presented in paper [11] is slightly lower than ours. This can be explained by different procedure used for experimental data analysis and the different measuring procedure. As we can see from the Table 3, K A values depend significantly on the adopted model of ion pairs. In the case of solvent-separated (SSIP) ion pairs, the K A and Λo values are higher. The data collected in Table 3 also show that the association constants increase with increasing temperature, and the effect is much more pronounced in the case of [emim][BF4]. This can be due to decrease in ILs-DCM interactions with increasing temperature.

In the case of [emim][BF4] and bmim][BF4] solutions in dimethyl sulfoxide [9] and N,N-dimethylformamide [6], the association constants are practically negligible; in methanol and acetonitrile [7–10], ion association is rather weak. In turn, in water [4], both ionic liquids are practically fully dissociated, whereas in 1-propanol [5] and especially in dichloromethane, they were definitely associated. The data are consistent with the classical ionic association theory of electrolytes [28]. Similar behavior of other ionic liquids in various solvents was also observed [1, 3, 29–34]. In turn, in very low-permittivity tetrahydrofuran (ε r = 7.58), ionic liquid (1-butyl-2,3-dimethylimidazolium tetrafluoroborate [bmmim][BF4]) form not only ion pairs but also triple ions [29]. It means that ions are more associated in the solvent possessing a low-relative permittivity. However, not only the relative permittivity of the solvent plays an essential role in the ionic association process, but also the participation of the ion–solvent interactions and the alkyl chain length of the ILs should be considered too.

From the temperature dependence of Λo, the Eyring activation enthalpy of charge transport, ΔH ‡λ , was obtained by using Eq. 5

$$ \ln {\varLambda}_{\mathrm{o}}+2/3\kern0.5em \ln \kern0.5em {\rho}_o=-\varDelta {H}_{\uplambda}^{\ddagger }\ /\ \mathrm{R}\mathrm{T}+D $$
(5)

where D is an empirical constant. From the slope of the linear dependencies of ln Λo + 2/3 ln ρ o versus the inverse of the temperature (1/T), which are shown in Fig. 3(a, b), we obtained the following ΔH ‡λ values 6,138 (CIP) and 6,142 (SSIP) for [emim][BF4] and 5,257 (CIP) and 5,271 (SSIP) for [bmim][BF4] (all in J · mol−1), respectively. For [emim][BF4], the value of ΔH ‡λ is thus higher than [bmim][BF4] by 881 (CIP) and 871 (SSIP) units. It is somewhat surprising, considering the fact that in other solvents [4–7, 9], the values of ΔH ‡λ are higher for [bmim][BF4] than [emim][BF4]. It is the result of the presence of a larger substituent in the [bmim]+ cation compared to [emim]+. In the case of dichloromethane, it may suggest that the effective ionic radius of [emim]+ is larger than the [bmim]+. Taking into account the values of the Eyring activation enthalpy of charge transport for other solvents, we can conclude that ΔH ‡λ depends mainly on the solvent. In the case of protic solvents (water and 1-propanol) values are very similar (about 16,000 J · mol−1) and almost twice or more higher than those for DMF, DCM, and ACN. It can be concluded that the value of ΔH ‡λ depends on the formation of hydrogen bonds between molecules of the solvent and its structure.

Fig. 3
figure 3

a, b Plot of ln Λo + 2/3 ln ρ o as a function of 1/T for a [emim][BF4] and b [bmim][BF4] in DCM: (), CIP, and (), SSIP

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The temperature dependence of the association constant was used to calculation of Gibbs-free energy of ion formation, ΔG oA

$$ \varDelta {G}_{\mathrm{A}}^{\mathrm{o}}\ (T)=-RT\ ln\ {K}_{\mathrm{A}}(T) $$
(6)

ΔG oA (T) can also be expressed by the polynomial

$$ \varDelta {G}_{\mathrm{A}}^{\mathrm{o}}\ (T)=A+BT+C{T}^2 $$
(7)

The values of parameters A, B, and C of Eq. (7) and correlation coefficients, r 2, are summarized in Table 5.

Table 5 Coefficients of Eq. (7) and correlation coefficients, r 2, for [emim][BF4] and [bmim][BF4] in DCM
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The entropy and enthalpy of ion association are defined as

$$ \varDelta {S}_{\mathrm{A}}^{\mathrm{o}} = -{\left(\partial \varDelta {G}_{\mathrm{A}}^{\mathrm{o}}\ /\ \partial T\right)}_p=-B-2CT $$
(8)
$$ \varDelta {H}_{\mathrm{A}}^{\mathrm{o}} = \varDelta {G}_{\mathrm{A}}^{\mathrm{o}}+T\varDelta {S}_{\mathrm{A}}^{\mathrm{o}}=A-C{T}^2 $$
(9)

The thermodynamic functions of the ion pair formation (ΔG oA , ΔS oA , ΔH oA ) at different temperatures are presented in Table 6 and in Figs. 4, 5, and 6, respectively.

Table 6 Thermodynamic functions of association of [emim][BF4] and [bmim][BF4] solutions in DCM at different temperatures
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Fig. 4
figure 4

Variation of Gibbs-free energy, ΔG oA , as a function of temperature T of [emim][BF4]: (), SSIP, (), CIP, and [bmim][BF4] in DCM, (), SSIP, (), CIP

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Fig. 5
figure 5

Variation of association entropies, ΔS oA , as a function of temperature of [emim][BF4], (), SSIP, (), CIP, and [bmim][BF4] in DCM, (), SSIP, () CIP

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Fig. 6
figure 6

Variation of enthalpies, ΔH oA , as a function of temperature of [emim][BF4], (), SSIP, (), CIP and [bmim][BF4] in DCM, (), SSIP, () CIP

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The values of ΔG oA presented in Table 6 and Fig. 4 indicate that the spontaneity of the ion pair formation in the case of both ionic liquids is comparable. The increase of temperature leads to more negative ΔG oA values, which means shifting the equilibrium toward the formation of ion pairs due to reduction in preferential solvation of ions by temperature (interactions between IL and DCM become weaker with increasing temperature).

The data collected in Table 4 show that the values of Gibbs-free energy of the studied ILs in other solvents are also negative (and become more negative as temperature increases).

As can be seen in Figs. 5 and 6, both the values of entropy and enthalpy of association are positive and greater for [emim][BF4]. Moreover, the values of ΔS oA and ΔH oA increase with increasing temperature for both tested electrolytes. Positive values of entropy prove that the transition from the free solvated ions into the ion pairs causes that system becomes less ordered. This is related to the partial desolvation of ions prior to the formation of ion pair. The positive values of ΔH oA indicate that the ion pair-forming processes are endothermic, particularly in the case of [emim][BF4]. From Eq. (10)

$$ \varDelta {G}_{\mathrm{A}}^{\mathrm{o}}\ (T)=\varDelta {H}_{\mathrm{A}}^{\mathrm{o}}\ (T)\hbox{--} T\varDelta {S}_{\mathrm{A}}^{\mathrm{o}}\ (T) $$
(10)

it follows that entropic effects seem to dominate over the enthalpic effects because the Gibbs-free energy, ΔG oA , is negative, and thus the ion pair formation is spontaneous in both cases. Furthermore, earlier studies [4–7, 19] confirm that in the case of other solvents, spontaneity of ionic association process results mainly from changes of the entropy.

Conclusions

Molar conductivities of very dilute solutions of 1-ethyl-3-methylimidazolium tetrafluoroborate and 1-butyl-3-methylimidazolium tetrafluoroborate in dichloromethane have been reported for the first time at T = 278.15 to 303.15 K. Conductivity data were analyzed using the Barthel’s low concentration Chemical Model (lcCM). The examined ionic liquids act like very weak electrolytes (K A ≈ 60 · 104 mol−1 dm3 for [emim][BF4] and ≈ 48 · 104 mol−1 dm3 for [bmim][BF4], respectively) in the low-permittivity solvent DCM at used temperature range. With increasing temperature, the tendency to form the ion pairs increases. [Emim][BF4] is more associated electrolyte than [bmim][BF4]. K A values depend significantly on the adopted model of ion pairs, (CIP) or (SSIP). The values of Λ for ionic liquids in DCM are smaller than in DMF [6], water [4], and 1-propanol [5] and change very slightly with a change of temperature. In turn, Λo values are much higher than corresponding values determined in 1-propanol, DMF, and water. The evaluated values of thermodynamic functions of association suggest the spontaneity of the association process. The values of ΔH oA are positive and suggest that the ion-pairing process is endothermic. Because the Gibbs-free energy is negative, entropic effects seem to dominate over the enthalpic effects, and thus, the ion pair formation of ionic liquids in DCM is spontaneous in both cases.