CC BY
1
UDK 541.8:544.623 DOI: 10.18698/1812-3368-2023-3-145-163
ELECTRICAL CONDUCTIVITY AND ASSOCIATION OF 1-BUTYL-3-METHYLPYRIDINIUM BIS{(TRIFLUOROMETHYL)SULFONYL}AMIDE IN SOME POLAR SOLVENTS
I.A. Karpunichkina1 Yu.M. Artemkina1 N.V. Plechkova2 V.V. Shcherbakov1
akimosha1@yandex.ru artemkina.iu.m@muctr.ru n.plechkova@qub.ac.uk shcherbakov.v.v@muctr.ru
1 Mendeleev University of Chemical Technology, Moscow, Russian Federation
2 Wellcome-Wolfson Institute for Experimental Medicine, The Queen's University of Belfast, Belfast, UK
Abstract
The influence of alternating current frequency in the determination of the electrical conductivity of ionic liquids' (ILs) dilute solutions in polar solvents has been considered. The frequency ranges in which the influence of polarization processes on electrodes occur and ionic relaxation occurs in the bulk of the solution have been excluded from the results of the electrical conductivity measurements. The association constants for Ka ILs in polar solvents published in literature were analyzed. A discrepancy between the values of K was noted, which is associated with the use of different calculation equations for electrical conductivity and the insufficiently correct consideration of the frequency dependance of the measured resistance. Based on the measured values of the electrical conductivity of dilute solutions of 1-butyl-3-me-thylpyridinium bis{(trifluoromethyl)sulfonyl}amide ([Bmpy][NTf2]) in acetonitrile (AN), dimethyl sulfoxide (DMSO) and dimethylformamide (DMF) in the 20-65 °C temperature range, the thermodynamic characteristics of the [Bmpy][NTf2] association were determined. The effect of temperature on the molar electrical conductivity of [Bmpy][NTf2] at infinite dilution h> and the association constant K have been considered. The Walden product (A,or|), where "q is the viscosity of the solvent, was also analysed. It was shown that in AN, DMSO, and DMF, A^q changes
Keywords
1-butyl-3-methylpyridinium bis{(trifluoromethyl)sulfonyl}amide, electrical conductivity, association, acetonitrile, dimethylsulfoxide, dimethylformamide
in different ways with increasing temperature; however, the value of A,or|/(£T) corrected for permittivity s and absolute temperature T does not depend on the temperature and nature of the solvent. As the temperature rises, the electrical conductivity of the dilute solutions of [Bmpy][NTf2] increases in direct propor- Received 16.11.2022 tion to the ratio of the permittivity to dipole dielectric Accepted 23.12.2022 relaxation time of the solvent © Author(s), 2023
The work is performed in the framework of the development program
Prioriyty 2030 of the Mendeleev University of Chemical Technology of Russia
Introduction. Ionic liquids (ILs) occupy a special place in the physical chemistry of liquid states, being both a solute and a solvent. Possessing a low vapor pressure, high thermal stability and that they remain liquid over a large temperature range [1], ILs replace volatile organic solvents not only in scientific research, but also in practical applications in various branches of chemistry and technology [2-7]. Possessing significant electrical conductivity (EC), ILs and their solutions in polar solvents show promise for use in various electrochemical devices — current sources and electric energy storage devices [8-10]. By combining various cations and anions of ILs, it is possible to obtain liquids with the suitable set of physical and chemical properties required for practical use. Therefore, ILs can be classified as "designer solvents" [3].
For the practical application of ILs, their mixtures and solutions in polar solvents, it is necessary to study their physicochemical properties in a wide range of temperatures and compositions. In the case of their application in electrochemical devices, information is needed on the conductivity of ILs, as well as their state in the processes of solvation and dissociation in solutions.
Based on the results of the EC measurements of dilute solutions, it is possible to determine the value of molar EC at infinite dilution X 0 and the association constant Ka of ILs in polar solvents. Currently, there are publications in literature related to the results of determining X0 and Ka mainly for the ILs based on the 1-alkyl-3-methylimidazolium cation ([Rmim]+, R = CnH2n + 1) [11-21]. It should be noted that if the values of X 0 in these publications are in good agreement with each other (the discrepancy between the values of A.0 does not exceed 5-10 %), then the association constants Ka can differ significantly (the error in determining the association constants, as a rule, is twice as large as the error ^0). As an example, let us compare the values of the molar EC at infinite dilution (^0, S cm2/mol) and the association constants (Ka, L/mol) of some ionic liquids based on the 1-butyl-3-methylimidazolium cation in methanol and acetonitrile at 25 °C (Table 1).
Table 1
Molar EC values of X0 and association constants Ka of ionic liquids based on 1-butyl-3-methylimidazolium ([Bmim]+) cation in methanol and acetonitrile
at 25 °C at infinite dilution
Ionic liquid Solvent X0, S cm2/mol Ka, L/mol References
[Bmim][BF4] Methanol 121.84 37.7 [11]
126.9 55.0 [12]
Acetonitrile 189.29 15.7 [13]
190.3 18.2 [14]
181.4 712 [15]
[Bmim][PF6] Acetonitrile 184.70 15.6 [13]
158.52 27.0 [16]
179.1 683 [15]
[Bmim]Cl Acetonitrile 196.52 88.5 [16]
178.45 725.21 [17]
In a methanolic solution of 1-butyl-3-methylimidazolium tetrafluoroborate ([Bmim][BF4]), K a according to the data of [11], turned out to be almost 1.5 times less than in [12]. The values of A, 0 according to [11, 12] differ by only 4 %. The association constants of the same IL in acetonitrile are close, according to the data of [13] and [14] (the difference between the Ka values does not exceed 15 %), but differ significantly from the Ka value (712 L/mol) of [Bmim][BF4] obtained in the work [15]. The same large difference is observed for the association constants of [Bmim][PF6] in this solvent according to the data of [15] (683 L/mol), [13] (15.6 L/mol) and [16] (27.0 L/mol). In acetonitrile, the association constants of [Bmim]Cl are 88.5 [16] and 725.21 L/mol [17], so they also differ significantly (more than eight times).
In dilute aqueous solutions, ionic liquids based on the imidazolium cation are weakly associated. According to [18], for imidazolium chlorides 2.5 < Ka < 6 L/mol. The association constant for 1-butyl-3-methylimi-dazolium halides is less than 10 L/mol [19]. For [Bmim][BF4] Ka = = 0.19 L/mol [20]. In [15], the association constant is clearly overestimated: it is 70-100 L/mol for 1-alkyl-3-methylimidazolium bromides (alkyl C4, C6, C8, C10, and C12) and 105 L/mol for [Bmim][BF4].
The discrepancy between the values of Ka published in various works is noted [14, 20, 21]. It is indicated that a possible reason for the variation in the association constants can be caused by a different procedure for processing conductometric data [14]. In particular, in [12, 14, 15], the Lee — Wheaton
electrical conductivity equation [22-24] is used to calculate the association parameters, and in [11, 13, 16, 18-20], the Fuoss — Justice equation is applied for the analysis of conductometric data in the framework of "Low Concentration Chemical Model" proposed by Barthel et al [25]. In [17], the X0 and Ka were calculated using the Fuoss equation [26]. The use of different electrical conductivity equations is the first reason for the discrepancy between the association constants noted above. In our opinion, these values should be compared only within the framework of one calculation equation, which, for example, was correctly carried out in [27].
The second reason for the discrepancy between the values of the association constants may be the use of different procedures for measuring the electrical resistance of the solution R, in particular, the analysis of its frequency dependance in order to exclude the influence of the polarisation processes. In [12, 14, 15, 17, 19], such an analysis was not carried out and R measurements were carried out at one frequency (1 kHz [12, 14, 17]; 1.1 kHz [15] and 1 MHz [19]).
The experimentally measured electrical resistance of the solution in the conductometric cell R decreases with increasing frequency F. To improve the accuracy of conductometric measurements, it is recommended to extrapolate the measured resistance to an infinite frequency, i.e., analyze the dependance of the measured resistance R on the frequency F in the coordinates R-1/F [28, 29]. This procedure was used in [11, 13, 18, 20]. At the same time, to eliminate the influence of polarization processes on the electrodes, the dependances R-1/F05 [30] and R-1/F2 [31] are also used. Analysis of the frequency influence on the accuracy of conductometric measurements was carried out in the experimental part of this work.
The brief analysis carried out above shows that the ionic association of mainly dialkylimidazolium ILs in polar solvents has been studied. The association of ILs based on other organic cations, in particular 1-alkyl-3-methylpyridinium, has practically not been studied. It is of practical interest to elucidate the nature of the association of the 1-butyl-3-methylpyridinium [bis{(trifluoromethyl)sulfonyl}amide, [Bmpy] [NTf?] ionic liquid. Solutions of ILs with this anion have a fairly high specific conductivity and a relatively wide electrochemical window [32].
In this work, we analyze the conductometric studies' results of the thermodynamic characteristics of [Bmpy][NTf2] association in acetonitrile (AN), dimethyl sulfoxide (DMSO), and dimethylformamide (DMF) and consider the relationship between the electrical conductivity of dilute solutions of this IL and the dielectric properties of the solvent.
Experimental part. [Bmpy][NTf2] (1-butyl-3-methylpyridinium bis{(trifluo-romethyl)sulfonyl}amide) (Fig. 1) was obtained by a metathesis reaction between the aqueous solutions of 1-butyl-3-methylpyridinium chloride and an excess of lithium bis{(trifluoromethyl)sulfonyl}amide at Queen's University of Belfast Ionic Liquid Laboratories (QUILL) in Northern Ireland.
The purity of the ionic liquids (99.5 %) was also monitored using NMR spectroscopy at QUILL. Characteristics of IL: molar mass 430.41 g/mol, melting point 8.15 °C and density 1.4187 g/cm3 (20 °C).
Before preparing the solutions, [Bmpy][NTf2] was dried in a vacuum fume hood at 60 °C for five hours. Solutions of [Bmpy][NTf2] were prepared by the gravimetric method; in this case, taken with an accuracy of ± 0.00001 g, a weighed portion of the ionic liquid was quantitatively transferred into a preliminarily prepared volumetric flask. After that, a solvent was added to this ionic liquid. The water content in the solvents used in this work (AN, DMSO, and DMF) was controlled by the Karl Fischer method and did not exceed 0.1 %.
The conductometric cell used in the work is made of Pyrex glass and is a glass tube with an inner diameter of « 10 mm, at the ends of which there are two spherical containers into which platinum electrodes are soldered. The length of the cell glass tube is « 45 mm. The cell is soldered into a glass jacket, through which liquid (water) is pumped from a thermostat. The accuracy of solution temperature control was ± 0.05 °C. The electrodes of the contact cell were platinised to reduce the polarisation resistance. The cell constant was determined by measuring the resistance of KCl aqueous solutions according to the standard procedure [28]. Its value is 0.1723 ± 0.0003 cm. The error in the specific EC of the solutions did not exceed 0.5 %. The solution resistance R was measured using an E7-20 digital AC bridge (immittance meter) in the 0.1-10 kHz frequency range with an error that did not exceed 0.1 %.
An important issue in determining the thermodynamic characteristics of the association (in addition to the choice of the equation X = f (c) considered above and the method of analysing conductometric data (using the procedure for calculating Ka and X0 from the dependance of the molar EC X
on the concentration c)) is also the restriction on the maximum concentration of solutions cmax and the requirements for high accuracy measurements of dilute ILs solutions' electrical conductivity in various polar solvents.
The highest concentration of the solution cmax, the molar EC of which is used in calculating the thermodynamic characteristics of the association, depends on the dielectric permittivity (DP) of the solvent s, the absolute temperature T, and the equation, describing the dependance of X on the concentration c. In [24], the following equation was proposed for estimating cmax (mol/L):
Cmax = 9.1-10_15(sT )3. (1)
In his work [33], Fuoss proposed to take into account only the dielectric permittivity of the solvent e when calculating cmax:
W = 3.2 -10"7 s3. (2)
The cmax values for the solvents used in this work are compared below.
The molar EC of IL solutions X is determined on the basis of specific EC k, which, in turn, is calculated using the value of the cell constant k and the measured solution resistance R. In this case: k = 1/(kR), X = k/c.
The measured electrical resistance of the solution Rmeas decreases with an increase in the frequency of the alternating current F, as a result of polarization processes on the electrodes [34, 35] and ionic relaxation in the volume of the solution [36]. Electrode polarization leads to the fact that the measured resistance Rmeas exceeds the resistance of the solution R [34, 35], while ionic relaxation in the volume of solutions reduces the measured resistance Rmeas compared to the value of R [36]. Therefore, the problem of correctly measuring the resistance R of ILs solutions, in particular, the analysis of the frequency dependance of this value, needs special consideration.
To exclude polarisation processes on the electrodes, the resistance of the solution is measured, as a rule, in the frequency range of 0.1-10 kHz and R is found by extrapolation to an infinite frequency in the Rmeas — 1/ F coordinates [11, 13, 18, 20, 28, 29]. When analyzing the frequency dependance of the measured resistance Rmeas of dilute IL solutions, it is also necessary to consider the ionic relaxation in the bulk of solution [36]. The procedure for accounting for this phenomenon will now be considered.
In the general case, the electrical equivalent circuit of a solution is represented in the form of solution resistance R and electric capacitance C connected in parallel that model its specific conductivity k and dielectric permittivity 8. At the same time [36]:
R = C = ksso, (3)
k k
where k is the proportionality factor having the dimension of length (conduc-tometric cell constant); s0 is the vacuum DP (s0 = 8.854 10 12 F/m).
The measured solution resistance Rmeas is related to the resistance R
and electrical capacitance C of the solution by the relation [36]:
R
Rmeas ~ " "" , (4)
1 + (ro CR)2 where Q = 2nF is the angular frequency.
The exclusion of polarization processes' influence on the measured solution resistance in the Rmeas -1/ F coordinates is valid under the condition ®CR «1. Only in this case, the measured solution resistance Rmeas will be equal to the desired resistance R [36].
Ionic relaxation in the volume of the solution leads to a decrease in the measured resistance Rmeas with increasing frequency and it affects the measurement results already under the ®CR > 0.1 condition. Under the ®CR = 1 condition, according to Eq. (4), the measured resistance Rmeas will be two times lower than the desired resistance R, which can be perceived as a twofold increase in the specific EC, and, consequently, the molar EC of dilute IL solutions. Such a sharp increase in the molar EC with decreasing concentration can occur in very dilute solutions of ILs in weakly polar solvents characterized by low DP values.
Equation (4) can be rewritten as:
1 = - + (ra C)2 R = - + AF2. (5)
Rmeas R R
Here A = (2tcc)2R. Accounting for ionic relaxation in precision conducto-metric measurements is carried out by extrapolating the inverse measured resistance 1/ Rmeas to zero frequency in the 1/ Rmeas -F2 coordinates [36]. Such accounting must be carried out in the frequency range in which the following inequality is satisfied:
0.1 <®CR <10. (6)
Equation (6) limits the frequency range in which it is necessary to consider the effect of ionic relaxation on the measured solution resistance in the 1/ Rmeas -F2 coordinates.
It should be noted that under the condition ©CR »1, Eq. (4) is transformed into the equality
Rmeas — , . . (7)
(aC )2 R
Thus, under the condition ©CR»1, the measured resistance Rmeas decreases in proportion to the square of the reciprocal frequency and is not equal to the desired solution resistance R. In this case, the solution resistance R must be calculated based on its measured value Rmeas, considering the angular frequency © and the electric capacitance of the solution C. From Eq. (7), we obtain:
R=—2-• (8)
(Q c) Rmeas
Equation (8) must be used, first of all, when determining the electrical conductivity of polar solvents, the electrical resistance of which is very high, and the inequality aCR » 1 for them is already satisfied at low frequencies.
The value of aCR is the ratio of displacement currents to conduction currents [36]. Using Eq. (3), we can write
OCR = (9)
K
Taking into account Eq. (9), inequality (6) can be written as
„ „ rassn 0.1 <-0 < 10.
K
Ionic relaxation leads to a decrease in the measured resistance with increasing frequency already under the ®ss0 > 0.1k condition. From here, one
can find the boundary cut-off frequency Fbound, at which the measured resistance of the solution begins to decrease due to ionic relaxation:
^ 0.1k 1.8-109 Abound ,inv
Fbound ^-=-. (10)
SS0 8
In Eq. (10), the specific conductivity is expressed in S/m, and the permittivity is expressed in relative units. From Eq. (10) for any frequency F, one can also find the boundary value of the specific electric field Kbound, below which ionic relaxation will affect the results of measuring the solution resistance in a conductometric cell:
Kbound < — < 5.56-10"10sF. (11)
0.1
In Table 2, for the solvents used in this work (AN, DMSO, and DMF) the values of DP s, calculated using Eq. (11), the boundary values of the specific
EC Kbound below which ionic relaxation begins to affect the results of resistance measurements at a frequency of 1 kHz, and also the maximum concentrations of solutions cmax (1) and cmax (2) calculated using equations (1) and (2) utilised in calculations of Ka and X0 are shown. For comparison, in Table 2 these values for aqueous solutions are also shown.
Table 2
Dielectric permittivity of solvents s, boundary specific electrical conductivity Kbound and maximum concentrations Cmax for some polar solvents; t = 25 0C
Solvent 6 [37] Abound, 105, S/m Cmax, mol/L
(1) (2)
AN 37.5 2.08 0.017 0.013
DMF 37.0 2.06 0.016 0.012
DMSO 47.0 2.61 0.033 0.025
Water 78.3 4.35 0.150 0.120
From the calculated values in Table 2, the following conclusions can be drawn. The limiting specific electrical conductivity Kbound is much higher than the conductivity of pure organic solvents [38]. Therefore, when measuring their specific electrical conductivity, it is necessary to consider ionic relaxation, which leads to an overestimation of the electrical conductivity. Such an overestimation will also take place in the case of the specific EC measurements of sufficiently dilute (c < 104 M) IL solutions under consideration. The maximum concentrations cmax calculated using Eqs. (1) and (2) are close and for the solvents used in the work do not exceed 0.02-0.04 mol/L.
An important conclusion from the data in Table 2 is also the fact that when determining the thermodynamic characteristics of ionic association based on the results of measuring the EC of dilute solutions, there are restrictions on both the maximum and minimum concentrations. The minimum concentration determines the value of the boundary EC of the solution Kbound, above which ionic relaxation does not affect the frequency dependance of the measured resistance. Since the measurements of the resistance R are carried out in the frequency range of 0.1-10 kHz, the minimum concentration of the studied solutions should be such that the value of their specific electrical conductivity should not fall below the value of kbound described by Eq. (11), which depends on the DP of the solvent s and the frequency F.
The desired resistance R of all solutions in this work was determined by extrapolation of its measured value to an infinite frequency in the R-1/F
coordinates [29]. The frequency interval was chosen so that for all the studied solutions the condition aCR ^ 1 is satisfied, under which ionic relaxation does not affect the results of measuring the resistance R. As the concentration increases, the measured resistance decreases, therefore, to fulfill the condition ©CR ^ 1, a transition to the region of higher frequencies is needed. Such a transition is also necessary when the measurement temperature rises, since with increasing temperature, the measured resistance Rmeas decreases.
To determine the molar electrical conductivity at infinite dilution A0, the ion association constant Ka and the parameter of the closest approach of ions R from the experimental conductometric data, we used the experimental data processing method [39], which consists of minimizing the function:
F =
■ t (x?eor ~Xexp )2 i = 1
where Xexp is the experimental value of the electrical conductivity; Xtheor is the theoretical value of the molar EC calculated using the Lee — Wheaton equation [22-24], which is a function of concentration c, permittivity s, viscosity temperature T, and the desired parameters A0, Ka and R. The values of A0, Ka and R were calculated using a programme compiled in Microsoft Office Excel [39],
in which the values of s, T and all measured molar EC Xexp at the corresponding concentrations ci were entered. As a result of the calculation, the numerical values of A0, Ka and R and the absolute error values of these quantities (± ÀÀ,0, ± AKa and ± ÀR) were obtained.
Results and discussion. The molar EC of [Bmpy][NTf2] solutions in AN, DMF, and DMSO decreases with increasing concentration. Figure 2 as an example shows the X-c1/2 dependances for the solutions of [Bmpy][NTf2] in DMF (Fig. 2, a) and DMSO (Fig. 2, b). In the entire studied range of concentrations and temperatures, the following pattern of change in molar conductivity is observed:
A AN > AdMF > ADMSO-This pattern is consistent with the results in the molar EC of dilute solutions changes of other ILs in AN, DMF, and DMSO [13, 21].
The molar EC calculated by the Lee — Wheaton method at an infinite dilution X0 [Bmpy][NTf2] in the studied solvents changes in the same way as the values of X, i.e., decrease upon going from AN to DMF and to DMSO. To explain the temperature dependance of A0, the Walden empirical rule [40] is usually used, according to which, the product of the molar EC at an infinite
X, S • cm2/mol X, S • cm2/mol
a b
Fig. 2. Dependance of the molar EC of [Bmpy][NTf2] solutions in DMF (a) and DMSO (b) on the square root of the concentration in the 20-65 °C
temperature range
dilution of X 0 and the solvent viscosity ^ is a constant value. Since the opposite pattern is observed for the viscosity of solvents ^AN <^DMF <^DMSO, one would expect that the values of the products X for the studied ILs in the temperature range (20-65 °C) would be the same for all three solvents. An analysis of the dependances of the product on temperature (Fig. 3) shows
9 —1
-mol -mPa-s
Fig. 3. Dependance of the Walden product ^o^ for solutions of [Bmpy][NTf2] in AN (1), DMF (2) and DMSO (3) on temperature (20-65 °C)
that these values do not coincide and vary in different ways depending on temperature: the value of passes through a minimum with increasing temperature in AN and DMF (curves 1 and 2, see Fig. 3) and passes through a maximum in DMSO (curve 3, see Fig. 3).
It should be noted that the Walden rule is also not valid for solutions of other ionic liquids in polar solvents [14, 20, 21].
60 77,1
In [41], it was proposed to analyze the temperature dépendance of X0 of non-aqueous electrolyte solutions depending on the dielectric properties of solvents, in particular, on the sT / ^ ratio. As a result, it turned out that with increasing temperature, X0 increases in direct proportion to the value of sT / r|. This pattern was also confirmed for IL solutions in polar solvents [42]. The dependance of X0 on the ratio sT / ц for [Bmpy][NTf2] solutions in three solvents (AN, DMF, and DMSO) in the 20-65 °C temperature range is shown in Fig. 4, a. The values of the molar EC at infinite dilution for AN, DMF, and DMSO fit into one straight line, i.e., the value of X0 increases in direct proportion to the ratio sT / r|. Similarly, in proportion to the value of sT/r\, the molar EC at infinite dilution X0 of [Bmim][BF4] increases in various polar solvents (see Fig. 4, b). The dependance in Fig. 4, b was plotted using the data for A0, s, and ^ provided in [21].
a b
Fig. 4. Dependance of the molar EC of [Bmpy][NTf2] at infinite dilution in the 20-65 °C temperature range (a) and [Bmim][BF4 ] at 25 °C (b) on the ratio sT/ц in AN (1), DMF (2), DMSO (3), methanol (4), dimethylacetamide (5), 1-propanol (6), 2-propanol (7) and 1-butanol (8)
Thus, the dependances, presented in Fig. 4, confirm the applicability of the previously established pattern, first for aqueous [43] and then for non-aqueous [41] electrolyte solutions, as well as for IL solutions in polar solvents [42]. This pattern establishes a relationship between the electrical conductivity of solutions and the dielectric properties of the solvent: as the temperature rises, the EC of the solutions increases in direct proportion to the ratio of the
permittivity s to the dipole dielectric relaxation time x of the solvent [41-43]. With regard to the specific EC, one can write [41-43]:
, sso , к = k-= k к0
(12)
were is the limiting high-frequency (HF) EC of a polar solvent, which is equal to the ratio of its absolute DP ss0 to the dipole relaxation time x.
The existence of the proportionality described by Eq. (12) means that with increasing temperature, the specific EC of [Bmpy][NTf2] solutions in the studied polar solvents should increase in proportion to the ratio 8 / x, i.e., proportional to the limiting HF EC k^ of the solvent. The dependances k-k^
for 0.1 M solutions of [Bmpy][NTf2] in AN, DMF, and DMSO are shown in Fig. 5. The considered dependances k-k^ differ in the value of the slope
к, S/m
Fig. 5. Dépendance of the specific EC of 0.1 M [Bmpy][NTf2] in AN (1), DMF (2), and DMSO (3) solutions on the limiting HF EC of the solvent
coefficient, which depends on the degree of ionic liquid dissociation and the concentration of solvent molecules in the solution [42].
Since, according to the Stokes — Einstein — Debye equation [44], the dipole dielectric relaxation time is proportional to the ratio ^ / T, taking into account Eq. (12) and the established dependance (see Fig. 5), the Walden rule can be supplemented by the values s and T:
sT
= const.
(13)
Equation (13) has been proposed to be used to compare the X 0 values of IL solutions in different solvents at different temperatures.
Based on the temperature dependance of the molar EC at infinite dilution, the activation enthalpy of activation for the Eyring electrical conductivity can be obtained AH^ [45]:
2 AH?
ln + 2ln p =--^ + B,
3 RT
were p is the density of the solvent, which takes into account the increase in the volume of the solution with increasing temperature [45].
The dependances of ln + 2 / 3 ln p on the reciprocal temperature are shown in Fig. 6, a and the Eyring conduction activation enthalpies calculated on the basis of these dependances are presented in Table 3.
In X0 + 2/3 In p In Ka
3.3 3.5
1000/Г, 1000/K
3.3 3.5
1000/71 1000/K
Fig. 6. Dependance of ln A,o + 2/3ln p (a) and ln Ka (b) of [Bmpy][NTf2] on the reciprocal temperature T in AN (1), DMF (2) and DMSO (3)
Table 3
Enthalpy of activation for electrical conductivity )
and thermodynamic characteristics of [Bmpy][NTf2] association (AH°, AS°) in polar solvents in the 20-65 °C temperature range
Solvent ДН0, kJ/mol ДН°, kJ/mol AS°, J/(mol-K)
AN 6.47 5.10 41.3
DMF 9.20 4.90 35.0
DMSO 13.3 11.1 41.1
The AH^ values of [Bmpy][NTf2] in AN and DMF are close to each other, and the Eyring activation energy for an IL solution in DMSO is about two times higher than in AN. It should be noted that the obtained values of AH^ are close
for other ionic liquids in AN and DMSO. For [Bmim][BF4] in AN, for example, AH^q = 6.24 kJ/mol [13], and for this IL in DMSO, AH£ = 13.37 kJ/mol [11].
The association constant Ka of the studied IL increases with increasing temperature in AN, DMF and DMSO (Fig. 6, b). In the studied temperature range, the following pattern of change in the association constants was observed:
Ka,AN > Ka,DMF > Ka,DMSO- (14)
The pattern of changes in the association constants described by inequality (14) in AN, DMF, and DMSO is also valid for other ionic liquids [21]. In general, [Bmim][BF4] is weakly associated in AN, DMF, and DMSO. Therefore, dilute solutions of [Bmim] [BF4] are close in their behavior to solutions of simple inorganic electrolytes [47].
Based on the dependances ln Ka -1/ T, the enthalpies and entropies
of [Bmpy][NTf2] association in solvents were also determined (see Table 3). The enthalpy of association of [Bmpy][NTf2] in DMSO is about two times higher than in AN and DMF, and the entropies of association are approximately the same. The values obtained for the enthalpies and entropies of association in AN and DMSO are of the same order of magnitude as for other ILs in these solvents [13, 25].
Conclusion. It was shown that the difference in the results of determining the association constants of ILs in polar solvents is caused by the use of different electrical conductivity equations and insufficiently correct consideration of the frequency dependance of the measured solution resistance. The frequency ranges in which the influence of polarization processes on the electrodes occurs and ionic relaxation in the bulk of the solution occur are excluded from the results of the electrical conductivity measurements. The thermodynamic characteristics of [Bmpy][NTf2] association in acetonitrile, dimethylsulfoxide, and dimethylformamide were determined by the conductometric method in the 20-65 °C temperature range. The effect of temperature on the molar electrical conductivity of [Bmpy][NTf2] at an infinite dilution X 0 and the association constant Ka have been considered. The Walden product has been analyzed. It was shown that in AN, DMSO, and DMF, changes in different ways with increasing temperature; however, the value of / (sT) corrected for permittivity s and absolute temperature T) does not depend on the temperature and nature of the solvent. As the temperature rises, the electrical conductivity of dilute solutions of [Bmpy][NTf2] in AN, DMSO, and DMF increases in direct proportion to the ratio of the permittivity to the dipole dielectric relaxation time of the solvent.
Acknowledments
The authors are grateful to Professor Vitaliy Lukich Chumak (National Aviation University of Ukraine) for providing the Microsoft Office Excel programme for calculating the À0, Ka and R parameters.
REFERENCES
[1] Aslanov L.A., Zakharov M.A., Abramycheva R.D. Ionnye zhidkosti v ryadu rastvoriteley [Ionic liquids in a range of solvents]. Moscow, MSU Publ., 2005.
[2] Rogers R.D., Seddon K.R., eds. Ionic liquids. Industrial applications to green chemistry. ACS, 2002.
[3] Plechkova N.V., Seddon K.R. Applications of ionic liquids in the chemical industry. Chem. Soc. Rev., 2008, vol. 37, iss. 1, pp. 123-150.
DOI: https://doi.org/10.1039/B006677J
[4] Torrecilla J.S. The role of ionic liquids in the chemical industry. Nova Science, 2012.
[5] Siriwardana A.I. Industrial applications of ionic liquids. In: Torriero A. (eds). Electrochemistry in Ionic Liquids. Cham, Springer, 2015, pp. 563-603.
DOI https://doi.org/10.1007/978-3-319-15132-8_20
[6] Jain N., Kumar A., Chauhan S., et al. Chemical and biochemical transformations in ionic liquids. Tetrahedron, 2005, vol. 61, iss. 5, pp. 1015-1060.
DOI: https://doi.org/10.1016/j.tet.2004.10.070
[7] Kustov L.M., Vasina T.V., Ksenofontov V.A. Ionic liquids as catalytic media. Ros-siyskiy khimicheskiy zhurnal, 2004, vol. 48, no. 6, pp. 13-37 (in Russ.).
[8] Matsumiya M., Song Y., Tsuchida Y., et al. Recovery of platinum by solvent extraction and direct electrodeposition using ionic liquid. Sep. Purif. Technol., 2019, vol. 214, pp. 162-167. DOI: https://doi.org/10.1016/jj.seppur.2018.06.018
[9] Ohno H. Electrochemical aspects of ionic liquids. Wiley, 2011.
[10] Qin J., Lan Q., Liu N., et al. A metal-free battery with pure ionic liquid electrolyte. iScience, 2019, vol. 15, pp. 16-27. DOI: https://doi.org/10.1016/jisci.2019.04.010
[11] Liu H., Yu H. Ionic liquids for electrochemical energy storage devices applications. J. Mat. Sci. Technol., 2019, vol. 35, iss. 4, pp. 674-686.
DOI: https://doi.org/10.1016/j.jmst.2018.10.007
[12] Bester-Rogac M., Hunger J., Stoppa A., et al. Molar conductivities and association constants of 1-butyl-3-methylimidazolium chloride and 1-butyl-3-methylimidazolium tetrafluoroborate in methanol and DMSO. J. Chem. Eng. Data, 2010, vol. 55, iss. 5, pp. 1799-1803. DOI: https://doi.org/10.1021/je900531b
[13] Voroshylova I.V., Smaga S.R., Lukinova E.V., et al. Conductivity and association of imidazolium and pyridinium based ionic liquids in methanol. J. Mol. Liq., 2015, vol. 203, pp. 7-15. DOI: https://doi.org/10.1016/j.molliq.2014.12.028
[14] Bester-Rogac M., Stoppa A., Buchner R. Ion association of imidazolium ionic liquids in acetonitrile. J. Phys. Chem. B, 2014, vol. 118, no. 5, pp. 1426-1435.
DOI: http://dx.doi.org/10.1021/jp412344a
[15] Kalugin O.N., Voroshylova I.V., Riabchunova A.V., et. al. Conductometric study of binary systems based on ionic liquids and acetonitrile in a wide concentration range. Electrochim. Acta, 2013, vol. 105, pp. 188-199.
DOI: http://dx.doi.org/10.1016/jj.electacta.2013.04.140
[16] Wang H., Wang J., Zhang S., et al. Ionic association of the ionic liquids [C4mim][BF4], [C4mim][PF6], and [Cnmim]Br in molecular solvents. Chem. Phys. Chem., 2009, vol. 10, iss. 14, pp. 2516-2523.
DOI: https://doi.org/10.1002/cphc.200900438
[17] Jan R., Rather G.M., Bhat M.A. Association of ionic liquids in solution: conductivity studies of [BMIM][Cl] and [BMIM][PF6] in binary mixtures of acetonitrile + methanol. J Solution Chem., 2013, vol. 42, no. 4, pp. 738-745.
DOI: https://doi.org/10.1007/s10953-013-9999-4
[18] Barman S., Datta B., Roy M.N. Investigation on solvation behavior of an ionic liquid (1-butyl-3-methylimidazolium chloride) with the manifestation of ion association prevailing in different pure solvent systems. Indian J. Adv. Chem. Sci., 2017, vol. 5, no. 3, pp.160-175.
[19] Bester-Rogac M., Fedotova M.V., Kruchinin S.E., et al. Mobility and association of ions in aqueous solutions: the case of imidazolium based ionic liquids. Phys. Chem. Chem. Phys, 2016, vol. 18, iss. 41, pp. 28594-28605.
DOI: https://doi.org/10.1039/c6cp05010g
[20] Shekaari H., Mousavari S.S. Conductometric studies of aqueous ionic liquids, 1-alkyl-3-methylimidazolium halides, solutions at T = 298.15-328.15 K. Fluid Phase Equilib., 2009, vol. 286, iss. 2, pp. 120-126.
DOI: https://doi.org/10.1016/jfluid.2009.08.0n
[21] Borun A., Fernandez C., Bald A. Conductance studies of aqueous ionic liquids solutions [emim][BF4] and [bmim][BF4] at temperatures from (283.15 to 318.15) K. Int. J. Electrochem. Sci., 2015, vol. 10, no. 3, pp. 2120-2129.
[22] Borun A. Conductance and ionic association of selected imidazolium ionic liquids in various solvents: a review. J. Mol. Liq., 2019, vol. 276, pp. 214-224.
DOI: https://doi.org/10.1016/j.molliq.2018.11.140
[23] Lee W.H., Wheaton R.J. Conductance of symmetrical, unsymmetrical and mixed electrolytes. Part 1. Relaxation terms. J. Chem. Soc. Faraday Trans. 2, 1978, vol. 74, pp. 743-766. DOI: https://doi.org/10.1039/F29787400743
[24] Lee W.H., Wheaton R.J. Conductance of symmetrical, unsymmetrical and mixed electrolytes. Part 2. Hydrodynamic terms and complete conductance equation. J. Chem. Soc. Faraday Trans. 2, 1978, vol. 74, pp. 1456-1482.
DOI: https://doi.org/10.1039/F29787401456
[25] Lee W.H., Wheaton R.J. Conductance of symmetrical, unsymmetrical and mixed electrolytes. Part 3. Examination of new model and analysis of data for symmetrical electrolytes. J. Chem. Soc. Faraday Trans. 2, 1979, vol. 75, pp. 1128-1145.
DOI: https://doi.org/10.1039/F29797501128
[26] Barthel J.M.G., Krienke H., Kunz W. Physical chemistry of electrolyte solutions. Springer, 1998.
[27] Fuoss R.M. Conductance-concentration function for the paired ion model. J. Phys. Chem, 1978, vol. 82, iss. 22, pp. 2427-2440. DOI: https://doi.org/10.1021/j100511a017
[28] Borun A, Bald A. Ionic association and conductance of [emimHBFJ and [bmim][BF4] in 1-butanol in a wide range of temperature. J. Chem. Thermodyn., 2016, vol. 96, pp. 175-180. DOI: https://doi.org/10.10167j.jct.2015.12.029
[29] Barthel J., Feuerlein F., Neueder R., et al. Calibration of conductance cells at various temperatures. J. Solut. Chem., 1980, vol. 9, no. 3, pp. 209-219.
DOI: https://doi.org/10.1007/BF00648327
[30] Bester-Rogac M., Habe D. Modern advances in electrical conductivity measurements of solutions. Acta Chim. Slov., 2006, vol. 53, no. 2, pp. 391-395.
[31] Stoppa A., Hunger J., Buchner R. Conductivities of binary mixtures of ionic liquids with polar solvents. J. Chem. Eng. Data, 2009, vol. 54, iss. 2, pp. 472-479.
DOI: https://doi.org/10.1021/je800468h
[32] Kanabuko M., Harris K.R., Tsuchihashi N., et al. Temperature and pressure dependence of the electrical conductivity of the ionic liquids 1-methyl-3-octylimidazolium hexafluorophosphate and 1-methyl-3-octylimidazolium tetrafluorob-orate. Fluid Phase Equilib., 2007, vol. 261, iss. 1-2, pp. 414-420.
DOI: https://doi.org/10.1016/j.fluid.2007.06.019
[33] Arkhipova E.A., Ivanov A.S., Maslakov K.I., et. al. Effect of cation structure of tetraalkylammonium- and imidazolium-based ionic liquids on their conductivity. Electrochim. Acta, 2019, vol. 297, pp. 842-849.
DOI: https://doi.org/10.1016/j.electacta.2018.12.002
[34] Fuoss R.M. Conductance-concentration function for associated symmetrical electrolytes. J. Phys. Chem, 1975, vol. 79, iss. 5, pp. 525-540.
DOI: https://doi.org/10.1021/j100572a020
[35] Lopatin B.A. Konduktometriya [Conductometry]. Novosibirsk, SB AS SSSR, 1964.
[36] Evans D.F., Matesich M.A. The measurement and interpretation of electrolytic conductance. In: Techniques of Electrochemistry. Vol. 2. Wiley, 1973.
[37] Shcherbakov V.V. Accounting for the electrical capacitance of a solution in the analysis of the impedance of an electrochemical cell. Elektrokhimiya, 1998, vol. 14, no. 1, pp. 121-124 (in Russ.).
[38] Akhadov Ya.Yu. Dielektricheskie parametry chistykh zhidkostey [Dielectric parameters of pure liquids]. Moscow, MAI Publ., 1999.
[39] Barthel J., Wachter R., Gores H.-J. Temperature dependence of conductance of electrolytes in nonaqueous solutions. In: Conway B.E., Bockris J.O. (eds). Modern Aspects of Electrochemistry. Boston, Springer, 1979, pp. 1-79.
DOI: https://doi.org/10.1007/978-1-4615-7455-2_1
[40] Chumak V.L., Maksimyuk M.R, Neshta T.V., et al. Designation of Lee — Wheaton coefficients for the electrical conductivity of electrical differences in the MS Excel medium. Vostochno-Evropeyskiy zhurnal peredovykh tekhnologiy [Eastern-European Journal of Enterprise Technologies], 2013, vol. 62, no. 5, pp. 59-63 (in Ukrainian).
[41] Robinson R.A., Stokes R.H. Electrolyte solutions. Dover, 2012.
[42] Shcherbakov V.V., Artemkina Yu.M. Limiting equivalent electrical conductivity of inorganic salt solutions and dielectric properties of a polar solvent. Russ. J. Inorg. Chem., 2013, vol. 58, no. 8, pp. 968-971.
DOI: https://doi.org/10.1134/S0036023613080214
[43] Shcherbakov V.V., Artemkina Yu.M., Akimova I.A., et al. Dielectric characteristics, electrical conductivity and solvation of ions in electrolyte solutions. Materials, 2021, vol. 14, iss. 19, art. 5617. DOI: https://doi.org/10.3390/ma14195617
[44] Shcherbakov V.V., Ermakov V.I., Artemkina Yu.M. Dielectric characteristics of water and electric conductivity of aqueous electrolytes. Russ. J. Electrochem., 2017, vol. 53, no. 12, pp. 1301-1306. DOI: https://doi.org/10.1134/S1023193517120102
[45] Dote J., Kivelson D., Schwartz R.N. A molecular quasi-hydrodynamic free-space model for molecular rotational relaxation in liquids. J. Phys. Chem., 1981, vol. 85, iss. 15, pp. 2169-2180. DOI: https://doi.org/10.1021/j150615a007
[46] Brummer S.B., Hills G.J. Kinetics of ionic conductance. Part 1. Energies of activation and the constant volume principle. Trans. Faraday Soc., 1961, vol. 57, pp. 18161822. DOI: https://doi.org/10.1039/TF9615701816
[47] Hefter G., Buchner R. Dielectric relaxation spectroscopy: an old-but-new technique for the investigation of electrolyte solutions. Pure Appl. Chem., 2020, vol. 92, no. 10, pp. 1595-1609. DOI: https://doi.org/10.1515/pac-2019-1011
Karpunichkina Irina Alekseevna — Post-Graduate Student, Department of General and Inorganic Chemistry, Mendeleev University of Chemical Technology (Miusskaya ploshchad 9, Moscow, 125047 Russian Federation).
Artemkina Yuliya Mikhailovna — Cand. Sc. (Chem.), Assoc. Professor, Department of General and Inorganic Chemistry, Mendeleev University of Chemical Technology (Miusskaya ploshchad 9, Moscow, 125047 Russian Federation).
Plechkova Natalia Vladimirovna — PhD (Chem.), Research Impact and Engagement Officer, Wellcome-Wolfson Institute of Experimental Medicine, Queen's University Belfast (Lisburn Road 97, Belfast BT9 7BL, UK).
Shcherbakov Vladimir Vasilievich — Dr. Sc. (Chem.), Professor, Department of General and Inorganic Chemistry, Mendeleev University of Chemical Technology (Miusskaya ploshchad 9, Moscow, 125047 Russian Federation).
Please cite this article as:
Karpunichkina I.A., Artemkina Yu.M., Plechkova N.V., et al. Electrical conductivity and association of 1-butyl-3-methylpyridinium bis{(trifluoromethyl)sulfonyl}amide in some polar solvents. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2023, no. 3 (108), pp. 145-163. DOI: https://doi.org/10.18698/1812-3368-2023-3-145-163
