CC BY
2DOI: 10.6060/ivkkt.20236612.6830
УДК: 541.8: 541.133
ЭНЕРГИЯ АКТИВАЦИИ ЭЛЕКТРОПРОВОДНОСТИ 1-БУТИЛ-3-МЕТИЛИМИДАЗОЛИЙ
БИС{(ТРИФТОРМЕТИЛ)СУЛЬФОНИЛ}АМИДА И 1-БУТИЛ-3-МЕТИЛПИРИДИНИЙ БИС{(ТРИФТОРМЕТИЛ)СУЛЬФОНИЛ}АМИДА И ИХ РАСТВОРОВ В АЦЕТОНИТРИЛЕ, ДИМЕТИЛСУЛЬФОКСИДЕ И ДИМЕТИЛФОРМАМИДЕ
Н.В. Плешкова, И.А. Карпуничкина, Ю.М. Артемкина, В.В. Щербаков
Наталья Владимировна Плешкова
Институт экспериментальной медицины Королевского университета Белфаста, 97 Lisbum Road, Belfast BT9 7BL, UK
E-mail: [email protected]
Ирина Алексеевна Карпуничкина, Юлия Михайловна Артемкина, Владимир Васильевич Щербаков (ORCID 0000-0002-6690-1966)*
Кафедра общей и неорганической химии Российского химико-технологического университета им. Д.И. Менделеева, Миусская пл. 9, Москва, Российская Федерация, 125047 E-mail: [email protected] [email protected] [email protected]*
На основании анализа литературных данных показано, что энергия активации электропроводности ионных жидкостей и их растворов увеличивается с повышением их концентрации, а температурная зависимость энергии активации не исследована. Согласно представлениям Литовица, эта энергия активации должна увеличиваться прямо пропорционально квадрату обратной абсолютной температуры. По уравнению Аррени-уса на основании результатов измерения электропроводности определена ее энергия активации двух ионных жидкостей - 1-бутил-3-метилимидазолий бис{(трифторметил). И далее сульфонил}амида и 1-бутил-3-метилпиридиний бис{(трифторметил) сульфо-нил}амида и их растворов в ацетонитриле (АН), диметилфлормамиде (ДМФА) и диме-тилсульфоксиде (ДМСО). Проанализирована погрешность расчета энергии активации. Показано, что энергия активации электропроводности уменьшается при повышении температуры и увеличивается с ростом концентрации ИЖ. На основании литературных данных по диэлектрическим свойствам рассчитана энергия активации предельной высокочастотной электропроводности АН, ДМФА и ДМСО, которая также уменьшается с ростом температуры. Установлено, что зависимости энергии активации растворов ионных жидкостей и предельной высокочастотной электропроводности растворителей подчиняются уравнению Литовица - их энергия активации увеличивается прямо пропорционально квадрату обратной температуры. Показано, что вклад растворителей в энергию активации электропроводности определяется температурной зависимостью их диэлектрических свойств - статической диэлектрической проницаемости и времени ди-польной диэлектрической релаксации, отношение которых и определяет предельную высокочастотную электропроводность полярного растворителя. Сопоставлены вклады различных полярных растворителей в энергию активации электропроводности растворов ионных жидкостей. Для растворов ионных жидкостей в воде, диметилсульфоксиде, диметилформамиде и пропиленкарбонате эта величина составляет 10 -15 кДж/моль. В аце-тонитрильныхрастворах ионных жидкостей этот вклад составляет 5,5 - 6,0 кДж/моль.
Ключевые слова: электропроводность, энергия активации, 1-бутил-3-метилимидазолий бис{(три-фторметил) сульфонил^мид, 1-бутил-3-метилпиридиний бис{(трифторметил) сульфонил^мид, растворы, ацетонитрил, диметилсульфоксид, диметилформамид
Для цитирования:
Плешкова Н.В., Карпуничкина И.А., Артемкина Ю.М., Щербаков В.В. Энергия активации электропроводности 1-бутил-3-метилимидазолий бис{(трифторметил) сульфонил^мида и 1-бутил-3-метилпиридиний бис{(трифторме-тил) сульфонил}8мида и их растворов в ацетонитриле, диметилсульфоксиде и диметилформамиде. Изв. вузов. Химия и хим. технология. 2023. Т. 66. Вып. 12. С. 82-90. DOI: 10.6060/ivkkt.20236612.6830.
For citation:
Plechkova N.V., Karpunichkina I.A., Artemkina Yu.M., Shcherbakov V.V. Activation energy of electrical conductivity for 1-butyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}amide and 1-butyl-3-methylpyridinium bis{(trifluorome-thyl)sulfonyl}amide and their solutions in acetonitrile, dimethyl sulfoxide, and dimethylformamide. ChemChemTech [Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol]. 2023. V. 66. N 12. P. 82-90. DOI: 10.6060/ivkkt.20236612.6830.
ACTIVATION ENERGY OF ELECTRICAL CONDUCTIVITY FOR 1-BUTYL-3-METHYLIMIDAZOLIUM BIS{(TRIFLUOROMETHYL)SULFONYL}AMIDE AND 1-BUTYL-3-METHYLPYRIDINIUM BIS{(TRIFLUOROMETHYL)SULFONYL}AMIDE AND THEIR SOLUTIONS IN ACETONITRILE, DIMETHYL SULFOXIDE, AND DIMETHYLFORMAMIDE
N.V. Plechkova, I.A. Karpunichkina, Yu.M. Artemkina, V.V. Shcherbakov
Natalia V. Plechkova
Wellcome-Wolfson Institute of Experimental Medicine, Queen's University Belfast, 97 Lisburn Road, Belfast BT9 7BL, UK
E-mail: [email protected]
Irina A. Karpunitchkina, Yulia M. Artemkina, Vladimir V. Shcherbakov*
Department of General and Inorganic Chemistry, Mendeleev University of Chemical Technology, Miusskaya sq., 9, Moscow, 125047, Russia
E-mail: [email protected], [email protected], [email protected]*
After the analysis of the relevant data in literature, it can be shown that the electrical conductivity activation energy of ionic liquids (ILs) and their solvent solutions increases with the increase in their concentration. The temperature dependence of the activation energy was not studied. According to Litowitz, this activation energy should increase in direct proportion to the square of the reciprocal of absolute temperature. The activation energy of two ionic liquids, 1-butyl-3-me-thylimidazolium bis{(trifluoromethyl)sulfonyl}amide and 1-butyl-3-methylpyridinium bis{(trifluo-romethyl)sulfonyl}amide, and their solutions was determined using the Arrhenius equation, based on the results of electrical conductivity measurements in acetonitrile (AN), dimethylflormamide (DMF) and dimethyl sulfoxide (DMSO). The error in the calculation of the activation energy was analysed. It was shown that the activation energy of electrical conductivity decreases with increasing temperature and increases with increasing IL concentration. Based on the literature data on the dielectric properties, the limiting high-frequency electrical conductivity activation energy of AN, DMF, and DMSO was calculated, which also decreases with increasing temperature. It has been established that the dependences of the activation energy of solutions of ionic liquids and the limiting high-frequency electrical conductivity of solvents obey the Litowitz equation - their activation energy increases in direct proportion to the square of the reciprocal temperature. It was shown that the contribution of solvents to the activation energy of electrical conductivity is determined by the temperature dependence of their dielectric properties - static permittivity and dipole dielectric relaxation time, the ratio of which determines the limiting high-frequency electrical conductivity of a polar solvent. The contributions of various polar solvents to the activation energy of the electrical conductivity of solutions of ionic liquids were compared. For solutions of ionic liquids in water, dimethyl sulfoxide, dimethylformamide, and propylene carbonate, this value is 10 -15 kJ/mol. In acetonitrile solutions of ionic liquids, this contribution is 5.5 - 6.0 kJ/mol.
Key words: electrical conductivity, activation energy, 1-butyl-3-methylimidazolium bis{(trifluorome-thyl)sulfonyl}amide, 1-butyl-3-methylpyridinium bis{(trifluoromethyl)sulfonyl}amide, solutions, acetonitrile, dimethylsulfoxide, dimethylformamide
INTRODUCTION
Ionic liquids (ILs) have high thermal stability, low vapor pressure, and a large range of liquidus states [1]. These properties allow them to replace volatile organic solvents in the fields of both scientific research and technology [2, 3]. Due to their relatively high electrical conductivity (EC), ILs and their solutions in polar solvents are promising for use in various electrochemical devices such as current sources and electric energy storage devices [4, 5]. The practical application of ILs and their solutions requires knowledge of their transport properties, in particular, their conductivities and its temperature dependences.
An increase in the specific electric conductivity (EC) of Type 2 conductors (melts and electrolyte solutions) with increasing temperature is qualitatively explained by an increase in the mobility of the ions and a decrease in the viscosity [6]. According to the theory of absolute reaction rates [7] and the "hole" theory of EC [8], the temperature dependence of the specific EC of solutions can be described by the Arrhenius equation: , E N
K = K maxeXP(-^X (1)
where Ek is the activation energy of a specific EC and Kmax is a pre-exponential factor, which can be considered as an EC at the absolute temperature T tending to infinity.
Activation energy is traditionally used to describe the temperature dependence of the conductivity of aqueous [9-11] and non-aqueous [12-14] electrolyte solutions. When analyzing the temperature dependences of the EC of ILs solutions in polar solvents, in addition to the Arrhenius equation (1), other equations are also required [15-31].
An analysis of the specific EC logarithm dependences on the reciprocal temperature showed that these dependences are not linear [15-22, 27, 31], and the temperature dependence of the specific EC of ILs solutions in polar solvents is better described by the Vogel-Tammann-Fulcher (VTF) equation [32], when, as applied to the specific EC, can be represented as [31]:
B E
k = AKexp(-——) = Kmaxgxp(- K ). (2) T -Tg -Tg)
In the the Vogel-Tammann-Fulcher (VTF) equation (2), Ak, B and Tg are empirical adjustable parameters. It should be noted that the VTF equation goes into the Arrhenius equation (1) under the Ak = Kmax, B = Ek /R and T = (T- Tg) condition.
The VTF equation (2) quite accurately describes the temperature dependence of the EC of IL solutions in polar solvents [20, 22-26, 28-30], but this
equation is unable to describe the dependence of the specific EC on the IL concentration.
For a simultaneous description of the specific EC dependence on the concentration and temperature, the equation (3) containing four adjustable parameters Bi - B4 was proposed in [26] :
k = x0^--^- + BT + B4 ), (3) 1 - B2
where x is the mole fraction of an IL in the solution and T is the absolute temperature.
Based on the analysis of the results of the temperature effect on the specific EC of solutions of 1-ethyl-3-methylimidazolium dicyanamide ([Emim][DCA]) solutions in propylene carbonate (PC) and y-Butyro-lactone (GBL), it was found in [26] that the activation energy of the EC of these solutions increases in direct proportion to the mole fraction x of [Emim] [DCA] in accordance with the equation:
ek = ek 0 + xek,il • (4)
Equation (4) contains two contributions to the EC activation energy: the independent of the [Emim][DCA] concentration contribution of the solvent EK0 and the molar fraction-dependent contribution of an IL Ek,il. The value of Ek,il in [26] is considered as a molar increase in the EC activation energy as a result of interionic interactions in solution. For [Emim][DCA] in propylene carbonate (PC), the values Ha in PC, the values EK0 and Ek,il turned out to be 12.6465 and 8.0085 kJ/mol, while for this IL in GBL they turned out to be almost the same, 10.0640 and 10.5796 kJ/mol [26]. It should be noted here that the accuracy of the values of activation energies given in [26] (5-6 digits), in our opinion, is clearly overestimated, since, as will be shown below, it sharply decreases due to the large contribution of the EC difference values to the EK error.
Equation (3) was also used in [28] to analyze the concentration and temperature dependences of the specific EC of six imidazolium IL solutions in GBL. As in [26], the concentration dependence of the activation energy is described by Eq. (3). The value of EK° obtained in [28] for a pure solvent (GBL) turned out to be 9.07-11.91 kJ/mol, which is in good agreement with the value of EK° = 10.640 kJ/mol for GBL given in [26].
Consisting of two components (solvent EK0 and electrolyte Ek,el) and described by equation (4), the EC activation energy is also used when considering the temperature dependence of the specific EC of electrolyte solutions in non-aqueous solutions [12-14]. For a solution of LiAsF6 in acetonitrile, as an example, EK0 = 5.5, and Ek,el = 28.16 kJ/mol [14].
It should be noted that the above-mentioned absence of a linear dependence of the EC logarithm on
the reciprocal absolute temperature indicates the possible existence of a dependence of the EC activation energy on temperature. The existence of such a dependence for the transport properties of solutions was first considered by Litowitz in [33] and used in the analysis of the temperature dependence of the EC of imid-azolium and tetraalkylammonium bis{(trifluorome-thyl)sulfonyl}amide solutions in acetonitrile in [30].
In his work [33], Litowitz suggested that the activation energy of the transport properties E is proportional to the inverse square of the temperature:
E = (5)
T2
and the dependence of the specific EC on temperature can be described by the equation [30]:
K = K max^P(-^3). (6)
The Litowitz constant Bl in equation (5) relates the EC activation energy Ek to temperature.
In order to determine the activation energy, the dependences lnK - 1/T, lnK - 1/(T - T0), and lnK - 1/T3 described by equations (1), (2), and (6) were considered in [30]. As a result, it was found that the highest activation energy (6.9-8.1 kJ/mol) is obtained using the Arrhenius equation (1). This value is 1.5-2 times greater than the activation energy (4.1-5.0 kJ/mol) obtained from the VTF equation (2). Finally, when using the Litowitz equation (6), the smallest value of Ek is obtained: 2.0-3.2 kJ/mol (the Bl constant in the Litowitz equation (6) is (2.4-2.8)105 kJ K2/mol [30]). A significant difference (by 2-4 times) in the Ek values obtained in [30] does not allow one to give preference to any of the equations (1), (2) or (6), and also does not make it possible to relate the EC activation energy of IL solutions with the nature of the solvent.
At the same time, an important result obtained in [30] is the presence of the dependence of the activation energy on temperature, described by Eq. (5). According to [30, 33], as the temperature rises, the activation energy decreases as a result of an increase in the thermal motion of molecules. It is also important to note that, using the Arrhenius equation (1) and the fact that the EC activation energy decreases with increasing temperature, one can try to describe the temperature dependence of the specific EC of ILs solutions. A similar way of describing the EC temperature dependence is used for aqueous electrolyte solutions [34]. In this work, this approach is used to analyze the EC temperature dependences of ILs solutions.
The above brief analysis of the EC activation energy Ek of ILs solutions shows that if the dependence of Ek on the concentration is established (Ek increases in proportion to the mole fraction of the IL, equation
(4)), then the temperature dependence of EC activation energy is practically not studied.
In [21], the dependence of Ek on the reciprocal absolute temperature (1/T) for six ILs based on the [Bmim]+ cation is given, according to which Ek decreases monotonically with decreasing 1/T (with increasing temperature) and with decreasing anion size. In this work, however, it is not indicated how the temperature dependence of Ek was obtained and why the EC activation energy decreases with increasing temperature and with decreasing anion size. It would also be expedient to analyze the dependence of the activation energy on the square of the reciprocal absolute temperature Ek = f(1/T2) and find out whether the dependence of the EC activation energy on temperature for pure ILs and for their solutions in polar solvents obeys equation (5).
The aim of this work is to establish the effect of temperature on the EC activation energy Ek of 1-butyl-3-methylimidazolium bis{ (trifluoromethyl)sulfonyl} amide ([Bmim][NTf2]) and 1-butyl-3-methylpyridinium bis{(trifluoromethyl)sulfonyl}amide ([Bmpy][NTf2]) and their solutions in acetonitrile (AN), dimethylfor-mamide (DMF), and dimethyl sulfoxide (DMSO). The choice of these ionic liquids is explained by the fact that ILs with bis{(trifluoromethyl)sulfonyl}imide anions are characterized by the maximum electrical conductivity both as pure ILs and their solutions [1, 30]. It is also of interest to compare the EC values and their activation energies for different [Bmim]+ and [Bmpy]+ cations while retaining the same [NTf2]- anion. ILs with this anion are promising for their use, since they are characterized by relatively low viscosities and high electrochemical stability [35].
AN, DMF, and DMSO were used as solvents for ILs. AN and DMF are taken for comparison, since they have close dielectric permittivities (DP) [36]. DMF and DMSO are characterised by close values of density and molar mass. Some of the properties of ILs and solvents used in this work are presented in Table 1 below.
EXPERIMENTAL TECHNIQUE AND PROCESSING OF RESULTS
Imidazolium ([Bmim][NTf2]) and pyridinium ([Bmpy] [NTf2]) bis{(trifluoromethyl)sulfonyl}amides were synthesized at QUILL (Queen's University Belfast Ionic Liquid Laboratories) in Northern Ireland. The purity of the ionic liquids (99.5%) was also monitored using NMR spectroscopy at QUILL.
Before measuring the EC of pure ILs and preparing their solutions, [Bmim][NTf2] and [Bmpy][NTf2] were dried for five hours in a vacuum fume hood at 60 °C. Solutions of ILs were prepared by the grav i-metric method; in this case, taken with an accuracy of
± 10-5 g, a weighed portion of IL was quantitatively transferred into a dry volumetric flask. After that, a weighed portion of the solvent was added to this ionic liquid. The water content in organic solvents (AN, DMSO, and DMF) was controlled by the Karl Fischer method and did not exceed 0.1%.
Measurements of the specific EC of ILs and their solutions were carried out using an E7-20 digital AC bridge (immittance meter) in the frequency range F 0.1-10 kHz. To eliminate the influence of polarization effects on the results of measuring the resistance of solutions R, the desired resistance was determined by extrapolating its measured value to an infinite frequency in the coordinates R - 1/F [37]. The temperature-controlled conductometric cell with platinum electrodes was made of Pyrex glass. In the 20-80 °C temperature range, distilled water was used as a ther-mostating liquid. At 90-210 °C temperatures, thermo-stating was carried out using glycerol. The cell constant was determined by measuring the resistance of aqueous KCl solutions according to the standard procedure [37]. Its value was 0.1723 ± 0.0003 cm. The error in determining the specific EC of ILs solutions did not exceed 0.5%.
The activation energy Ek was calculated based on the analysis of the temperature dependence of the specific EC, measured with a step of 5 degrees. In particular, if the values of K1, K2, and K3 are experimentally measured at temperatures T1, T2, and T3, then the specific EC activation energy of Ek is [34]:
E =RT2
(7)
K2 (T3 - T)
In equation (7), R is the universal gas constant, T is the absolute temperature, K. The most important issue in the procedure for determining Ek is the choice of the temperature step (value AT). The calculation error of the EC activation energy SEk according to equation (7) depends on the error in determining the difference Ak = K3 - K1. With a decrease in AT, the difference Ak decreases and the calculation error Ek increases significantly, which is determined by the expression [34]:
ЬЕ =5„
(8)
In expression (8), 5k is the relative error in determining the specific EC (0.5%).
To reduce the error sEk, it is desirable to increase the value of AT = T3 - T1. However, in this case, the calculated value of Ek decreases, i.e. the accuracy of the analysis of the activation energy temperature dependence decreases. Our analysis shows that if we use a temperature step of less than five degrees (AT < 10 K), then the calculation error sEk increases sharply due to
a decrease in the difference K3 - ki and can reach several tens of percent. An analysis of the error 5EK described by equation (8) shows that the optimal value of AT is 10 K (temperature step five degrees). In this case, if 5k = 0.5%, then the calculation error 5Ek does not exceed 5%.
When discussing the results in this work, some additional physicochemical properties of ILs and polar solvents are used, which are presented in Table 1. The physical meaning of the values of the limiting high-frequency (HF) EC k„ and its activation energy к» is considered below in the discussion of results.
Table 1
Molar mass M (g/mol), density p (g/cm3), molar concentration c (mol/l), dielectric constant £, activation energy EC Ek of ionic liquids and activation energy of limiting high-frequency electrical conductivity Ek (kJ/mol) of the solvents; t=25 °C Таблица 1. Молярная масса М (г/моль), плотность p (г/см3), молярная концентрация с (моль/л), диэлектрическая проницаемость £, энергия активации ЭП Ек ИЖ и предельной высокочастотной ЭП Ек
Compound М P с £ Ek»
[Bmim][NTf2] 419.4 1.436 3.42 15.0[38] 35.4*
[Bmpy][NTf2] 430.4 1.414 3.28 - 37.7*
AN 41.05 0.7875 19.18 35.9[36] 5.8
DMF 73.09 0.9445 12.92 36.8[36] 8.8
DMSO 78.13 1.1004 14.08 46.4[36] 13.7
Note: *The values of the specific EC activation energy Ek of ionic liquids are given
Примечание: *Приведены величины энергии активации удельной ЭП Ek ИЖ
Comparing the properties presented in Table 1 of the studied ILs and polar solvents, the following can be noted. The molar concentration of pure ILs is 4-6 times lower than the molar concentration of pure polar solvents (AN, DMF, and DMSO). In [Bmim][NTf2] solutions in AN, DMF, and DMSO, the molar concentration of IL will increase from zero to its maximum value of 3.42 mol/L, and in [Bmpy][NTf2] solutions, from zero to 3.28 mol/L. The activation energy of the limiting HF EC Ek» of polar solvents is 3-6 times lower than the value of EK of ILs. Therefore, it can be expected that in solutions of IL in AN, DMF, and DMSO, Ek will increase from the value of Ek» of a polar solvent to Ek of a pure IL, In solutions of [Bmim] [NTf2] in AN, for example, Ek will increase from 5.8 to 35.4 kJ/mol, and in solutions of [Bmim][NTf>] in DMSO, from 13.7 to 37.7, Table 1.
DISCUSSION OF RESULTS
According to the concepts of Litovitz [33], the activation energy of the transport properties of solutions should decrease with increasing temperature; the
K3 -K1
linear dependence of the EC activation energy on the square of the reciprocal absolute temperature should take place as well, described by Eq. (5). Before considering the dependences of Ek on t and on 1/T2 of pure ILs and their solutions in AN, DMF, and DMSO, it is necessary to note the different nature of the dependencies of specific EC (k) on temperature (t) for pure ILs and their solutions in polar solvents. In pure ILs, the specific EC sharply increases with increasing temperature due to a significant decrease in their viscosity and the dependencies k - t are concave curves [39-43], while in solutions of polar solvents these dependencies are almost linear or are slightly convex curves [9, 11, 16]. At the same time, the dependencies of the EC activation energy of pure ILs and their solutions on temperature practically do not differ in character.
The temperature dependencies of the activation energies of ILs and their solutions will now be considered. Fig. 1 shows the Ek dependencies of [Bmim][NTf2] (curve 1) and [Bmpy][NTf2] (curve 2) on temperature (Fig. 1a) and on the square of the reciprocal absolute temperature (Fig. 1b).
The activation energy of pure ILs decreases monotonically with increasing temperature, and in the temperature range under study (20-200 °C), the Ek of [Bmpy] [NTf2] is greater than the Ek of [Bmim] [NTf2], Fig. 1a. With regard to the EC activation energy of pure ILs, it should be noted that the Litowitz equation (5) is valid for [Bmim][NTf2] and [Bmpy][NTf2] only in the 50-120 °C temperature range. At t < 50 °C and at t > 120 °C, there is a systematic deviation of the Ek = fl/T2) dependence from the direct proportionality described by equation (5).
The EC activation energy of [Bmim][NTf2] and [Bmpy][NTf2] solutions in AN, DMF, and DMSO also decreases with increasing temperature. However, in contrast to the Ek of pure ILs, the linear dependence of Ek (described by equation (5)) on the square of the reciprocal of absolute temperature is observed for the ionic liquid solutions in AN, DMF and DMSO. As an example, the dependence of the specific EC activation energy of [Bmpy][NTf2] solutions is shown in Fig. 2.
Fig. 1. Dependencies of the EC activation energy EK of [Bmim][NTf2] (1) and [Bmpy][NTf2] (2) on temperature (a) and
on the square of the reciprocal absolute temperature (б) Рис. 1. Зависимости энергии активации ЭП Ек [Bmim][NTf2] (1) и [Bmpy][NTf2] (2) от температуры (а) и от квадрата обратной абсолютной температуры (б)
0.6 0.9 105/Т:
Fig. 2. Dependence of EC activation energy Ek 0.1 M of [Bmpy][NTf2] solutions on temperature (a) and on the square of the
reciprocal temperature (б) in AN (1), DMF (2), and DMSO (3) Рис. 2. Зависимость энергии активации ЭП Ек 0,1 M растворов [Bmim][NTf2] от температуры (а) и от квадрата обратной температуры (б) в АН (1), ДМФА (2) и ДМСО (3)
The specific EC activation energy Ek monoton-ically increases with an increase in the molar concentration с of an IL. Fig. 3a shows the dependence of Ek of [Bmpy] [NTf2] on molarity in AN, DMF, and DMSO as an example.
0 3 6 9
с г (molL)
Fig. 3. Dependence of electrical conductivity activation energy Ек of [Bmpy] [NTf2] solutions on the concentration (a) and the squared concentration (б) in (1) AN, (2) DMF, and (3) DMSO; t=25 °С
Рис. 3. Зависимость энергии активации удельной ЭП растворов [Bmpy][NTf2] в АН (1), ДМФА (2) и ДМСО (3) от концентрации (а) и квадрата концентрации (б); t=25 °С
The curves shown in this Figure are easily straightened if the square of the molar concentration is used as an argument, Fig. 3b. All three dependencies presented in this figure are described by a single equation:
Ек = Ек0 + К с2, (9)
where Ек0 is its contribution to the activation energy determined by the dielectric properties of the solvent (5.9, 9.1, and 13.8 kJ/mol, respectively, for AN, DMF, and DMSO) and K is the contribution of the IL to the activation energy, which is the same for all solvents and is (1.50±0.07) kJmol/L2.
The contribution of the solvent to the activation energy Ek0 is determined by the temperature dependence of the dielectric properties of the solvent, in particular, the static permittivity (DP) Ss and the dipole dielectric relaxation time t. The ratio of these quantities determines the limiting high-frequency (HF) EC of a polar solvent [44]:
e„en
(10)
In equation (10), so is the absolute DP of vacuum (so = 8.854 1012 F/m).
The activation energy of the limiting HF EC Екш of acetonitrile was determined in [45] and at 25 °C is 5.8 ± 0.8 kJ/mol. The limiting HF EC of DMF and DMSO, as well as its activation energies, were derived from the dielectric properties of these solvents, as published in [46-50]. The limiting HF EC and its activation energy AN, DMF, and DMSO are shown in Table 2.
Table 2
Limiting high-frequency electrical conductivity к (S/m) and its activation energy Ек (kJ/mol) of acetonitrile, di-
methylformamide and dimethyl sulfoxide Таблица 2. Предельная высокочастотная электропроводность к (См/м) и энергия ее активации Ек (кДж/моль) ацетонитрила, диметилформамида и
/, °С AN DMF DMSO
Кда Екш Кда Екш кш Екш
20 81.2 - 23.4 - 19.8 -
25 82.1 5.8 24.8 8.8 21.9 13.5
30 82.9 5.7 26.3 8.6 24.1 12.9
35 83.7 5.5 27.8 8.4 25.8 12.3
40 84.6 5.4 29.3 8.2 28.2 11.8
45 85.4 5.2 30.7 8.1 29.9 11.4
50 86.3 5.1 32.2 7.9 31.9 11.0
55 87.1 5 33.7 7.8 34.3 10.6
60 87.9 4.9 35.2 7.7 36.2 10.4
65 88.8 4.9 36.7 7.6 38.1 10.1
70 - - 38.1 7.5 40.2 9.9
It should be noted that the Ek values that cut off on the j-axis at the concentrations of [Bmpy][NTf2] and [Bmim][NTf2] tending to zero coincide quantitatively with those given in Table 2 Ek«, values of AN, DMF, and DMSO. Consequently, the contribution of solvents to the EC activation energy EK0 is determined by the temperature dependence of their dielectric characteristics, in particular, by the temperature dependence of the limiting high-frequency EC of the solvent, determined by equation (10).
The values of the EC activation energy EK0 of various polar solvents published in literature and obtained in this work are summarized in Table 3.
k „ =
t
Table 3
EC activation energy Ек0 (kJ/mol) of various polar solvents; t=25 °C Таблица 3. Энергия активации ЭП Ек0 (кДж/моль)
различных полярных растворителей; t=25 °C
Solvent Ек0 Solvent Ек0
Water 14.0 [18] GBL 10.06 [26]
Water 14.8 [45] GBL 9.07-11.91[28]
PC 12.13 [14] AN 5.5 [14]
PC 12.2 [18] AN 5.9
PC 12.65 [26] DMF 10.3 [18]
DMSO 13.8 DMF 9.1
The Ек0 values for various polar solvents published in different works are in good agreement with each other, Table 3. For solutions of ionic liquids in water, dimethyl sulfoxide, dimethylformamide and propylene carbonate, this value is 10-15 kJ/mol. In ac-etonitrile solutions of ionic liquids, this contribution is 5.5-6.0 kJ/mol. Since the Ек0 values obtained in this work coincide with the HF EC activation energies Ек» of AN, DMF, and DMSO, it can be assumed that for other polar solvents, the Ек0 values will also be determined by the temperature dependence of the dielectric properties of the solvent, as shown in Table 3.
CONCLUSIONS
It is shown from analysis of the results of determining the electrical conductivity (EC) activation energy Ек of ionic liquids (ILs) and their solutions in polar solvents that these values increase with an increase in the concentrations of ILs. The temperature dependance of the EC activation energy of ILs solutions has not been studied, although, according to the ideas of Litowitz [33], the Ек of solutions should increase in direct proportion to the square of the reciprocal absolute temperature.
The specific EC activation energy Ек of the two ionic liquids and their solutions in acetonitrile (AN), dimethylflormamide (DMF), and dimethyl-sulfoxide (DMSO) was determined using the Arrhe-nius equation. It was shown that Ек decreases with increasing temperature and increases with increasing IL concentration. Based on the literature data on the dielectric properties, the limiting high-frequency (HF) EC activation energy Ек» of AN, DMF, and DMSO was calculated, which also decreases with increasing temperature. It has been found that the EC activation energy Ек of ILs solutions and the limiting HF EC activation energy Ек<x, of the solvent obey the Litowitz equation (5), i.e. Ек and Ек» increase in direct proportion to the square of the reciprocal temperature.
It is shown that the contribution of solvents to the EC activation energy EK° is determined by the temperature dependance of their dielectric properties -static dielectric permittivity Ss and the dipole dielectric relaxation time т. The ratio of these values determines the limiting high-frequency electrical conductivity of a polar solvent к», equation (10).
The work was performed in the framework of the development program "Prioriyty-2030" of the Mendeleev University of Chemical Technology ofRussia.
The authors declare the absence a conflict of interest warranting disclosure in this article.
Работа выполнялась в рамках программы развития «Приоритеты-2030» Российского химико-технологического университета имени Менделеева.
Авторы заявляют об отсутствии конфликта интересов, требующего раскрытия в данной статье.
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Поступила в редакцию 10.03.2023 Принята к опубликованию 17.05.2023
Received 10.03.2023 Accepted 17.05.2023
