Study of ion-pair and triple-ion origination of an ionic liquid ([bmmim][BF₄]) predominant in solvent systems

Abstract

Electrolytic conductivities, densities, viscosities, and FT-IR spectra of 1-butyl-2,3 dimethylimidazolium tetrafluoroborate ([bmmim][BF₄]) have been studied in tetrahydrofuran, dimethylacetamide and methyl cellosolve at different temperatures. The limiting molar conductivities, association constants, and the distance of closest approach of the ions have been evaluated using the Fuoss conductance equation (1978). The molar conductivities observed were explained by the formation of ion pairs and triple ion formation. Ion–solvent interactions have been interpreted in terms of apparent molar volumes and viscosity B-coefficients which are obtained from the results supplemented with densities and viscosities, respectively. The limiting apparent molar volumes, experimental slopes derived from the Masson equation and viscosity A and B coefficients using the Jones–Dole equation have been interpreted in terms of ion–ion and ion–solvent interactions respectively. However, the deviation of the conductometric curves (Λ vs. √c) from linearity in tetrahydrofuran indicated triple-ion formation and therefore corresponding conductance data have been analyzed by the Fuoss–Kraus theory of triple ions. The limiting ionic conductances have been estimated from the appropriate division of the limiting molar conductivity value of tetrabutylammonium tetraphenylborate as the “reference electrolyte” method along with a numerical evaluation of ion-pair and triple-ion formation constants (K_P ≈ K_A and K_T). The FT-IR spectra for the solvents as well as the solute in solvents have also been studied. The results are discussed in terms of ion–dipole interactions, hydrogen bond formation, structural aspects, and configurational theory.

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1. Introduction

In general, ionic liquids (ILs) are liquid electrolytes that consist of combinations of organic–organic or organic–inorganic cations/anions. Because of their unique physicochemical properties, such as the favourable solubility of organic and inorganic compounds, low vapour pressures, low melting points, high thermal stability, good solvent characteristics for organic, inorganic and polymeric materials, adjustable polarity, selective catalytic effects, chemical stability, non-flammability and high ionic conductivity, ILs have generated significant interest in a wide range of industrial applications.

The solvents used in this study find wide industrial usage. N,N-dimethylacetamide (DMA) is commonly used as a solvent for fibres and in the adhesive industry, in the production of pharmaceuticals and plasticizers as a reaction medium, and in the manufacture of adhesives, synthetic leathers, fibres, films, and surface coatings. Tetrehydrofuran (THF) is used as a precursor to polymers. The other main application of THF is as an industrial solvent for PVC and in varnishes. 2-Methoxyethanol or methyl cellosolve (MC) is used as a solvent for many different purposes such as varnishes, dyes, and resins.

In continuation of our earlier investigations,^1–5 we study here the density, viscosity, conductance and FT-IR spectra of an ionic liquid, namely 1-butyl-2,3-dimethylimidazolium tetrafluoroborate ([bmmim][BF₄]) in various solvents to investigate the solvation consequences analysed by different appropriate equations.

2. Experimental

2.1 Source and purity of samples

The room temperature IL selected for the present work was of puriss grade procured from Sigma-Aldrich, Germany and was used as purchased. The mass fraction purity of the IL was ≥0.99.

All the solvents of spectroscopic grade were procured from Sigma-Aldrich, Germany and were used as received. The mass fraction purity of the solvents was 0.995. The purities of the liquids were checked by measuring their density, viscosity and conductivity values, which were in good agreement with the literature values as shown in Table 1.

Table 1 Density (ρ), viscosity (η) and relative permittivity (ε) of the different solvents dimethylacetamide (DMA), tetrahydrofuran (THF) and methyl cellosolve (MC) at different temperatures

Solvent	Temp. (K)	ρ × 10^−3/kg m^−3	η/mPa s	ε
DMA	298.15	0.93680	0.923	37.78
	303.15	0.93343	0.871	—
	308.15	0.92908	0.7262	—
THF	298.15	0.88074	0.463	7.58
	303.15	0.87731	0.381	—
	308.15	0.87179	0.369	—
MC	298.15	0.96002	1.541	15.4
	303.15	0.95836	1.522	—
	308.15	0.95374	1.509	—

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2.2 Apparatus and procedure

All the stock solutions of the electrolyte (IL) in the studied solvents were prepared by mass (weighed by a Mettler Toledo AG-285 with uncertainty of 0.0003 g). For conductance measurements, the working solutions were obtained by mass dilution of the stock solutions.

The densities of the solvents and experimental solutions (ρ) were measured by means of a vibrating U-tube Anton Paar digital density meter (DMA 4500M) with a precision of ±0.00005 g cm⁻³ maintained at ±0.01 K of the desired temperature. Calibration was by triply distilled water and passing dry air.

The viscosities were measured using a Brookfield DV-III Ultra programmable rheometer with spindle size 42 fitted to a Brookfield Digital TC-500 bath. The viscosities were obtained using the following equation:

η = (100/RPM) × TK × torque × SMC

where RPM, TK (0.09373) and SMC (0.327) are the speed, viscometer torque constant and spindle multiplier constant, respectively. The instrument was calibrated against the standard viscosity samples supplied with the instrument, water and aqueous CaCl₂ solutions.¹⁷ Temperature of the solution was maintained to within ±0.01 °C using a Brookfield Digital TC-500 temperature thermostat bath. The viscosities were measured with an accuracy of ±1%. Each measurement reported herein is an average of triplicate reading with a precision of 0.3%.

The conductance measurements were carried out with a Systronics-308 conductivity bridge of accuracy ±0.01%, using a dip-type immersion conductivity cell, CD-10, having a cell constant of approximately (0.1 ± 0.001) cm⁻¹. Measurements were made in a thermostat water bath maintained at T = (298.15 ± 0.01) K. The cell was calibrated by the method proposed by Lind et al. and cell constant was measured based on 0.01 M aqueous KCl solution. During the conductance measurements, the cell constant was maintained within the range 1.10–1.12 cm⁻¹. The conductance data were obtained at a frequency of 1 kHz and the accuracy was ±0.3%. During all the measurements, the uncertainty of temperatures was ±0.01 K.

Infrared spectra were recorded with an 8300 FT-IR spectrometer (Shimadzu, Japan). The details of the instrument have been previously described.⁵

3. Results and discussion

The solvent properties are given in Table 1. The concentrations and molar conductances (Λ) of the IL in MC, DMA and THF at different temperatures are given in Table 2. The molar conductance (Λ) has been obtained from the specific conductance (κ) value using the following equation:

Λ = (1000κ)/c (1)

Table 2 The concentration (c) and molar conductance (Λ) of [bmmim][BF₄] in methyl cellosolve, dimethylacetamide and tetrahydrofuran at 298.15, 303.15, and 308.15 K

c × 10^4/mol dm^−3	Λ × 10^4/S m^2 mol^−1	c × 10^4/mol dm^−3	Λ × 10^4/S m^2 mol^−1	c × 10^4/mol dm^−3	Λ × 10^4/S -m^2 mol^−1
Methyl cellosolve		Dimethylacetamide		Tetrahydrofuran
298.15 K
3.3672	141.54	3.5044	92.82	3.97	52.31
3.9641	141.50	4.4521	92.77	4.74	51.21
4.7350	141.46	5.1938	92.72	5.52	50.31
5.7600	141.41	5.8081	92.69	6.21	49.50
6.6203	141.37	6.2001	92.68	6.82	49.20
7.3984	141.33	6.9169	92.64	7.21	48.90
8.2254	141.29	7.7841	92.60	7.84	48.50
9.0721	141.27	8.7557	92.55	8.28	48.00
10.1188	141.25	9.6534	92.51	9.00	46.40
11.1422	141.25	10.6406	92.48	9.45	45.50
11.9578	141.25	11.8542	92.44	10.24	44.70
13.2642	141.27	13.3810	92.40	11.02	43.11
14.2129	141.28	15.0777	92.38	11.90	42.90
15.5000	141.31	16.4106	92.39	12.90	42.80
16.4106	141.34	17.7241	92.42	14.98	42.00
303.15 K
3.3672	144.54	3.5044	94.82	3.97	56.31
3.9641	144.50	4.4521	94.77	4.74	54.21
4.7350	144.46	5.1938	94.72	5.52	52.31
5.7600	144.41	5.8081	94.69	6.21	51.50
6.6203	144.37	6.2001	94.68	6.82	50.20
7.3984	144.33	6.9169	94.64	7.21	49.90
8.2254	144.29	7.7841	94.60	7.84	48.50
9.0721	144.27	8.7557	94.55	8.28	48.00
10.1188	144.25	9.6534	94.51	9.00	46.40
11.1422	144.25	10.6406	94.48	9.45	45.50
11.9578	144.25	11.8542	94.44	10.24	44.70
13.2642	144.27	13.3810	94.40	11.02	43.11
14.2129	144.28	15.0777	94.38	11.90	42.90
15.5000	144.31	16.4106	94.39	12.90	42.80
16.4106	144.34	17.7241	94.42	14.98	42.00
308.15 K
3.3672	148.54	3.5044	98.82	3.97	58.31
3.9641	148.50	4.4521	98.77	4.74	58.21
4.7350	148.46	5.1938	98.72	5.52	58.31
5.7600	148.41	5.8081	98.69	6.21	58.50
6.6203	148.37	6.2001	98.68	6.82	58.20
7.3984	148.33	6.9169	98.64	7.21	48.90
8.2254	148.29	7.7841	98.60	7.84	48.50
9.0721	148.27	8.7557	98.55	8.28	48.00
10.1188	148.25	9.6534	98.51	9.00	48.40
11.1422	148.25	10.6406	98.48	9.45	48.50
11.9578	148.25	11.8542	98.44	10.24	48.70
13.2642	148.27	13.3810	98.40	11.02	48.11
14.2129	148.28	15.0777	98.38	11.90	48.90
15.5000	148.31	16.4106	98.39	12.90	48.80
16.4106	148.34	17.7241	98.42	14.98	48.00

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Linear conductance curves (Λ versus √c) were obtained for the electrolyte in MC and DMA and extrapolation of √c = 0 was used to evaluate the starting limiting molar conductance for the electrolyte.

3.1 Ion-pair formation

The ion-pair formation in the case of conductometric study of [bmmim][BF₄] in MC and DMA was analysed using the Fuoss conductance equation.⁶ With a given set of conductivity values (c_j, Λ_j; j = 1…n), three adjustable parameters, i.e., Λ₀, K_A and R, have been derived from the Fuoss equation. Here, Λ₀ is the limiting molar conductance, K_A is the observed association constant and R is the association distance, i.e., the maximum centre-to-centre distance between the ions in the solvent-separated ion pairs. There is no precise method⁷ for determining the R value but in order to treat the data in our system, R is assumed to be given by R = a + d, where a is the sum of the crystallographic radii of the ions and d is the average distance corresponding to the side of a cell occupied by a solvent molecule. The distance d is given by⁸

d = 1.183(M/ρ)^1/3 (2)

where M is the molecular mass and ρ is the density of the solvent. Thus, the Fuoss conductance equation may be represented as follows:

Λ = PΛ₀[(1 + R_X) + E_L] (3)

P = 1 − α(1 − γ) (4)

γ  = 1 − K_Acγ²f² (5)

−ln f = βκ/2(1 + κR) (6)

β = e²/(ε_rk_BT) (7)

K_A = K_R/(1 − α) = K_R/(1 + K_S) (8)

where Λ₀ is the limiting molar conductance, K_A is the observed association constant, R is the association distance, R_X is the relaxation field effect, E_L is the electrophoretic counter-current, k is the radius of the ion atmosphere, ε is the relative permittivity of the solvent mixture, e is the electron charge, c is the molarity of the solution, k_B is the Boltzmann constant, K_S is the association constant of the contact pairs, K_R is the association constant of the solvent-separated pairs, γ is the fraction of solute present as unpaired ions, α is the fraction of contact pairs, f is the activity coefficient, T is the absolute temperature and β is twice the Bjerrum distance.

The computations were performed using the program suggested by Fuoss. The initial Λ₀ values for the iteration procedure are obtained from Shedlovsky extrapolation of the data.⁹ Input for the program is the number of data, n, followed by ε, η (viscosity of the solvent mixture), initial Λ₀ value, T, ρ (density of the solvent mixture), mole fraction of the first component, molar masses, M₁ and M₂ along with c_j, Λ_j values where j = 1, 2…n and an instruction to cover preselected range of R values.

In practice, calculations are performed by finding the values of Λ₀ and α which minimize the standard deviation, δ, where.

δ² = ∑[Λ_j(cal) − Λ_j(obs)]²/(n − m) (9)

for a sequence of R values and then plotting δ against R. The best-fit R corresponds to the minimum of the δ–R versus R curve. So, an approximate sum is made over a fairly wide range of R values using 0.1 increments to locate the minimum, but no significant minimum is found in the δ–R curves. Thus R is assumed to be R = a + d, with terms having their usual significance. Finally, the corresponding limiting molar conductance (Λ₀), association constant (K_A), co-sphere diameter (R) and standard deviations of experimental Λ(δ) obtained from the Fuoss conductance equation for [bmmim][BF₄] in MC and DMA at 298.15 K, 303.15 K and 308.15 K are given in Table 3.

Table 3 Limiting molar conductance (Λ₀), association constant (K_A), co-sphere diameter (R) and standard deviations of experimental Λ(δ) obtained from Fuoss conductance equation for 1-butyl-2,3-dimethylimidazoliun tetrafluoroborate in methyl cellosolve and DMA at 298.15, 303.15, and 308.15 K

Solvent	Λ0 × 10^4/S m^2 mol^−1	KA dm^−3 mol^−1	R/Å	Δ
298.15 K
Methyl cellosolve	23.29	422.24	7.44	0.25
DMA	24.27	421.14	6.83	0.14
303.15 K
Methyl cellosolve	23.49	423.24	7.54	0.26
DMA	24.67	422.14	6.93	0.15
308.15 K
Methyl cellosolve	33.29	453.24	8.54	0.16
DMA	34.67	443.14	8.23	0.14

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Table 3 shows that K_A values increase with increasing temperature in the case of MC and DMA. In the case of MC and DMA, with increasing temperature the number of free ions per unit volume decreases and hence the tendency of ion-pair formation increases.

The standard Gibbs free energy change of solvation, ΔG^o, for [bmmim][BF₄] in MC and DMA is given by the following equation:¹⁰

ΔG^o = −RT ln K_A (10)

It is observed from Table 4 that the value of the Gibbs free energy is entirely negative for MC and DMA at all temperatures. This can be explained by considering the participation of specific covalent interaction in the ion-association process.

Table 4 Walden product (Λ₀η) and Gibbs energy change (ΔG^o) of 1-butyl-2,3-dimethylimidazoliun tetrafluoroborate in methyl cellosolve and DMA at 298.15 K, 303.15 K and 308.15 K

Solvent	Λ0η × 10^4/S m^2 mol^−1 mPa	ΔG^o/kJ mol^−1
298.15 K
Methyl cellosolve	94.44	−30.31
DMA	86.94	−29.21
303.15 K
Methyl cellosolve	95.44	−31.31
DMA	85.94	−30.21
308.15 K
Methyl cellosolve	105.44	−32.31
DMA	104.24	−30.11

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Table 5 shows the value of ionic conductance (λ^±₀) and ionic Walden product (λ^±₀η) (product of ionic conductance and viscosity of the solvent) along with Stokes radii (r_s) and crystallographic radii (r_c) of [bmmim][BF₄] in MC and DMA at different temperatures.

Table 5 Limiting ionic conductance (λ^±₀), ionic Walden product (λ^±₀η), Stokes radii (r_s), and crystallographic radii (r_c) of 1-butyl-2,3-dimethylimidazoliun tetrafluoroborate in methyl cellosolve and DMA at 298.15 K, 303.15 K and 308.15 K

Solvent	ion	λ^±0 (S m^2 mol^−1)	λ^±0η (S m^2 mol^−1 mPa)	rs (Å)	rc
298.15 K
Methyl cellosolve	Bmmim^+	10.05	21.51	3.44	5.78
	BF4^−	21.01	42.15	1.50	2.06
DMA	Bmmim^+	10.15	22.51	3.64	5.88
	BF4^−	21.71	48.15	1.70	2.16
303.15 K
Methyl cellosolve	Bmmim^+	10.15	22.51	3.54	5.78
	BF4^−	21.71	46.15	1.50	2.06
DMA	Bmmim^+	10.15	23.11	3.74	5.88
	BF4^−	21.71	47.05	1.70	2.12
308.15 K
Methyl cellosolve	Bmmim^+	9.15	20.51	3.24	5.87
	BF4^−	20.71	48.15	1.70	2.15
DMA	Bmmim^+	8.25	22.51	3.11	5.42
	BF4^−	19.71	48.15	1.70	2.12

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3.2 Triple-ion formation

For the electrolyte in THF, a deviation in the conductance curve was obtained, showing a decrease in conductance values up to a certain concentration, reaching a minimum and then increasing, indicating triple-ion formation.

The conductance data for the electrolyte in THF have been analysed using the classical Fuoss–Kraus equation¹¹ for triple-ion formation:

β′ = 1.8247 × 10⁶/(εT)^1.5 (13)

In the above equations, Λ₀ is the sum of the molar conductance of the simple ions at infinite dilution; Λ^T₀ is the sum of the conductances of the two triple ions bmmim⁺BF₄⁻ and bmmim⁺(BF₄)₂⁻. K_P ≈ K_A and K_T are the ion-pair and triple-ion formation constants. To make eqn (11) applicable, the symmetrical approximation of the two possible constants of triple ions being equal to each other has been adopted¹² and Λ₀ values for the studied electrolytes have been calculated.¹³ Λ^T₀ is calculated by setting the triple ion conductance equal to 2/3Λ₀.¹⁴

The ratio Λ^T₀/Λ₀ was thus set equal to 0.667 during linear regression analysis of eqn (2). Limiting molar conductance of triple ions (Λ^T₀), slope and intercept of eqn (2) for [bmmim][BF₄] in THF at different temperatures are given in Table 6.

Table 6 The calculated limiting molar conductance of ion pairs (Λ₀), limiting molar conductance of triple ion Λ^T₀, experimental slope and intercept obtained from Fuoss–Kraus equation for 1-butyl-2,3-dimethylimidazoliun tetrafluoroborate in THF at 298.15 K, 303.15 K and 308.15 K

Solvent	Λ0 × 10^4/S m^2 mol^−1	Λ^T0 × 10^4/S m^2 mol^−1	Slope × 10^−2	Intercept × 10^−2
298.15 K
THF	55.34	38.25	0.09	0.42
303.15 K
THF	60.34	40.25	0.11	0.45
308.15 K
THF	61.34	41.25	0.14	0.48

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Linear regression analysis of eqn (2) for the electrolytes with an average regression constant R² = 0.9653 gives intercepts and slopes. These permit the calculation of other derived parameters such as K_P and K_T listed in Table 7. It is observed that Λ passes through a minimum as c increases. The K_P and K_T values predict that a major portion of the electrolyte exists as ion pairs with a minor portion as triple ions (neglecting quadrupoles).

Table 7 Salt concentration at the minimum conductivity (C_min) along with the ion-pair formation constant (K_P) and triple-ion formation constant (K_T) for 1-butyl-2,3-dimethylimidazoliun tetrafluoroborate in THF at 298.15 K

Solvent	cmin × 10^4/mol dm^−3	log cmin	KP × 10^−5/(mol dm^−3)^−1	KT/(mol dm^−3)^−1	KT/KP × 10^5	log KT/KP
298.15 K
THF	8.14	−2.8343	1.76	63.33	35.9	−2.83425
303.15 K
THF	8.24	−2.9343	1.86	65.33	36.9	−2.93425
308.15 K
THF	8.34	−2.9353	1.96	66.33	38.9	−2.83425

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At very low permittivity of the solvent (ε < 10) electrostatic ionic interactions are very large. So the ion pairs attract the free +ve and −ve ions present in the solution medium as the distance of the closest approach of the ions becomes a minimum. This results in the formation of triple ions, which acquire the charge of the respective ions in the solution,¹⁵ i.e.

M⁺ + A⁻ ↔ M⁺⋯A⁻ ↔ MA (ion pair) (15)

MA + M⁺ ↔ MAM⁺ (triple ion) (16)

MA + A⁻ ↔ MAA⁻ (triple ion) (17)

where M⁺ and A⁻ are respectively bmmim⁺ and BF₄⁻. The effect of ternary association thus removes some non-conducting species, MA, from solution, and replaces them with triple ions which increase the conductance manifested by non-linearity observed in conductance curves for the electrolyte in THF.

Furthermore, the ion-pair and triple-ion concentrations, C_P and C_T, respectively of the electrolyte have also been calculated at the minimum conductance concentration of [bmmim][BF₄] in THF using the following relations:¹⁶

α = 1/(K_P^1/2c^1/2) (18)

α_T = (K_T/K_P^1/2)c^1/2 (19)

c_P = c(1 − α − 3α_T) (20)

C_T = (K_T/K_P^1/2)c^3/2 (21)

Here α and α_T are the fractions of ion pairs and triple ions present in the salt solutions respectively and are given in Table 8. Thus, the values of C_P and C_T also given in Table 8 indicate that the ions are mainly present as ion pairs even at high concentration with a small fraction existing as triple ions. The ion-pair fraction (α), triple-ion fraction (α_T), ion-pair concentration (C_P) and triple-ion concentration (C_T) have also been calculated over the whole concentration range of [bmmim][BF₄] in THF and are provided in Table 8.

Table 8 Salt concentration at the minimum conductivity (c_min), ion-pair fraction (α), triple-ion fraction (α_T), ion-pair concentration (c_P) and triple-ion concentration (c_T) for 1-butyl-2,3-dimethylimidazoliun tetrafluoroborate in THF at 298.15 K, 303.15 K and 308.15 K

Solvent	cmin × 10^4/mol dm^−3	α × 10^−5	αT × 10^3	cP × 10^−4/mol dm^−3	cT × 10^−6/mol dm^−3
298.15 K
THF	8.14	6.61	4.82	9.01	4.2
303.15 K
THF	8.24	6.71	4.92	9.11	4.4
308.15 K
THF	8.34	6.83	4.87	9.35	4.6

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From Table 7, it is observed that with increasing temperature the number of free ions per unit volume decreases resulting in an increase of K_P and K_T values. Interactions between ionic liquid and different solvents are represented in Scheme 1.

Scheme 1 Consequence of solvation between ionic liquid and each of the solvents.

4. Apparent molar volume

The measured values of densities of [bmmim][BF₄] in MC, DMA and THF at 298.15, 303.15 and 308.15 K are reported in Table 1. The densities of the electrolytes in different solvents increase linearly with the concentration at the studied temperatures. For this purpose, the apparent molar volumes ϕ_V were determined from the solution densities using the following equation with the values being given in Table 9:

ϕ_V = M/ρ − (ρ − ρ₀)/mρ₀ρ (22)

where M is the molar mass of the solute, m is the molality of the solution, and ρ and ρ₀ are the densities of the solution and solvent, respectively. The apparent molar volumes ϕ_V were found to decrease with increasing molality (m) of the IL in different solvents and increase with increasing temperature for the system under study. The limiting apparent molar volumes ϕ⁰_V were calculated using a least-squares treatment of the plots of ϕ_V versus √c using the following Masson equation:¹⁷

ϕ_V = ϕ⁰_V + S^*_V√c (23)

where ϕ⁰_V is the limiting apparent molar volume at infinite dilution and S^*_V is the experimental slope.

Table 9 Concentration, c, density, ρ, apparent molar volume, ϕ_V, limiting apparent molar volume, ϕ⁰_V, and experimental slope for 1-butyl-2,3-dimethylimidazoliun tetrafluoroborate in methyl cellosolve, dimethylacetamide and tetrahydrofuran at 298.15 K, 303.15 K and 308.15 K

Solvent	c/mol dm^−3	ρ × 10^−3/kg m^−3	ϕV × 10^6/m^3 mol^−1	ϕ^0V × 10^6/m^3 mol^−1	S^*V × 10^6/m^3 mol^−3/2 dm^3/2
298.15 K
Methyl cellosolve	0.010	0.99849	440.58	67.38	−98.01
	0.025	1.00000	438.58
	0.040	1.00155	437.15
	0.055	1.00312	436.17
	0.070	1.00472	435.19
	0.085	1.00634	434.32
Dimethylacetamide	0.010	0.87629	449.65	55.70	−91.58
	0.025	0.87854	444.51
	0.040	0.88086	441.49
	0.055	0.88324	438.91
	0.070	0.88566	436.82
	0.085	0.88814	434.66
Tetrahydrofuran	0.010	1.16303	219.191	35.31	−78.46
	0.025	1.16328	216.48
	0.040	1.16369	214.67
	0.055	1.16421	213.24
	0.070	1.16484	212
	0.085	1.16550	210.9
303.15 K
Methyl cellosolve	0.010	0.99849	440.58	70.14	−128.31
	0.025	1.00000	438.58
	0.040	1.00155	437.15
	0.055	1.00312	436.17
	0.070	1.00472	435.19
	0.085	1.00634	434.32
Dimethylacetamide	0.010	0.87629	449.65	62.02	−122.04
	0.025	0.87854	444.51
	0.040	0.88086	441.49
	0.055	0.88324	438.91
	0.070	0.88566	436.82
	0.085	0.88814	434.66
Tetrahydrofuran	0.010	1.16303	457.18	40.20	−86.78
	0.025	1.16328	450.30
	0.040	1.16369	445.39
	0.055	1.16421	441.53
	0.070	1.16484	438.00
308.15 K
Methyl cellosolve	0.010	0.99849	440.58	73.03	−158.57
	0.025	1.00000	438.58
	0.040	1.00155	437.15
	0.055	1.00312	436.17
	0.070	1.00472	435.19
	0.085	1.00634	434.32
Dimethylacetamide	0.010	0.87629	449.65	69.07	−151.78
	0.025	0.87854	444.51
	0.040	0.88086	441.49
	0.055	0.88324	438.91
	0.070	0.88566	436.82
	0.085	0.88814	434.66
Tetrahydrofuran	0.010	1.16303	457.18	47.92	−108.51
	0.025	1.16328	450.30
	0.040	1.16369	445.39
	0.055	1.16421	441.53
	0.070	1.16484	438.00

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The plots of ϕ_V against the square root of the molar concentration √c were found to be linear with negative slopes. The values of ϕ⁰_V and S^*_V are reported in Table 9. From Table 9 it is observed that ϕ⁰_V values for this electrolyte are generally positive for all the solvents and is highest in case of [bmmim][BF₄] in MC. This indicates the presence of strong ion–solvent interactions and the extent of interactions increases from THF to MC.

On the contrary, S^*_V indicates the extent of ion–ion interactions. The values of S^*_V show that the extent of ion-ion interaction is highest in the case of THF and is lowest in the case of MC. From a quantitative comparison, the magnitudes of ϕ⁰_V are much greater than S^*_V, for all solutions. This suggests that ion–solvent interactions dominate over ion–ion interactions in all the solutions. The values of ϕ⁰_V also support the fact that a higher ion–solvent interaction in MC leads to lower conductance of [bmmim][BF₄] in it than in DMA and THF, discussed earlier.

Temperature-dependent limiting apparent molar volume.

The variation of ϕ⁰_V with the temperature of the IL in different solvents can be expressed by the general polynomial equation as follows:

ϕ⁰_V = a₀ + a₁T + a₂T² (24)

where a₀, a₁, a₂ are empirical coefficients depending on the solute and mass fraction (w₁) of the cosolute IL, and T is the temperature range under study in kelvin. The values of these coefficients of the above equation for the IL in THF, DMA and MC are reported in Table 10.

Table 10 Values of empirical coefficients (a₀, a₁, and a₂) of eqn (24) for IL in different solvents (MC, DMA, THF) at 298.15 K to 308.15 K

Solvent mixture	a0 × 10^6/m^3 mol^−1	a1 × 10^6/m^3 mol^−1 K^−1	a2 × 10^6/m^3 mol^−1 K^−2
THF + IL
298.15	4859.46	−33.050	0.0566
303.15	4859.46	−33.050	0.0566
308.15	4859.46	−33.050	0.0566
DMA + IL
298.15	998	−7.515	0.0146
303.15	998	−7.515	0.0146
308.15	998	−7.515	0.0146
MC + IL
298.15	137.80	−1.011	0.0026
303.15	137.80	−1.011	0.0026
308.15	137.80	−1.011	0.0026

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The limiting apparent molar expansibilities, ϕ⁰_E, can be obtained by the following equation:

ϕ⁰_E = (δϕ⁰_V/δT)_P = a₁ + 2a₂T (25)

The limiting apparent molar expansibilities, ϕ⁰_E, change in magnitude with a change of temperature. The values of ϕ⁰_E for different solutions of the studied IL at 298.15, 303.15, and 308.15 K are reported in Table 11. The table reveals that ϕ⁰_E is positive for IL in all the studied solvents and studied temperatures. This fact can ascribed to the absence of caging or packing effect for the IL in solutions.

Table 11 Limiting apparent molal expansibilities (φ⁰_E) for IL in different solvents (THF, DMA, THF) at 298.15 K to 308.15 K

Solvent mixture	ϕ^0E × 10^6/m^3 mol^−1 K^−1			(∂ϕ^0E/∂T)P × 10^6/m^3 mol^−1 K^−2
THF + IL
T/K	298.15	303.15	308.15
	0.701	1.267	1.833	0.113
DMA + IL
T/K	298.15	303.15	308.15
	1.191	1.337	1.483	0.269
MC + IL
T/K	298.15	303.15	308.15
	0.539	0.565	0.591	0.309

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During the past few years it has been emphasized by different workers that S^*_V is not the sole criterion for determining the structure-making or -breaking nature of any solute. Hepler¹⁸ developed a technique of examining the sign of (δϕ⁰_E/δT)_P for the solute in terms of long-range structure-making and -breaking capacity of the solute in mixed solvent systems using the general thermodynamic expression

(δϕ⁰_E/δT)_P = (δ²ϕ⁰_V/δT²)_P = 2a₂ (26)

If the sign of (δϕ⁰_E/δT)_P is positive or a small negative value, then the molecule is a structure maker; otherwise, it is a structure breaker.¹⁹ As is evident from Table 11 the (δϕ⁰_E/δT)_P values for IL in all the solvents under investigation are positive so are predominantly structure makers in all of the experimental solutions.

5. Viscosity calculation

Another transport property of the solution is viscosity, which has been studied for comparison and confirmation of the solvation of the electrolyte in the chosen solvents. The viscosity data have been analyzed using Jones–Dole equation:²⁰

(η/η₀ − 1)/√c = A + B√c (27)

where η and η₀ are the viscosities of the solution and solvent respectively. The values of A-coefficient and B-coefficient are obtained from the straight line of plots of (η/η₀ − 1)/√c against √c which are reported in Table 12. The viscosity B-coefficient is a valuable tool to provide information concerning the solvation of solutes and their effects on the structure of the solvent. From Table 12 it is evident that the values of the B-coefficient are positive, thereby suggesting the presence of strong ion-solvent interactions, and strengthened with an increase the solvent viscosity value, in agreement with the results obtained from ϕ⁰_V values discussed earlier. The values of the A-coefficient are found to increases slightly with temperature and with an increase in mass of IL in the solvent mixture. These results indicate the presence of very weak solute–solute interactions. These results are in excellent arrangement with those obtained from S^*_V values.

Table 12 Concentration, c, viscosity, η, , and viscosity A and B coefficients for 1-butyl-2,3-dimethylimidazoliun tetrafluoroborate in methyl cellosolve, dimethylacetamide and tetrahydrofuran at 298.15 K, 303.15 K and 308.15 K

Solvent	c/mol dm^−3	η/mPa s		B/dm^3 mol^−1	A/dm^3/2 mol^−1/2
298.15 K
Methyl cellosolve	0.010	1.57	0.186	2.2891	0.1701
	0.025	1.62	0.323
	0.040	1.65	0.352
	0.055	1.69	0.411
	0.070	1.73	0.462
	0.085	1.78	0.531
Dimethylacetamide	0.010	0.91	0.225	2.1324	0.1528
	0.025	0.93	0.284
	0.040	0.95	0.337
	0.055	0.97	0.383
	0.070	0.99	0.425
	0.085	1.02	0.501
Tetrahydrofuran	0.005	0.48	0.324	1.9876	0.1448
	0.020	0.50	0.505
	0.035	0.51	0.508
	0.050	0.53	0.617
	0.065	0.55	0.686
	0.080	0.56	0.711
303.15 K
Methyl cellosolve	0.010	1.53	0.052	2.3535	0.2086
	0.025	1.55	0.116
	0.040	1.57	0.157
	0.055	1.59	0.190
	0.070	1.61	0.218
	0.085	1.66	0.311
Dimethylacetamide	0.010	0.89	0.218	2.2154	0.1954
	0.025	0.91	0.283
	0.040	0.92	0.281
	0.055	0.94	0.338
	0.070	0.95	0.343
	0.085	0.98	0.429
Tetrahydrofuran	0.010	0.40	0.394	2.0734	0.1831
	0.025	0.41	0.498
	0.040	0.43	0.617
	0.055	0.44	0.649
	0.070	0.46	0.744
	0.085	0.47	0.783
308.15 K
Methyl cellosolve	0.010	1.52	0.073	2.4329	0.2313
	0.025	1.55	0.172
	0.040	1.58	0.235
	0.055	1.63	0.342
	0.070	1.67	0.403
	0.085	1.73	0.502
Dimethylacetamide	0.010	0.75	0.331	2.3015	0.2214
	0.025	0.76	0.296
	0.040	0.78	0.372
	0.055	0.80	0.440
	0.070	0.82	0.489
	0.085	0.83	0.491
Tetrahydrofuran	0.010	0.38	0.298	2.2007	0.2119
	0.025	0.40	0.548
	0.040	0.41	0.556
	0.055	0.42	0.589
	0.070	0.44	0.727
	0.085	0.45	0.753

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The extent of solute–solvent interaction in the solution calculated from the viscosity B-coefficient²¹ gives valuable information regarding the solvation of the solvated solutes and their effects on the structure of the solvent in the local vicinity of the solute molecules in the solutions. From Table 12 it is evident that the values of the B-coefficient are positive and much higher than those of the A-coefficient, thereby suggesting the solute–solvent interactions are dominant over the solute-solute interactions. The higher B-coefficient values for higher viscosity values is due to the solvated solute molecules associated by the solvent molecules all round to the formation of associated molecule by solute-solvent interaction. Further, these types of interactions are strengthened due to the rise in temperature. These results are in good agreement with those obtained from ϕ⁰_V values discussed earlier.

Thus, the trend of ion–solvent interaction is MC > DMA > THF. The viscosity A- and B-coefficients are in excellent agreement with the results obtained from the volumetric studies.

6. FT-IR spectroscopy

With the aid of FT-IR spectroscopy the molecular interaction existing between the solute and the solvent can be studied. At first the IR spectra of the pure solvents were studied. The stretching frequencies of the key groups are given in Table 13 and the spectra are shown in Fig. 1–3.

Table 13 Stretching frequencies of the functional groups present in the pure solvent and change of frequency after addition of 0.05 M concentration of [bmmim][BF₄] in THF, DMA and MC

Solvent	Stretching frequencies (cm^−1)
	Pure solvent	Solvent + [bmmim][BF4]
THF	C–O (1084)	C–O (1098.2)
DMA	C=O (1670)	C=O (1695.4)
MC	C–O (1060)	C–O (1071.5)

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Fig. 1 IR spectra of pure THF and its binary mixture with ionic liquid.

Fig. 2 IR spectra of pure DMA and its binary mixture with ionic liquid.

Fig. 3 IR spectra of pure methyl cellosolve and its binary mixture with ionic liquid.

In the case of THF, a sharp peak is observed at 1084.4 cm⁻¹ for C–O which shifts to 1098.2 cm⁻¹ on addition of 0.05 M of the electrolyte, [bmmim]BF₄, due to the interaction of [bmmim]⁺ with the C–O dipole showing ion–dipole interaction which is formed due to the disruption of H-bonding interaction in THF molecules.

Similar types of interactions are observed in the case of DMA where the sharp peak for C=O shifts from 1670.2 cm⁻¹ to 1698.1 cm⁻¹ on addition of [bmmim]BF₄ due to ion–dipole interaction between [bmmim]⁺ and the C=O dipole.

The FT-IR spectrum of the IL in MC shows that the peak for C–O at 1060 cm⁻¹ shifts to 1071.5 cm⁻¹ for [bmmim]BF₄ due to the disruption of weak H-bonding interaction between the two MC molecules²² leading to the formation of ion–dipole interaction between [bmmim]⁺ and the C–O dipole.

7. Conclusion

The extensive study of the IL [bmmim][BF₄] in MC, DMA and THF leads to the conclusion that the salt is more associated in MC than in the other two solvents. It can also be seen from the conductometric studies in THF that [bmmim][BF₄] mostly remains as triple ions rather than ion pairs, but in MC and DMA [bmmim][BF₄] remains as ion pairs. There is a stronger ion–solvent interaction in MC than in DMA. The experimental values obtained from the volumetric and viscometric studies suggest that the ion–solvent interaction dominant over the ion–ion interaction. And the extent of ion–solvent interactions of studied ionic liquid in the chosen solvents is as follows: MC > DMA > THF.

Acknowledgements

The authors are grateful to the Departmental Special Assistance Scheme, Department of Chemistry, NBU under the University Grants Commission, New Delhi (no. 540/27/DRS/2007, SAP-1) for financial support and instrumental facilities in order to continue this research work. Tanusree Ray is also grateful to “Rajiv Gandhi National Fellowship,” UGC, New Delhi Ref UGC Letter no. F1-17.1/2013-14/RGNF-2013-14-SC-WES-52926, for sanctioning research fellowship and financial assistance. Milan Chandra Roy is alsograteful to “UGC Research Fellowship in Science for Meritorious Students” Ref UGC Letter no. F4-1/2006(BSR)/7-133/2007(BSR) under SAP, for sanctioning research fellowship and financial assistance. One of the authors, Prof. M. N. Roy, is grateful to the University Grant Commission, New Delhi, Government of India for being awarded a one-time grant under Basic Scientific Research via the Grant-in-Aid no. F4-10/2010 (BSR) regarding his active service for augmenting of research facilities to facilitate further research work.

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