Measurement and Modelling of Carbon Dioxide in Triflate-Based Ionic Liquids: Imidazolium, Pyridinium, and Pyrrolidinium

Abstract

Carbon dioxide, the primary greenhouse gas responsible for global warming, represents today a critical environmental challenge for humans. Mitigating CO₂ emissions and other greenhouse gases is a pressing global concern. The primary goal of this study is to investigate the potential of particular ionic liquids (ILs) in capturing CO₂ for the sweetening of natural and other gases. The solubility of CO₂ was measured in three distinct ILs, which shared a common anion (triflate, TfO) but differed in their cations. The selected ionic liquids were {1-butyl-3-methylimidazolium triflate [BMIM][TfO], 1-butyl-1-methylpyrrolidinium triflate [BMP][TfO], and 1-butyl-4-methylpyridium triflate [MBPY][TfO]}. The solvents were screened based on results from a molecular computational study that predicted low CO₂ Henry’s Law constants. Solubility measurements were conducted at 303.15 K, 323.15 K, and 343.15 K and pressures up to 1.5 MPa using a gravimetric microbalance (IGA-003). The CO₂ experimental results were modeled using the Peng–Robinson Equation of state with three mixing rules: van der Waals one (vdWI), van der Waals two (vdWII), and the non-random two-liquid (NRTL) Wong–Sandler (WS) mixing rule. For the three ILs, the NRTL-WS mixing rule regressed the data with the lowest average deviation percentage of 1.24%. The three solvents had similar alkyl chains but slightly different polarities. [MBPY][TfO], with the largest size, exhibited the highest CO₂ solubility at all three temperatures. Calculation of its relative polarity descriptor (N) shows it was the least polar of the three ILs. Conversely, [BMP][TfO] showed the highest Henry’s Law constant (lowest solubility) across the studied temperature range. Comparing the results to published data, the study concludes that triflate-based ionic liquids with three fluorine atoms had lower capacity for CO₂ compared to bis(trifluoromethylsulfonyl) imide (Tf2N)-based ionic liquids with six fluorine atoms. Additionally, the study provided data on the enthalpy and entropy of absorption. A final comparison shows that the ILs had a lower CO₂ capacity than Selexol, a solvent widely used in commercial carbon capture operations. Compared to other ILs, the results confirm that the type of anion had a more significant impact on solubility than the cation.

1. Introduction

The release of carbon dioxide (CO₂) into the atmosphere has adverse environmental consequences, since it contributes to the greenhouse effect, leading to global warming [1]. Substantial cuts in CO₂ emissions are imperative within the industrial and energy sectors to reduce greenhouse gas emissions significantly by 2050 [2].

Due to their distinctive attributes, ionic liquids (ILs) are considered viable solvents in gas-sweetening operations. Their attributes include notable capacity for CO₂ absorption and lower co-absorption of methane and ethane, low vapor pressure, chemical stability, a broad range of operational temperatures in a liquid state, and adaptability. Two fundamental categories of ILs exist: task-specific ILs (TSILs) and room-temperature ILs (RTILs). The principal contrast between these two types of sorbents lies in their absorption mechanisms. While RTILs follow conventional physical gas absorption governed by Henry’s Law, TSILs exhibit a dual absorption mechanism, encompassing both physical and chemical processes, potentially enabling them to capture more CO₂ [2].

Over time, multiple technologies have been employed to reduce carbon dioxide emissions. Among these approaches is the process of carbon dioxide capture and storage (CCS), which utilizes a blend of aqueous amines in commercial plants. However, these solvents have several disadvantages, such as high cost, volatility, substantial energy consumption, and corrosive nature [3,4]. ILs are unique salts that exist as liquids at ambient temperature, a characteristic that is well-suited for various applications, and are gaining popularity as environmentally friendly and reusable absorbents for capturing CO₂. These non-volatile ILs are more ecologically sustainable than traditional organic solvents [5]. They are composed of anions and cations. Their extremely low vapor pressure, which makes them eco-friendly, has earned them the name “Green Solvents” [6]. One of the fundamental features of ILs is their ability to customize properties like density, conductivity, viscosity, hydrophobicity, gas solubility, and hydrogen-bonding capability by modifying the type of constituent ions or functionalizing them. This adaptability allows ILs to find extensive applications in various industrial sectors [1].

Selection of Ionic Liquids

Analyzing a set of 2701 ionic liquids at the molecular level identified three promising triflate-based ionic liquids chosen for this research. The study also explored the relationships between Henry’s Law constants and the properties of these ionic liquids. Utilizing COSMO-RS (COnductorlike Screening Model for Real Solvents), our research group employed a thermodynamic approach to predict the Henry’s Law constants for CO₂, CH₄, and N₂ [7]. The obtained values and the polarity parameters of the cations and anions used to explain CO₂–IL interactions will be discussed in the next section.

2. Materials and Methods

2.1. Materials

Information about the solvents used in this study is listed in

Table 1. List of substances used in this study, their chemical structures, abbreviations, suppliers, and purity levels.

Ionic Liquids	Abbreviation	Structures	Suppliers and Purities
Carbon dioxide	CO2		Linde Inc., Regina, SK, Canada (>99.99 wt.%)
1-Butyl-3-methyl-imidazolium triflate (C9H15-F3N2O3S)	[BMIM][TfO]		Iolitec, Heilbronn, Germany (>99.0 wt.%, 343 ppm water)
1-Butyl-1-methyl-pyrrolidinium triflate (C10H20-F3NO3S)	[BMP][TfO]		Iolitec, Heilbronn, Germany (>99.0 wt.%, 643 ppm water)
1-Butyl-4-methyl-pyridinium triflate (C11H16-F3NO3S)	[MBPY][TfO]		Iolitec, Heilbronn, Germany (>99.0 wt.%, 1586 ppm water)

.

2.2. Solubility Measurement

This work describes experiments investigating gas solubility in ionic liquids using an IGA-003 Intelligent Gravimetric Analyzer (Hiden Isochema Ltd., Warrington, UK). The experiments were computer-aided and performed under elevated pressures reaching up to 1.5 MPa at 343 K. The IGA-003 measured weight changes in an ionic liquid when gas was injected into the system, and these changes were used to determine the solubility.

The setup encompassed diverse elements: an IGA-003 microbalance, a mass flow control, a gas cylinder, a vacuum pump, a pressure control, a functional computer, and a water bath (Polyscience, Niles, IL, USA) to control the temperature. A key aspect of these experiments was accounting for the buoyancy effect on the sample’s weight, as gravitational forces could introduce errors in solubility measurements. A counterbalance container was used to reduce the impact of buoyancy, and a mathematical formula was used to calculate the buoyancy force.

Figure 1 provides a detailed schematic diagram of the IGA-003. The study notes the potential impact of volume expansion at high temperatures and emphasizes the importance of considering sample expansion when calculating solubility. Information about buoyancy and other forces can be found in reference [8].

2.3. Thermodynamic Modelling

2.3.1. Correlation of the Model

We used the Peng–Robinson Equation of State (PR EoS) to correlate the experimental solubility values of CO₂ in ILs.

$$P={\displaystyle \frac{\mathrm{R}\mathrm{T}}{\mathrm{v}-{\mathrm{b}}_{\mathrm{m}}}}-{\displaystyle \frac{{\mathrm{a}}_{\mathrm{m}}\left(\mathrm{T}\right)}{\mathrm{v}\left(\mathrm{v}+{\mathrm{b}}_{\mathrm{m}}\right)+{\mathrm{b}}_{\mathrm{m}}\left(\mathrm{v}-{\mathrm{b}}_{\mathrm{m}}\right)}}$$

(1)

The equation provided symbolizes the general Peng–Robinson equations of state. The intermolecular attractive force is denoted by a_m, and b_m represents the van der Waals co-volume factor.

Using different mixing methods, the Peng–Robinson Equation of State (PR EoS) was used to correlate the experimental data [9].

These rules are the following:

• van der Waals one with a single binary interaction parameter (vdWI)
• Two binary van der Waals interactions with two parameters (vdWII)
• The NRTL model combined with Wong–Sandler mixing rules (WS-NRTL)

2.3.2. Van Der Waals Mixing Rules

The calculation of mixing parameters (a_m and b_m) was carried out using the van der Waals one (vdWI) and van der Waals two (vdWII) mixing methods [9]. The following equations govern the mixing rules for vdWI and vdWII:

$$a_m={\sum }_i{\sum }_j{x}_i{x}_j{a}_{ij}$$

(2)

$$b_m={\sum }_i{x}_i{b}_i$$

(3)

$$b_m={\sum }_i{\sum }_j{x}_i{x}_j{b}_{ij}$$

(4)

$$a_{ij}=\sqrt{a_{ii}{a}_{jj}}\left(1-k_{ij}\right)$$

(5)

$$b_{ij}={\displaystyle \frac{b_i+b_j}{2}}\left(1-l_{ij}\right)$$

(6)

In this context, Equation (2) was employed to compute the combined attractive parameter (a_m). Equation (5) was used to derive the temperature-dependent binary interaction parameter (k_ij), which involves estimation of a_ij. The co-volume factor for the van der Waals one (vdWI) method was determined through Equation (3), and the co-volume for van der Waals two (vdWII) was obtained using Equation (4), where b_ij was calculated according to Equation (6) [9].

2.3.3. Wong–Sandler Mixing Rule

The model employed Wong–Sandler mixing rules, incorporating the following equations.

In Equations (7) and (8), the parameter of attractive force “a” of the mixture and the co-volume parameter “b” were each given. As indicated, the activity coefficient and excess Gibbs energy were computed using the non-random two liquid (NRTL) model [9]. The mixing parameters were determined using the binary parameters ${\tau }_{ji}$, ${\tau }_{ij}{,\mathrm{a}\mathrm{n}\mathrm{d}k}_{ij}$, where ${\tau }_{ji}$ and ${\tau }_{ij}$ are the NRTL parameters, and$g_{ij}$ and $g_{ji}$ represent the interaction energies between molecules “i” and “j”, respectively [9].

$$a=RT\left({\displaystyle \frac{QD}{1-D}}\right)$$

(7)

$$b=\left({\displaystyle \frac{Q}{1-D}}\right)$$

(8)

$$Q={\sum }_i{\sum }_j{x}_i{x}_j{b}_{ij}\left(b-{\displaystyle \frac{a}{RT}}\right)$$

(9)

$$D={\sum }_i{x}_i\left({\displaystyle \frac{a_i}{b_{i}RT}}\right)+\left({\displaystyle \frac{G^{ex}}{CRT}}\right)$$

(10)

$$C=-ln ln\left(\left(1+\sqrt{2}\right)/\sqrt{2}\right)$$

(11)

$${\left(\mathrm{b}-{\displaystyle \frac{\mathrm{a}}{\mathrm{R}\mathrm{T}}}\right)}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{1}{2}}\left[\left({\mathrm{b}}_{\mathrm{i}}-{\displaystyle \frac{{\mathrm{a}}_{\mathrm{i}}}{\mathrm{R}\mathrm{T}}}\right)+\left({\mathrm{b}}_{\mathrm{j}}-{\displaystyle \frac{{\mathrm{a}}_{\mathrm{j}}}{\mathrm{R}\mathrm{T}}}\right)\right]\left(1-{\mathrm{k}}_{\mathrm{i}\mathrm{j}}\right)$$

(12)

$${\displaystyle \frac{{\mathrm{G}}^{\mathrm{e}\mathrm{x}}}{\mathrm{R}\mathrm{T}}}={\mathrm{x}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{j}}\left({\displaystyle \frac{{\mathsf{\tau }}_{\mathrm{j}\mathrm{i}}{\mathrm{G}}_{\mathrm{j}\mathrm{i}}}{{\mathrm{x}}_{\mathrm{i}}+{\mathrm{x}}_{\mathrm{j}}{\mathrm{G}}_{\mathrm{j}\mathrm{i}}}}+{\displaystyle \frac{{\mathsf{\tau }}_{\mathrm{i}\mathrm{j}}{\mathrm{G}}_{\mathrm{i}\mathrm{j}}}{{\mathrm{x}}_{\mathrm{j}}+{\mathrm{x}}_{\mathrm{i}}{\mathrm{G}}_{\mathrm{i}\mathrm{j}}}}\right)$$

(13)

$${\mathrm{G}}_{\mathrm{i}\mathrm{j}}=\mathrm{e}\mathrm{x}\mathrm{p}(-{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}{\mathsf{\tau }}_{\mathrm{i}\mathrm{j}})$$

(14)

$${\mathrm{G}}_{\mathrm{j}\mathrm{i}}=\mathrm{e}\mathrm{x}\mathrm{p}(-{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}{\mathsf{\tau }}_{\mathrm{j}\mathrm{i}})$$

(15)

$${\mathsf{\tau }}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{({\mathrm{g}}_{\mathrm{i}\mathrm{j}}-{\mathrm{g}}_{\mathrm{j}\mathrm{j}})}{\mathrm{R}\mathrm{T}}}$$

(16)

$${\mathsf{\tau }}_{\mathrm{j}\mathrm{i}}={\displaystyle \frac{({\mathrm{g}}_{\mathrm{j}\mathrm{i}}-{\mathrm{g}}_{\mathrm{i}\mathrm{i}})}{\mathrm{R}\mathrm{T}}}$$

(17)

$$\mathrm{l}\mathrm{n}{\mathsf{\gamma }}_{\mathrm{i}}={\mathrm{x}}_{\mathrm{j}}^2\left[{\mathsf{\tau }}_{\mathrm{j}\mathrm{i}}{\left({\displaystyle \frac{{\mathrm{G}}_{\mathrm{j}\mathrm{i}}}{{\mathrm{x}}_{\mathrm{i}}+{\mathrm{x}}_{\mathrm{j}}{\mathrm{G}}_{\mathrm{j}\mathrm{i}}}}\right)}^2+{\displaystyle \frac{{\mathsf{\tau }}_{\mathrm{i}\mathrm{j}}{\mathrm{G}}_{\mathrm{i}\mathrm{j}}}{{\left({\mathrm{x}}_{\mathrm{j}}+{\mathrm{x}}_{\mathrm{i}}{\mathrm{G}}_{\mathrm{i}\mathrm{j}}\right)}^2}}\right]$$

(18)

$$\mathrm{l}\mathrm{n}{\mathsf{\gamma }}_{\mathrm{j}}={\mathrm{x}}_{\mathrm{i}}^2\left[{\mathsf{\tau }}_{\mathrm{i}\mathrm{j}}{\left({\displaystyle \frac{{\mathrm{G}}_{\mathrm{i}\mathrm{j}}}{{\mathrm{x}}_{\mathrm{j}}+{\mathrm{x}}_{\mathrm{i}}{\mathrm{G}}_{\mathrm{i}\mathrm{j}}}}\right)}^2+{\displaystyle \frac{{\mathsf{\tau }}_{\mathrm{j}\mathrm{i}}{\mathrm{G}}_{\mathrm{j}\mathrm{i}}}{{\left({\mathrm{x}}_{\mathrm{i}}+{\mathrm{x}}_{\mathrm{j}}{\mathrm{G}}_{\mathrm{j}\mathrm{i}}\right)}^2}}\right]$$

(19)

2.4. Critical Property Calculations

The modified Lydersen–Joback–Reid method calculates the ionic liquids’ acentric factor (ω) and critical properties. This method is an extension of Lydersen’s work, which integrated equations for critical pressure (Pc) and volume from Lydersen with those for normal boiling (T_b) and critical temperature (Tc) from Joback and Reid. A notable advantage of this approach is its ability to determine the high-molecular-weight critical properties accurately of ionic liquids [10]. The three ionic liquids’ critical properties were computed and are shown in

Table 2. Critical characteristics of ionic liquids and gases utilized in this study.

Component	Molecular Weight (g/mol)	Critical Temperature (K)	Critical Pressure (Bar)	Acentric Factor
[BMIM][TfO]	288.29	1023.5	29.5	0.4046
[BMP][TfO]	291.33	933.4	25.9	0.6099
[MBPY][TfO]	299.13	997.8	26.9	0.4153
CO2	44.01	304.1	73.8	0.239

.

2.5. Optimization of Binary Interaction Parameters

Nath and Sumon coded the thermodynamic model in MATLAB (2017a), utilizing a bubble point algorithm based on the three mixing rules [9]. As depicted in Equation (20), the simulations involved optimizing the binary interaction parameters to minimize the error in the objective function (Err). These binary interaction parameters were adjusted within the 0.1 to 1.5 MPa pressure range.

$$\mathrm{E}\mathrm{r}\mathrm{r}={\displaystyle \frac{100}{\mathrm{n}}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left[{\displaystyle \frac{{\mathrm{P}}_{\mathrm{E}\mathrm{x}\mathrm{p},\mathrm{i}}-{\mathrm{P}}_{\mathrm{C}\mathrm{a}\mathrm{l},\mathrm{i}}}{{\mathrm{P}}_{\mathrm{E}\mathrm{x}\mathrm{p},\mathrm{i}}}}\right]$$

(20)

2.6. Henry’s Law Constants, Entropy of Solvation, and Enthalpy

We used the solubility data to compute Henry’s Law constants for the three ionic liquids employed in this study. For each temperature, we plotted the fugacity of CO₂ against the mole fractions. Henry’s Law constants were determined by examining the limiting slope of the second-order polynomial dataset.${\mathrm{H}}_{\mathrm{i}}$of the solute (i) in the solvent (j) is represented by the ratio at infinite dilution of the solute’s fugacity (i) to its mole fraction. In this context, ${\mathrm{f}}_{\mathrm{i}}^{\mathrm{L}}$ and ${\mathrm{f}}_{\mathrm{i}}^{\mathrm{V}}$ indicate the fugacities in the liquid and vapor phases, respectively, while ${\mathrm{x}}_{\mathrm{i}}$ and ${\mathrm{y}}_{\mathrm{i}}$ denote the mole fractions of solute (i) in the liquid and vapor phases, respectively, as described in reference [11]. Assuming only CO₂ is present in the gas phase, Henry’s Law constant is expressed as

$${\mathrm{H}}_{\mathrm{i}}=\underset{{\mathrm{x}}_{\mathrm{i}}\to 0}{\mathrm{Lim}}{\displaystyle \frac{{\mathrm{f}}_{\mathrm{i}}^{\mathrm{L}}\left(\mathrm{T},\mathrm{P},{\mathrm{x}}_{\mathrm{i}}\right)}{{\mathrm{x}}_{\mathrm{i}}}}=\underset{{\mathrm{x}}_{\mathrm{i}}\to 0}{\mathrm{Lim}}{\displaystyle \frac{{\mathrm{f}}_{\mathrm{i}}^{\mathrm{V}}\left(\mathrm{T},\mathrm{P}\right)}{{\mathrm{x}}_{\mathrm{i}}}}$$

(21)

Once the Henry’s Law constant is established from the solubility data, the subsequent step involves calculating the enthalpy of solvation (ΔH^∞) at infinite dilution and the entropy of solvation (ΔS^∞) at infinite dilution using the following equations:

$$∆{\mathrm{H}}^{\mathrm{\infty }}=\mathrm{R}{\left({\displaystyle \frac{\partial \left(\ln H\right)}{\partial \left(1/\mathrm{T}\right)}}\right)}_{\mathrm{P}}$$

(22)

$$∆{\mathrm{S}}^{\mathrm{\infty }}=-\mathrm{R}{\left({\displaystyle \frac{\partial \left(\ln \mathrm{H}\right)}{\partial \left(\ln \mathrm{T}\right)}}\right)}_{\mathrm{P}}$$

(23)

In these equations, ΔH^∞ represents the enthalpy of solvation at infinite dilution, while ΔS^∞ stands for the entropy of solvation at infinite dilution. R denotes the universal gas constant, while H represents Henry’s Law constant.

3. Results

3.1. Densities of the Ionic Liquids

We tested the densities of the three different ionic liquids used in this study at various temperatures ranging from 20 to 70 °C, increasing in 5 °C steps. The measurements were taken at an average atmospheric pressure of 98.5 kPa using an Anton Paar DSA 5000 density meter calibrated with air and water. As expected, the densities of all three liquids decreased as the temperature increased. Among the ILs, [BMIM][TfO] had the highest density, followed by [MBPY][TfO] and [BMP][TfO]. Density data are reported in the Supplementary Material section (Table S1) and plotted in Figure 2.

3.2. Validation of the CO₂ Solubility Measurements

A validation test was conducted to verify proper operation of the IGA-003 and adherence to the relevant experimental procedures. This validation test employed the ionic liquid [BMIM][BF4] to validate CO₂ solubility at 323.15 K. The experiment’s results were compared with the data published by Shiflett and Yokozeki [8]. They used the same ionic liquid and provided density information in their literature. The comparison yielded an absolute average deviation (AAD) of 0.024%.

Figure 3 demonstrates a quasi-perfect match between the experimental data and those reported in reference [8].

3.3. CO₂ Solubility in Ionic Liquids

The investigation involved assessing the solubility of CO₂ in [BMIM][TfO], [BMP][TfO], and [MBPY][TfO] under various conditions, including temperatures of 303.15 K, 323.15 K, and 343.15 K and pressures of up to 1.5 MPa. The plots were generated and are presented in Figure 4, Figure 5 and Figure 6 using the data collected for these three ionic liquids. Detailed experimental data are reported in Tables S2–S4.

Figure 4, Figure 5 and Figure 6a–c represent plots of the experimental data and those obtained using the three models at the three temperatures for each ionic liquid.

4. Discussion

Table 3. Relative overall polarity (N) and electrostatic polarity (sig 2) of anions and cations.

Compound	N	Sig 2
TfO	−19.66	119.07
Tf2N	6.22	99.10
1-Butyl-3-methylimidazolium [BMIM]	32.79	84.40
1-Butyl-3-methypyrrolidium [BMP]	33.10	72.79
1-Butyl-3-methylpyridium [MBPY]	33.52	77.34

summarizes the properties of the ionic liquids screened for their capacity to absorb CO₂ based on the results of our group’s computational simulation [7]. COSMO-RS is a quantum chemistry-based equilibrium thermodynamics method that predicts the chemical potential μ of liquids. It processes the screening charge density σ on the surface of molecules to calculate the chemical potential μ_i of each species in solution. The temperature-dependent relative polarity descriptor (N) would be the residual pseudo-chemical potential of an ion at its infinite dilution in a protic polar solvent like water (reported in

Table 4. Henry’s Law constants, enthalpies, and entropies for the solvation of CO₂ in ionic liquids under infinite dilution conditions.

Ionic Liquid	$\mathbf{H}\mathbf{e}\mathbf{n}\mathbf{r}\mathbf{y}\mathbf{\text{'}}\mathbf{s} \mathbf{L}\mathbf{a}\mathbf{w} \mathbf{C}\mathbf{o}\mathbf{n}\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{t}$ (MPa)				$∆{\mathbf{H}}^{\mathbf{\infty }}$ (kJ/mol)	$∆{\mathbf{S}}^{\mathbf{\infty }}$ (J/mol·K)
	T = 303.15 K	T = 323.15 K	T = 343.15 K	T = 298.15 K Predicted [7]
[BMIM][TfO]	5.0	7.3	10.0	5.3	−14.6	−46.1
[BMP][TfO]	5.3	7.3	10.0	4.1	−13.8	−42.8
[MBPY][TfO]	5.0	7.1	9.2	4.3	−13.2	−40.8

). It quantifies the degree of chemical affinity of water with the ion due to various interactions (vdW, misfit, and H-bond). The polarity of ILs is considered the linear sum of the polarity of its constituent ions. The more negative the value of N, the more polar the ion is [7].

In other terms, COSMO-RS is an excess Gibbs energy model for liquid mixtures based on surface charge interaction [7]. The surface of a molecule or ion is divided into segments of a standard area. Each segment is identified by its average screening charge obtained from COSMO calculation. A histogram that shows the number of segments versus the corresponding screening charge density of a molecule or ion is called the sigma profile [7]. The σ profile of a mixture is a mole fraction average of the σ profiles of the pure compounds. Such a profile gives the relative amount of surface with polarity σ on the molecule’s surface, providing detailed information about the molecular polarity distribution. The lowest energy conformer’s second sigma (sig2) moment is a polarity descriptor (reported in

Table 5. Determined binary interaction parameters for different models and calculated the average absolute deviation percentage (AAD%).

Compound	Temperature (K) and Pressure (MPa)	Mixing Rule	${\mathbf{k}}_{12}$ a	${\mathbf{l}}_{12}$ b	${\mathsf{\tau }}_{12}$	${\mathsf{\tau }}_{21}$	AAD%
CO2(1) + [BMIM][TfO](2)	303.15 and 0.1–1.2	vdWI	−0.0034	-	-	-	3.12
		vdWII	0.0596	0.0188	-	-	1.14
		WS + NRTL	0.6665	-	4.966	−1.1026	1.12
	323.15 and 0.1–1.2	vdWI	−0.0084	-	-	-	1.73
		vdWII	0.0134	0.0065	-	-	1.41
		WS + NRTL	0.4315	-	4.0594	−0.8902	1.33
	343.15 and 0.1–1.2	vdWI	−0.0109	-	-	-	1.52
		vdWII	−0.0134	−0.0007	-	-	1.52
		WS + NRTL	0.2972	-	3.331	−0.7393	1.46
CO2(1) + [BMP][TfO](2)	303.15 and 0.1–1.2	vdWI	0.0015	-	-	-	2.11
		vdWIi	0.029	0.0088	-	-	1.27
		WS + NRTL	0.471	-	4.3505	−0.8425	1.57
	323.15 and 0.1–1.2	vdWI	0.0085	-	-	-	2.4
		vdWII	0.0616	0.0169	-	-	0.87
		WS + NRTL	0.6357	-	4.7698	−1.0227	0.86
	343.15 and 0.1–1.2	vdWI	−0.0012	-	-	-	1.62
		vdWII	0.029	0.0083	-	-	1.4
		WS + NRTL	0.451	-	3.652	−0.8614	1.36
CO2(1) + [MBPY][TfO](2)	303.15 and 0.1–1.5	vdWI	0.0099	-	-	-	4.36
		vdWII	0.692	0.0185	-	-	0.72
		WS + NRTL	0.9736	-	−01431	−0.0504	0.65
	323.15 and 0.1–1.5	vdWI	0.0057	-	-	-	3.39
		vdWII	0.0692	0.0185	-	-	0.80
		WS + NRTL	0.6793	-	4.5475	−1.055	0.80
	343.15 and 0.1–1.5	vdWI	−0.00027	-	-	-	3.84
		vdWII	0.0999	0.027	-	-	1.98
		WS + NRTL	0.7664	-	4.7769	−1.1622	1.99

^a: ${\mathrm{k}}_{12}$ = ${\mathrm{k}}_{21}$; ^b: ${\mathrm{l}}_{12}$ = ${\mathrm{l}}_{21}$.

). The 3D distribution of the polarization charges σ of each molecule is converted into a surface composition function (σ profile). Corresponding sigma potentials of the solvents can be used to ascertain the affinity of solvents to a solute [7].

Our earlier study [7] predicted that [TfO], with a more negative N, was more polar than [Tf2N] and had a lower capacity for CO₂, as confirmed by comparison with data published earlier [11] and this study. This study reports that CO₂ solubility decreases with an increase in polarity. Table 4 shows that the least polar cation is [MBPY], with the highest CO₂ solubility, followed by [BMP] and [BMIM]. The infinite dilution enthalpies and entropies of solvation for CO₂ in the anions and cations used in this study were reported in reference [7].

4.1. Factors That Affect CO₂ Solubility

4.1.1. Effect of Cations

Nath et al. [9] confirmed that different cations did not notably alter the solubility of gases in an ionic liquid. The outcomes of their study remained broadly consistent, primarily due to the uniformity of the anion used. In a similar study, Taguiri et al. [11] investigated the impact of various cations, all of which shared the common anion [Tf2N]. Their findings suggested that the choice of cation had minimal influence on the solubility of CO₂. In this study, the cations present were very similar in the number of carbons, varying only from C9 to C11. This slight difference was enough to rank the ILs, with the one with the highest solubility having the largest number of carbons.

4.1.2. Effect of Anions

In this investigation, three distinct ionic liquids share a common anion, [TfO]. The comparison in Figure 7 illustrates that all three ionic liquids exhibit a similar trend in CO₂ solubility, with very close values. This consistency can be ascribed to the common anion. [TfO] had a very negative value of N (−19.66), making it a more polar anion compared to [Tf2N], for example. [Tf2N] with more fluorine atoms exhibits high CO₂ capacity.

4.1.3. Pressure and Temperature

As evidenced by the data presented in Figure 4, Figure 5 and Figure 6, the solubility of gases in an ionic liquid is significantly affected by variations in both temperature and pressure. The collective findings from these figures unequivocally demonstrate that an increase in pressure results in a corresponding increase in CO₂ solubility. Conversely, solubility decreases as the temperature rises for all three ionic liquids under study.

4.1.4. Alkyl Chain Length

In studies published by Aghaie et al. [12] and Ramdin et al. [13], it was found that the length of the cation’s alkyl chain significantly affects the solubility of CO₂ in ionic liquids. A longer alkyl chain in the cation corresponds to higher CO₂ solubility. In this research, where ionic liquids share the same anion, the alkyl chains are the same for all three ionic liquids, resulting in similar solubility. Quaye et al. [14] observed that ionic liquids with longer alkyl chains exhibit enhanced CO₂ solubility due to increased van der Waals interactions and surface area. Their study also concluded that 1-hexadecyl-3-methyl imidazolium bis (trifluoromethyl sulfonyl imide) with 21 carbons [IL2, C₂₁H₄₀F₆N₃O₄S₂] had a superior CO₂ solubility (based on Henry’s Law constants) compared to 1-decyl-3-methyl-imidazolium bis (trifluromethylsulfonyl imide with 15 carbons (IL1, C₁₅H₂₆F₆N₃O₄S₂), which resulted in a lower Henry’s Law constant. The experimental results presented in Figure 7 show very close solubility data.

4.2. Henry’s Law Constants, Enthalpies, and Entropies

Henry’s Law constants were determined by plotting the fugacity against the mole fraction and fitting a second-order trend line to the data. The slope of this equation, obtained through differentiation, showed that Henry’s Law constants increased with higher temperatures, as shown in Table 4. In this study, the slope was utilized to compute the enthalpy. The determined Henry’s Law constants were plotted against the reciprocal of temperature (1/T), and the slope of this graph was used to calculate the absorption enthalpy. This enthalpy value was multiplied by the universal gas constant (8.314 J/mol·K). Table 4 demonstrates that, among the three temperatures investigated, among the three ionic liquids, [MBPY][TfO], the least polar and with the most significant size (number of carbons and hydrogens), exhibits the highest solubility, followed by [BMIM][TfO] and [BMP][TfO]. Note that [BMIM][TfO] and [BMP][TfO] had identical values at 323.15 K and 343.15 K.

Figure 8 compares the CO₂ Henry’s Law constants determined in this study with those obtained from the literature [6,14,15]. The ionic liquid featuring the highly fluorinated [Tf2N] as its anion exhibited higher CO₂ solubility than the ionic liquids used in this study (TfO-based) across the three temperatures of 303.15 K, 323.15 K, and 343.15 K. Values of the enthalpy and entropy at infinite dilution were determined to be negative, indicating exothermic absorption and an increase in system order.

Finally, Henry’s Law constants of [MBPY][TfO] were compared with those of a widely used physical solvent known as Genesorb 1753 (Selexol^©). This particular solvent was selected for comparison due to its extensive use in gas-sweetening plants, waste air treatment, and purification of synthesis gases, as noted by [16]. Henry’s Law constants for Selexol/Genesorb are reported for comparison [16] and presented in Figure 9. [MBPY][TfO] was chosen in this comparative analysis because it possesses the lowest Henry’s Law constant among the studied ionic liquids. Selexol/Genesorb 1753 had a lower Henry’s Law constant than [MBPY][TfO], and therefore a higher capacity for CO₂.

Table 5 summarizes the calculated interaction binary parameters and their corresponding average absolute deviations for each mixing rule. The average absolute deviations for the vdWI, vdWII, and WS-NRTL mixing rules applied to CO₂ in ionic liquids were determined to be 2.67%, 1.27%, and 1.24%, respectively. Among these mixing rules, the Wong–Sandler (WS-NRTL) mixing rule exhibited the least average absolute deviation, signifying its superiority as the favored option.

5. Conclusions

This study examines the solubility of CO₂ in three promising ionic liquids ([BMIM][TfO], [BMP][TfO], and [MBPY][TfO]) at various temperatures and pressures. This study also reports the densities of these ionic liquids at different temperatures. The results indicated that CO₂ solubility decreased with increasing temperature and increased with higher pressure. With the same [TfO] cation and the same alkyl chain, the three ILs presented very close absorption capacities. Based on Henry’s Law constants, [MBPY][TfO], the least polar, had slightly higher solubility among the three ionic liquids. The measured Henry’s Law constants were close to those predicted using COSMO-RS. Compared to Selexol/Genesorb 1753, [MBPY][TfO] exhibited a higher Henry’s Law constant, indicating that it was less effective in absorbing CO₂. Based on several studies reported in the literature, the Henry’s Law constants of the ionic liquids determined in this study were higher when compared to [Tf2N]-based ionic liquids at all temperatures.

Additionally, binary interaction coefficients were regressed using the Peng–Robinson equation of state (PR-EoS), and three mixing rules (vdWI, vdWII, and WS-NRTL) were evaluated. The Wong–Sandler mixing rule had the lowest average absolute deviation (AAD).

Values of the enthalpy and entropy of absorption were negative, indicating exothermic absorption and an increase in system order. The enthalpy of absorption ranged from −25.9 kJ/mol for [MBPY] to −42.2 kJ/mol for [BMP], while the entropies varied from −8.3 kJ/mol·K for [MBPY] to −13.7 kJ/mol·K for [BMP].