Effect of Ionic Liquids on the Solubility of Lithium Bromide in Aqueous Solution: Experimental Measurement and Prediction

Abstract

The paper presents experimentally determined solubility results of lithium bromide in ionic liquid + water and assesses the effect of the addition of ionic liquids (ILs) on the solubility of lithium bromide (LiBr) in water. The solubility of LiBr in pure water has been determined and compared to the literature data. It is known that LiBr aqueous solutions are widely used as working fluids in low-temperature thermal energy recovery systems. However, the aqueous LiBr solution is easy to crystallize, which could cause equipment corrosion. One of the possibilities for improving the properties of the H₂O/LiBr refrigerant system is the use of an additive to increase the solubility of LiBr in water. Three ILs were selected as an additive: 1-ethyl-3-methylimidazolium acetate ([EMIM]­[OAc]), 1-ethyl-3-methylimidazolium bromide ([EMIM]­Br), and 1-butyl-3-methylimidazolium bromide ([BMIM]­Br). In this study, new empirical parameters for the calculation of LiBr solubility in water were provided. A reasonable prediction of phase equilibrium data is made using the COSMO-SAC model. The NRTL equation is also calculated. The maximum deviation of COSMO-SAC is 7.56%, and the deviation of the other calculations is less than 2%. These experimental and theoretical findings offer valuable insights into the selection and optimization of working fluids in absorption cycle systems.

1. Introduction

Absorption refrigeration systems have gained prominence in industrial waste heat recovery and sustainable cooling applications due to their energy-efficient operation and compatibility with low-grade thermal sources. In these systems, the thermodynamic properties of the working fluids significantly influence efficiency and performance. − Lithium bromide absorption chillers, which use lithium bromide–water as the absorbent–refrigerant pair, are commonly employed in applications with evaporation temperatures above 0 °C. , These systems are widely used in air conditioning, industrial cooling, temperature control, and waste heat recovery. − The advantages of water/lithium bromide chillers include high efficiency, low working pressure, nonpolluting operation, high thermal efficiency, low energy consumption, and safe operation. ,, However, the aqueous lithium bromide solutions have a crystallization risk at low temperatures or high concentrations, which can cause corrosion to metals. , Additionally, noncondensable gases produced during corrosion can severely affect system performance. , As a result, additives are necessary to mitigate the crystallization problem.

To enhance the operational performance of the water/lithium bromide refrigerant pair system, the addition of third or fourth components, such as inorganic salt mixtures, organic solvents, and alcohols or ionic liquids (ILs), can improve the anticrystallization properties of lithium bromide aqueous solutions. , Previous studies explored multicomponent systems to enhance LiBr solutions, including inorganic salt mixtures, − organic solvents and alcohols, − and ionic liquids. − The research situation is presented in Table . Inorganic salt mixtures can increase solubility but risk introducing additional corrosive ions. Organic solvents expand operating ranges but reduce the vapor pressure suppression efficiency. ILs have emerged as the most promising additives due to their tunable properties, yet underexplored strategy.

1. Researches on Additives for LiBr Aqueous Solution.

Authors	test object	additives	refs
Koo and Lee	solubilities, vapor pressures, densities, viscosities	lithium iodide + lithium chloride
Salavera et al.	solubility, heat capacity, density	lithium iodide + lithium nitrate + lithium chloride
Arabi and Dehghani	solubility, density	lithium chloride, sodium formate
Park et al.	solubility, vapor pressure, density, viscosity	potassium nitrate + 1,3-propanediol	−
Inada et al.	crystallization temperature, vapor pressure, density, viscosity	lithium iodide + ethylene glycol
Królikowska et al.	solubility	lithium acetate, lithium lactate, lithium trifluoroacetate
		crown ethers, glycols
		ionic liquids, zwitterionic compounds,	−
Li et al.	absorption cycle performance	1,3-dimethylimidazolium chloride, 1,3-dimethylimidazolium tetrafluoroborate
Kim et al.	solubility	1-butyl-3-methylimidazolium ammonium
Latorre-Arca et al.	solubility	ethylammonium nitrate, propylammonium nitrate, ethylammonium chloride, 1-butyl-3-methylimidazolium bromide, 1,3-dimethylimidazolium chloride
Tariq et al.	anticrystallization	1,3-dimethylimidazolium chloride

Existing research has primarily focused on ILs containing halide anions or nitrate-based and tetrafluoroborate-based cations, which demonstrate enhanced lithium bromide solubility and crystallization suppression. However, comparisons of ILs with different anions and alkyl chain lengths are limited. Meanwhile, no systematic screening methods for ionic liquids have been established.

The screening of ILs in this paper is carried out through calculation, which was derived from our previous work. The screening strategy is verified through experimental measurement and prediction. We selected 1-butyl-3-methylimidazolium bromide ([BMIM]­Br), 1-ethyl-3-methylimidazolium acetate ([EMIM]­[OAc]), and 1-ethyl-3-methylimidazolium bromide ([EMIM]­Br) by the COSMO-SAC model based on the infinite dilution activity coefficient of ionic liquids in water. This approach contrasts with previous empirical trials. The connection between the IL structure and solubility is expounded through interaction strength analysis. Based on this, the current study investigated the solubility of lithium bromide in both water and the corresponding IL aqueous solutions. Furthermore, different empirical and theoretical models were employed to represent the experimental data, thereby enabling the prediction of the effect of ionic liquids on the solubility of lithium bromide in aqueous solution. Additionally, the performance of ILs as absorbents or anticrystallization additives for lithium bromide was systematically assessed, providing valuable insights into the design and development of absorption cycle processes using lithium bromide as the absorbent.

2. Experimental Section

2.1. Materials

Lithium bromide (LiBr, CAS No. 7550–35–8) was purchased from Aladdin Bio Chem. and Tech. (Shanghai) Co., Ltd. with mass fraction purity >0.99. The deionized water used for the solubility experiment was made by a reverse osmosis unit integrated with an ion-exchange system with a conductivity of 0.05 μS·cm^–1. The three ILs [EMIM]­[OAc], [EMIM]­Br, and [BMIM]Br were supplied by Monils Chem. Eng. Sci. and Tech. (Shanghai) Co., Ltd., and the purity of the compounds is higher than 99.0%. The water mass fraction in ILs was determined by a Karl Fischer titrator (KF831 made by Metrohm Herisau Switzerland) with an accuracy of 0.1 μg. To reduce the water content, before the experiment, each IL was dried for 24 h in a vacuum drying oven at a temperature of T = 363.15 K and under pressure P = 5 kPa, generated by a vacuum pump. No decomposition of the ILs was observed under the experimental conditions. The purity and moisture content of ionic liquids can introduce systematic errors in solubility measurements. To mitigate this, Karl Fischer titration was used throughout the experiments to monitor moisture content stability. Furthermore, the residual water mass was accounted for in the solubility calculations, as shown in Table S1 of the Supporting Information. The detailed information on the compounds used in this work is presented in Table .

2. Specifications of the Compounds in This Work.

chemicals	water	[EMIM][OAc]	[EMIM]Br	[BMIM]Br	LiBr
CAS No.	7732–18–5	143314–17–4	65039–08–9	85100–77–2	7550–35–8
mass percentage purity	>99.9%	>99.9%	>99.9%	>99.9%	>99.9%
purification method		Vacuum desiccation
water mass fraction		4.26%	0.32%	0.36%
source	own source	Monils (Shanghai)			Aladdin(Shanghai)

^a1-Ethyl-3-methylimidazolium acetate.

^b1-Ethyl-3-methylimidazolium bromide.

^c1-Butyl-3-methylimidazolium bromide.

^dKarl Fischer titrator.

2.2. Experimental Apparatus and Method

The experiment was conducted using the laser turbidity method ,, to determine the solubility of LiBr in water and three aqueous ionic liquid (IL) solutions. The experimental setup is shown in Figure . A glass-phase equilibrium kettle with a jacket was used, which is connected to a constant-temperature water bath. After preparing aqueous IL solutions, predetermined masses of LiBr and solution were added to the phase equilibrium kettle under magnetic stirring. The mass of LiBr remained constant throughout the experiment. To prevent supersaturation, the solution must be turbid initially at the measurement temperature. The mixture was first heated to 343.15 K (20 K above the target temperature) for 20 min until complete dissolution. The temperature was then reduced to measurement levels with continuous stirring for 30 min. Ionic liquid solutions are added until the solution becomes clear, with real-time tracking of laser intensity changes using a precalibrated He–Ne laser system. The collimated He–Ne laser beam is vertically incident on the sample solution. Suspended particles in the solution scatter the light, with the forward-scattered light collected by detectors positioned along the forward axis. Transmittance stabilization (laser intensity variation <0.1 mV/min) indicated saturation. Three measurement cycles were conducted at each temperature (323.15–313.15 K), with equilibrium verification through reversible cloud-clarity transitions by the transformation of heating and cooling.

1.

Schematic diagram of the phase balance experimental device: 1. thermometer, 2. water bath glass jacket, 3. phase equilibrium chamber, 4. magnetic rotor, 5. magnetic stirrer, 6. water outlet to bath, 7. water inlet from bath, 8. laser transmitter, and 9. laser receiver.

The temperature was measured by using a mercury thermometer. The temperature uncertainty comes from the reading error and repeatability error. The error in the reading is 0.01 K, which follows a uniform distribution, u ₁ = 0.01/√3 ≈ 0.006 K. The reading error of the nonvertical line of sight is ±0.01 K, which follows the arcsine distribution, u ₂ = 0.01/√2 ≈ 0.007 K. The standard deviation calculated from repeated measurement data is 0.03 K. Thus, the relative standard uncertainty of temperature in the paper can be expressed as follows

$$u(T)=\sqrt{{(u_1)}^2+{(u_2)}^2+{(0.03)}^2}\approx 0.032\mathrm{K}$$

The electronic balance undergoes calibration using its built-in autocalibration feature and verified 100 g standard weights. The uncertainty of the electronic balance comes from the instrument resolution u(m ₁) = 0.01/2√3 ≈ 0.03 mg, the uncertainty of the standard weights u(m ₂) = 0.053/2√3 ≈ 0.016 mg, and measurement repeatability u(m ₃) = 0.071 mg. The relative standard uncertainty of mass is as follows

$u(m)=\sqrt{{(u(m_1))}^2+{(u(m_2))}^2+{(u(m_3))}^2}\approx 0.079\mathrm{mg}$

Deionized water was selected as the calibration fluid, and its laser intensity was 0.60 mV. Before the experiment, the dynamic range (upper and lower limits) and the water’s transmittance were measured to ensure the normal operation of the laser monitoring system. The accuracy of the laser receiver is ±0.01 mV, and the uncertainty of the laser light intensity is u = 0.01/2√3 ≈ 0.0029 mV.

3. Results and Discussion

To validate the experimental method, the solubility of LiBr in pure water was determined at 293.15, 303.15, 313.15, and 323.15 K. The measured values were in good agreement with the literature data, , showing consistency within the experimental temperature range. The graphical presentation of the binary system is presented in Figure .

2.

Comparison between this work and literature data on the solubility for the LiBr + H₂O binary system.

The main purpose of the work is to determine the effect of ILs on the solubility of LiBr in water. The solubility data of the LiBr + ILs + H₂O system with different IL mole fractions from x ₂ = 0.001 to 0.02 were determined by the laser turbidity method at a temperature range from 293.15 to 323.15 K. The experimental results are listed in Table , and the original experimental data are listed in Table S1. To be better applied in the industry, it would be required to further expand the temperature and mole fraction range in future work. The experiment clearly shows that different ILs have varying enhancements on the solubility of LiBr in water. Specifically, [EMIM]­[OAc] exhibits the highest solubility enhancement, followed by [EMIM]­Br, while [BMIM]Br shows the least effect. At 323.15 K and a mole fraction of 0.02, LiBr has the highest solubility in the [EMIM]­[OAc] aqueous solution, approximately 69 wt %. In contrast, at 293.15 K, in the [BMIM]Br aqueous solution (x ₂ = 0.001), the solubility of LiBr is close to that in pure water under the same conditions, and the solubility increases the least. The solubility of LiBr in water is closely dependent on temperature and the IL content, with solubility increasing as both the temperature and the mole fraction of the IL increase. The increase of the IL’s mole fraction increases the solubility of LiBr in water.

3. Experimental and Calculated Solid–Liquid-Phase Equilibrium for the LiBr (1) + ILs (2) + H₂O (3) Ternary System.

		S/g·(100gH2O)−1
T/K	x 2	exp.	model 1	model 2	COSMO-SAC
[EMIM][OAc]
293.15	0.000	150.3	150.3
	0.001	153.4	151.6	152.5	162.0
	0.005	155.7	155.4	154.6	166.9
	0.008	156.3	157.5	155.2	170.8
	0.010	158.5	158.6	157.3	173.3
	0.015	161.9	161.1	161.2	179.8
	0.020	163.7	164.0	162.9	186.6
303.15	0.000	161.5	161.5
	0.001	166.3	162.9	169.3	164.3
	0.005	167.3	167.1	170.5	169.2
	0.008	168.1	169.7	171.5	172.9
	0.010	170.9	171.2	174.3	175.4
	0.015	176.1	174.7	178.4	181.9
	0.020	178.0	178.5	180.4	188.4
313.15	0.000	184.2	184.2
	0.001	186.1	184.6	183.0	166.8
	0.005	187.0	187.1	183.7	171.6
	0.008	188.3	189.5	184.7	175.2
	0.010	192.1	191.1	188.6	177.7
	0.015	194.6	194.6	192.3	184.0
	0.020	196.1	196.2	193.7	190.4
323.15	0.000	190.2	190.2
	0.001	191.8	190.2	192.9	169.7
	0.005	192.7	192.4	193.9	174.5
	0.008	193.3	195.23	194.5	178.1
	0.010	198.3	197.1	199.5	180.6
	0.015	201.3	201.0	202.1	186.9
	0.020	201.4	201.5	202.3	193.3
AAD/%			0.51	1.12	6.82
[EMIM]Br
293.15	0.000	150.3	150.3
	0.001	151.1	150.7	150.1	161.8
	0.005	152.0	152.0	150.9	165.0
	0.008	152.5	152.6	151.4	167.5
	0.010	152.9	152.9	151.9	168.9
	0.015	153.8	153.7	152.7	172.8
	0.020	154.6	154.7	153.4	176.6
303.15	0.000	161.5	161.5
	0.001	164.2	162.6	167.4	164.2
	0.005	164.8	165.1	168.3	167.2
	0.008	165.5	166.0	168.7	169.8
	0.010	166.2	166.1	169.4	171.1
	0.015	166.7	166.3	170.2	175.0
	0.020	166.8	166.9	170.5	178.6
313.15	0.000	184.2	184.2
	0.001	185.2	184.7	181.8	166.7
	0.005	186.2	186.0	182.6	169.8
	0.008	186.4	186.8	183.0	172.2
	0.010	187.1	187.1	183.7	173.5
	0.015	188.1	187.8	184.5	177.2
	0.020	188.5	188.6	184.6	180.9
323.15	0.000	190.2	190.2
	0.001	191.5	190.7	192.6	169.6
	0.005	192.1	192.1	193.3	172.7
	0.008	192.4	192.7	193.5	175.1
	0.010	193.0	192.9	194.2	176.5
	0.015	193.5	193.3	194.7	180.1
	0.020	193.8	193.9	195.1	183.9
AAD/%			0.14	1.32	7.34
[BMIM]Br
293.15	0.000	150.3	150.3
	0.001	150.4	150.5	149.1	157.9
	0.005	151.0	151.0	149.8	162.0
	0.008	151.2	151.3	149.9	165.3
	0.010	151.5	151.4	150.5	167.2
	0.015	151.6	151.6	150.5	173.1
	0.020	151.8	151.8	150.8	179.1
303.15	0.000	161.5	161.5
	0.001	162.4	161.8	166.1	160.1
	0.005	162.7	162.9	166.4	164.2
	0.008	163.0	163.6	166.8	167.4
	0.010	164.7	164.0	167.9	169.2
	0.015	164.8	164.9	167.9	175.0
	0.020	165.6	165.6	168.6	180.6
313.15	0.000	184.2	184.2
	0.001	184.4	184.3	180.5	162.6
	0.005	184.4	184.6	180.6	166.6
	0.008	184.9	184.9	180.9	169.7
	0.010	185.3	185.1	182.0	171.6
	0.015	185.4	185.6	182.1	177.1
	0.020	185.8	185.8	182.7	182.6
323.15	0.000	190.2	190.2
	0.001	190.4	190.2	191.7	165.5
	0.005	190.3	190.4	191.7	169.4
	0.008	190.5	190.6	191.9	172.5
	0.010	190.9	190.8	192.0	174.4
	0.015	191.1	191.1	192.2	179.9
	0.020	191.2	191.2	192.2	185.7
AAD/%			0.08	1.35	7.56
the relative standard uncertainty: u(T) = 0.032 K, u(m) = 0.079 mg
error range of x : x 1 (0.14–0.20) × 10–6

^a x ₂ is the mole fraction of IL in water.

^bModel 1 is an empirical model in Section .

^cModel 2 is the Apelblat model in Section .

^dCOSMO-SAC is a predictive model in Section .

^eexp. is the experimental value in this work.

^fThe AAD represents the average absolute deviation between the experimental and calculated values. $\mathrm{AAD}=(\sum _{i=1}^n|{\mathrm{value}}_{\mathrm{cal},i}-{\mathrm{value}}_{\exp .,i}|/{\mathrm{value}}_{\exp .,i})/n$ .

^gDerived from u(m) of the electronic balance $\mathrm{\Delta }{x}_i=\frac{u(m)}{M_i{n}_{\mathrm{total}}}$ . Detailed calculation values are shown in Table S6.

Additionally, the solubility is significantly influenced by the alkyl chain length of the cationic substituents in the ILs and the atomic type and structure of the anions. The increase in the alkyl chain decreases the solubility of LiBr; see Figure . This is because longer alkyl chains making the ILs are more hydrophobic. The anions with hydrogen-bond donor atoms can form ion pairs with bromine ions, thus increasing the solubility of lithium bromide. The anions with larger molecular weight and complex structure have a more stronger steric hindrance, which are more difficult to form ion pairs, and decrease the solubility of LiBr. However, when [OAc]⁻ in the tested system is closely linked to the bromine ion, its relatively complex structure can better enclose the bromine ion and improve the solubility of LiBr.

3.

Comparison of the mole fraction of LiBr in binary and ternary systems at an absorber operating temperature of 303.15 K (IL’s mole fraction in water: 0.02).

Since bromine ions are present in both LiBr and ILs, the salting-out effect must be considered. However, experimental results reveal an increase in the LiBr solubility. This indicates that there are unaccounted ion-pair interactions in the system. Imidazolium salts typically provide at least three hydrogen-bond-donating sites. The imidazolium cations act as additional hydrogen-bond donors, forming ion pairs with bromide ions and weakening their association with lithium ions. These imidazolium–bromide interactions may therefore drive enhanced LiBr solubility. While the bromide ion acts as a common ion, inevitably inducing a common ion effect that would suppress solubility enhancement. However, the bromide common ion effect and the specific interactions of imidazolium-based ionic liquids collectively determine the solubility trend of LiBr. This suppression is counterbalanced by specific imidazolium–bromide interactions, ultimately increasing the LiBr solubility. Experimental data from this work further confirm these conclusions. At the same temperature, [EMIM]­[OAc] exhibited higher solubility enhancement for LiBr compared to [EMIM]­Br.

The typical operating temperature of the absorber is 303.15 K. At this temperature, the binary system (LiBr + H₂O) can remain liquid only within a limited range of concentrations. When the mole fraction of LiBr exceeds 0.2509, the aqueous solution of lithium bromide will crystallize and form a solid phase. The experimental results clearly show that the addition of ionic liquid can significantly improve the solubility of lithium bromide and effectively inhibit crystallization. Figures and show a comparison of the solubilities of lithium bromide. It is observed that lithium bromide has the best solubility in water when [EMIM]­[OAc] is added (x ₁ = 0.2697), and the worst effect was observed for [BMIM]­Br (x ₁ = 0.2520) for IL to LiBr mole fraction is 0.001. These findings suggest that adding ILs as anticrystallization additives to LiBr aqueous solutions can help extend the operating range of LiBr absorption refrigeration systems.

4.

Comparison of the mole fraction of LiBr in binary and ternary systems at an absorber operating temperature of 303.15 K (IL’s mole fraction in water: 0.001–0.02).

The incorporation of ILs into lithium bromide solutions significantly improves absorption refrigeration systems by addressing crystallization challenges while enhancing operational efficiency. ILs increase lithium bromide solubility, allowing the solution to retain more water per unit mass and thereby improving heat transfer in absorbers and generators. This modification also enables a higher refrigerant delivery to the evaporator, directly increasing the cooling capacity and overall system efficiency (COP). Crucially, ILs inhibit lithium bromide crystallization through supersaturation control, minimizing maintenance issues caused by pipe blockages.

4. Computational Model

4.1. Empirical Model

In practical applications, the simpler the fitting formula for solubility data, the more widely used. For the system in the paper, since the pressure and temperature are determined, the solubility is mainly determined by the composition of the solution. By fitting solubility data with polynomial equations, a suitable calculation model for the solubility of ternary systems is derived. This model is known as the four-parameter semiempirical formula. Ma et al. used the empirical equation to calculate the solid–liquid equilibria of maleic anhydride in chain dicarboxylic acid diester. All have a small calculation deviation. The empirical model is suitable for interpolating data without an extrapolation function. However, it has the advantages of strong adaptability and a wide application range. It plays an important role in the preliminary research

$$S=a+\mathit{bw}+c{w}^2+d{w}^3$$ 1

where S represents the solubility of LiBr in g/100g of H₂O, and w represents the mass fraction of the IL in the mixed solution. The empirical parameters a, b, c, and d were obtained through least-squares fitting by the Levenberg–Marquardt algorithm, and the values are listed in Table .

4. First-Order Fitting Parameters of Model 1.

T/K	a	b	c	d	RMSE	R 2
[EMIM][OAc]
293.15	150.2881	358.3675	–4719.5852	37480.5466	0.9578	0.95
303.15	161.4537	391.1752	–3940.3591	33124.9287	1.6754	0.90
313.15	184.2226	90.7392	7120.1543	–88379.9684	0.8873	0.95
323.15	190.1707	–32.4510	14086.4916	–175337.8110	1.1482	0.93
[EMIM]Br
293.15	150.2881	107.7601	–1465.3808	10307.3033	0.1934	0.98
303.15	161.4537	277.8190	–5454.2603	36373.1235	0.7197	0.82
313.15	184.2226	124.1539	–1585.3320	10189.7410	0.2948	0.95
323.15	190.1707	149.1900	–2661.3180	18591.8721	0.3501	0.91
[BMIM]Br
293.15	150.2881	37.8517	–373.5196	1488.5653	0.0720	0.98
303.15	161.4537	69.0894	–243.1199	28.8600	0.4934	0.85
313.15	184.2226	9.8010	451.5917	–4110.4591	0.1354	0.94
323.15	190.1707	3.0993	487.2601	–4566.9566	0.1098	0.91

Parameter a in eq is fixed as the solubility of LiBr in pure water at each temperature based on the physical constraint S = a when the ionic liquid mole fraction is zero. This approach ensures that the model balances theoretical validity and practical utility. However, at 313.15 and 323.15 K, the model calculates slightly lower solubility for the [EMIM]­[OAc] system compared to that of [EMIM]­Br. This discrepancy occurs because the solution environment in the low IL concentration range (0.001–0.008) is nearly identical to pure water, leading to an experimentally subtle distinction. Under these conditions, the current model might not fully resolve subtle differences in the IL–solvent interactions. These differences could depend on both the experimental uncertainties and model limitations.

To systematically evaluate the model’s holistic applicability and intuitively reflect the magnitude of average deviation in computational outcomes, this study adopts the root-mean-square error (RMSE) as the primary evaluation metric. Its mathematical formulation is as follows

$$\mathrm{RMSE}=\sqrt{\frac{1}{n}\sum _i^n{(y_{\exp ,i}-y_{\mathrm{cal},i})}^2}$$ 2

where y _exp,i denotes the experimental observed value, y _cal,i represents the model-computed value, and n signifies the total sample size. RMSE effectively mitigates the influence of outliers on evaluation outcomes so as to provide a quantitative basis for comparing the actual prediction performance of different models.

The four-parameter semiempirical formula can describe the solid–liquid-phase equilibrium of LiBr(1) + ILs(2) + H₂O­(3) ternary solutions. It is used for calculating the relationship between the solubility of LiBr and the IL’s mass fraction at a given temperature. The calculated results are shown in Table , and the maximum of the average absolute deviation (AAD) is 0.49%. Furtherly, the RMSE of eq ranges from 0.06 to 1.68 at different temperatures and in different IL aqueous solutions, indicating a good correlation, as shown in Table . The R-squared is also given. The minimum values for all three systems occur at 303.15 K, which is 0.90 ([EMIM]­[OAc]), 0.82 ([EMIM]­Br), and 0.85 ([BMIM]­Br), respectively. And the maximum value occurs at 293.15 K.

To enhance the generality of the solubility model for the ternary system, further processing of the fitting parameters for model 1 is carried out. Based on the connection between S and a, we think it is possible that a depends on the temperature. Through an analysis of the relationship between the fitting parameters, temperature, and the mass fraction of IL, the following equation has been derived

$$\ln (a/86.85)=a_1+a_2/T+a_3\ln T$$ 3

$$b=10(b_1+b_2{T}^2+b_3{T}^{2.5}+b_4{T}^3)$$ 4

$$c=100(c_1+c_2{T}^2+c_3{T}^{2.5}+c_4{T}^3)$$ 5

$$d=1000(d_1+d_2{T}^2+d_3{T}^{2.5}+d_4{T}^3)$$ 6

where a, b, c, and d are the first-order fitting parameters of eq . a _i , b _i , c _i , and d _i (i = 1, 2, 3, or 4) are the parameters of (eqs –), which are called the second-order fitting parameters of eq . T represents the absolute temperature in °C.

Equations – can be used to calculate the first-order parameters of eq at specified temperatures, thereby obtaining solubility data of LiBr at different mass fractions of IL under isothermal conditions. The root-mean-square error (RMSE) for different ternary systems is shown in Table . And the calculation results are listed in Table S2.

5. Second-Order Fitting Parameters of Model 1.

parameters	[EMIM][OAc]	[EMIM]Br	[BMIM]Br
a 1	–1.0157	–1.0157	–1.0157
a 2	4.9718	4.9718	4.9718
a 3	0.4379	0.4379	0.4379
R 2	1	1	1
RMSE	0.0183	0.0183	0.0183
b 1	–80.7336	–122.2109	–31.5002
b 2	0	1.9639	0.5407
b 3	–0.5148	–0.5280	–0.1468
b 4	0.0359	0.0365	0.0102
R2	1	1	1
RMSE	2.12 × 10–11	1.47 × 10–13	9.88 × 10–14
c 1	270.5147	313.9361	18.0042
c 2	0	–4.9033	–0.3887
c 3	1.4588	1.3232	0.1101
c 4	–0.1016	–0.0918	–0.0079
R2	1	1	1
RMSE	1.96 × 10–10	1.20 × 10–12	6.76 × 10–14
d 1	–315.3956	–209.7162	–8.3844
d 2	0	3.2980	0.1905
d 3	–1.5821	–0.8914	–0.0549
d 4	0.1095	0.0619	0.0040
R2	1	1	1
RMSE	4.96 × 10–10	5.75 × 10–13	4.13 × 10–14

As can be seen from Figure , eq , that is, the degree of correlation between the first-order fitting and experimental solubility results is higher than that between the second-order fitting. It has high computational reliability at each experimental temperature point. The second-order fitting is more general, considering both the temperature and the mass fraction of IL in solution. Both the RMSE value and R-squared are smaller than the first-order fit. It is worth noting that all R-squared is 1.

5.

Solubility curve of the LiBr (1) + ILs (2) + H₂O (3) ternary system (T = 293.15 K-323.15 K, w _IL = 0.001–0.02). (a) [EMIM]­[OAc], (b) [EMIM]­Br, and (c) [BMIM]­Br.

4.2. Apelblat Model

Based on the principles of phase equilibrium, Apelblat and Manzurola supposed that the solution could be treated as an ideal solution. They proposed neglecting the effect of the solute activity coefficient under normal pressure and assumed a linear relationship between temperature and the mole enthalpy change of the solution. Consequently, solubility was determined to be solely dependent on temperature ,

$$\ln (x_1)=100(A+B/T+C\ln T)$$ 7

where x ₁ represents the mole fraction of LiBr, T is the absolute temperature in K, and A–C are the dissolution parameters determined by fitting the experimental data. The solubility calculation results are shown in Table , and the AAD is in the range of 1.12–1.35%. This model describes the variation of the LiBr mole fraction with temperature within the mole fraction range of IL aqueous solutions with small RMSE values. The fitting parameters, correlation errors, and R-squared are presented in Table . Comparing the RMSE values of model 1 and model 2, it can be concluded that model 2, which prioritized temperature, has a better prediction ability for experimental data. It can be found that the influence of the temperature on solubility is very important. The model that gives priority to the temperature can describe the solubility more accurately.

6. First-Order Fitting Parameters of Model 2.

x 2	A	B	C	RMSE	R 2
[EMIM][OAc]
0.020	1.1981	–59.5817	–0.1775	0.001934	0.99
0.015	1.0502	–53.0250	–0.1555	0.001881	0.99
0.010	0.9144	–47.0670	–0.1352	0.002843	0.97
0.008	0.9782	–49.7835	–0.1448	0.002843	0.97
0.005	0.8613	–44.4502	–0.1274	0.002683	0.98
0.001	1.0607	–53.7624	–0.1569	0.002527	0.98
[EMIM]Br
0.020	1.0237	–52.1650	–0.1514	0.003153	0.97
0.015	1.1122	–56.2692	–0.1645	0.002941	0.97
0.010	1.1032	–55.9122	–0.1631	0.002739	0.98
0.008	1.0731	–54.5375	–0.1587	0.002764	0.98
0.005	1.0680	–54.3504	–0.1579	0.002891	0.97
0.001	1.0578	–53.9294	–0.1564	0.002766	0.98
[BMIM]Br
0.020	1.2633	–63.1895	–0.1870	0.002550	0.98
0.015	1.1411	–57.6369	–0.1688	0.002713	0.98
0.010	1.1604	–58.5108	–0.1717	0.002691	0.98
0.008	0.9635	–49.5626	–0.1424	0.003232	0.97
0.005	0.9058	–46.9225	–0.1338	0.003175	0.97
0.001	0.9594	–49.4664	–0.1417	0.003158	0.97

On the basis of the Apelblat model, the effect of IL concentration in water is considered. We modified the model to the following

$$A=A_1+A_2/x_2+A_3/{x_2}^2+A_4/{x_2}^3+A_5/{x_2}^4$$ 8

$$B=B_1+B_2/x_2+B_3/{x_2}^2+B_4/{x_2}^3+B_5/{x_2}^4$$ 9

$$C=C_1+C_2/x_2+C_3/{x_2}^2+C_4/{x_2}^3+C_5/{x_2}^4$$ 10

where x ₂ represents the mole fraction of IL in water, and A _i , B _i , and C _i (i = 1, 2, 3, 4, or 5) are the parameters of eqs –, which are called the second-order fitting parameters of eq . The second-order dissolution parameters are determined by fitting the mole fraction of IL in water and A, B, C. The solubility calculation results are shown in Table S3, and the fitting parameters and errors are listed in Table .

7. Second-Order Fitting Parameters of Model 2.

parameters	[EMIM][OAc]	[EMIM]Br	[BMIM]Br
A 1	2.5545	0.3539	1.1233
A 2 × 10	–0.4320	0.2246	0.0648
A 3 × 103	0.3837	–0.2125	–0.1036
A 4 × 106	–1.2270	0.6903	0.3865
A 5 × 109	0.8848	–0.4996	–0.2895
R 2	0.99	0.94	0.90
RMSE	0.0112	0.0073	0.0419
B 1	–119.2520	–21.1119	–56.8061
B 2	1.9004	–1.0400	–0.2954
B 3 × 102	–1.6870	0.9826	0.4716
B 4 × 104	0.5398	–0.3190	–0.1758
B 5 × 107	–0.3894	0.2308	0.1317
R 2	0.99	0.94	0.90
RMSE	0.4753	0.3327	1.9035
C 1	–0.3805	–0.0521	–0.1662
C 2 × 103	6.4641	–3.3296	–0.9638
C 3 × 104	–0.5742	0.3151	0.1541
C 4 × 106	0.1836	–0.1024	–0.0575
C 5 × 1010	–1.3242	0.7409	0.4305
R 2	0.99	0.94	0.90
RMSE	0.0017	0.0011	0.0062

The fitting results for the Apelblat model show good agreement with the experimental values, as shown in Figure . It can be observed that the content of LiBr increases with the increase in the component concentration of the IL in the mixed solution. And when [EMIM]­[OAc] is added, the growth trend is the largest, followed by [EMIM]­Br, and finally [BMIM]­Br. The similarity between the first-order fit and second-order fit of the Apelblat model is very high. Therefore, the second-order fitting is successful, and parameters A, B, C can be calculated from the mole fraction of IL in water; these parameters can calculate the solubility of LiBr at different temperatures.

6.

Mole fraction curve of the LiBr (1) + ILs (2) + H₂O (3) ternary system (T = 293.15 K-323.15 K). (a) [EMIM]­[OAc], (b) [EMIM]­Br, and (c) [BMIM]­Br.

4.3. COSMO-SAC Model

The COSMO-SAC model , is a predictive model that can be used to correct for the nonideality of solutions. To further investigate the effects of different ILs on the solubility of LiBr in water, the COSMO-SAC model was employed to predict the solubility data for the ternary system LiBr + ILs + H₂O. COSMO-SAC bridges quantum mechanics and macroscopic thermodynamics by calculating segment interactions using surface charge densities derived from the COSMO calculations. It avoids the reliance on predefined interaction parameters, making it suitable for novel ionic liquids or complex solvents where experimental data are scarce. In the COSMO-SAC model, the activity coefficients of molecular fragments are calculated by calculating the solvation free energy of the obtained solution molecules. The expression is as follows

$$\ln {\gamma }_{i/s}=n_i\left\{\sum _{\sigma }{p}_i({\sigma }_n){\mathrm{\Gamma }}_i({\sigma }_n)\exp \left[\frac{-\mathrm{\Delta }W({\sigma }_m,{\sigma }_n)}{\mathit{RT}}\right]\right\}$$ 11

$$\ln {\mathrm{\Gamma }}_i({\sigma }_m)=-\ln \left\{\sum _{{\sigma }_n}{p}_i({\sigma }_n){\mathrm{\Gamma }}_i({\sigma }_n)\exp \left[\frac{-\mathrm{\Delta }W({\sigma }_m,{\sigma }_n)}{\mathit{RT}}\right]\right\}$$ 12

$$\ln {\mathrm{\Gamma }}_s({\sigma }_m)=-\ln \left\{\sum _{{\sigma }_n}{p}_s({\sigma }_n){\mathrm{\Gamma }}_s({\sigma }_n)\exp \left[\frac{-\mathrm{\Delta }W({\sigma }_m,{\sigma }_n)}{\mathit{RT}}\right]\right\}$$ 13

$$\mathrm{\Delta }W({\sigma }_m,{\sigma }_n)=\left(\frac{{\alpha }^{\prime }}{2}\right){({\sigma }_m+{\sigma }_n)}^2+c_{\mathrm{hb}}\max [0,{\sigma }_{\mathrm{acc}}-{\sigma }_{\mathrm{hb}}]\min [0,{\sigma }_{\mathrm{don}}+{\sigma }_{\mathrm{hb}}]$$ 14

where n _i is the effective segment number, which is equal to the ratio of the surface area of molecule i to the effective segment surface area. p _i (σ _n ) and p_s (σ _n ) represent the probability of finding a fragment of the surface charge density σ _n in pure liquid i and solution S, respectively, that is, σ-profile. Γ­(σ _m ) and Γ _s (σ _m ) are the activity coefficient of the fragment of charge density in pure fluid i and solution S, respectively. ΔW(σ _m ,σ _n ) is the exchange energy between the fragments m and n. R is the universal gas constant, and T is the temperature. The c _hb and σ_hb are the energy-type constant and cutoff value for the hydrogen-bonding interaction, respectively. The σ_acc and σ_don are the maximum and minimum values of surface charge density, respectively. α′ accounts for the misfit energy.

The size and shape differences of the molecules are accounted for in the combinatorial part and calculated by the Staverman–Guggenheim term as follows

$$\ln {\gamma }_{i/S}^{\mathrm{SG}}=\ln \left(\frac{\phi }{x_i}\right)+\frac{z}{2}{q}_i\ln \left(\frac{{\theta }_i}{{\phi }_i}\right)+l_i-\frac{{\phi }_i}{x_i}\sum _j{x}_j{l}_j$$ 15

$${\theta }_i=\frac{x_i{q}_i}{\sum _j{x}_j{q}_j};{\phi }_i=\frac{x_i{r}_i}{\sum _j{x}_j{r}_j}$$ 16

$$l_i=\frac{z}{2}[(r_i-q_i)-(r_i-1)]$$ 17

$$r_i=\frac{V_i^{\mathrm{COSMO}}}{r};q_i=\frac{A_i^{\mathrm{COSMO}}}{q}$$ 18

In the above expressions, q _i and r _i are related to the cavity volume of component i and the total surface area of molecule i obtained from the COSMO file. r = 66.69 × 10^–3 nm³,q = 79.53 × 10^–2 nm². z is usually 10; x _i is the mole fraction of component i.

All of the equations for determining the activity coefficient have been provided. Parameters used in the COSMO-SAC model are from the literature. The application of COSMO-SAC is based on the establishment of σ-profile data for ionic liquids or solvents. This study was obtained through the DMol3 analysis in Materials Studio. The COSMO-SAC model is not suitable for very high pressures (>25 kbar) or high temperatures (>423.15 K). It can be modified in conjunction with molecular dynamics simulations. It should be noted that the implicit treatment of hydrogen bonding by COSMO-SAC may lead to inaccuracies in strongly polar solvents.

The COSMO-SAC solvent model can be applied with the DMol3 module in Materials Studio (MS) to calculate the surface charge density distribution (σ-profile) and frontier orbital levels, which describe intermolecular interactions. As shown in Figure , the horizontal coordinate represents the charge density σ, and the vertical coordinate represents the probability P(σ) of the charge density distribution; σ < −0.0082 e/Ų indicates the hydrogen-bond donor region, while σ > 0.0082 e/Ų indicates the hydrogen-bond acceptor region, reflecting the strengths of the anions and cations as hydrogen-bond donors and acceptors, respectively. The further the peaks deviate from ±0.0082 e/Ų, the stronger the capacities for hydrogen-bond donation or acceptance. It is evident that the hydrogen-bond donor and acceptor abilities of water are relatively balanced. The [EMIM]⁺ cation exhibits a more pronounced peak at −0.007 e/Ų compared to [BMIM]⁺, indicating that it has a slightly stronger hydrogen-bond donor capability. The order of potential hydrogen-bond acceptors and donors is as follows: [OAc]⁻ > [Br]⁻ and Li⁺ > [EMIM]⁺ > [BMIM]⁺; see Figure a. This sequence suggests that Li⁺ and [OAc]⁻ can form the most stable hydrogen bonds in solution, which could enhance the solubility of LiBr. A more obvious graphical representation is shown in Figure b. The ability to form strong hydrogen bonds is as follows: [EMIM]­[OAc] > [EMIM]Br > [BMIM]­Br.

7.

Surface charge density distribution (σ-profile): (a) anions and cations; (b) ionic liquids, lithium bromide, and water.

In addition, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) can also well present the interaction between molecules. The parameters are listed in Table S4. Low LUMO levels correspond to strong electron acceptor capabilities. High HOMO levels correspond to a strong electron donor capacity. As shown in Figure , [EMIM]⁺ has the lowest LUMO, and [OAc]⁻ has the highest HOMO. For ionic liquids, the ability to form strong electron pairs is as follows: [EMIM]­[OAc] > [EMIM]Br > [BMIM]­Br. This is consistent with the analysis of hydrogen-bond strength and the solubility enhancement order obtained from the experiment.

8.

Highest occupied and lowest unoccupied molecular orbitals for ILs (HOMO/LUMO).

The activity coefficient of the solute was calculated by COSMO-SAC, and the solubility of LiBr was predicted by the formula of the solid–liquid equilibrium. In the solid–liquid equilibrium, the solid solubility is calculated according to the following equation

$$\ln ({\gamma }_i{x}_i)=\frac{\mathrm{\Delta }{H}_{\mathrm{m}}^{\mathrm{fus}}}{R}\left(\frac{1}{T_{\mathrm{m}}}-\frac{1}{T}\right)-\frac{\mathrm{\Delta }{C}_{\mathrm{pm}}}{R}[\ln \left(\frac{T_{\mathrm{m}}}{T}\right)-\frac{T_{\mathrm{m}}}{T}+1]$$ 19

where γ _i denotes the activity coefficient, x _i signifies the mole fraction of the solute, ΔH _m is the enthalpy of fusion, quantified in J·mol^–1, ΔC _pm is the isobaric heat capacity difference between the solid and liquid states of LiBr solute, expressed in J·mol^–1·K^–1, T _m is the melting point, and T is the system temperature; the unit is K. The gas constant R is utilized as 8.314 J·mol^–1·K^–1. The melting point of LiBr is 825.15 K. Detailed predictions for the solubility data are shown in Table , and the maximum of AAD is 7.56%. The enthalpy of fusion and the isobaric heat capacity are set as adjustable parameters, predicted by COSMO-SAC. They are independent of temperature and IL concentration, which are averages over the temperature range, shown in Table .

8. Fusion Enthalpy and Isobaric Heat Capacity of LiBr in IL Aqueous Solution.

ILs	ΔH m (J·mol–1)	ΔC pm (J·mol–1·K–1)
[EMIM]Br	26745.86	0.7565
[EMIM][OAc]	26796.14	0.7582
[BMIM]Br	27343.08	0.7974

Additionally, the relative error between the predicted value and the experimental value is shown in Figure ; positive deviations occur at lower mole fractions of LiBr, and negative deviations occur at higher mole fractions. The results show that the COSMO-SAC model demonstrates an acceptable predictive accuracy. However, it exhibits relatively significant deviations compared to other models. These deviations primarily originate from its parameter settings and system complexity. Specifically, the COSMO-SAC employs fixed parameters obtained from quantum chemical calculations, which are simultaneously used for predicting solubility for specific systems without temperature-dependent adjustments. This approximation leads to error accumulation across wide temperature ranges. Meanwhile, systems with intricate molecular interactions also present computational challenges, which constrain accuracy and predictive capability.

9.

Relative error between the experimental value and the calculated value of the COSMO-SAC model.

4.4. NRTL Model

NRTL model is an activity coefficient model widely used in chemical thermodynamics calculation, proposed by Renon and Prausnitz. , It can predict the thermodynamic behavior of nonideal solutions by describing the nonrandom interactions between molecules in the liquid phase. It is suitable for polar systems, partially miscible systems, and azeotrope systems. NRTL model is based on the theory of local composition, which holds that the interaction between molecules in solution is not completely random, but there is a phenomenon of local molecular aggregation. The NRTL model is calculated as follows

$$\ln {\gamma }_i=\frac{\sum _j({\tau }_{\mathit{ji}}{G}_{\mathit{ji}}{x}_j)}{\sum _k(G_{\mathit{ki}}{x}_k)}+\sum _j\frac{G_{\mathit{ij}}{x}_j}{G_{\mathit{kj}}{x}_k}\left[{\tau }_{\mathit{ij}}-\frac{\sum _i({\tau }_{\mathit{ij}}{G}_{\mathit{ij}}{x}_i)}{\sum _k(G_{\mathit{kj}}{x}_k)}\right]$$ 20

$${\tau }_{\mathit{ij}}=\frac{g_{\mathit{ij}}-g_{\mathit{ji}}}{\mathit{RT}}=\frac{\mathrm{\Delta }{\lambda }_{\mathit{ij}}}{\mathit{RT}}$$ 21

$$G_{\mathit{ij}}=\exp (-{\alpha }_{\mathit{ij}}{\tau }_{\mathit{ij}})$$ 22

$${\alpha }_{\mathit{ij}}={\alpha }_{\mathit{ji}}$$ 23

α is an empirical parameter, with a value ranging from 0.20 to 0.47. In this article, α = 0.20. Δλ _ij is the energy parameter of binary interaction. The binary interaction energy parameter Δλ _ij can be obtained by combining eqs –, and the results are listed in Table .

9. Binary Interaction Parameters of the Ternary System in the NRTL Model.

i	j	Δλ ij	Δλ ji	RMSE	R 2
LiBr + [EMIM][OAc] + H2O
LiBr	[EMIM][OAc]	–8865.81	2407.03
LiBr	H2O	8291.95	–19046.02	0.0065	0.86
H2O	[EMIM][OAc]	6720.13	–19046.02
LiBr + [EMIM]Br + H2O
LiBr	[EMIM]Br	–1475.13	698.39
LiBr	H2O	7518.96	–18850.23	0.0065	0.87
H2O	[EMIM]Br	1454.54	2282.15
LiBr + [BMIM]Br + H2O
LiBr	[BMIM]Br	1765.60	28153.87
LiBr	H2O	8339.35	–19348.51	0.0064	0.87
H2O	[BMIM]Br	–1080.31	17935.25

The results show that six parameters are needed to reproduce the experimental solubility of the ternary system. Although the solubility data obtained at high temperatures are slightly skewed, the overall description is acceptable. The maximum AAD value of the NRTL model is 1.99%, and the maximum RMSE value is 0.0065. Detailed calculation values are shown in Table S5. The results show that the total error of NRTL is smaller than that of COSMO-SAC. The enthalpy of fusion and the difference between isobaric heat capacity required during the calculation are difficult to find. However, COSMO-SAC predictions can be calculated directly by skipping experiments, as shown in Table . Therefore, the joint calculation of COSMO-SAC and the typical activity coefficient model will be the future trend.

5. Conclusions

In this research, the solubility of LiBr was investigated in IL aqueous solutions over a wide composition range at various temperatures. To verify the experimental method, the solubility of an aqueous lithium bromide solution was measured, which is consistent with the available literature data. Through COSMO-SAC modeling and molecular interaction analysis, the study revealed that the anion hydration capacity critically determines LiBr solubility in IL solutions. The optimal combination involved cations with short alkyl chains and strong hydrophilic anions. Three ionic liquids were identified as effective additives for H₂O + LiBr systems: [EMIM]­Br, [EMIM]­[OAc], and [BMIM]­Br. It was found that the addition of three kinds of ILs can increase LiBr solubility to varying extents, which has a high possibility of performance alleviating the crystallization problem of LiBr in the system. The solubility decreased in the tested system in the following order: [EMIM]­[OAc] > [EMIM]Br > [BMIM]­Br. At the typical operating temperature for the absorber of 303.15 K, the maximum liquid-phase composition expanded from x ₁ = 0.2509 (in pure water) to x ₁ = 0.2697 with [EMIM]­[OAc], followed by [EMIM]Br (x ₁ = 0.2570), and the narrowest for [BMIM]Br (x ₁ = 0.2557), highlighting the critical role of IL selection. Moreover, the study shows that longer alkyl chains and weak hydrogen-bonding ability will reduce the solubility of the test system.

Additionally, the experimental data showed strong agreement with the four-parameter empirical model and the Apelblat model and were predicted by the COSMO-SAC and NRTL models. These findings provide essential phase equilibrium data and modeling tools to advance working fluid design in absorption refrigeration.

Importantly, the enhanced performance of ionic liquids (ILs) demonstrates their potential to transform industrial absorption chillers. For engineering applications, adding a small amount of ionic liquid to the traditional H₂O/LiBr system can change the liquid-phase composition range. Expanding the operating range can reduce the level of LiBr crystallization-related maintenance. This not only enables energy-saving, high-concentration operation but also enhances system reliability to minimize downtime.

The measurement of solubility is the first step of research in this field; future work will prioritize mixed solution properties, dynamic cycling tests, and cost–benefit analyses.

The data supporting the findings of this study are included in this article and its Supporting Information.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c00488.

• Original experimental data (Table S1); the calculation results of second-order fitting for model 1 (Table S2); the calculation results of first-order fitting and second-order fitting for model 2 (Table S3); orbital energy level analysis of ionic liquids (Table S4); the calculation results of NRTL model (Table S5); and error range comparison (Table S6) (PDF)

Z.W.: Conceptualization, formal analysis, investigation, software, and writingreview and editing. C.H.: Formal analysis, software, and writingreview and editing. L.L.: Experiment and data curation. J.C.: Validation and writingreview and editing. Y.L.: Validation and review and editing. Q.Y.: Supervision, review and editing. J.L.: Supervision, data curation, resources, and writingreview and editing.

The authors declare no competing financial interest.