Modelling study on phase equilibria behavior of ionic liquid-based aqueous biphasic systems

The ability to predict the phase equilibria behavior is of crucial relevance in the early design stage of biphasic liquid-liquid systems. Ionic liquid-based aqueous biphasic systems (IL-ABS) have demonstrated superior performance in many applications such as the recovery of bio-products and the recycling of hydrophilic ILs from aqueous solutions. In order to better utilize these novel biphasic liquid-liquid systems, modelling studies on phase equilibria behavior are carried out in this work. First, the IL database developed in our previous work is extended to these unconventional biphasic systems. In total, 17,449 experimental binodal data points covering 171 IL-ABS at different temperatures (278.15 K-343.15 K) are collected. Then, all involved IL-ABS are correlated using a popular three-parameter mathematical description and the optimal parameters of each IL-ABS are obtained. Afterwards, we try to build a linear group contribution (GC) model to predict the phase equilibria behavior of IL-ABS, but it fails due to the high complexity of these biphasic systems. For this reason, we finally turn to applying a well-known machine learning algorithm, i.e., artificial neural network (ANN), to build a nonlinear GC model for such a purpose. This model gives a mean absolute error (MAE) of 0.0175 and squared correlation coefficient (R) of 0.9316 for the 13,789 training data points, and for the 3,660 test data points they are 0.0177 and 0.9195, respectively. The results indicate that the proposed nonlinear ANN-GC model, to some extent, is capable to predict the phase equilibria behavior of IL-ABS. Besides the efforts of building GC models, we also discuss somemain issues that govern the phase equilibria behavior of ILABS, which could be a guidance in the design of IL-ABS. 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).


Introduction
Ionic liquids (ILs) are being considered as potential alternatives to conventional organic solvents due to their attractive properties such as negligible volatility, non-flammability, exhibiting good solubility and selectivity for a wide range of organic and inorganic chemicals (Rogers and Seddon, 2003). The replacement of volatile organic solvents by ILs is able to lower the energy consumption in solvent recycle and reduce the solvent loss to the atmosphere, thereby decreasing the environmental footprint and even reducing the cost of the process in some cases (Chen et al., 2019a(Chen et al., , 2019bLiu et al., 2020;Lei et al., 2021). Moreover, ILs have been recognized as ''designer solvents" (Plechkova and Seddon, 2007) since their properties can be tailored by tuning the molecular structure and this feature allows the possibility of designing suitable ILs with desired properties for specific tasks. So far, ILs have been widely studied in many fields such as chemistry, pharmaceuticals and materials, where they can play different roles such as solvents in separations , media and/or catalysts in reactions (Vekariya, 2017;Meng et al., 2019) and functional material (Liu and Jin, 2016).
Currently, IL-based separations are the most widely studied approaches involving ILs. Among them, IL-based liquid-liquid extractions (LLE) and IL-based aqueous biphasic systems (ABS) extractions are being paid more attention in many separation and purification processes, particularly in bioprocesses. To date, these separation approaches have been applied to recover various bioproducts ranging from small organic compounds (e.g., phenolic acids, alkaloids, amino acids, lipids and other hydrophobic compounds) (Bi et al., 2012;Pei et al., 2012;Zafarani-Moattar and Hamzehzadeh, 2011;Wu et al., 2015;Wang et al., 2005;Absalan et al., 2010;Yang et al., 2009Yang et al., , 2012Yang et al., , 2013Liang et al., 2013) to more complex molecules (e.g., nucleic acids, proteins, enzymes, antibodies) (Fister et al., 2015;Pei et al., 2009;Lin et al., 2013;Yan et al., 2014;Ren et al., 2015;Xu et al., 2014;Ito et al., 2013;Dreyer and Kragl, 2008). A variety of ILs have been synthesized for such purposes by many researchers, especially Coutinho's group from University of Aveiro. Recently, a critical review on IL-mediated extraction and separation processes for bioactive compounds was published and it demonstrates that, if properly selected/designed, ILs can provide higher extraction yields and purification factors compared to conventional organic solvents . Generally, LLE with hydrophobic water-immiscible ILs are initially used for water-rich biomass extracts (Absalan et al., 2008). However, the number of available hydrophobic ILs is much more limited when compared to hydrophilic ones and they tend to be very costly . On the other hand, ABS with hydrophilic water-miscible ILs are usually recognized as biocompatible, non-denaturing and benign media for cells, cell organelles and biologically active substances, and they have demonstrated superior performance as alternative extraction platforms. So far, most of the successfully extractions using ILs for natural compounds recovery from biomass are carried out by this type of IL-based technique .
ABS refer to two aqueous-rich phases which are ternary systems composed of water and two solutes. They are clean alternatives for traditional organic-water solvent extraction systems and have gained an increasing interest due to their potential in biotechnological applications (Raja et al., 2011). The main advantages of ABS technique can be summarized as: (i) they provide mild conditions that do not harm or denature unstable/labile biomolecules; (ii) they enable rapid phase separation and compounds partition, and have far lower interfacial stress than water-organic solvent systems which allow less damage to the molecules to be extracted; (iii) specialized systems can be tailored by varying factors (e.g., temperature, presence of certain ions) to favor the enrichment of a specific compound into one of the two phases; (iv) they are able to give high recovery yield and is easily to scale up (Raja et al., 2011;Iqbal et al., 2016;Grilo et al., 2016;Goja et al., 2013). To date, ABS have been successfully used as non-denaturing and benign separation media to recover various biomolecules such as proteins, enzymes and antibiotics from crude cell extracts or other mixtures (Asenjo and Andrews, 2012;Nadar et al., 2017;Magalhães et al., 2020). However, challenges such as how to obtain reliable phase behavior predictions of ABS, how to reuse of the phase-forming components and how to incorporate other operation units in downstream processing need to be addressed to take their place at the industrial level (Magalhães et al., 2020). Besides these, find low cost, low toxicity and high-performance phase forming agents is another issue needs to be taken into account.
ABS with water-miscible ILs were firstly proposed by Rogers and co-workers (Gutowski et al., 2003) in 2003 and these systems are reported to have potential to replace the typical polymer-based ABS due to their unique system properties such as low toxicity, low viscosity, and tailored selectivity. The main applications of ILbased ABS can be summarized as: (i) the recovery and recycling of ILs from aqueous solutions, (ii) new separation techniques and (iii) carrying out metathesis reactions in the formation of new ILs (Freire, 2016). To date, most ILs investigated in ABS are composed of well-known cations (e.g., imidazolium, pyridinium, ammonium, phosphonium) and anions including halogens, sulphates, sulphonates, alkanoates, tetrafluoroborate and triflate. On the other hand, inorganic salts such as NaH 2 PO 4 , K 3 PO 4 and (NH 4 ) 2 SO 4 are the most widely used second phase-forming agents in IL-based ABS, while a certain number of more benign species such as organic salts, amino acids, carbohydrates and polymers are being studied as alternatives to high-charge-density inorganic salts in the formation of second phase . As both IL and phase-forming agent have influence on the system's properties, it is challenging to rationally design IL-based ABS for specific tasks. Therefore, a systematic understanding of the relationship between the property of IL-based ABS and its composition is essential to promote its wide application. The optimal design of compounds through manipulating properties at the molecular level is often the key to considerable scientific advances and improved process systems performance (Alshehri et al., 2020). Recently, the computer-aided ionic liquid design (CAILD) method has been widely applied to design suitable ILs for various processing tasks (Song et al., 2018(Song et al., , 2019Chen et al., 2018aChen et al., , 2018bChen et al., , 2020cLiu et al., 2021). When using CAILD for the optimal design of IL-based ABS, the development of reliable models to describe the property of these systems is essential.
Rogers and co-workers (Gutowski et al., 2003) were the first to use a mathematical description (Eq. (1)) to correlate the experimental coexisting curve of IL-based ABS which was initially proposed by Merchuk et al. (Merchuk et al., 1998) to describe polymer-based ABS. Then, many researchers used Eq. (1) to describe various IL-based ABS since it can satisfactorily reproduce their experimental binodal boundaries. Zafarani-Moattar and Hamzehzadeh Hamzehzadeh, 2009, 2010) further expressed the dependence of the coefficients A, B and C of Eq. (1) as a function of temperature and as a function of pH, respectively. They found that these temperature/pH associated descriptions are able to provide good correlations of the binodal experimental curves with different temperature and pH. Nonetheless, current correlation studies of the binodal experimental curves are limited to a single ABS. It means that different IL-based ABS have their own correlation coefficients, and they cannot be used interchangeably. Therefore, a mathematical description with same coefficients that is capable to describe all IL-based ABS is highly desirable due to the fact it can provide quantitative information of structure-property for the optimal design of IL-based ABS. In this regard, group contribution (GC) methods may have the potential since both IL and phase-forming agent in ABS can be described as the occurrences of functional groups in the molecule. In addition, GC models can be easily combined in the computer-aided design method, (Gani, 2019) which make it possible to use CAILD for the optimal design of IL-based ABS.
Most properties are initially associated with the group numbers using a linear GC model. However, some of them cannot be properly described by linear model expressions and nonlinear GC models are needed to achieve more reliable predictions in such cases. In this respect, machine learning (ML) algorithms such as artificial neural networks (ANN) and support vector machine that are capable to build complex nonlinear GC or QSPR models have been widely used for various properties including gas solubility (Sedghamiz et al., 2015;Tatar et al., 2016;Faúndez et al., 2016;Zhao et al., 2016;Song et al., 2020), surface tension (Mulero et al., 2017) and toxicity of ILs (Cao et al., 2018;Wang et al., 2021). ANNs have also been used by many scientists in the phase equilibrium calculations. So far, no investigations of using GC methods to study IL-based ABS have been reported, it is the pur-pose of this work to investigate such possibilities. Besides the efforts of building GC models, we also discuss some main issues that govern the phase equilibria behavior of IL-ABS, which could be a guidance in the design of IL-ABS.

Experimental data sets
For the purpose of building GC models to predict the phase equilibria behavior of IL-based ABS, the IL database developed in our previous works (Chen et al., 2019a(Chen et al., , 2020b(Chen et al., , 2020c) is extended to these unconventional aqueous biphasic systems. In total, 17,449 experimental binodal data points of 171 IL-based aqueous biphasic systems covering 56 ILs and 43 s phase-forming agents (summarized in Table 1) from 278.15 K to 343.15 K are collected. All involved IL-ABS together with their experimental binodal data are provided in the Supporting Information. Similar to our previous work of developing GC models for physical properties, (Chen et al., 2019a(Chen et al., , 2020b(Chen et al., , 2020c IL molecules in ABS are also decomposed into three types of building groups (i.e., cation cores, cation substituents, anions) considering the design space and the flexibility of ILs. For the second phase-forming agents, organic/inorganic salts are decomposed into cations and anions, while amino acids and carbohydrates are regarded as whole molecular groups. It should be noted that cations and anions decomposed from ILs and organic/inorganic salts are different. In order to distinguish them, we use salt cation(s) and salt anion(s) to, represent the cations and anions decomposed from organic/inorganic salts in this work. Fig. 1 gives the structure of IL-ABS described by building blocks from the concept of GC model.
In total, 71 different building groups are obtained from the decomposition of all involved ILs and the second phase-forming agents, wherein 34 are IL building groups (6 cation cores, 23 anions, 5 substituents) and the remaining 37 groups belonging to the second phase-forming agents including inorganic/organic salts, carbohydrates, amino acids, as shown in Table 2. All building groups with their numbers of occurrence in each IL-ABS are given in the Supporting Information. Testing is an essential part of the model development and therefore we divide the experimental binodal data into a training set and a test set. The training set accounts for nearly 80% of the data points and the remaining data points (test set) are used to evaluate the predictive performance of the developed linear/nonlinear GC model. The training set and test set are, respectively, provided in Table S4 and Table S5 (Supporting  Information).

Linear model
In this section, we use a three-parameter mathematical description, as shown in Eq. (1), to fit the experimental coexisting curves of IL-ABS. This equation was initially proposed by Merchuk et al. (Merchuk et al., 1998) to describe polymer-based aqueous biphasic systems and then Rogers and co-workers (Gutowski et al., 2003) were the first to introduce it to IL-based aqueous biphasic systems. Since then, this equation has been successfully applied to describe various IL-ABS. Zafarani-Moattar and Hamzehzadeh Hamzehzadeh, 2009, 2010) and Wang et al. (Wang et al., 2010) further extended this equation to IL-ABS with different temperatures and the three fitting parameters of Eq. (1) are expressed as a function of temperature in a linear form as Eqs. (2)-(4).
where Y and X are the weight fraction percentages of the IL and the second phase-forming agent and A, B and C are fitting parameters which can be calculated from following T-dependent equations.
where T represents the temperature (K) of the studied ABS system and T 0 denotes the reference temperature (=273.15 K). A 0 , A 1 , B 0 , B 1 , C 0 and C 1 are T-independent adjustable parameters which can be directly obtained by correlating the experimental data points into Eq.
(1) or can be indirectly calculated from Eq. (5) when using the GC-based linear model to describe the IL-ABS. For the first of all, each of the involved IL-ABS are, separately, correlated using Eq. (1). The resulting mean absolute error (MAE) of the correlation is 0.0086 with a squared correlation coefficient (R 2 ) of 0.9849, showing that the IL-ABS can be described well by this three-parameter model. The comparison between the experimental and Eq. (1)-calculated weight fraction of IL in ABS is presented in Fig. 2 and the error between experimental value of IL weight fraction (x Exp: IL ) and correlated value of IL weight fraction (x Cor: IL ) in ABS from Eq. (1) is given in Fig. 3. For a better illustration of the correlation performance of this three-parameter equation, we also provide the histogram of the regression deviations, as shown in Fig. 4. The obtained parameters (A 0 , A 1 , B 0 , B 1 , C 0 , C 1 ) of all studied IL-ABS are provided in Table S3 (see Supporting Infor mation). Some calculation examples of Eqs. (1)-(4) using these parameters are presented in Figs. 9-12. Although Eqs. (1)-(4) with these obtained parameters are able to provide reliable correlations, they are limited to a single IL-ABS. It means that different IL-based ABS have their own correlation coefficients, and they cannot be used interchangeably. Thus, it's impossible to use them to predict the phase equilibria behavior of those experimental data unavailable IL-ABS. In fact, the number of all reported IL-ABS is very small when compared to that of the possible existing IL-ABS, and some of them may have great potential in many specific applications. Therefore, a mathematical description with same coefficients that is capable to describe all IL-based ABS is highly desirable due to the fact it can provide quantitative information of structure-property for the optimal design of IL-based ABS. On the other hand, the introduction of GC methods would significantly improve the design space of IL-ABS, which means that we have more opportunities to find suitable IL-ABS with desired properties. For this purpose, we try to use GC-based method to simultaneously regress all involved IL-ABS. Unfortunately, the proposed GC-based linear model (with a MAE of 0.4827) fails to describe the phase composition of IL-ABS.

Nonlinear GC model
ANN inspired by biological neural systems, currently, are widely used in many technical fields due to their simplicity, flexibility and ability in the modeling systems (Sedghamiz et al., 2015;Lashkarbolooki et al., 2011). It is characterized by layered architec- Table 1 Various IL-ABS with different phase -forming agent(s) involved in this work.

Ionic liquid
The second phase-forming agent tures and feed-forward connections between neurons, or back connections. Weights are assigned to these connections between the neurons of one layer and the next. The benefits of using ANN can be summarized as: (i) ANN can learn organically. This means their outputs aren't limited entirely by inputs and they have the ability to generalize their inputs; (ii) nonlinear systems have the capability of finding shortcuts to reach computationally expensive solutions; (iii) ANN have the potential for high fault tolerance; (iv) ANN can do more than routing around parts of the network that no longer operate. (https://www.allerin.com/blog/4-benefits-ofusing-artificial-neural-nets) The advantages of ANN are highlighted when a large experimental data in the wide ranges of variables is available. To date, a series of ANN-based nonlinear GC models have been developed for the prediction of various properties and results show that they are able to provide better performance than linear models (Zhao et al., 2014;Peng and Picchioni, 2020). For this reason, here we try to use ANN for building a nonlinear GC model to describe the phase properties of IL-ABS. In this work, a popular ANN architecture that comprises of a three-layer feed forward network is used (see Fig. 5). The input layer reads the structure information of IL and the second phase-forming agent involved in IL-ABS (denoted as 71 group numbers) and the weight fraction of IL and the second phase-forming agent and the temperature, which totally giving an input vector with a size of 73 Â 1. The hidden layer transfers and delivers this input information to the output layer where the phase composition of IL-ABS is estimated, and the summation of errors between experimental and model-estimated weight fractions of IL are quantified. For a given input vector p, the output from the hidden layer f 1 (a 1 ) is calculated by Eq. (6) and the output of the output layer f 2 (a 2 ) is determined by Eq. (7).
As reported, (Song et al., 2020) combining the application of tansig transfer function (see Eq. (8)) in the hidden layer with the application of purelin transfer function (see Eq. (9)) in the output layer is a very effective way to build a three-layer neural network in MATLAB. For this reason, such a combination is also employed to build the ANN-GC model in this work.
In ANN, selecting a suitable number of neurons in the hidden layer is essential due to the network with too few neurons may not be powerful enough for achieving good predictions, while the network with too large number of neurons tends to perform over-fitting. Typically, this number is specified before the regression of the weight matrices (W 1 , W 2 ) and bias vectors (b 1 , b 2 ). In order to identify the number of neurons in the hidden layer, we train the ANN-GC model with a series of neurons in the hidden  layer. Finally, the network with 2 neurones in the hidden layer is identified has the best performance. Based on this number of neurons, weight and bias parameters are optimized using the Levenberg-Marquardt algorithm (in MATLAB), in which the minimization of the summation of absolute errors between the experimental and model-predicted weight fraction of IL in the training dataset is taken as the objective function. The values of W 1 ,W 2 , b 1 , and b 2 are given in the Supporting Information.   This nonlinear GC model gives a MAE of 0.0175 and R 2 of 0.9316 for the 13,789 training data points, and for the 3,660 test data points they are 0.0177 and 0.9195, respectively. The comparison between the experimental and model-predicted weight fraction of the second phase-forming agent for both training set and test set are presented in Fig. 6. Meanwhile, Fig. 7 gives the errors between the experimental (x Exp: agent ) and model-predicted (x Pre: agent ) weight fraction of the second phase-forming agent. For a better illustration of the model performance, we also provide the histogram of the prediction deviations, as shown in Fig. 8. In general, the proposed ANN-GC model is able to describe phase composition of various IL-ABS at different temperature. An example of using this nonlinear ANN-GC model to predict the ternary phase diagram of three different IL-ABS is provided in Appendix.

Results and discussions
From Figs. 1 and 2, it is clear that Eq. (1) can well describe each of the IL-ABS at different temperatures. However, on the other hand, the linear GC model based on this three-parameter mathematical description is unable to simultaneously represent the phase property of IL-ABS. This can be explained by the complexity of these biphasic systems. On the other hand, the proposed nonlinear ANN-GC model provides acceptable MAE and R 2 for both training set (0.0173, 0.9316) and test set (0.0177, 0.9195). Among all predictions from this nonlinear ANN-GC model, most of them have small deviations (close to zero) and only a very limited number of them have absolute errors higher than 0.1 which may be attributed to experimental deviations among different measurements, as shown in Fig. 8. Despite the developed ANN-GC model is able to provide reliable predictions, we should not ignore that unlike the traditional models such as UNIFAC and NRTL, this ANN-GC model    is not derived from thermodynamic principles. Therefore, we use it as a predictive tool/model rather than a thermodynamic model.
Besides the efforts of building linear/nonlinear GC model to describe the phase property of IL-ABS, we also investigate the influence of IL and the second phase-forming agent on the phase formation of IL-ABS from the group level. As we know, the closer to the axis origin a binodal curve is, the greater is the ability of an IL to phase split. Fig. 9 indicates that the ability of IL with different cations to form ABS in the presence of K 2 CO 3 , follow the order: [C 4 mIm] [Cl]. Similar trend has also been observed when using other salts (e.g., K 3 PO 4 , K 2 HPO 4 ) as the second phase-forming agent. (Bridges et al., 2007;Louros et al., 2010) This is due to the phosphonium/ammonium-based ILs have highly shielded charges and mostly located on the heteroatom surrounded by four alkyl chains, which results in a higher tendency toward salting out from water solution. (Bridges et al., 2007) Similarly, the charge of a pyridinium-based IL mostly locates on the nitrogen atom, but it generally has less shielding when compared to the phosphonium /ammonium-based ILs. In contrast, the charge of an imidazolium-based IL disperses evenly along the entire hete-rocycle, and this cation can also interact with water through hydrogen-bonding.  As the other ion in IL, the anion also has influence on the ability of the IL to produce ABS. As reported, the ability of an IL anion to form ABS generally follows the decrease in their hydrogen-bond accepting strength or electron pair donation ability. (Ventura et al., 2009) Fig. 10 presents the experimental phase diagrams of water-K 2 HPO 4 -IL with different anions; it reveals that in the region with low salt concentration, the ability of the anions to form ABS increases in the order: [N (CN)  Similar to many other properties such as viscosity, toxicity of ILs, the cation alkyl chain length also has big influence on the phase behaviour of IL-based ABS. Generally, the hydrophobicity of an IL increases with the increase of the cation alkyl chain length, and therefore ILs with longer cation alkyl side chain tends to have less Fig. 8. Distribution of the prediction error of the nonlinear GC model. Fig. 9. Ternary phase diagrams for ABS composed of chloride-based ILs + K 2 CO 3 +-H 2 O at room temperature. Symbols are experimental data (Zafarani-Moattar and Hamzehzadeh, 2010;Sintra et al., 2014) and lines are calculated values from Eqs.1-4 using the parameters obtained in this work.  [C 4 mIm]-based ILs + K 2 HPO 4 +-H 2 O at room temperature. Symbols are experimental data Mourão et al., 2012; and lines are calculated values from Eqs. (1)-(4) using the parameters obtained in this work. Fig. 11. Ternary phase diagrams for ABS composed of [C n mIm][N(CN) 2 ] + K 3 TO 7 +-H 2 O at room temperature (n = 2,3,4,6). Symbols are experimental data  and lines are calculated values from Eqs. (1)-(4) using the parameters obtained in this work.
Y. Chen, X. Liang, J.M. Woodley et al. Chemical Engineering Science 247 (2022) 116904 solubility in water. For this reason, ILs with longer cation alkyl side chain require less salt for salting-out and are more easily excluded from the salt-rich phase to the ionic-liquid-rich phase.  It means that the ability of the ILs to form ABS generally increases with the increase in cation alkyl chain length, an example of this trend is presented in Fig. 11. It is to be noted that this trend only works under a certain number of the cation alkyl chain (e.g., hexyl, octyl) due to the ABS may not exist when the cation alkyl chain of the ILs is too long. On the other side, temperature also plays an important role on the creation of ABS containing IL. Fig. 12 gives an example of the influence from temperature on the phase diagrams of ionic-liquid-based ABS. Obviously, the lower the temperature, the less the IL and salting-out agent are required for the phase split. This phenomenon has also been observed by other authors and it can be attributed to the fact that the interaction between the IL and water increases with the increase of temperature, and therefore improving their mutual solubilities Hamzehzadeh, 2009, 2010;Wang et al., 2010;Sadeghi et al., 2010). However, it should be noted that temperature has no major influence on the phase separation of some aqueous systems containing IL. Nonetheless, lower temperatures are favourable to induce the formation of IL-ABS is a general agreement . Besides the influences of the cation and anion of the IL, and the temperature on the formation of ABS, the effect of the second phase-forming agent also needs to be taken into accounted in the preparation of IL-ABS. Currently, most studied IL-ABS use conventional salt as the second phase-forming agent, a few of them involving amino acids and carbohydrates. The amount of salt required to produce ABS largely depends on the salting-out strength of the salt. Fig. 13 gives an example of the salt anion influence on the creation of IL-ABS, while the salt cation influence is presented as another example (see Fig. 14). As reported,  salt anions with higher valence have higher saltingout ability than those with lower one because the latter are more hydrated. However, the binodal curves shown in Fig. 13 indicate that salt anions in some IL-ABS do not follow this rule. On the other hand, it seems that the salt cation has little influence on the phase split in IL-ABS. However, salts with different cations exhibit different salting-out capabilities in some other IL-ABS (Shill et al., 2011). In conclusion, there is no general rule to guide the salt cation and anion influence on the formation of ABS, and they need to be care-fully evaluated in the preparation of ABS with different ILs. Nonetheless, the salting-out in IL-ABS is an entropically driven process, as the idea proposed for hydrophobic ionic liquids and a wide range of salts (Tomé et al., 2009;.

Conclusion
The ionic liquid database developed in our previous work has been extended to IL-based aqueous biphasic systems. In total, 17,449 experimental binodal data points covering 171 IL-ABS at different temperatures (278.15 K-343.15 K) are collected. All involved IL-ABS are correlated using a popular three-parameter mathematical description and the optimal parameters of each IL-ABS are obtained. Based on this mathematical description, we try to build a linear GC model to predict the phase equilibria behavior of IL-ABS, but it fails due to the high complexity of these biphasic systems. On the other hand, the proposed nonlinear ANN-GC model gives a MAE of 0.0175 and R 2 of 0.9316 for the 13,789 train- Fig. 12. Ternary phase diagrams for ABS composed of [C 4    and lines are calculated values from Eqs. (1)-(4) using the parameters obtained in this work.  ing data points, and for the 3,660 test data points they are 0.0177 and 0.9195, respectively. The results suggest that this nonlinear GC model, to some extent, can give reliable predictions on the phase equilibria behavior of IL-ABS. This model provides the possibility of using computer-aided design method in the optimal design of IL-ABS, which would significantly improve the opportunity of finding optimal IL-ABS for specific tasks.
Besides the efforts of building GC models, we also discuss some main issues that govern the phase equilibria behavior of IL-ABS. The quaternary phosphonium/ammonium-based ILs have higher ability to create ABS than that of pyridinium and imidazoliumbased ILs, while the ability of an IL anion to form ABS generally follows the decrease in their hydrogen-bond accepting strength or electron pair donation ability. On the other hand, the ability of an IL to produce ABS generally increases with the increase in cation alkyl chain length and lower temperatures are favorable to induce the formation of IL-ABS is a general agreement, although temperature has no major influence on the phase split of some IL-ABS. In addition, salt anions with higher valence are reported have higher salting-out ability than those with lower one because the latter are more hydrated, but some IL-ABS do not follow this rule. Meanwhile, salts with different cations exhibit different salting-out capabilities in different IL-ABS. Therefore, there is no general rule to guide the salt cation and anion influence on the formation of ABS, and they need to be carefully evaluated in the preparation of ABS with different ILs. All conclusions mentioned above could be a guidance in the design of IL-ABS.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.