Model Performances Evaluated for Infinite Dilution Activity Coefficients

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Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX pubs.acs.org/IECR

Model Performances Evaluated for Inﬁnite Dilution Activity Coeﬃcients Prediction at 298.15 K Thomas Brouwer and Boelo Schuur*

Sustainable Process Technology group, Process and Catalysis Engineering Cluster, Faculty of Science and Technology, University of Twente, PO Box 217, 7500AE, Enschede, The Netherlands

*S Supporting Information

fi ffi γ∞ ABSTRACT: The in nite dilution activity coe cient ( i ) is often applied to characterize solvent−solute interactions, and, when accurately predicted, it can also serve as an early-stage solvent selection tool. Ample data are available on the use of a variety of models, which complicates decision making on which model to apply and when to apply it. A comparative study was performed for eight predictive models at 298.15 K, including the Hildebrand parameter and the Hansen solubility parameters. Also, three group contribution methods based on UNIFAC, COSMO-RS, the Abraham model, and the MOSCED model were evaluated. Overall, the MOSCED model and the Abraham model are most accurate for molecular solvents and ionic liquids, respectively, with average relative deviations of 16.2% ± 1.35% and 65.1% ± 4.50%. γ∞ Therefore, cautious decision making based on predicted i in ionic liquids should always be done, because of the expected significant deviations. A MOSCED model for ionic liquids could be a potential approach for higher accuracy.

1. INTRODUCTION coefficients are composition-dependent and a limiting case is where a solute is infinitely diluted in a solvent. The nonideal The global community relies on the chemical industry for the fi production of goods from complex raw materials, such as oil behavior of the solute at in nite dilution is solely induced by solvent−solute interaction, i.e., the effect of the molecular and biomass. The separation processes required in these ffi production routes account for up to 50% of the total energy properties of the solvent on the activity coe cient of the fi 1 ffi solute. The activity coefficient in this limiting case is called the costs in re neries, and improving the e ciency of separations fi ffi γ∞ 12 fi in nite dilution activity coe cient ( i ). can signi cantly reduce the environmental impact of the ffi chemical industry.2 This can only be achieved when the Various methods are in use to estimate activity coe cients. Downloaded via UNIV TWENTE on May 16, 2019 at 11:42:03 (UTC). separation processes are understood on the molecular level, Eight models were evaluated, as these are most commonly which includes a good description of thermodynamic used. Seven of them having many similarities and one has a equilibria. An accurate description of these equilibria is completely separate theoretical framework. Three solvation possible with models such as UNIQUAC and NRTL, but models (SMs) are chosen, which are, in order of increasing

See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. complexity, the Hildebrand parameter, the Hansen solubility requires labor-intensive experimental data. For initial stages of fi process design, including solvent selection and/or design, less- parameter (HSP), and the Modi ed Separation of Cohesive labor-intensive approaches for understanding intermolecular Energy Density (MOSCED) model. These models attempt to interactions are desired. A range of predictive models is describe the intermolecular interaction strength by increasingly available to provide engineers with first estimates for more molecular parameters. The group contribution methods − ff (inter)molecular behavior.3 11 (GCMs) are similar in form to SMs, but di er in origin. GCMs An appropriate indicator of intermolecular interactions attempt to describe the intermolecular interactions by fi ffi underlying thermodynamic equilibria is the infinite dilution empirical tting of binary interaction coe cients of segments activity coefficient.12 Activity coefficients describe the of the interacting molecules. The three GCMs that are thermodynamic nonideality between two substances due to included in this work are the original Universal Quasichemical ffi intermolecular interactions. These intermolecular interactions Functional-group Activity Coe cients (UNIFAC) method, 13−15 fi are induced by van der Waals interactions and electro- and two modi cations thereof (Lyngby and Dortmund). static interactions, such as intermolecular or intramolecular 16 hydrogen bonding effects, consequently causing either Received: February 5, 2019 positive or negative deviation from Raoult’s law. Net attractive Revised: March 29, 2019 interactions result in an activity coefficient (γ) below unity, and Accepted: April 29, 2019 net repulsive interactions result in a γ above unity. Activity Published: April 29, 2019

Figure 1. Number of publications where both the model and activity coefficient is mentioned extracted from Scopus. The search terms where “model” AND “infinite dilution activity coefficient” retrieved on December 3, 2018.

Despite these differences, all of these models still use the same GCMs make use of combinatorial and residual contributions entropic formulations. Next to these, a software package called that find their origin in the Flory−Huggins model; this model the Conductor-like screening model for realistic solvents and the variations thereof are first discussed. (COSMO-RS) is also evaluated. COSMO-RS has an entirely 2.1. Flory−Huggins-Based Models. Nonideal behavior different theoretical framework and does not require any input in mixtures can be induced by intermolecular interactions such parameters from the user besides the molecular structures. as polarity, as well as by shape differences,16 The simplest Similar to GCMs, COSMO-RS also divides molecules in cause of nonideal behavior is due to shape differences without segments. COSMO-RS divides the surface of molecules, as polarity differences. This situation occurs in alkane mixtures calculated by the quantum chemical density functional theory for which activity coefficients can be described by the Flory− (DFT) approach in segments, and calculates the interaction Huggins theory (eq 1), where the combinatorial contribution energy for each segment. The molecular properties are then to the activity coefficient is formulated solely in terms of calculated by taking the integral over all segments. molecular volume differences.25,26 GCMs such as variations on UNIFAC, and COSMO-RS are most commonly applied, as can be seen in Figure 1. However, c Φi Φi lnln1γi = +− this does not imply that these models are always most accurate xxi i (1) γ∞ 6,17−24 in predicting the i . Because the existing literature is where Φ and x are the volume fraction and molar fraction of inconclusive, the aim of this contribution is to extensively i ji i zy compound i,j respectively.z compare the performance of all these fundamentally different j z γ∞ The Flory−kHuggins{ combinatorial approach assumes a very approaches for prediction of the i of (a)polar solutes in (a)polar solvents. The performances of all evaluated models in large number of nearest-neighbor sites, hence ignoring the fact that neighboring sites can be occupied by a segment of the predictions for a variety of chemical systems were evaluated − and explained on the basis of their fundamental assumptions. same molecule. Consequently, the Flory Huggins correlation overestimates the combinatorial contribution.27 The Staver- Examples of such assumptions include that the entropy of the − fi system does not differ from the ideal entropy, that the volume mann Guggeheim modi cation attempts to correct this by of the molecule does not change in a changing environment, or incorporating the probability of vacant sites for polymer that there is no distinction between hydrogen-bond-accepting segments, although the combinatorial term is still over- estimated, because the coordination number of all molecules and hydrogen-bond-donating molecules. 28 fi The extensive evaluation of model performances yielded is set. The Kikic modi cations attempted to correct the correlation by adding an exponent to the number of lattice insight in the applicability of the models for systems with 29 variations in intermolecular interactions and which models give sites, but this resulted in an underprediction of the γ∞ combinatorial term. Recently, Krooshof et al.28 generalized the most accurate description of i at 298.15 K. A heuristic fi approach for the model choice is given for all binary the approach of Guggeheim and set loose the xed combinations of solute and solvent classes, e.g., apolar coordination number. For this approach, the coordination number of all molecules in the system must be additionally compounds, aromatic compounds, halogenated compounds, fi polar aprotic compounds, and polar protic compounds. speci ed. When there is also a difference in the polarity of the molecules in the mixture, a residual correction can be added. 2. THEORETICAL FRAMEWORK This can be described by the Flory−Huggins free-energy χ ffi In this section, all of the models that were compared for parameter ( 12), as equated in eq 2. The activity coe cient γ∞ prediction of i are described. The models can be categorized resulting from both combinatorial and residual terms is given into solvation models, GCMs, linear solvation energy relations, in eq 3. and COSMO-RS predictions that are of statistical thermody- ln γχR =Φ2 namic nature. Because both the solvation models and the i 12 i (2)

B DOI: 10.1021/acs.iecr.9b00727 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX Industrial & Engineering Chemistry Research Article

cR where, initially, α was taken to be 1, although Lindvig et al.9 lnlnlnγγii=+ γ i (3) showed that an α value of 0.6 increases the average accuracy of Starting from eq 3, a wide range of models have been the model. γc γR fi developed that vary in their formulation of i and i .Inthe The Modi ed Separation of Cohesive Energy Density next subsections, the most relevant solvation models and (MOSCED) model may be one of the most-extensive 21 GCMs are described. solvation models. In the MOSCED model, additional 2.2. Solvation Models (SM). In an early attempt to contributions to the Flory−Huggins parameter are considered describe and understand the strength of intermolecular that arise from significant variations in the cybotactic region interactions, Hildebrand7 defined the cohesive pressure or due to the local organization, as a result of electrostatic cohesive energy density (c) as the net result of the sum of all interactions, such as hydrogen bonding. This local organization intermolecular interactions between the molecules. As a causes the geometric mean assumption not to be valid 21 measurable quantity for the cohesive energy density in liquids anymore for highly polar and associating compounds. To below their boiling point, the molar vaporization energy account for hydrogen bonding, the MOSCED model Δ Δ 30 α β ( Uvap) or enthalpy ( Hvap) is considered, and correlated to distinguishes acidic ( )andbasic()contributionsto the Hildebrand parameter (δ), according to eq 4. hydrogen bonding. Similar to the HSP model, the summation of the terms results in the Hildebrand parameter, as can be 32 ΔUvap Δ−HRTvap seen in eq 8. δ ==−c = i i 22iii 2 2 Vm Vm (4) δλτ=++β() α (8) i iλ iτ where Vm is the molar volume of the molecule i. where the dispersion constant and polarity constant are iδ iδ The cohesive pressure is the sum of all attractive identical to the HSP parameters d and P, respectively. In interactions, which must be broken to vaporize the liquid, addition, the interaction between induced dipoles is accounted and large δ values are therefore obtained for highly polar for by the induction parameter, iq. The model furthermore substances and small δ values are obtained for weakly contains two empirical asymmetry factors: ψ and ξ. More interacting substances (e.g., fluorocarbons).30 Considering information on the MOSCED parameters can be found in eqs mixtures, the difference in δ of the constituents of that mixture S1−S8 in the Electronic Supporting Information (ESI).6 The can be interpreted as the difference in nature of these resulting MOSCED-based equation for the Flory−Huggins molecules and may be used as a measure for nonideality. In the parameter is given in eq 9: Hildebrand−Scatchard equation (eq 5),7 the difference in δ is i ij22 i T j T2 used in the expression for the Flory−Huggins free-energy V m ij2 qq()ττ− χ χλλ12 =−+() i parameter ( 12): RT ψ j Ä V ijijÅ TTTT m ij2 ()()ααββÅ −− χδδ12 =−() Å (5) + Å i RT Å ξ ÇÅ 1 (9) where iδ and jδ are, respectively, the Hildebrand parameters of ÑÉ 2.3. Group Contribution MethodsÑ (GCMs). Also, the the solute and solvent. Ñ 8 fi Ñ Hansen proposed an extension of the Hildebrand GCMs of UNIFAC and modi cationsÑ thereof are the sum of a δ δ combinatorial part and a residual part.ÖÑ Each GCM model uses parameter by separating the dispersion ( D), polar ( P), and ff hydrogen bonding (δ ) contribution. These three parameters adierent description for the combinatorial term. The HB UNIFAC and the modified UNIFAC(Do) models use the are called the Hansen solubility parameters (HSP) and are − 33 linked to the Hildebrand parameter, as defined in eq 6. Guggenheim Stavermann term (eqs 10 and 11), while the modified UNIFAC(Ly) uses the Kikic modification,29 as given i 2 iii2 2 2 in eq 12. δδ=++D δP δHB (6) UNIFAC: Often, the dispersive component was determined by homomorph methods, which estimates the dispersive param- Φ Φ lnln()1γc =Φ+−Φ− 51q −i + lni eter by evaluating an apolar molecule with almost the same size i iii θθi i (10) and shape of the polar compound.30 The remainder can be ÅÄ ÑÉ subtracted from the Hildebrand parameter and split into the modified UNIFAC(Do): Å i yÑ Å j zÑ polar and hydrogen-bonding term. By optimizing the Å j zÑ Å j zÑ miscibility description an optimal split between both terms c ÇÅ Φi k Φi{ÖÑ 30 lnln()1γ =Φ′ +−Φ′ −− 51q + ln was chosen. i iii θθ Common practice in using HSP is to plot the solute and i i (11) ÅÄ ÑÉ solvents in a 3D Hansen space. The spatial distance between modified UNIFAC(Ly): Å i yÑ Å j zÑ solute and solvent can be correlated to the solvation capability Å j zÑ c ′′ ′′ Å j zÑ of the solvent, where shorter distances in the Hansen space lnln()1γi =Φ+−ΦiiÇÅ k {ÖÑ (12) allow better solubility. Hansen31 also suggested that the Flory− Huggins parameter can be determined using eq 7: where Φ, θ, and q are, respectively, the volume fraction, surface fraction, and the coordination number, which is often set at 10. iV The modified UNIFAC(Do) model also has a modified χα=[−+m (ij δδ )2 0.25( ij δδ −+ )2 0.25( i δ − j δ )2] 12 RT dd pp HB HB volume fraction, on which more information is given in the (7) ESI.

C DOI: 10.1021/acs.iecr.9b00727 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX Industrial & Engineering Chemistry Research Article

The residual contribution of all UNIFAC models is always to perform quantum mechanical calculations to obtain determined via eqs 13 and 14: the state of the geometrically optimized molecule. This step must be done only once, and the result can be stored in a lnγνR =Γ−Γ()i (ln ln ()i ) i ∑ k k k database. The second step estimates the interaction energy of (13) k the optimized molecules with other molecules and can γ∞ henceforth estimate molecular properties such as the i θ Ψ 40 ln1lnΓ=Q −∑∑θ Ψ − mkm parameter. k k mmk ∑ θ Ψ m m n nnm (14) The energy of this state can be determined via dielectric continuum solvation methods. However, empirical parameters where Γ is thei overalli activity ofy moiety k, Γ(i) they activity of k j j z k z (e.g., atomic radii) are required to construct the molecular moiety k solelyj surroundedj by moietyz i, ν(i) the occurrencez of j j z k z cavity within the conductor exterior. COSMO-RS implements each moiety k kin surroundedk by moiety{ i, Qk the van{ der Waals element-specific radii, which are ∼17% larger than van der surface of group k, and Ψ the group binary interaction Waals radii. The state of the molecule is consequently parameter.4,5,11 determined using any Self-Consistent Field (SCF) model, 2.4. Linear Solvation Energy Relationship (LSER). − Linearly combining solute and solvent descriptors was e.g., Hartree Fock (HF) and density functional theory (DFT). − pioneered by Kamlet, Abboud, and Taft,34 38 and later Combining the COSMO approach with a SCF model results in Abraham3 introduced a now widely used LSER that consisted not only the total energy of the molecule, but also the fi fi polarization charge density, or σ.40 of ve solute and ve solvent descriptors (eq 15). An extension σ fi “ ” is made for ILs, where both the cation and anion have five The -pro le is frozen into place, while the conductor “ ” fi unique solvent descriptors (see eq 16).39 The Abraham model environment is squeezed out . A thin lm of a conductor is ff can be used to obtain either the gas-solvent partition left in place where di erent molecules will have an interface. ffi ffi σ σ σ′ coe cient (KS) or the water-solvent partition coe cient (Ps). The sum of the -value at the interface, ( + ), is then the net polarization charge density. As the conductor is removed, log(PceEsSaAbBvVS ) =+ + + + + the polarization charge density differences resemble intermolecular interactions with local contact energy, which may be log(KceEsSaAbBlLS ) =+ + + + + (15) described by

log(PceeEssSaaAScacaca )=+ ( + ) + ( + ) + ( + ) EEEcontact(,σσ′= ) misfit (, σσ ′+ ) hb (, σσ ′ ) (18) ++()()bbBvvVca ++ ca An interaction distinction is made between the misfit energy log(KceeEssSaaAScacaca )=+ ( + ) + ( + ) + ( + ) ff (Emisfit) and the energy that is due to hydrogen bonding e ects ++()()bbBllL ++ ca ca (Ehb). Both energy terms dissipate when the conjugant (16) polarization charge densities are equal. If not, the misfit The capital variables in eqs 15 and 16 are defined as the between both σ-values represents the electrostatic interaction solute descriptors and the lowercase variables are the solvent energy between those segments. Additional interaction energy descriptors. While the c-variable is a fitting constant, the latter can be induced by two very polar surfaces with opposite signs terms are respectively the excess molar refraction [dm3 mol−1/ via hydrogen bonding. The capability of COSMO-RS to 10], the dipolarity/polarizability, hydrogen-bond acidity and predict a large number of chemical potentials of solutes in − basicity, the McGowan characteristic volume (dm3 mol 1/ either a pure or mixed solvent enabled fast and versatile − ffi γ∞ 40 100), and the gas hexadecane partition coe cient at 298.15 predictions regarding various equilibria and also i . K. The descriptors describe the tendency to interact via σ- and π -electrons (e/E), the tendency to interact with (induced) 3. METHODS multipole moments (s/S), the tendency to accept hydrogen γ∞ bonds or donate electrons (A/b), the tendency to donate For all i predictions, a systematic assessment was done at hydrogen bonds or accept electrons (a/B), and the tendency 298.15 K and all model specific parameters were imported to either form (V/L) or the work required to form (v/l) from literature sources, as can be seen in the ESI. All cavities. simulations with COSMO-RS were performed with COSMO- The determination of solute and solvent descriptors is done thermX C30_1705, in which a pure solvent phase was defined γ∞ ffi by multilinear regression of experimental i data of either a set and the activity coe cient of the solute in that phase was of solutes in a solvent or a solute in various solvents. The gas− estimated. Molecules that were not available in the databases solvent partition coefficient can consequently be linked to the were created with TurboMole TmoleX 3.4, using the TZVPD- γ∞ 39 i parameter by eq 17: Fine parametrization. RT log(γ∞ )= log− log(K ) 4. RESULTS i PV°j s j m (17) 4.1. General Averaged Model Predictions. The where P° and V are,i respectively,y the vapor pressure and molar accuracy of all models was determined by comparing the j j j z volume of the purej solvent.z predictions with experimental values taken from the literature. j z 2.5. Conductor-likek { Screening Model for Real Sol- An extensive overview of all experimental data is presented in vents (COSMO-RS). The ab initio method developed by the ESI. The accuracy of the models is evaluated by Klamt et al.,40 called COSMO-RS, predicts chemical potentials, determining the average relative deviation (ARD) between γ∞ fi γ∞ which can be used to calculate the value of i . The rst step is the predicted and experimental i values, as given in eq 19.

D DOI: 10.1021/acs.iecr.9b00727 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX Industrial & Engineering Chemistry Research Article

γ∞ Figure 2. Evaluation of various predictive models for i for (A) molecular solvents and (B) ionic liquids (ILs) at 298.15 K. On the y-axis, the ARD is presented within the boxes the total amount of comparisons made. The experimental γ∞ is collected in the ESI. The integrated scatter plot i − − depicts similar comparison made in the literature for various models, e.g., modiﬁed UNIFAC(Ly),17 19 UNIFAC,17 22,42,43 COSMO-RS,18,44 − − modiﬁed UNIFAC(Do),17,19,22,23,45 47 and MOSCED.6,20 22,24

∞∞ ()γγ− () more elaborate description of the various intermolecular ∑N iimodel experimental i=1 γ∞ interactions via all descriptors. ()i experimental ARD = For ILs, the ARD of all models (see Figure 2b) increase due N (19) to the presence of not only dispersion, dipole, and hydrogen γ∞ bonding interactions, but also ionic interactions between the The ARD for prediction of i for all solutes in molecular fi ionic species and the solute. The ARD of the HSP model is solvents and ILs by each model, and their 95% con dence determined to be 168% ± 54.5%, while the GCM methods intervals, are depicted in Figure 2. For molecular solvents, eight perform better with an ARD of 86.2% ± 14.6%, 86.5% ± predictive models have been evaluated; for ILs, seven 15.7%, and 122% ± 55.9%, respectively, for the modified predictive models due to lack of MOSCED parameters for UNIFAC(Ly), UNIFAC, and modified UNIFAC(Do). ILs have been evaluated. The ARD of the various models ff fi Although COSMO-RS performed for molecular solvents is di ers signi cantly, as can be seen in Figure 2. For both the comparable to that of the GCMs, for ILs, the ARD is larger molecular solvents and the ILs, the most inaccurate model is (182% ± 16.7%). The larger ARD for ILs is known to be (at the Hildebrand model. Evidently, using only the evaporation least partly) caused by neglecting long-range ion−ion ffi enthalpy and the molar volume is insu cient to accurately interactions and insufficient description of extreme polarization γ∞ describe i in systems where intermolecular interactions such charge densities of ions.10 The Abraham model performs most 41 fi as hydrogen bonding occur. This accumulates in a signi cant accurately for ILs, with an ARD value of 65.1% ± 4.50%. The 5 γ∞ ARD of >10 % in the i prediction. accuracy of the Abraham model is interesting for solvent γ∞ fi Using the HSP to calculate the i with eq 7 is a signi cant screenings purpose, because of the availability of ion-specific improvement, compared to the Hildebrand model (eq 5), Abraham parameters for 60 cations and 17 anions, allowing which is due to taking into account hydrogen bonding and rapid assessment of 1020 ILs, since they are binary ff 8 ± polarity e ects. Still, an ARD of 66.4% 14.4% is observed combinations of these ions. (see the ESI). for molecular solvents. This may be explained by the inability The ARDs reported in Figure 2 appear to be larger than 6 − − to differentiate between hydrogen acidity and basicity effects. errors described in various literature sources.6,17 24,42,43,45 48 Further refining the model using hydrogen acidity and Similar comparisons have been made by Gmehling et al.,17 hydrogen basicity, as well as polarizability effects, as taken who assessed the accuracy of the UNIFAC models, and into account in the MOSCED model, which shows from Thomas et al.,20 who assessed the accuracy of the MOSCED Figure 2a to be, on average, the most accurate model, with an model. They reported lower ARD values, correspondingly ARD of 16.2% ± 1.35%. Unfortunately, no parameters for ILs 25.8% (instead of 31.1% ± 1.66%) and 9.10% (instead of are available, and therefore this model could not be evaluated 16.2% ± 1.35%). Because the error calculation method is the for ILs. The three group contribution models that were also same, and only the used dataset differs, the logical conclusion ± γ∞ evaluated showed comparable ARD values of 32.2% 1.84%, is that the dataset used in this work includes i with a higher 31.1% ± 1.66%, and 24.3% ± 1.63%, respectively, for the average error margin. This will be the case for each of the modified UNIFAC(Ly), UNIFAC, and modified UNIFAC- assessed models; hence, these error margins in the dataset will (Do) for molecular solvents. The ARD of COSMO-RS is not affect the comparison of the relative accuracies between all within 28.3% ± 1.07%, which is similar to that observed for the models. For comparison with the work of Gmehling et al.,17 GCM methods. The Abraham model is more accurate than there is a difference in the selected data, because they state that ± γ∞ GCM methods and COSMO-RS with an ARD of 21.7% i values of >100 were excluded, whereas, in this manuscript, 1.19%. The better accuracy of the Abraham model is due to a these values were included.

E DOI: 10.1021/acs.iecr.9b00727 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX Industrial & Engineering Chemistry Research Article

Table 1. Accuracy of Eight Predictive Models Diﬀerentiated Towards Aliphatic, Aromatic, Halogen, Aprotic Polar, and Protic a Polar Compounds in Molecular Solvents

aAll 25 binary solute-solvent combinations have been made at 298.15 K. The colors are indicative: white, ARD < 100%; light gray, 100% < ARD < 300%; medium gray, 300% < ARD < 500%; dark gray, 500% < ARD < 103%; and black, ARD >105%.

4.2. Molecular Solvents. Although from the averaged hydrogen bonding basicity and acidity separately, as well as γ∞ model predictions, one general guideline for model selection including polarizability, predict i with increasing accuracy. All can be distilled, a more-detailed analysis of subgroups of of these models show the largest ARD for protic compounds, solutes and solvents allows one to provide a more-sophisticated including amines, alcohols, and aldehydes, which is a logic directive to the use of thermodynamic models for the result due to the number and type of intermolecular γ∞ fi prediction of i for various speci c chemical families. To interactions occurring in these systems. fi fi γ∞ this end, all solvents and solutes were classi ed into ve There is no single model that predicts i most accurately for categories, i.e., aliphatic compounds, aromatic compounds, all solvent and solute category combinations. Each of the compounds containing a halogen atom, polar aprotic models, except for the Hildebrand and HSP models, most compounds and polar protic compounds, and the model accurately predicts a category of solute−solvent pairs. accuracies were evaluated per combination of solvent and COSMO-RS performs best in systems with only (induced) solute class. dipole interactions and in the absence of hydrogen bonding In Table 1, all model evaluations are shown per combination formation. When polarity and hydrogen bonding systems are of solvent and solute categories. Comparison of the concerned, COSMO-RS becomes less accurate. The Hildebrand, HSP, and MOSCED models clearly shows that MOSCED and Abraham models perform much better in models with increasing complexity, i.e., taking hydrogen hydrogen bonding systems, because of the multiple parameters bonding and polarity into account, and describing the that describe these directional interactions. The various

F DOI: 10.1021/acs.iecr.9b00727 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX Industrial & Engineering Chemistry Research Article

Table 2. Accuracy of Five Predictive Models Diﬀerentiated Towards Aliphatic, Aromatic, Halogen, Aprotic Polar, and Protic a Polar Compounds in Ionic Liquids with Various Nonfunctionalized and Functionalized Cations

aAll 25 binary solute−solvent combinations have been made at 298.15 K. Color legend: white, ARD <100%; light gray, 100% < ARD < 300%; medium gray, 300% < ARD < 500%; dark gray, 500% < ARD < 103%; and black, ARD >105%.

UNIFAC models appear to be most accurate for a few performances are listed in Table 2. A larger ARD is generally categories of chemical interaction systems, which may arise obtained for FILs, because of the fact additional intermolecular from the empirical nature of the UNIFAC models based on and intramolecular interactions occur with the moieties present fitting the model parameters to experimental data. The on the cation tails. Also, COSMO-RS clearly has severe ffi γ∞ variation between the UNIFAC models can also arise from di culties in predicting accurate i values. Analogous to the the different fitting procedures for the determination of their trends observed in molecular solvents, the ARD increase from empirical constants. Finally, the differences in the formulation apolar to polar solutes, because of hydrogen bonding effects. of their combinatorial term can induce variation in activity Overall, the performance of the Abraham model is superior to coefficient prediction. that of the other models, although some systems can be more γ∞ 4.3. Ionic Liquids. Overall, the ARD in predicted i in ILs accurately described using a variant of UNIFAC. For instance, is larger than that observedin molecular solvents. Not only is the predictions for aliphatic, aromatic, and halogen solutes in the additional electrostatic intermolecular interaction of the imidazolium cations are more accurately predicted with charges on the ions with the solutes responsible for this, but modified UNIFAC(Do). This is most likely due to the large also the additional competition between the solute-related dataset available for imidazolium cations, hence improving the intermolecular interactions and the interactions between the empirical fit of the modified UNIFAC(Do). ions in the IL plays an important role. Furthermore, ILs with a 4.3.2. Anions. The nature of the anion in ILs has been fi γ∞ cation containing, besides the central ionic moiety, also a identi ed as a key factor determining the i parameter for second moiety (e.g., ether, hydroxyl, or unsaturated bond), are solutes;49 therefore, it is also important to list the anion- fi γ∞ collectively evaluated as functionalized ionic liquids (FILS). category-speci c ARD in the predictions of i , which is done 4.3.1. Cations. A systematic analysis was made for various in Table 3. By combining the information in Table 2 with the classes of cations, and the cation class-specificmodel information in Table 3, it becomes clear that the large ARD

G DOI: 10.1021/acs.iecr.9b00727 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX Industrial & Engineering Chemistry Research Article

Table 3. Accuracy of Five Predictive Models Diﬀerentiated Towards Aliphatic, Aromatic, Halogen, Aprotic Polar, and Protic a Polar Compounds in Ionic Liquids with Various Anions

aAll 25 binary solute−solvent combinations have been made at 298.15 K.

Table 4. Overview of the Most Accurate Predictive Model of Each Speciﬁc Category of Binary Molecular Solvent−Solute Mixtures

Best Practice Solute solvent aliphatic aromatic halogen aprotic polar protic polar aliphatic modified UNIFAC(Do) modified UNIFAC(Do) Abraham COSMO-RS Abraham aromatic COSMO-RS COSMO-RS MOSCED Abraham UNIFAC halogen MOSCED MOSCED COSMO-RS MOSCED Abraham aprotic polar MOSCED MOSCED MOSCED MOSCED Abraham protic polar Abraham MOSCED Abraham MOSCED modified UNIFAC(Ly)

H DOI: 10.1021/acs.iecr.9b00727 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX Industrial & Engineering Chemistry Research Article observed with various UNIFAC models and the Abraham 6. CONCLUSIONS model originate from very large ARD observed for a few Several models have been assessed for their ability to predict anions. ARD values of >100% are caused by the bis- the infinite dilution activity coefficient (γ∞) for solutes of fl fl i (tri uoromethane)sulfonimide [NTf2], tetra uoroborate various classes, in molecular solvents categorized in the same [BF4], and diethylene glycolmonomethyl ether sulfate classes, and in ionic liquids (ILs). A larger ARD was observed [MDEGSO4] anions, which indicates that improving these for ILs than for molecular solvents, because of the additional correlations will greatly improve the overall average accuracy of ionic interactions. Averaged overall, the MOSCED model was γ∞ these models. COSMO-RS appears to have difficulties in each the most accurate model for the prediction of i of all solute anion, indicating that the problems of COSMO-RS do not classes in molecular solvents, with an ARD of 16.2% ± 1.35%. arise from a particular intermolecular interaction induced by The UNIFAC group contribution methods (GCMs), one or more specific anion(s). COSMO-RS, and the Abraham models perform comparably, with ARD values of 24.3%−32.2%. Models using the Hildebrand parameter and the Hansen solubility parameters 5. MODEL SELECTION (HSP) are significantly less accurate, because of an insufficient In Table 4, for each combination of chemical systems, the description of intermolecular interactions such as hydrogen γ∞ model that most accurately predicts for that combination of bonds. To predict the i in ILs, overall, the Abraham model is chemical classes is listed. However, this is not the only the most accurate model, with an ARD value of 65.1% ± selection criteria of importance. Solvation models, such as 4.50%. The GCMs are less accurate, with ARD values of − MOSCED and the Abraham model, can only be used when all 86.2% 122%, while COSMO-RS is far less accurate, with an ± fi molecular parameters are known. GCMs and COSMO-RS are ARD value of 182% 16.7%, because of a de cient description much more flexible, in the sense that (almost) every molecular of long-range interactions. ∞ Upon classification of solutes and molecular solvents and structure can be drawn and the γ parameter can be predicted. i evaluating the model prediction accuracy for each of the To improve the applicability range of MOSCED and the ff solvent and solute classes, it is observed that each of the Abraham model, recent e orts are made to predict the models, except for the Hildebrand parameter and HSP, is most molecular parameters for MOSCED by using a GCM50 or by fi − 51,52 accurate for speci c classes of binary solute solvent pairs, using quantum mechanical charge density calculations. although the accuracy decreases with the polarity of the solute. Moreover, isobaric vapor−liquid predictions using MOSCED For ILs, using the overall averages, the Abraham model is most have been shown to outperform UNIFAC.32 Regarding the accurate, although several cations are more accurately Abraham model, it has been shown that solute parameters can described with modified UNIFAC(Ly) or modified UNIFAC- be predicted by multilinear regression analysis and computa- (Do). The large ARD values from the UNIFAC models and tional neural networks.53 The limited temperature range of, the Abraham model are mainly due to large ARD values for the often, only 298.15 K is a drawback for SMs and LSER, and [NTF2], [BF4], and [MDEGSO4] anions. Hence, improving attempts have been made toward temperature-independent the prediction of these anions will greatly increase their overall parameters;54 however, this is not generalized yet. prediction accuracy. In addition, the most accurate model for It should be taken into consideration that the accuracy for molecular solvents (MOSCED) could not be assessed for ILs. γ∞ γ∞ Therefore, an extension of MOSCED toward ILs may become predicting i by GCMs can be improved when only i data γ∞ are regressed and not the thermodynamic data of other forms an accurate tool in predicting accurate i values in ILs. These evaluation results are applicable when each molecular (excess enthalpy for example). However, this will reduce the 4 parameter is either known or accurately predicted. If so, the accuracy for other thermodynamic properties. Therefore, a γ∞ γ∞ fi most accurate model for estimation of i is dependent on both suggestion could be made to regress a separate i -speci c the solute and solvent categories under evaluation. Still, using a γ∞ ∞ GCM that can obtain the most accurate i predictions. model to predict γ for IL screening should be done with γ∞ i Overall, the model choice for the most accurate i must be caution, since these, on average, easily exceed deviations of a stepwise procedure. First, it should be ascertained whether all 65%. molecular parameters of the chosen molecules are available in the literature. If this is not the case, they may be predicted ■ ASSOCIATED CONTENT using theoretical or regression methods, although the accuracy *S Supporting Information of these methods should always be taken into consideration. The Supporting Information is available free of charge on the When satisfactory molecular parameters are available, the best ACS Publications website at DOI: 10.1021/acs.iecr.9b00727. practice matrix in Table 4 can be used to select the best model. Specific parameters, equations, and predictions for the When the molecular parameters are lacking or are questionable γ∞ various models; all experimental i used in the (strongly deviating from the same parameters for comparable comparison, along with the corresponding references molecules), then GCMs or COSMO-RS should be used for the (PDF) prediction. Regarding ILs, the Abrahams model is the most accurate model when the molecular parameters are known. ■ AUTHOR INFORMATION Otherwise, GCMs of COSMO-RS must be used, although this will significantly increase the probability of deviation from the Corresponding Author * true value. Tel.: +31 6 14178235. E-mail: [email protected]. Lastly, the application should be taken into consideration. ORCID GCMs and COSMO-RS are able to predict a much wider Thomas Brouwer: 0000-0002-3975-4710 range of molecular properties than the SMs and LSER. Boelo Schuur: 0000-0001-5169-4311

I DOI: 10.1021/acs.iecr.9b00727 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX Industrial & Engineering Chemistry Research Article

Notes α = empirical constant added to Hansen solubility The authors declare no competing financial interest. parameters, as reported by Lindvig et al.9 c = cohesive pressure or cohesive energy density ■ ACKNOWLEDGMENTS c = fitting constant of the Abraham model N = number of data points This has been an ISPT (Institute for Sustainable Process Δ Uvap = molar vaporization energy Technology) project (TEEI314006/BL-20-07), cofunded by Δ Hvap = molar vaporization enthalpy the Topsector Energy by the Dutch Ministry of Economic i Affairs and Climate Policy Vm = molar volume of compound i T = temperature (K) −1 −1 ■ NOMENCLATURE R = universal gas constant; R = 8.3145 J K mol iλ = MOSCED dispersion constant for compound i Abbreviations iτ = MOSCED polarity constant for compound i AD = average deviation iq = MOSCED induction constant for compound i ARD = average relative deviation iα = MOSCED hydrogen bond acidity constant for UNIQUAC = Universal Quasichemical compound i UNIFAC = UNIQUAC Functional-group Activity Coef- iβ = MOSCED hydrogen bond basicity constant for ficients compound i COSMO-RS = Conductor like Screening Model for Real iτT = temperature-corrected MOSCED polarity constant for Solvents compound i DFT = density functional theory iαT = temperature-corrected MOSCED hydrogen bond ESI = electronic Supporting Information acidity constant for compound i MOSCED = Modified Separation of Cohesive Energy iβT = temperature-corrected MOSCED hydrogen bond Density basicity constant for compound i ILs = ionic liquids iξ = MOSCED empirical asymmetric constant for FILs = functionalized ionic liquids compound i NRTL = nonrandom two-liquid model iψ = MOSCED empirical asymmetric constant for GCM = group contribution method compound i θ HSP = Hansen solubility parameters i = surface fraction of compound i − HF = Hartree Fock qi = coordination number of compound i fi ν(i) SCF = self-consistent eld k = occurrence of each moiety k in surrounded by moiety i Γ SM = solvation models k = overall activity of moiety k fi ζ Γ(i) TZVPD-Fine = ne grid triple- valence polarized basis set k = activity of moiety k solely surrounded by moiety i fl [NTf2] = bis(tri uoromethylsulfonyl)imide Qk = van der Waals surface of moiety k fl [BF4] = tetra uoroborate Rk = van der Waals volume of moiety k Ψ [SCN] = thiocyanate mk = group binary interaction parameter between moieties fl [CF3SO3] = tri uoromethanesulfone m and k σ π [MDEGSO4] = 2-(2-methoxyethoxy)ethyl sulfate ec/a,E=Abrahamdescriptorsfor -and -electron [OSO4] = octyl sulfate interactions (subscripts c and a indicate cationic and anionic fl [PF6] = hexa uorophosphate species, respectively) [B(CN)4] = tetracyanoborate sc/a, S = Abraham descriptors for (induced) multipole [TFA] = trifluoroacetate moments interactions (subscripts c and a indicate cationic [DMPO4] = dimethylphosphate and anionic species, respectively) [DCA] = dicyanamide ac/a, A = Abraham descriptors for tendency to accept Symbols hydrogen or donate electron (subscripts c and a indicate γ ffi cationic and anionic species, respectively) i = activity coe cient of compound i γ∞ fi ffi b , B = Abraham descriptors for tendency to donate i =in nite dilution activity coe cient of compound i c/a γc ffi hydrogen or accept electron (subscripts c and a indicate i = combinatorial term of the activity coe cient of compound i cationic and anionic species, respectively) γR ffi v , V = Abraham descriptors for the work/tendency i = residual term of the activity coe cient of compound i c/a required to form cavities (subscripts c and a indicate xi = molar fraction of compound i Φ cationic and anionic species, respectively) i = volume fraction of compound i Φ’ fi l , L = Abraham descriptors for the work/tendency i = modi ed volume fraction of compound i, reported by c/a Weidlich et al.4 required to form cavities (subscripts c and a indicate Φ″ fi cationic and anionic species, respectively) i = modi ed volume fraction of compound i, reported by 5 o Larsen et al. Pi = vapor pressure of the pure solvent − ffi χ =Flory−Huggins interaction parameter between KS = gas solvent partition coe cient 12 − ffi compounds 1 and 2 PS = water solvent partition coe cient iδ = Hildebrand parameter of compound i Econtact = local contact energy fi iδ = Hansen parameter for dispersion interactions of Emisfit = mis t energy D ff compound i EHB = energy due to hydrogen bonding e ects σ iδ = Hansen parameter for hydrogen bonding interactions = polarization charge density HB σ′ of compound i = polarization charge density on the opposite side iδ P = Hansen parameter for polar interactions of compound i

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L DOI: 10.1021/acs.iecr.9b00727 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX