Abstract Efficient Early Stage Chemical Process

ABSTRACT

EFFICIENT EARLY STAGE CHEMICAL PROCESS DESIGN

by Pratik Dhakal

Design of any chemical processes on a large scale such as distillation, extraction requires tremendous amount of data. Such data can be obtained either through literature review (if available), experiments, molecular, property prediction tools. Conducting experiments on a large scale for multicomponent mixtures at different variables can be quite expensive and time consuming, while molecular simulation is still computationally demanding even though it can provide accurate molecular level details. Property prediction tools are simple analytical model based on empirical relations or thermodynamics relations that can provide accurate estimates, which is why they are used throughout the industry. However, most commons property predictions tools provide no qualitative insight on a molecular level that could be extremely useful for process intensifications. Thus, this research is focused on a analytical model called MOSCED that has shown tremendous capability in providing accurate property predictions and qualitative molecular insights that could guide chemical process design during early stage.

EFFICIENT EARLY STAGE CHEMICAL PROCESS DESIGN

Thesis

Submitted to the

Faculty of Miami University

in partial fulfillment of

the requirements for the degree of

Master of Science

Pratik Dhakal

Miami University

Oxford, Ohio

2018

Advisor: Dr.Andrew Paluch

Reader: Catherine Almquist

Reader: Dr Shashi Lalvani

This thesis titled

EFFICIENT EARLY STAGE CHEMICAL PROCESS DESIGN

Pratik Dhakal

has been approved for publication by

The College of Engineering and Computing

and

Department of Chemical, Paper and Biomedical Engineering

______Dr. Andrew Paluch

______Dr. Catherine Almquist

______Dr. Shashi Lalvani

Contents 1.Introduction ...... 1 1.1 Motivation ...... 1 1.2. Background ...... 2 2. Application of MOSCED to Predict Limiting Activity Coefficients, Hydration Free Energies, Henry’s Constants, Octanol/Water Partition Coefficients, and Isobaric Azeotropic Vapor-Liquid Equilibrium ...... 6 2.1 Introduction ...... 6 2.2 Computational Methods ...... 6 Solvation Free Energy ...... 6 Henry’s Constant ...... 7 Partition Coefficient ...... 8 Binary Vapor-Liquid Equilibrium ...... 9 2.3 Result and Discussions...... 12 Association/hydrogen bonding term ...... 12 Limiting Activity Coefficient, Solvation Free Energy, and Henry’s Constant ...... 16 Partition Coefficients ...... 23 Azeotropic vapor/liquid equilibrium...... 25 3.4 Conclusion ...... 32 2.5 References ...... 34 3.Expansion of MOSCED using new UNIFAC based Group Contribution Method and Linear Solvation Energy Relationship (LSER). Application: Predicting Activity Coefficient at Infinite Dilution for Non-Hydrogen Bonding Molecules ...... 41 3.1 Introduction...... 41 3.2 LSER correlation: ...... 42 3.3 Correlating LSER parameters with MOSCED...... 43 Data Collection ...... 44 Correlation: ...... 44 UNIFAC based Group Contribution Method: ...... 45 3.4 Result and Discussions...... 47 Application: ...... 52 3.5 Conclusion: ...... 55 iii

3.6 References: ...... 55 4. Expansion of MOSCED to Ionic Liquids for Efficient Early Stage Chemical Process Design: Application such as selecting Entrainers, breaking Azeotropic Vapor Liquid Equilibria ...... 58 4.1 Introduction ...... 58 4.2 Methodology ...... 61 Data Collection ...... 61 Regression ...... 62 Quantifying Errors ...... 63 4.3 Computational Methods ...... 63 Ternary Vapor-Liquid Equilibrium Modelling ...... 63 Selectivity Coefficient and Distribution Coefficient ...... 65 4.4 Result and Discussion ...... 66 MOSCED Parameters ...... 66 Ternary Vapor Liquid Equilibrium Result ...... 74 Selectivity ...... 79 4.5 Conclusion ...... 81 4.6 References: ...... 81

List of Tables

11 Table 1: MOSCED association parameters for chloroform, acetone, methanol, and N- 1/2 3 1/2 methylpyrrolidone, where αi and βi have units of MPa or (J/cm ) ...... 12 Table 2 : A summary of the number of solutes (N) for which log limiting activity coefficients (ln휸ퟐ∞) were calculated in water, the average absolute error (AAE) and the corresponding standard deviation (SD), and Pearson’s correlation coefficient (R2) of the calculations versus the reference data45...... 17 Table 3 : A summary of the number of solutes (N) for which hydration free energies were calculated, the average absolute error (AAE) and the corresponding standard deviation (SD), 17,18,20 and Pearson’s correlation coefficient (R2) of the calculations versus the reference data , where all hydration free energy calculations were in units of kJ/mol...... 19 Table 4 : A summary of the number of solutes (N) for which log Henry’s constan2,1) were calculated in water, the average absolute error (AAE) and the corresponding standard deviation (SD), and 2 45 Pearson’s correlation coefficient (R ) of the calculations versus the reference data , where H21 was calculated in units of kPa...... 21 Table 5 : A summary of the number of solutes (N) for which log octanol(I)/water(II) partition coefficients (ln PI/II) were calculated, the average absolute error (AAE) and the corresponding standard deviation (SD), and Pearson’s correlation coefficient (R2) of the calculations versus the reference 45 data , where molar concentrations (moles/volume) were used in the calculation of ln PI/II...... 23 Table 6 : A summary of the percent average absolute relative error (AARE) in the volatility of components 1 (K1) and 2 (K2) in the dilute region, x1 < 0.3 and x2 < 0.3, respectively, of the predictions versus reference data51–56. For each system, N corresponds to the number of experimental data points available for comparison, and predictions were made using mod-UNIFAC and using MOSCED to parameterize NRTL, Wilson’s, and TK-Wilson equations as described in the text. For all cases, in the system name the first component corresponds to component 1. In the last line of the table, we calculate the average of AARE for all of the systems studied...... 28 Table 7: UNIFAC GC groups for MOSCED parameters with example molecule...... 47 Table 8 : Stats in correlating activity coefficient at infinite dilution method...... 51 Table 9 : Activity Coefficient at Infinite Dilution Stats for Non-Hydrogen Bonding Set ...... 53 Table 10: Stats for multifunctional molecule using different methods...... 55 Table 11: MOSCED parameters for the Ionic Liquids with its standard anion name, where cation [EMIM] stands for 1 ethyl-3methyl imidazolium [EMIM], 1 butyl-3methyl imidazolium [BMIM] and 1 alkyl-3methyl imidazolium [HMIM]. Lambda, tau, alpha, beta is in units of (J/cm3)1/2 and molar volume(v) is in cm3/mol...... 67 Table 12: Stats for all the Ils RMSE in log gamma, AARD in gamma, NO of data points by MOSCED and * indicates LSSVM method. Average error is given at the end of sheet and total no of data points used for correlation ...... 69 Table 13 : MOSCED hydrogen bonding parameters and the cross-interactions term ...... 71

Table 14 : Hydrogen bonding basicity data, where beta1 is taken from reference [38], beta2 is taken from reference [39], Ehb data taken from COSMO-RS as mentioned in reference[30], and MOSCED beta ...... 72 Table 15: Binary Vapor Liquid Equilibria data for Methyl Acetate(1) and Methanol(2) at 101.3 KPa(where x1 is liquid mole fraction of component 1, y1 liquid mole fraction, gamma1(풚ퟏ)is activity predicted using MOSCED& WILSON, gamma1*(풚ퟏ)* is experiment activity, gamma2((풚ퟐ) is activity predicted using MOSCED & WILSON, gamma2*(풚ퟐ)* is experiment activity, T is temperature in Kelvin predicted using MOSCED & WILSON, T* is experimental temperature in Kelvin...... 75 Table 16: Binary Vapor Liquid Equilibria data for Methyl Acetate(1) and Methanol(2) + 0.1 mole frac [C4MIM][Cl] of at 101.3 KPa(where x1 is liquid mole fraction of component 1, y1 liquid mole fraction, gamma1(풚ퟏ)is activity predicted using MOSCED& WILSON, gamma1*(풚ퟏ)* is experiment activity, gamma2((풚ퟐ) is activity predicted using MOSCED & WILSON, gamma2*(풚ퟐ)* is experiment activity, T is temperature in Kelvin predicted using MOSCED & WILSON, T* is experimental temperature in Kelvin...... 76 Table 17: Binary Vapor Liquid Equilibria data for Methyl Acetate(1) and Methanol(2) + 0.2 mole frac [C4MIM][Cl] of at 101.3 KPa(where x1 is liquid mole fraction of component 1, y1 liquid mole fraction, gamma1(풚ퟏ)is activity predicted using MOSCED& WILSON, gamma1*(풚ퟏ)* is experiment activity, gamma2((풚ퟐ) is activity predicted using MOSCED & WILSON, gamma2*(풚ퟐ)* is experiment activity, T is temperature in Kelvin predicted using MOSCED & WILSON, T* is experimental temperature in Kelvin...... 77 Table 18: Binary Vapor Liquid Equilibria data for Methyl Acetate(1) and Methanol(2) + 0.3 mole frac [C4MIM][Cl] of at 101.3 KPa(where x1 is liquid mole fraction of component 1, y1 liquid mole fraction, gamma1(풚ퟏ)is activity predicted using MOSCED& WILSON, gamma1*(풚ퟏ)* is experiment activity, gamma2((풚ퟐ) is activity predicted using MOSCED & WILSON, gamma2*(풚ퟐ)* is experiment activity, T is temperature in Kelvin predicted using MOSCED & WILSON, T* is experimental temperature in Kelvin...... 78

List of Figures

Figure 1: Plots of pxy diagrams for acetone(1)/chloroform(2) at 298.15 K, acetone(1)/methanol(2) at 323.15 K, and methanol(1)/Nmethylpyrrolidone(2) at 393.15 K. Circles are experimental reference data,8,42,43 and solid lines correspond to predictions made using MOSCED11 to parametrize Wilson’s equation. The dotted red line corresponds to the bubble line predicted using Raoult’s law and is drawn for convenience...... 15 Figure 2 : Parity Plot of ln γ2 ∞ for organics in water predicted using MOSCED [11] and mod- UNIFAC [21][36] versus reference values from ref 45. The dashed lines indicate an error of ±2 log units...... 18 Figure 3: Parity plot of the solute solvation free energy in water (hydration free energy, ΔG2solv), predicted using MOSCED,11 modUNIFAC,[21−26],[36] and molecular simulation [17],[18],[20] versus reference data.[17],[18],[20] The dashed lines indicate an error of ±5 kJ/mol or approximately 2RT...... 20 Figure 4: Parity plot of log Henry’s constants (ln 2,1 / ) for organics in water, predicted using MOSCED11 and mod-UNIFAC21−26,36 versus reference data from ref 45. The dashed lines indicate an error of ±2 log unit ...... 22 Figure 5: Parity plot of log octanol(I)/water(II) partition coeﬃcients (ln P2I/II), predicted using MOSCED11 and mod-UNIFAC21−26,36 versus reference data from ref 45. The dashed lines indicate an error of ±2.8 log units. This is indicative of an error of approximately 2RT in ΔG2I,solv and ΔG2II,solv...... 24 Figure 6: A plot of the relative volatility (α1,2 = K1/K2) and the volatility of each component (K1 and K2) for the binary system cyclohexane(1)/1,2-dichloroethane(2) at 1.013 bar. The solid black line is experimental reference data51−56 and the dotted black lines are drawn for convenience as ±20% error in the reference data. The dashed lines correspond to predictions made using mod- UNIFAC21−26,36 and using MOSCED to parametrize NRTL (α = 0.3), TK−Wilson, and Wilson’s equation, as indicated. The horizontal gray line in the top plot corresponds to α1,2 = 1 and is useful for locating the azeotrope. The vertical gray line in the bottom two plots corresponds to x1 = 0.3 and x2 = 0.3, respectively, and is used to identify the dilute region...... 26 Figure 7 : Activity Coefficient at Infinite Dilution Predicted for the original test...... 52 Figure 8: Activity Coefficient at Infinite Dilution for Non-Hydrogen bonding set using different method...... 54 Figure 9: 1-Ethyl 3-methylimidazolium Ethyl Sulfate ...... 61 Figure 10:Correlation of Activity Coefficient Data ...... 66 Figure 11 : Vapor Liquid Equilibria for Methyl Acetate + Methanol + [EMIM][Cl] at 101.3 KPa ... 75 Figure 12 : Ln Selectivity of aromatic/aliphatic using IL ...... 80

vii

Dedication

To mom, dad, brother, and Rina.

viii

Acknowledgements

All of this work wouldn’t have been a possibility without the collaboration of Maria Lucas, Jeremy Phifer, Sydnee Roese, Brook Long, Cassie O’Dell, Anthony Weise, Raechel Ollier, Erin Stalcup, Joanthan Ouimet, Natalie Folkins and Martin Fritsch.

1.Introduction 1.1 Motivation Separation and puriﬁcation of chemical mixtures are an essential but a costly factor procedure in the chemical industry. Often such processes require the use of solvents that are expensive on a large scale, as a result engineers are continuously in search of economic and effective solvents. Addition to solvent selection, design of chemical processes, understanding toxicity, contamination removal and design of pharmaceutical drugs requires the knowledge of important thermodynamic properties. For several properties, experiments on a small scale can be conducted at a low expense but dealing with numerous mixtures at a given time can be extremely time consuming and tedious. State-of-the-art molecular simulations can provide molecular level insight but are often computationally demanding and still not accessible to everyone. Thus, property estimation tool could be a convenient way for property prediction. There are several kind of property prediction tools available. Conventional group contribution model such as MOD-UNIFAC, UNIFAC are some of the most popular methods that are often used to predict mixture properties, however these models fail to provide any kind of physical intuition on a molecular level. Powerful quantum methods such as COSMO-RS and COSMO-SAC are another popular method that provide accurate and powerful insight on a molecular level, but these techniques are only available on a commercial level and are complex methods. Then we have solubility parameter methods which quantity molecular interaction behavior of each compounds that allows property estimation and qualitative molecular insight. This valuable insight could be extremely powerful for chemical process design toll during solvent selection and process intensification. Some of the common methods are Regular Solution Theory, Hansen and MOSCED. So, a major motivation of this thesis work is to find a simple, accurate, reliable property solubility parameter method and demonstrate on how it can provide quantitative and qualitative insight which might be extremely valuable during early stage chemical process design. Thus, by efficient early stage process design, we mean using property prediction tool to cut down cost completely during early stage and then guide experiments in the final stage.

1.2. Background Solubility parameter-based methods were first introduced in the Scatchard-Hildebrand regular solution theory. Regular solution theory assumes the excess volume and entropy are zero, and therefore that the excess Gibbs free energy is equal to the excess internal energy [1] [2]. While the contribution to the excess Gibbs free energy due to the excess volume is typically minute, the contribution of the excess entropy may be significant, especially for cases where the size and shape of the solvent and solute differ greatly. To remedy this shortcoming, one may add to the regular solution theory equation the athermal Flory-Huggins equation (or one of its various extensions), derived assuming the excess Gibbs free energy is equal to the excess entropy [1]. For a binary mixture of species 1 and 2, this leads to the following expression for the limiting (or infinite

∞ dilution) acticity coefficient of component 2, γ2 :

∞ 푣2 2 푣2 푣2 푙푛훾2 = (훿1 − 훿2) + 푙푛 ( ) + 1 − ( ) (1) 푅푇 푣1 푣1 where R is the ideal gas constant, T is the absolute temperature, δi is the solubility parameter of component i, defined as the square root of the component’s cohesive energy density, and vi is the liquid molar volume of component i, where i = {1, 2}. An equivalent expression may be written for component 1 by switching the subscript indices. Following the work of Abrams and Prausnitz[3], eq. (1) may be interpreted as the sum of a residual (RES) and combinatorial (COMB) contribution:

∞ ∞,푅퐸푆 ∞,퐶푂푀퐵 푙푛훾2 = 푙푛훾2 + 푙푛훾2 (2) The first term of eq. (1) (i.e., regular solution theory) is the residual contribution and results from intermolecular interactions; it corresponds to the partial molar excess internal energy. For all ∞,푅퐸푆 cases, 푙푛훾2 ≥ 0. The greater the dissimilarity in intermolecular interactions between two

∞,푅퐸푆 components, the greater the value of 푙푛훾2 . The latter terms (i.e., Flory-Huggins theory) are the combinatorial contribution and results from the size dissimilarity of the components, which

∞,퐶푂푀퐵 corresponds to the partial molar excess entropy. For all cases, 푙푛훾2 ≤ 0. The greater the size ∞,퐶푂푀퐵 dissimilarity between the two components, the more negative the value of 푙푛훾2 . An ideal ∞ ∞ solution (푙푛훾2 = 푙푛훾1 = 0) results when the components have similar intermolecular interactions (δ1 = δ2) and are comparable in size (v1 = v2). 2

While eq. (1) has been successfully used for a wide range of applications, its major limitation is the residual term only accounts for molecules interacting via dispersion interactions. Higher order interactions may be accounted for by re-writing the cohesive energy density as a sum of contributions (or partial solubility parameters) [2][4][6]. Perhaps the most well-known expansion is that of the Hansen Solubility Parameters (HSP) [5][7]:

2 2 2 2 2 2 2 훿푖 = 훿푖,퐷 + 훿푖,푃 + 훿푖,퐻 = 휆푖 + 휏푖 + (훼푖훽푖) (3)

where δi,D, δi,P , and δi,H correspond to the solubility parameter resulting from dispersion, polar, and association (or hydrogen bonding) interactions, respectively. We equivalently write our dispersion and polar solubility parameters as λi and τi, respectively, and write the association solubility parameter as the product of the contribution due to hydrogen bond acidity (αi) and basicity (βi). This results in: 푣 푙푛훾∞,푅퐸푆 = 2 [(휆 − 휆 )2 + (휏 − 휏 )2 + (훼 훽 − 훼 훽 )2] (4) 2 푅푇 1 2 1 2 1 1 2 2

∞,푅퐸푆 0. It follows that ln 푙푛훾∞,푅퐸푆, the term resulting where we still have for all case 푙푛훾2 ≥ 2 from intermolecular interactions, can only contribute toward positive deviations from Raoult’s law, ∞,퐶푂푀퐵 while 푙푛훾2 can only contribute toward negative deviations from Raoult’s law. As an example of where this is not correct, consider the the binary system acetone/chloroform which is well known to exhibit negative deviations from Raoult’s law and a maximum boiling azeotrope [8]. Recently, using neutron diffraction, this was confirmed to be caused by the association of acetone and chloroform ∞,푅퐸푆 molecules [9]. Using HSP, 푙푛훾2 and the association term may only contribute toward positive deviations from Raoult’s law and is therefore unable to capture the underlying physics of this system. A major difference between MOSCED (MOdified Separation of Cohesive Energy Density) and HSP is that MOSCED separates the association term, resulting in the following system of ∞ equations for γ2 in a binary mixture [10] [11]:

2 2( 푇 푇)2 ( 푇 푇)( 푇 푇) 푎푎2 푎푎2 ∞ 푣2 2 푞1 푞2 휏1 − 휏2 훼1 − 훼2 훽1 − 훽2 푣2 푣2 푙푛훾2 = [(휆1 − 휆2) + + ] + 푙푛 ( ) + 1 − ( ) 푅푇 휓1 휉1 푣1 푣1

2 (푇) (푇) (푇) 푎푎2 = 0.953 − 0.002314 [(휏2 ) + 훼2 훽2 ]

293퐾 0.8 293퐾 0.8 293퐾 0.4 훼(푇) = 훼 ( ) , 훽(푇) = 훽 ( ) , 휏(푇) = 휏 ( ) 푖 푖 푇 푖 푖 푇 푖 푖 푇 (5) where i = {1 or 2}

(푇) (푇) 휓1 = 푃푂퐿 + 0.002628훼1 훽1

1.5 (293퐾/푇)2 휉1 = 0.68(푃푂퐿 − 1) + [3.4 − 2.4 exp(−0.002687(훼1훽1) )]

3 4 (푇) 푃푂퐿 = 푞1 [1.15 − 1.15 exp(−0.002337(휏1 ) ] + 1

where an equivalent expression can be written for component 1 by switching the subscript indices.

The induction parameter, qi, reflects the ability of the nonpolar part of a molecule to interact with a

polar part. The terms ψ1 and ξ1 are empirical (solvent dependent) asymmetry terms to modify the

residual contribution for polar and hydrogen bonding interactions, and aa2 is an empirical (solute dependent) term to modify the size disimilarity in the combinatorial contribution for polar and hydrogen bonding interactions. These additional empirical terms are not adjustable but are

functions of the other parameters (τi, αi, βi and qi). For all cases aa2 ≤ 0.953, effectively reducing the ∞,퐶푂푀퐵 size dissimilarity and magnitude of 푙푛훾2 , with the value smaller for polar and associating compounds. The superscript (T ) is used to indicate temperature dependent parameters, where the temperature dependence is computed using the empirical correlations provided in eq. (5). As

suggested by the equations, MOSCED adopts a reference temperature of 293 K (20 ◦C). An important difference between MOSCED and HSP is that by splitting the association (or ∞,푅퐸푆 hydrogen bonding) term, the contribution to 푙푛훾2 due to association (or hydrogen bonding interactions) may be either positive or negative. The term resulting from intermolecular interactions, ∞,푅퐸푆 푙푛훾2 , may now contribute toward both positive and negative deviations from Raoult’s law. This

4 subtle difference allows MOSCED to capture the underlying physics of solvation of associ-ating compounds. This will be explored in greater detail in the subsection “Association/hydrogen bonding term,” including a discussion of the system acetone/chloroform.

2. Application of MOSCED to Predict Limiting Activity Coefficients, Hydration Free Energies, Henry’s Constants, Octanol/Water Partition Coefficients, and Isobaric Azeotropic Vapor- Liquid Equilibrium

2.1 Introduction ∞ In this present study we relate 훾2 to the solute solvation free energy. This relation between ∞ solvation free energy and 훾2 is valuable for two reasons. First, the solute solvation free energy is a direct measure of solute–solvent intermolecular interactions, which will allow us to focus solely on MOSCED’s ability to capture the challenging solute-solvent intermolecular interactions. The (Lewis/Randall normalized) limiting activity coefficient is a measure of solute– solvent intermolecular interactions, however, these interactions are normalized with respect to the interaction of the solute with itself (i.e., solute–solute interaction). Second, the solvation free energy is a quantity from statistical mechanics that may readily be computed using molecular simulation free energy calculations or electronic structure calculations in a continuum solvent. This therefore provides a route by which molecular simulation and electronic structure calculations may be used to parameterize MOSCED, creating a truly predictive method [12] [13] [14] [15] [16], or to use MOSCED as a tool to guide molecular simulation and to help interpret results. Moreover, reference solvation free energy values are valuable in the optimization of molecular simulation force fields; the importance of such has resulted in the recent development of the FreeSolv and CompSol Databanks for this purpose [17] [18] [19].

2.2 Computational Methods Solvation Free Energy

In the context of classical molecular simulation free energy calculations, we have shown 푠표푙푣 previously that the solvation free energy of a solute (component 2, ∆퐺2 or equivalently the residual chemical potential at infinite dilution, may be related to the limiting (or infinite dilution) activity coefficient of the solute as[12] [28] [29] [30]: 6

(6)

where f 0 is the pure liquid fugacity of the solute. The pure liquid fugacity may be related to the 2 푠푒푙푓 12 solute “self”-solvation free energy (∆퐺2 ) as :

(7)

At low pressures we may assume the vapor phase in equilibrium with the liquid phase at T is an ideal gas (such that the fugacity coefficient is unity) and the Poynting correction is negligible such

퐿 푠푎푡 푠푎푡 1 that 푓2 ≈ 푝2 , where 푝2 is the (pure component) liquid saturation pressure . Solving eq. (6) 푠표푙푣 for ∆퐺2 , we have:

(8)

Note that we define the solvation free energy as the change in free energy of taking a solute from an ideal gas to solution at the same molecular density (or concentration).

Henry’s Constant

The activity coefficient of the solute can be related to the Henry’s constant of the solute (H2,1) by equating the solution phase fugacity computed using a Lewis/Randall (Raoult’s law) and Henry’s law standard state[1]:

(9)

∗ where 훾2is the (asymmetical) activity coefficient of the solute normalized with respect to a ∗ Henry’s law standard state; in the infinite dilution limit, 훾2 = 1. At low pressures we may again assume that the vapor phase in equilibrium with the liquid phase at T is an ideal gas (such that the

fugacity coefficient is unity) and the Poynting correction is negligible such that f L ≈ psat.

Solving for 퐻2,1 in the infinite dilution limit we have:

(10)

Following the previous section, the Henry’s constant can be related to the solute solvation free energy as [31]:

(11)

Partition Coefficient

The distribution of a solute between two immiscible solvents may be described by the solute par-

tition coefficient1. Equating the solute fugacity in solvent I and II at equilibrium, we have:

(12)

Solving for the relative concentration in phase I relative to phase II, and assuming the solute concentration in each solvent is sufficiently small so as to be considered infinitely dilute, we obtain I/II the solute partition coefficient (K2 ):

(13)

The partition coefficient may equivalently be seen as the relative solubility in solvent I relative to I/II solvent II. While K2 is a dimensionless quantity, it is dependent on the units of concentration used. It is common to use molar (mole/volume) or mass concentrations (mass/volume) instead of mole fractions. Having assumed the solute is infinitely dilute, we can readily convert from mole 퐼 퐼 퐼퐼 퐼퐼 fractions to molar or mass concentrations as 푐2 = 푥2/푣퐼and 푐2 = 푥2 /푣퐼퐼. This results in the final expression for the partition coefficient using molar or mass concentrations:

(14)

The partition coefficient can equivalently be computed using solvation free energies as [32] [33]:

(15)

I/II Written in this form, we see that ln P2 is a direct measure of solute–solvent II intermolecular interactions relative to solute-solvent I intermolecular interactions.

Binary Vapor-Liquid Equilibrium

At low pressures we may again assume the vapor phase in equilibrium with the liquid phase at T is an ideal gas (such that the fugacity coefficient is unity) and the Poynting correction is negligible, resulting in the “modified”-Raoult’s law (γ − ϕ approach) to model VLE. Equating the fugacity of

each species i in the liquid and vapor phase, we have1:

sat xiγi (xi,T,p)p i= yip (16)

where yi is the vapor-phase mole fraction of component i and i = {1, 2}. While MOSCED predicts limiting activity coefficients, composition dependent activity coefficients are required for

eq. (16). As suggested by Schreiber and Eckert34, the infinite dilution activity coefficients of a 9 binary pair can be used to parameterize a binary interaction excess Gibbs free energy model. In the present study we will investigate the use of Wilson’s, TK-Wilson, and NRTL (α12 = 0.3) equations[1] [35]. For Wilson’s equation, we have1:

(17)

where Λ12 and Λ21 are adjustable parameters which may be related to the binary (intermolecular) interaction parameters (BIPs) of the system (a12 and a21).

(18)

At infinite dilution, eq. (17) reduces to:

∞ lnγ1 = −ln(Λ12) + 1 − Λ21 (19)

∞ lnγ2 = −ln(Λ21) + 1 − Λ12

∞ ∞ Calculating lnγ1 and lnγ2 using MOSCED, eq. (19) provides a system of two equations with two unknowns (Λ12 and Λ21 or a12 and a21). Solving for Λ12 and Λ21, eq. (17) may be used to calculate composition dependent activity coefficients. Similar expressions for the TK-Wilson and NRTL equations are provided in the Supporting Information accompanying the electronic version of this manuscript. Note that we have not evaluated UNIQUAC as we seek to use methods that may be parameterized solely using information from MOSCED[3].

While the present study is limited to binary VLE, this approach may readily be generalized to model multi-component VLE. The Wilson’s, TK-Wilson, and NRTL equations all have two binary parameters for each pair in the multi-component system, where MOSCED may be used to parameterize each binary pair [1]. This is the approach used by the process simulator CHEMCAD[36], where binary interaction parameters optimized for a binary system are combined to model multicomponent systems. For all VLE calculations, the pure component vapor pressure of each component was computed using the Antoine equation parameters from ref. 37. When predicting isothermal VLE (pxy), ∞ ∞ MOSCED calculations were performed at the temperature of the reference data (lnγ1 and lnγ2 ), which were then used to obtain Λ12 and Λ21 for Wilson’s equation. When predicting isobaric VLE (Txy), MOSCED calculations were performed at 10 equally spaced temperatures between ∞ ∞ the saturation temperature of component 1 and 2. At each temperature, lnγ1 and lnγ2 were used to solve for the BIPs for Wilson’s, TK-Wilson, and NRTL (α12 = 0.3) equations. While all three equations contain a temperature dependence, we performed a linear correlation of the temperature dependent BIPs (i.e., a12 = c0 + c1T ). With the Wilson’s and TK-Wilson equations, we assume the ratio of molar volumes is insensitive to temperature, and use the molar volumes used by MOSCED at 20 ◦C[38].

VLE was then computed by specifying x1 over the range 0 to 1 in increments of 0.05, and then solving for y1 and p or T, for the isothermal and isobaric case, respectively. While we used an equal spacing of x1 for our calculations, this was not necessarily the case in the reference data. To quantitatively compare the predicted values of y1 and p or T to the reference data, we used (1-D) spline interpolation to interpolate the predicted values of y1 and p or T with respect to x1 using

GNU Octave [39][40]. Spline interpolation was used to make predictions at the values of x1 where reference data was available, allowing a direct comparison of the predicted values of y1 and p or T to the reference data.

For all of the calculations (of all properties), reference calculations were additional performed with mod-UNIFAC [21] [26]. All of these calculations were performed using CHEMCAD 7.1.0.9402[36].

For VLE calculations, calculations were performed in increments of x1 of 0.05 mole fractions. To

calculate solvation free energies, Henry’s constants, and partition coefficients, mod-UNIFAC was used to predict limiting activity coefficients. For all solvation free energy and Henry’s constant calculations (using MOSCED and mod-UNIFAC), vapor pressure data was taken from ref. 37.

The necessary molar volumes were assumed constant and taken directly from MOSCED11,38. All of the calculations (of all properties) using MOSCED and mod-UNIFAC are tabulated in the Supporting information of this manuscript along with the reference data to which comparison is made. We additionally tabulate the MOSCED [11] and Antoine parameters[37] for all 130 organic solvents and water for which MOSCED is parameterized. 2.3 Result and Discussions.

Association/hydrogen bonding term

As already mentioned, solubility parameter-based methods are powerful in that they can both make quantitative predictions and give qualitative, molecular-level insight which may be used for intuitive solvent selection and formulation. Comparing MOSCED and HSP, a major difference is ∞,RES MOSCED separates the association (or hydrogen bonding) term in ln γ2 . We will illustrate how this is able to better describe the underlying physics of associating fluids using three examples: acetone/chloroform, methanol/acetone, and methanol/N-methylpyrrolidone. In this discussion re- ∞,RES member that ln γ2 results from intermolecular interactions and compares 2–1 (solute–

solvent) interactions relative to solute–solute (2–2) interactions. MOSCED αi and βi values may be found in table 1. Here our focus is on the ability of MOSCED to capture positive and negative deviations from Raoult’s law, and the interpretation of the results. While it is possible to observe deviations from Raoult’s law using isobaric VLE, we will consider isothermal VLE for which it is easier to visually observe the deviations.

11 Table 1: MOSCED association parameters for chloroform, acetone, methanol, and N- 1/2 3 1/2 methylpyrrolidone, where αi and βi have units of MPa or (J/cm ) .

Species (i) αi βi chloroform 5.80 0.12

acetone 0.00 11.14 methanol 17.43 14.49 N-methylpyrrolidone 0.00 24.22

First, consider the binary system of acetone(1)/chloroform (2). Chloroform has three weak C-

H hydrogen bond donating sites (proton donor, α2), and a weaker C-Cl halogen bonding site

(proton donor and acceptor, α2 and β2). On the other hand, acetone has a moderately strong C=O 41 hydrogen bond accepting site (β1) . We find that α2 > α1 while β2 < β1, indicating that chloroform would prefer to associate with acetone and acetone would prefer to associate with chloroform, then either component with itself. Favorable cross-interactions are expected to lead to negative deviations from Raoult’s law (ln γ1 < 0 and ln γ2 < 0). Looking at the association ∞,RES term in ln γ2 , we find that (α1 − α2) (β1 − β2) < 0. It follows that the association2 term is ∞ ∞ negative; the favorable cross-interactions result in a negative contribution to ln γ1 and ln γ2 , contributing toward negative deviations from Raoult’s law.

The self-association of each species is given by the product α1β1 and α2β2. For acetone, this product is 0, indicating that it does not associate with itself. For chloroform, this product is 0.696

J/cm3, suggesting weak association (C-H· · · Cl-C and C-Cl· · · Cl-C) interactions. It is exactly 2 this difference in self-association terms that is compared in HSP: (α1β1 − α2β2) . This results only in contributions to ln γ∞ and ln γ∞ that are greater than 0. HSP can only predict values of ∞,RES ∞,RES ln γ2 and ln γ2 greater than or equal to zero. Therefore, the only term that can contribute to negative deviations from Raoult’s law is the combinatorial term (COMB) which results from size and shape dissimilarities and is not due to intermolecular interactions. We see that as compared to HSP, the splitting of the association term in MOSCED allows us to better capture the underlying physics of the process, which we ultimately expect to lead to better quantitative predictions for associating fluids. We may additionally obtain an alternative (but equivalent) interpretation of the MOSCED association term by expanding and re-arranging it:

̅̅̅̅ ̅̅̅̅ (훼1 − 훼2)(훽1 − 훽2) = −(훼1훽2 + 훼2훽1) + (훼1훽1 + 훼2훽2) = −2(훼훽푐푟표푠푠 − 훼훽푠푒푙푓) (20)

where we have defined αβcross and αβself to be the mean “cross” and “self” association term (or energy), respectively:

(21)

In this light, we observe positive deviation from Raoult’s law for binary mixtures in which the components prefer to associate with themselves, where the mean self-association term is greater than the mean cross-association term (αβself > αβcross). On the other hand, we observe negative deviation from Raoult’s law for binary mixtures in which the components prefer to associate with each other rather than themselves, where the mean cross-association term is greater than the mean self-association term (αβcross > αβself ). This can be compared directly to HSP where the squared difference of the self-association term of each species is computed.

In the top pane of fig. 1 we plot the pxy phase-diagram for acetone(1)/chloroform(2). The system exhibits negative deviations from Raoult’s law and a minimum boiling azeotrope, with the predictions made using MOSCED in close agreement with experiment8. Observed recently using neutron scattering, the dominant contribution to the minimum boiling azeotrope is the strong association (hydrogen bonding) between chloroform and acetone9. This is in exact agreement 3 with MOSCED; α2β1 = 64.612 J/cm , which is two orders of magnitude greater than either self- association term.

Consider next the binary system of methanol(1)/acetone (2). The O-H group of methanol is a

moderately strong hydrogen bond donor and acceptor, and we find that α1 > α2 and β1 > β2. We therefore expect methanol to prefer to associate with itself rather than with acetone, which

would result in positive deviations from Raoult’s law (ln γ1 > 0 and ln γ2 > 0). This is exactly

captured by MOSCED where (α1 − α2) (β1 − β2) > 0. In the middle pane of fig. 1 we plot the pxy phase-diagram for methanol(1)/acetone (2), and find the predictions made using MOSCED result in positive deviations from Raoult’s law in agreement with experiment[42].

It follows that if we seek a species (component 2) that when mixed with methanol (component 1) results in negative deviations from Raoult’s law, we need to find a species such that either

α2 > α1 or β2 > β1, such that (α1 − α2) (β1 − β2) < 0. One candidate that fits this requirement is N-

methylpyrrolidone, for which β2 > β1. In the bottom pane of fig. 1 we plot the bubble line (px) for methanol(1)/N-methylpyrrolidone(2), and find the predictions made using MOSCED result in negative deviations from Raoult’s law in agreement with experiment[43].

Limiting Activity Coefficient, Solvation Free Energy, and Henry’s Constant

In the 2005 MOSCED parameterization, parameters were regressed for 130 organic solvents using ∞ 6441 reference limiting activity coefficients. The root mean squared error (RMSE) for ln훾2 was ∞ 11,44 0.148, and the average absolute error (AAE) for 훾2 was 10.6% . With the MOSCED parameters for the 130 organic solvents set, the authors then regressed MOSCED parameters for water using reference limiting activity coefficients for organic solutes in water, and obtained a much ∞ 11,44 larger AAE for 훾2 of 41.1% . Given the inferior performance for water, we will consider the ∞ specific case of solvation in water. We first compare the ability of MOSCED to predict ln훾2 for organics in water to reference data from ref. 45, mostly at 25 ◦C. Of the systems in the MOSCED database, predictions could be made for 88 solutes. The results of the predictions are summarized ∞ in table 2 and fig. 2. We obtain an AAE for ln 훾2 of 0.83 with a standard deviation (SD) of 0.75, and a Pearson’s correlation coefficient of R2 = 0.96. Predictions could be made for 58 of the systems using mod-UNIFAC. With this reduced set we obtain an AAE of 2.31 with an of 2.15, and R2 = 0.78.

Table 2 : A summary of the number of solutes (N) for which log limiting activity coefficients ∞ (ln휸ퟐ ) were calculated in water, the average absolute error (AAE) and the corresponding standard deviation (SD), and Pearson’s correlation coefficient (R2) of the calculations versus the reference data45. METHOD N AAE SD R2 MOSCED 88 0.83 0.75 0.96 MOD-UNIFAC 58 2.31 2.15 0.78

Figure 2 : Parity Plot of ln γ2 ∞ for organics in water predicted using MOSCED [11] and mod-UNIFAC [21][36] versus reference values from ref 45. The dashed lines indicate an error of ±2 log units.

Next, we focus the calculation of solvation free energies, which are a direct measure of solute– solvent intermolecular interactions. For the specific case of solvation in water, this corresponds to hydration free energies. We compare predictions using MOSCED to reference

values at 25 ◦C from the FreeSolv database [17] [18] [20] with the results summarized in table 3. Of the systems in the database, MOSCED predictions could be made for 73 solutes. We obtain an AAE of 2.04 kJ/mol with an SD of 2.73 kJ/mol, and R2 = 0.94. The FreeSolv database also contains predictions using state-of-the-art molecular simulation methods which has been used to assess the accuracy of conventional molecular models. For the same set of 73 solutes, the simulation results obtain an AAE of 2.85 kJ/mol with an SD of 3.69 kJ/mol, and R2 = 0.94. We find that the predictions made using MOSCED are comparable to the much more computationally expensive and more detailed molecular simulation results, with MOSCED resulting in a smaller overall AAE. The FreeSolv database additionally includes the uncertainty of the experimental measurements [20]. For the set of 73 solutes studied here, the mean uncertainty is 2.33 kJ/mol with an SD of 0.51 kJ/mol. We find that the mean uncertainty in the experimental data is greater than the AAE for the MOSCED predictions. With mod-UNIFAC, of the 73 solutes examined using MOSCED, groups were available to model 60 of the solutes. For this reduced set we obtain an AAE of 7.95 kJ/mol with an SD of 9.31 kJ/mol, and R2 = 0.70.

Table 3 : A summary of the number of solutes (N) for which hydration free energies were calculated, the average absolute error (AAE) and the corresponding standard deviation (SD), and 17,18,20 Pearson’s correlation coefficient (R2) of the calculations versus the reference data , where all hydration free energy calculations were in units of kJ/mol.

METHOD N AAE SD R2 MOSCED 73 2.04 2.73 0.94 MOD-UNIFAC 60 7.95 9.31 0.7

MOLECULAR 73 2.85 3.69 0.94 SIMULATION

While in the 2005 MOSCED parameterization MOSCED was found to perform the worst when water was the solvent, we find here that the predicted hydration free energies are superior to mod- UNIFAC and comparable to results obtained using molecular simulation. This is additionally illustrated in the parity plot of the predictions versus the reference data provided in fig. 3.

Figure 3: Parity plot of the solute solvation free energy in water (hydration free energy, ΔG2solv), predicted using MOSCED,11 modUNIFAC,[21−26],[36] and molecular simulation [17],[18],[20] versus reference data.[17],[18],[20] The20 dashed lines indicate an error of ±5 kJ/mol or approximately 2RT. Likewise, we next compute log Henry’s constants (ln H2,1) for organic solutes (2) in water (1). From eq. (11), we see that ln H2,1 is equal to the dimensionless solvation free energy (here hydration free energy) plus the log of the solvent molar volume. ln H2,1 may therefore additionally be used as a direct measure of solute–solvent intermolecular interactions. This affords us the opportunity to both demonstrate the calculation of an additional property and to compare to an independent database from ref. 45. As compared to our hydration free energy calculations, with both MOSCED and mod-UNIFAC, we are able to make predictions for an additional eight solutes. When calculating ln H2,1, H2,1 had units of kPa.

The results of predicting ln H2,1 using both MOSCED and mod-UNIFAC are summarized in table 4 and are shown graphically in the parity plot of the predictions versus the reference data in fig. 4. With MOSCED, we obtain an AAE of 0.74 with an SD of 1.07, and R2 = 0.97. With mod- 2 UNIFAC, we obtain an AAE of 1.44 with an SD of 1.93, and R = 0.71. The results for ln H2,1 ∞ are consistent with our hydration free energy and ln 훾2 calculations; predictions made using MOSCED have a smaller AAE and SD as compared to mod-UNIFAC, and have an R2 value closest to 1.

Table 4 : A summary of the number of solutes (N) for which log Henry’s constan2,1) were calculated in water, the average absolute error (AAE) and the corresponding standard deviation (SD), and 2 45 Pearson’s correlation coefficient (R ) of the calculations versus the reference data , where H21 was calculated in units of kPa. METHOD N AAE SD R2 MOSCED 81 0.74 1.07 0.97 MOD-UNIFAC 68 1.44 1.93 0.71

Figure 4: Parity plot of log Henry’s constants (ln 2,1 / ) for organics in water, predicted using MOSCED11 and mod-UNIFAC21−26,36 versus reference data from ref 45. The dashed lines indicate an error of ±2 log unit

Partition Coefficients

Next, we consider the ability of MOSCED to predict octanol/water (I/II) partition coefficients (ln PI/II). The study of octanol/water partition coefficients are of particular interest because of 2 their utility to correlate biological activity, which has resulted in compilations of volumes of reference data[46]. More importantly, in the present study, octanol/water parition coefficients allow us to probe the ability of MOSCED to model the intermolecular interactions between the solute and water relative to the solute and 1-octanol (a lipophilic reference solvent). We will use eq. (14) and ignore the mutual solubility of water and 1-octanol, consistent with refs. 46,47.

I/II We compare predictions of ln P2 using MOSCED to reference values at 25 ◦C from ref. 45, with the results summarized in table 5. Of the systems in the database, MOSCED predictions could be made for 117 solutes. We obtain an AAE of 0.92 with an SD of 1.43, and R2 = 0.93. Of the 117 solutes examined using MOSCED, mod-UNIFAC groups were available to model 96 of the solutes. For this reduced set we obtain an AAE of 1.95 with a SD of 3.04, and R2 = 0.60. The results are also summarized graphically in fig. 5.

Table 5 : A summary of the number of solutes (N) for which log octanol(I)/water(II) partition coefficients (ln PI/II) were calculated, the average absolute error (AAE) and the corresponding standard deviation (SD), and Pearson’s correlation coefficient (R2) of the calculations versus the reference 45 data , where molar concentrations (moles/volume) were used in the calculation of ln PI/II. METHOD N AAE SD R2 MOSCED 117 0.92 1.43 0.93 MOD-UNIFAC 96 1.95 3.04 0.60

Figure 5: Parity plot of log octanol(I)/water(II) partition coeﬃcients (ln P2I/II), predicted using MOSCED11 and mod-UNIFAC21−26,36 versus reference data from ref 45. The dashed lines indicate an error of ±2.8 log units. This is indicative of an error of approximately 2RT in ΔG2I,solv and ΔG2II,solv.

I/II Notice in fig. 5 that the predictions break from the trend for reference values of ln P2 < 0. A 2 value of ln PI/II < 0 would indicate a hydrophilic solute; a solute that prefers water. For these cases the MOSCED predictions appear to over-predict the solute affinity for water (hydrophilicity). However, we can understand this deviation if we consider as an example ternary liquid-liquid equilibrium with water/methanol/1-octanol at 25 ◦C. Starting with the binary water/1-octanol, the aqueous-phase is pure water while the organic phase is 0.732 mole fractions 1-octanol. As the amount of methanol added to this system increases, the amount of water in the organic phase also increases. When we have a mole fraction of methanol of 0.3995 in the organic phase, the solute-free mole fraction of octanol has decreased to 0.2390 mole fractions. At the same time, the solute-free mole fraction of water in the aqueous phase is 0.9815, very close to 1[48]. We expect similar behavior for the other hydrophilic solutes. For these cases, the assumptions of immiscible solvents and an infinitely dilute solute used to derive eq. (14) are not appropriate. The actual value of the reported partition coefficient will also be sensitive to the conditions used to make the measurement [48]. Likewise, since the assumption of a pure 1-octanol phase is inadequate, ref. 49 has cautioned against using octanol/water partition coefficients as a means to compute limiting activity coefficients. Nonetheless, for these systems MOSCED still predicts the correct qualitative behavior that the solutes prefer water over 1-octanol.

Overall, we find that MOSCED is able to model a wider range of solutes and offers superior predictions. While the MOSCED parameters for the 117 solutes for which predictions were made were regressed using experimental data, this result is encouraging as it suggests that MOSCED is able to accurately balance the hydrophilic and hydrophobic interactions of a molecule.

Azeotropic vapor/liquid equilibrium

Last, we consider the use of MOSCED to predict binary isobaric (Txy) azeotropic VLE. Azeotropic VLE results from deviations from ideality, with either favorable of disfavorable cross interactions.

Additionally, the prediction of isobaric VLE offers the additional challenge of accurately calculating temperature dependent activity coefficients. 25

We looked at a total of 17 binary systems [50], which are summarized in table 6. These systems were selected by searching through parts 1, 2a, 2b, 2h and 7 of the DECHEMA “Vapor- Liquid Equilibrium Data Collection”[51][52][53][54] and the DECHEMA “Recommended Data of 56 Selected Compounds and Binary Mixtures” for all possible binary pairs that could be modeled using the existing MOSCED parameters for 130 organic solvents plus water[11][44][57].

Figure 6: A plot of the relative volatility (α1,2 = K1/K2) and the volatility of each component (K1 and K2) for the binary system cyclohexane(1)/1,2-dichloroethane(2) at 1.013 bar. The solid black line is experimental reference data51−56 and the dotted black lines are drawn for convenience as ±20% error in the reference data. The dashed lines correspond to predictions made using mod-UNIFAC21−26,36 and using MOSCED to parametrize NRTL (α = 0.3), TK−Wilson,26 and Wilson’s equation, as indicated. The horizontal gray line in the top plot corresponds to α1,2 = 1 and is useful for locating the azeotrope. The vertical gray line in the bottom two plots corresponds to x1 = 0.3 and x2 = 0.3, respectively, and is used to identify the dilute region.

The agreement between the predictions and reference data was quantified by comparing the computed volatility of component 1, K1, when component 1 is dilute, where here we take x1 <

0.3 to mean dilute [58][59]. We also compare the computed volatility of component 2, K2, when component 2 is dilute (x2 < 0.3 ), where

푦푖 퐾푖 = = 훾푖 (22) 푥푖 푝 we see that the volatility is directly proportional to the activity coefficient, where p is constant 푠푎푡 and 푝푖 is computed using reference Antoine equation parameters from ref. 37. A plot of the relative volatility (α1,2), K1, and K2 versus x1 is provided in fig. 6 for the representative system cyclohexane(1)/1,2-dichloroethane(2). This system was chosen because it had the largest number of reference data. We find in the plots for K1 and K2 that the predictive methods exhibit the largest deviation from the reference data in the dilute region, with all of the predictions in close agreement with the reference data outside this region. We additionally find in the plot for α1,2 that all of the predictive methods are able to predict the composition of the azeotrope in good agreement with the reference data. Txy and McCabe-Thiele (yx) diagrams are also provided in the Supporting In- formation accompanying the electronic version of this manuscript for four representative systems. A summary of the quantitative agreement between the predictions and reference data is provided in table 6. The percent average absolute relative error (AARE) is computed as

|퐾푟푒푓−퐾푝푟푒푑| 푁 푖 푖 퐴퐴푅퐸 = ∑푖 푟푒푓 (23) 퐾푖 where the superscript “ref” and “pred” indicated reference and predicted data, respectively, where the summation is over all N compositions for which reference data is available for comparison. A summary of agreement between the predictions and reference data in terms of error in y1 and T is additionally provided in the Supporting Information accompanying the electronic version of this manuscript. For the MOSCED predictions, we find that the best overall predictions are made using Wilson’s equation. This is consistent with ref. 60 which found for the entire DECHEMA “Vapor- Liquid Equilibrium Data Collection”, Wilson’s equation was on 27

average able to best correlate VLE data. Comparing our MOSCED predictions using Wilson’s equation to mod-UNIFAC, we find that mod-UNIFAC on average performs better. However, the

difference is small. The average differance in K1 and K2 in the dilute region is 5.5 and 2.7%,

respectively. The average difference in AAE for y1 and T is 0.009 mole fractions and 0.568 K, respectively. Comparing to mod-UNIFAC, we therefore conclude that MOSCED with Wilson’s equation performs well, especially given the non-ideality of the systems studied.

Table 6 : A summary of the percent average absolute relative error (AARE) in the volatility of components 1 (K1) and 2 (K2) in the dilute region, x1 < 0.3 and x2 < 0.3, respectively, of the predictions versus reference data51–56. For each system, N corresponds to the number of experimental data points available for comparison, and predictions were made using mod-UNIFAC and using MOSCED to parameterize NRTL, Wilson’s, and TK-Wilson equations as described in the text. For all cases, in the system name the first component corresponds to component 1. In the last line of the table, we calculate the average of AARE for all of the systems studied.

System Ki mod- NRTL WILSO TK- N UNIFAC N WILSON cyclohexane/1,2- 1 8.644 3.446 6.953 6.924 14 dichloroethane 2 3.943 6.643 4.322 4.322 14 1&2 6.294 5.044 5.638 5.623 28 ethanol/1,2- 1 5.307 8.055 4.547 4.764 6 dichloroethane 2 4.480 13.025 6.163 5.993 6 1&2 4.831 10.541 5.355 5.378 12 ethanol/water 1 2.666 15.578 22.203 29.462 6 2 1.033 7.407 9.414 26.632 2 1&2 2.258 13.670 19.006 28.755 8 1-propanol/water 1 2.341 18.509 15.265 17.333 5 2 2.293 18.414 12.953 12.825 3 1&2 2.323 18.473 14.398 15.642 8 2-propanol/water 1 25.266 55.217 52.771 52.220 5

2 3.590 11.224 2.904 38.269 4 1&2 15.632 33.321 25.067 46.020 9 2-butanone/water 1 30.151 37.359 32.213 37.316 8 2 6.870 4.586 8.143 28.219 4 1&2 22.391 25.442 24.189 34.284 12 acetonitrile/water 1 30.924 42.422 44.970 45.259 6 2 15.612 25.29 33.2566 34.144 5 1&2 23.620 34.637 39.646 40.207 11 benzene/2-propanol 1 9.219 6.835 14.737 14.717 9 2 26.027 25.039 26.277 26.277 7 1&2 17.623 14.799 19.786 19.775 16 chloroform/methano 1 3.103 28.122 14.637 14.479 7 l 2 2.788 8.702 5.730 5.605 6 1&2 2.958 19.159 10.526 10.392 13 cylohexanone/phen 1 52.045 168.82 39.047 39.070 5 ol 2 2 46.290 279.09 40.025 40.025 3 6 1&2 50.123 210.17 39.423 39.547 8 5 ethyl-acetate/water 1 45.123 50.134 49.849 44.375 4 2 64.983 93.242 65.229 110.067 3 1&2 53.635 68.609 56.440 72.529 7 methanol/benzene 1 5.944 13.187 11.800 5.944 7 2 11.538 17.200 20.103 11.538 7 1&2 8.741 15.194 15.952 8.741 14 methanol/cyclohexa 1 7.025 9.305 7.260 4.328 5 ne 2 29.209 20.714 14.702 5.558 6 29

1&2 19.125 15.528 11.319 4.998 11 water/pyridine 1 18.761 20.978 24.308 28.547 1 2 45.916 66.722 70.709 73.532 9 1&2 43.201 62.148 66.609 69.034 10 ethanol/acetonitrile 1 1.089 12.554 1.570 1.550 4 2 2.385 16.616 4.812 4.801 3 1&2 1.459 13.714 5.293 5.293 7 benzene/acetonitrile 1 2.036 12.432 3.330 2.990 8 2 10.168 4.078 9.519 8.251 5 1&2 4.538 9.647 5.580 5.014 13

methanol/tetrahydro 1 –50 3.484 10.643 15.523 2 furan 2 7.029 6.683 10.046 5 –50 1&2 6.016 7.814 11.601 7 –50 average 1 15.603 29.791 20.947 21.459 2 17.327 36.766 20.056 25.653 1&2 17.422 32.775 21.884 24.873

Earlier, we found that MOSCED predictions of limiting activity coefficients in water, hydration free energies, Henry’s constants in water, and octanol/water partition coefficients were in better agreement with reference data than mod-UNIFAC. All of these calculated properties were directly related to limiting activity coefficients, which could be directly computed using MOSCED. This suggests that MOSCED was better able to predict limiting activity coefficients, while mod- UNIFAC is better able to predict VLE. When predicting VLE with MOSCED, we are dependent on an excess Gibbs free energy model to predict composition dependent activity coefficients. Schreiber and Eckert[34] previously looked at the ability to use Wilson’s equation parameterized using infinite dilution activity coefficients to predict binary isothermal (pxy) VLE for 31 miscible pairs. Overall, they found the predictions were in good agreement with experiment, and that one may use relatively imprecise ∞ ∞ values of 훾1 and 훾2 and still obtain good VLE predictions. Correlating isothermal VLE data, they obtained 30

an overall AAE in y1 of 0.0075 mole fractions using Wilson’s equation. When they instead used ∞ ∞ experimental values of 훾1 and 훾2 to parameterize Wilson’s equation, they obtained an overall AAE in y1 of 0.0086 mole fractions, an increase of 15%. Here, for isobaric (Txy) VLE, we ∞ expect the deviation to be larger as a result of requiring temperature dependent values 훾1 and ∞ 훾2 . This result is consistent with the findings of the first mod-UNIFAC paper [21]. In that work, the authors first attempted to use only limiting activity coefficient data to parameterize mod- UNIFAC. The authors were then able to predict this set of limiting activity coefficients with an overall AAE of 5.3%. Using this set of parameters, they were able to to predict VLE with an overall AAE of y1 of 0.0096 mole fractions. If they additionally included VLE data in the parameterization, the overall AAE for limiting activity coefficients increased slightly to 5.6%, and the overall AAE of y1 decreased to 0.0079 mole fractions. However, both sets of parameters performed poorly when predicting excess enthalpies. When excess enthalpy data was included in the parameterization, the predictions improved considerably. It follows that to improve the prediction of a particular property, experimental values of that property should be included in the parameterization. This comes at the slight expense of the other properties used in the parameterization. This is consistent with the results of the present study. We expect MOSCED to perform best when predicting limiting activity coefficients because MOSCED was parameterized using only limiting activity coefficient data, with only about 15% of the limiting activity coefficients from VLE [11]. Nonetheless, the value of the limiting activity coefficients from VLE are sensitive to the excess Gibbs free energy model used to correlate the data. On the other hand, mod-UNIFAC [21][26] is parameterized using limiting activity coefficients, VLE, liquid-liquid equilibrium, solid-liquid equilibrium, azeotropic data, excess enthalpies, and excess heat capacities. While MOSCED is in better agreement with experimental data when predicting limiting activity coefficients, mod-UNIFAC performs better when predicting azeotropic VLE.

3.4 Conclusion

In the present study, we assessed the ability of MOSCED to predict solvation free energies (specifically hydration free energies) and Henry’s constants for solutes in water, and octanol/water partition coefficients. It was shown how Henry’s constants and partition coefficients may be directly related to solvation free energies, allowing us to probe directly MOSCED’s ability to accurately capture solute–solvent intermolecular interactions. Comparison of the computed hydration free energies to state-of-the-art molecular simulations demonstrated that MOSCED was able to predict hydration free energies in greater agreement with experiment. We propose that MOSCED and molecular simulation may be used as two complementary tools. MOSCED may be used to save computational time by performing solvation free energy calculations and computing phase- equilibria, computationally intensive tasks to perform using molecular simulation. Additionally, by relating solvation free energies to infinite dilution activity coefficients, we present the opportunity to use molecular simulation free energy calculations or electronic structure calculations in a continuum solvent to obtain missing MOSCED parameters, making MOSCED a truly predictive method. The computed hydration free energies, Henry’s constants, and partition coefficients were additionally compared to mod-UNIFAC. For all of these cases, the predictions made with MOSCED were found to be superior to that of mod-UNIFAC. Of the reference sets examined, MOSCED was able to model more compounds than mod-UNIFAC. However, at present, MOSCED is limited to 130 organic solvents and water while mod-UNIFAC is a group contribution method, so mod-UNIFAC would be able to model additional compounds outside this set. Be that as it may, the ability to use molecular simulation or electronic structure calculations in a continuum solvent to parameterize MOSCED presents an opportunity to expand the MOSCED parameter database. Moreover, MOSCED is parameterized for a wide range of chemical classes, making the development of a group contribution MOSCED an intriguing possibility. The excellent performance of MOSCED as compared to molecular simulation and mod-UNIFAC is additionally encouraging because during the 2005 parameterization of MOSCED, errors in the

predictions where water was a solvent were substantially larger than for any other case. Here

32 we find that while MOSCED performs worst when water is the solvent, this is still improved as compared to molecular simulation and mod-UNIFAC. Additionally, MOSCED’s ability to predict octanol/water partition coefficients in good agreement with experiment suggests that MOSCED is able to accurately balance a compound’s hydrophobic and hydrophilic interactions. Comparison to mod-UNIFAC was additionally made to compute binary isobaric azeotropic vapor-liquid equilibrium. Azeotropic vapor-liquid equilibrium corresponds to significant deviations from ideality, and isobaric vapor-liquid equilibrium presents the additional challenge of predicting temperature dependent activity coefficients. Overall for the examined reference set, we find that predictions made using mod-UNIFAC are in better agreement with the reference data than MOSCED, although the difference is not large. This performance is expected. While MOSCED is parameterized solely using infinite dilution activity coefficients, mod-UNIFAC additionally includes vapor-liquid equilibrium and azeotropic data in its parameterization. In addition to making quantitative predictions, the use of solubility parameter-based methods are advantageous as they provide qualitative insight into the underlying molecular-level driving forces for the behavior of a system. This allows us to both understand the observed behavior from a molecular level, in addition to allowing for intuitive solvent selection and design by comparing solubility parameters. As compared to regular solution theory and Hansen Solubility Parameters, the use of MOSCED is advantageous as it splits the association term into contributions due to hydrogen bond acidity and basicity. We demonstrated how this subtle difference allows MOSCED to better model the molecular interactions of associating fluids. Additionally, to facilitate the adoption and use of MOSCED, an interactive software suite (MOSCED-CAD) has been developed. MOSCED-CAD can be used to calculate all of the properties described in the present study, in addition to binary interaction parameters for the Wilson and NRTL equations for use in a process simulator. A copy of the current user manual is provided in the Supporting Information accompanying the electronic version of this manuscript, which includes instructions for downloading from our personal website[27].

2.5 References

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(13) Phifer, J. R.; Solomon, K. J.; Young, K. L.; Paluch, A. S. Computing MOSCED parameters of nonelectrolyte solids with electronic structure methods in SMD and SM8 continuum solvents. AIChE J. 2017, 63, 781–791.

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(16) Diaz-Rodriguez, S.; Bozada, S. M.; Phifer, J. R.; Paluch, A. S. Predicting cyclohexane/water distribution coefficients for the SAMPL5 challenge with MOSCED and the SMD solvation model. J. Comput.-Aided Mol. Des. 2016, 30, 1007–1017.

(17) Mobley, D. L.; Guthrie, J. P. FreeSolv: a database of experimental and calculated hydration free energies, with input files. J. Comput.-Aided Mol. Des. 2014, 28, 711–720.

(18) Matos, G. D. R.; Kyu, D. Y.; Loeffler, H. H.; Chodera, J. D.; Shirts, M. R.; Mobley, D. L.

Approaches for Calculating Solvation Free Energies and Enthalpies Demonstrated with an Update of the FreeSolv Database. J. Chem. Eng. Data 2017, 62, 1559–1569.

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(20) FreeSolv: Experimental and Calculated Small Molecule Hydration Free Energies, Version

0.51 (June 11, 2017). https://github.com/MobleyLab/FreeSolv.

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Ind. Eng. Chem. Res. 1987, 26, 1372–1381.

(22) Gmehling, J.; Li, J.; Schiller, M. A Modified UNIFAC Model. 2. Present Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Eng. Chem. Res. 1993, 32, 178– 193.

(23) Gmehling, J.; Lohmann, J.; Jakob, A.; Li, J.; Joh, R. A Modified UNIFAC (Dortmund) Model.

3. Revision and Extension. Ind. Eng. Chem. Res. 1998, 37, 4876–4882.

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(25) Jakob, A.; Grensemann, H.; Lohmann, J.; Gmehling, J. Further Development of Modified UNIFAC (Dortmund): Revision and Extension 5. Ind. Eng. Chem. Res. 2006, 45, 7924–7933.

(26) Constantinescu, D.; Gmehling, J. Further Development of Modified UNIFAC (Dortmund): Revision and Extension 6. J. Chem. Eng. Data 2016, 61, 2738–2748.

(27) A Better Solution Ahead: Welcome to MOSCED. https://sites.google.com/ view/mosced, (accessed December 1, 2017).

(28) Paluch, A. S.; Maginn, E. J. Predicting the Solubility of Solid Phenanthrene: A Combined Molecular Simulation and Group Contribution Approach. AIChE J. 2013, 59, 2647–2661.

(29) Fuerst, G. B.; Ley, R. T.; Paluch, A. S. Calculating the Fugacity of Pure, Low Volatile Liquids via Molecular Simulation with Application to Acetanilide, Acetaminophen, and Phenacetin. Ind. Eng. Chem. Res. 2015, 54, 9027–9037.

(30) Noroozi, J.; Paluch, A. S. Microscopic Structure and Solubility Predictions of Multifunctional Solids in Supercritical Carbon Dioxide: A Molecular Simulation Study. J. Phys. Chem. B 2017, 121, 1660–1674.

(31) Paluch, A. S.; Maginn, E. J. Efficient Estimation of the Equilibrium Solution-Phase Fugac- ity of Soluble Nonelectrolyte Solids in Binary Solvents by Molecular Simulation. Ind. Eng. Chem. Res. 2013, 52, 13743–13760.

(32) Paluch, A. S.; Vitter, C. A.; Shah, J. K.; Maginn, E. J. A comparison of the solvation thermodynamics of amino acid analogues in water, 1-octanol and 1-n-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids by molecular simulation. J. Chem. Phys. 2012, 137, 184505.

(33) Paluch, A. S.; Parameswaran, S.; Liu, S.; Kolavennu, A.; Mobley, D. L. Predicting the excess solubility of acetanilide, acetaminophen, phenacetin, benzocaine, and caffeine in binary water/ethanol mixtures via molecular simulation. J. Chem. Phys. 2015, 142, 044508.

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(36) CHEMCAD 7.1.0.9402. http://www.chemstations.com.

(37) Yaws, C. L.; Narasimhan, P. K.; Gabbula, C. Yaws’ Handbook of Antoine Coefficients for Vapor Pressure (2nd Electronic Edition); Knovel, 2009.

(38) For water, in MOSCED calculations we use a molar volume of v = 36 cm3/mol. For VLE calculations with Wilson’s and TK-Wilson equations, and octanol/water partition coefficient

calculations, we use a molar volume of v = 18 cm3/mol.

(39) Eaton, J. W.; Bateman, D.; Hauberg, S. GNU Octave version 3.0.1 manual: a high-level interactive language for numerical computations; CreateSpace Independent Publishing Platform, 2009; ISBN 1441413006.

(40) When quantitatively comparing the predicted T and y1 to reference data, data at x1 = 0 and

x1 = 1 were excluded.

(41) Jeffrey, G. A. An Introduction to Hydrogen Bonding; Oxford University Press, Inc.: New York, NY, 1997.

(42) Góral, M.; Kolasin´ska, G.; Warycha, P. O. S. Vapor-Liquid Equilibria. II. The Ternary System Methanol-Chloroform-Acetone at 313.15 and 323.15 K. Fluid Phase Equilib. 1985, 23, 89– 116.

(43) Horstmann, S.; Fischer, K.; Gmehling, J. Isothermal Vapor-Liquid Equilibrium and Ex- cess Enthalpy Data for the Binary System Water+Sulfolane and Methanol+N-Methyl-2- pyrrolidone. J. Chem. Eng. Data 2004, 49, 1449–1503.

(44) Lazzaroni, M. J. Optimizing Solvent Selection for Separation and Reaction. Ph.D. thesis, Georgia Institute of Technology, 2004.

(45) Yaws, C. L. Yaws’ Handbook of Properties for Aqueous Systems; Knovel, 2012.

(46) Sangster, J. Octanol-Water Partition Coefficients of Simple Organic Compounds. J. Phys. Chem. Ref. Data 1989, 18, 1111–1227.

(47) Campbell, J. R.; Luthy, R. G. Prediction of Aromatic Solute Partition Coefficients Using the UNIFAC Group Contribution Model. Environ. Sci. Technol. 1985, 19, 980–985.

(48) Arce, A.; Blanco, A.; Souza, P.; Vidal, I. Liquid-Liquid Equilibria for Water + Methanol + 1-Octanol and Water + Ethanol + 1-Octanol at Various Temperatures. J. Chem. Eng. Data 1994, 39, 378–380.

(49) Sherman, S. R.; Trampe, D. B.; Bush, D. M.; Schiller, M.; Eckert, C. A.; Dallas, A. J.; Li, J.; Carr, P. W. Compilation and Correlation of Limiting Activity Coefficients of Nonelectrolytes in Water. Ind. Eng. Chem. Res. 1996, 35, 1044–1058.

(50) Confirmed using the “Group Assignment” tool online provided by DDBST at http:

//www.ddbst.com/unifacga.html, mod-UNIFAC groups exist for tetrahydrofuran (THF). However, these groups were not available in CHEMCAD. VLE calculations with mod- UNIFAC were therefore not performed for methanol/THF.

(51) Gmehling, J., Onken, U., Eds. Vapor-Liquid Equilibrium Data Collection, Part 1: Aqueous- Organic Systems; DECHEMA: Frankfurt am Main, Germany, 1977.

(52) Gmehling, J., Onken, U., Eds. Vapor-Liquid Equilibrium Data Collection, Part 2a: Organic Hydroxy Compounds: Alcohols; DECHEMA: Frankfurt am Main, Germany, 1977.

(53) Gmehling, J., Onken, U., Arlt, W., Eds. Vapor-Liquid Equilibrium Data Collection, Part 2b: Organic Hydroxy Compounds: Alcohols and Phenol; DECHEMA: Frankfurt am Main, Germany, 1978.

(54) Gmehling, J., Onken, U., Eds. Vapor-Liquid Equilibrium Data Collection, Part 2h: Alco- hols: Ethanol and 1,2-Ethanediol, Supplement 6; DECHEMA: Frankfurt am Main, Germany, 2006.

(55) Gmehling, J., Onken, U., Arlt, W., Eds. Vapor-Liquid Equilibrium Data Collection, Part 7: Aromatic Hydrocarbons; DECHEMA: Frankfurt am Main, Germany, 1980.

(56) Stephen, K., Hildwein, H., Eds. Recommended Data of Selected Compounds and Binary Mixtures, Part 1+2; DECHEMA: Frankfurt am Main, Germany, 1987.

(57) When more than one set of data was available for a binary pair, we chose the set with a pressure closest to 1 bar. If more than one set was available at this pressure, we chose the set for which DECHEMA was able to best correlate the data. For each binary, we compare to only a single set of reference data. The reference data used is tabulated along with the page number from DECHEMA in the supporting information accompanying this manuscript.

(58) Mathias, P. M. Guidlines for the Analysis of Vapor-Liquid Equilibrium Data. J. Chem. Eng. Data 2017, 62, 2231–2233.

(59) Mathias, P. M. Effect of VLE uncertainties on the design of separation sequences by distillation – Study of the bezene-chloroform-acetone system. Fluid Phase Equilib. 2016, 408, 265–272.

(60) Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth Publishers: Stoneham, MA, 1985.

3.Expansion of MOSCED using new UNIFAC based Group Contribution Method and Linear Solvation Energy Relationship (LSER). Application: Predicting Activity Coefficient at Infinite Dilution for Non-Hydrogen Bonding Molecules. 3.1 Introduction. Prediction of thermodynamic properties such as Phase Equilibria, Aqueous Solubility and Limiting Activity Coefficient are important for the design and optimization of chemical separation processes. Determining such data through experimental process can be time consuming and expensive for various number of molecules on a large scale. Thus, predictive methods are an important tool for predicting properties and guiding engineers on designing efficient separation reactors and columns. MOSCED (Modified Separation of Cohesive Energy Density) is a solubility parameter method known to calculate activity coefficient at infinite dilution method [1] [2]. Activity coefficient at infinite dilution limit is an extremely important quantity which describes solute- solvent interaction without the interference of any solute-solute interaction. This property gives a numerical representation on the molecule interaction between solute-solvent and can be used to determine whether the interaction is favorable or not. Along with such quantitative prediction, MOSCED can be also used to understand molecule interaction on a qualitative level through its parameters such as dispersion parameter, polar parameter and hydrogen bonding parameter. However, before any prediction can be made through MOSCED, it requires to have MOSCED parameters. The revised MOSCED paper regressed MOSCED parameters for 130 organic solvents using 6451 experiment activity coefficients at infinite dilution data. Although the regression yielded accurate MOSCED parameters, collecting activity coefficient at infinite dilution experiment data to expand MOSCED database further can be a daunting task and not feasible for newer compounds with very little to none experiment data. Thus, along with regressing MOSCED parameters through experiment data, when available, new methods are needed to expand MOSCED database. In our earlier paper [3], we showed on how Group Contribution method can be used to expand MOSCED database based on functional groups. Although this GC method allowed us to expand MOSCED database to a larger number of

41 compounds, it didn’t cover a wide variety of compounds and a lot of functional groups were required for multifunctional molecules. Thus, this paper introduces two new methods to expand MOSCED database further to cover wide range of organic compounds using various correlation. The first method is through using linear solvation energy method (LSER) and the second method is using a new GC method based on UNIFAC groups. 3.2 LSER correlation:

Like MOSCED, Quantitative structure relationships (QSAR) models are an important and popular predictive tool for predicting chemical properties, screening chemicals and getting valuable molecular insight. Kamlet-Taft linear solvation energy relationship (LSER) is one of the earliest and popular QSAR method for predicting properties [4]. The model takes in account for solute-solvent interaction using a linear equation model and with that several properties such as aqueous solubility, octanol-water partition coefficient and toxicity could be calculated [5][6][7]. Such LSER equation usually takes the form of: (XYZ Property of the solvent) = cavity term+ dipolar term+ hydrogen bonding term. Equation 1

Due to easy availability of chromatographic methods, Gas-Liquid Chromatography (GLC) and high-performance liquid chromatography (HPLC) method can be used to obtain descriptors for molecules based on its physical properties. M.H Abraham showed on how solvachormatic descriptors could be used in a LSER form to calculate solvent properties shown below [8]. ∗ 푆푃 = 푆푃표 + 푚푉 + 푠휋2 + 푏훽2 + 푎훼2 Equation 2

∗ Where, SP is a solubility or solvent-dependent property, SP0 is a constant, V, 휋2 , 훽2, 훼2 , characterizes the solutes and the coefficients m, s, b, a characterize the solvent. This LSER model however couldn’t be used for compounds that were associated, it also couldn’t be used for solids and gases, and lastly it had difficulty over solute hydrogen bond acidity parameters. Thus, a new modified Abraham descriptor were obtained for solutes to calculate solute properties in the form of: 42 푆푃 = 푐 + 푒퐸 + 푠푆 + 푎퐴 + 푏퐵 + 푣푉푥 Equation 3 Where, Vx(McGowan Volume): M.H.Abhram in his paper[5] found that computer calculated intrinsic volumes , calculated from solute conformation derived from X-Ray Structures , were accurate in correlation properties using the LSER equation(2) as compared to regular bulk molar volume. Mostly because regular bulk molar volume couldn’t accurately represent the cavity term and it was hard dealing with solutes that were solid. [9][10][11]

E: It is the refractive index of the molecule calculated using McGowan’s volume Vx,

MRx: molar refraction of an alkane with the same McGowan’s volume which can be defined as the following equation.

(ŋ2−1) 푀푅 = 10 [ ] 푉푥 Equation 4 푥 (ŋ2+2)

Where n is the refractive index of the molecule at 20 C, Vx is McGowan’s molecule with a unit of (cm3 mol-1)/100.

And MRx(alkane) can be calculated using the following equation [12]:

(푀푅푋)푎푙푘푎푛푒 = 2.83195푉푥 − 0.52553 Equation 5

Using that E can be computed using the following equation:

퐸 = (푀푅푋)푎푙푘푎푛푒 − 2.83195푉푥 + 0.52553 Equation 6

S: It is dipolarity/polariability of the solute that describes the polar ability of a molecule. A: This descriptor represents the hydrogen bonding acidity or proton donating ability of the molecule. B: While B represents the hydrogen bonding basicity or proton accepting ability of the molecule.

3.3 Correlating LSER parameters with MOSCED.

43 Data Collection: To correlate MOSCED with LSER, we decided to use 130 compounds present in MOSCED database for correlation. As for collecting LSER for the all the molecules available in the revised MOSCED database [1], we used UFZ-LSER database [13] for Abraham parameters which has parameters for more than 3700 molecules. Induction parameter(q) was excluded from the correlation. The website provides all the Abraham parameters along with the reference for given molecule. We were able to tabulate LSER parameters for 125 MOSCED molecules except Squalane ; Caprolactone; 1-EthylPyrrolidin-2-one ; 1,5-Dimethyl-2- Pyrrolidinone ; Sulfolane , for which LSER parameters were missing. The objective function was minimized using global optimizer method known as differential evolution [14] , implemented in GNU Octave [15] .

푛 푅푒푓 푃푟푒푑 2 푂퐵퐽 = ∑푗=1(푦푗 − 푦푗 ) Equation 8 Quantifying Errors.

|푋푟푒푓−푋푝푟푒푑| 푁 푖 푖 퐴푅퐸 = ∑푖−1 푟푒푓 Equation 9 퐾푖

|푋푟푒푓−푋푝푟푒푑| 퐴퐴퐸 = ∑푁 푖 푖 Equation 10 푖−1 푁

2 푅푀푆퐸. = √∑(푋푒푠푡 − 푋푒푥푝) /푁 Equation 11 Correlation: Molar Volume(V): Since molar volume of a molecular is required in the MOSCED equation, we decided to correlate the molar volume of a molecule through McGowan’s Volume

(Vx) which took the following form:

V = c1*Vx + c2, where c1 = 122.797 and c2 = 3.6179 Equation 12

Lambda (휆푖) : It is a MOSCED descriptor that takes in account for polarizability of the molecule associated with instantaneous dipoles. The original MOSCED correlation [2] used refractive index to calculate polarizability parameter, however in the revised MOSCED [ 1], they decided to remove this correlation and fit to individual molecule based on experiment data. However, in our LSER correlation we decided to use refractive index to calculate polarizability as suggested by several paper [16] [17] which uses refractive index to calculate solubility parameters. As shown in ref [13], solubility parameter can be calculated using the following equation.

44 푛2−1 훿 ≅ √퐶 Equation 13 푛2+2

And using equation(4) (13) from LSER, we can calculated MRx ,Which results in the following final equation…

푀푅푋 휆 = √퐶3 ∗ Equation 14 푉푋

Where C3= 95.782.

Tau(휏1) : In MOSCED, tau represents dipole moment of a molecule. The original MOSCED paper [2] correlated tau using the dipole moment of the molecule multiplied to a constant and then divided by the molar volume scaled to ¾. Like that, in our correlation we used the following form.

퐶4 푆 휏1 = Equation 15 √푉푋 Where C4 = 6.4844 Alpha (α) : The hydrogen bonding accepting ability is captured through alpha in MOSCED and the correlation takes the following form. 퐶 퐴 α = 5 Equation 16 √푉푋 where C5 = 23.766. Beta (훽) : The hydrogen bonding basicity ability is captured through beta in MOSCED, and the correlation takes the following form. 퐶 퐵 훽 = 6 Equation 17 √푉푋 Where C6 = 17.453. With all the correlation done for LSER, all the stats of the correlation and application are provided in the later section. UNIFAC based Group Contribution Method: The revised MOSCED has 130 organic compounds with unique MOSCED parameters covering a wide variety of compounds. In our earlier work [18] , we showed how these pure

45 component properties could be used to devise a group contribution method to expand MOSCED database to cover even more larger variety of molecules. We used Gani and co-workers method [19] as our GC framework because Gani’s group allowed us to divide groups into three categories; first order group as the regular group, while second and third order group to take in account for isomers and ring position. This lead to an accurate GC method that captured the correct trend for various application as shown in our paper. However, on the down side of using Gani’s GC method is that it requires many groups for big complex molecules. So, we decided to use UNIFAC groups [20] as our new GC method with because it is easily accessible, and it covers wider range of molecules. So the way we want to use these both group contribution method is as follows, if the groups are available then Gani’s GC method is the perfect tool for predicting MOSCED properties, however if the groups aren’t available then UNIFAC based method can be a guiding tool for property prediction during early stage process design. Since MOSCED separates the cohesive energy into additive contribution, we decided to follow the same steps for correlation as our earlier GC paper correlation which is correlating the cohesive energy contribution rather than correlating cohesive energy density properties such as lambda, tau, alpha, beta. And the reason for doing this is because firstly because of trying to make the model as simple as possible: correlating cohesive energy contribution allowed us to use a single general equation, while when we tried to correlate cohesive energy density, we found each property had a unique equation with various constants, secondly if we use cohesive energy density in our correlation , then we would predict infinite cohesive energy density in the infinite limit which is not true, rather it would be a constant in the infinite limit. More about this is discussed in the later section and briefly in our earlier GC paper[19] .As for q(induction parameter), the original MOSCED work suggested to set 1 for saturated molecule, 0.9 for unsaturated molecule such as alkenes , aromatics while halogens value were parameterized for best fit. However, to make sure we have a GC tool that can be automated we model q as well in our GC method. The GC equation took the following form during fitting.

퐺퐶 푦 = ∑ 푛푖푤푖 푖

Where wi is the weight of the functional group i, ni is the number of times the functional group occurs in the molecule and 푦퐺퐶 is the total estimated property of the molecule. 46

A total of 39 groups were assigned based on the Main Group of UNIFAC groups. The groups were taken from DDBST, Group Assignment page. Since we want a generalize group method that covers a wide range of compounds, we only take in account for Main Group. Water was defined as its own group, so no group was necessary for water molecule All the groups value was bound to positive value during the regression to ensure we obtain positive MOSCED properties. The groups weight was minimized using the following objective function.

푛 푅퐸퐹 퐺퐶 2 푂퐵퐽 = ∑(푦푗 − 푦푗 ) 푗=1 All the tabulated group weights are shown in table (7). These groups are cohesive energy properties, while to calculate cohesive energy density, we could use the equation shown below.

∑ 푛 푣휆2 휆2 = 푖 푖 푖 ∑푖 푛푖푣푖 ∑ 푛 푣푟2 푟2 = 푖 푖 푖 ∑푖 푛푖푣푖 ∑ 1/2 2 푖 푛푖푣 훼푖 훼 = 1/2 (∑푖 푛푖푣푖) ∑ 1/2 2 푖 푛푖푣 훽푖 훽 = 1/2 (∑푖 푛푖푣푖)

3.4 Result and Discussions.

Table 7: UNIFAC GC groups for MOSCED parameters with example molecule.

Groups volume lambd tau q_grou alpha_group beta_grou Example Group Order group a group p kJ/mol p kJ/mol Molecule cm3/mol group kJ/mol kJ/mol CH2 19.124 4.4506 0 0 0 0 Octane 8CH2

47 CdbC 25.758 6.4114 0 0.0122 0 0.12911 Hexene 4CH2 + 43 1CdbC ACH 12.685 3.7738 0.1984 0.0091 0.03142 0.01227 Benzene 6ACH 6 03 ACCH2 35.41 9.907 0.2962 0.0338 0.22082 0.18786 Isopropyl 2CH2 + 8 27 benzene 5ACH + 1ACCH2 OH 14.843 1.9702 0.4089 0 2.76545 3.13224 Ethanol 2CH2 +1OH 6 ACOH 22.16 7.148 0.7674 0.0421 7.8949 1.00002 Phenol 5ACH+1ACO 6 22 H CH2CO 42.176 8.8716 3.5014 0 0.06803 2.63757 Acetone 1CH2+1CH2 2 CO CHO 28.569 4.8065 3.6424 0 0 1.43566 Acetaldeh 1CH2+1CHO 4 yde CCOO 51.555 10.630 4.8086 0.0034 0 2.60679 Methyl 1CH2+1CCO 3 4 43 Acetate O HCOO 42.976 17.474 4.2677 0 0.0922 2.14809 Methyl 1CH2+1HCO 7 7 Formate O CH2O 28.621 7.7728 1.8944 0.0002 0.00148 1.43038 1,4- 2CH2+2CH2 3 16 Dioxane O (ACH2) 76.77 23.153 8.6107 0 0.16558 7.46845 N- 1CH2 + NCO 3 1 methylpy 1(ACH2)NC rrolidone O (C)3N 44.081 7.0786 0.1453 0 0 2.87799 Triethyl 5CH2+1(C)3 4 Amine N ACNH2 28.173 6.0991 7.1187 0.0544 1.8132 1.85748 Aniline 5ACH+1ACN 2 83 H2 PYRIDI 75.703 20.343 2.8250 0.0878 0.44288 4.28157 2,6- 2CH2+1Pyrid

48 NE 2 1 62 dimethyl ine pyridine CH3CN 43.954 9.5839 7.1753 0 0.48826 1.72346 Propanen 1CH2+1CH3 1 itrile CN COOH 38.476 8.4404 0.6009 0 5.7672 1.8 Acetic 1CH2+1COO 4 Acid H CCL 41.306 11.125 1.6152 0.024 0.2799 0.22689 Chlorobu 3CH2+1CCl 3 tane CCL2 64.988 17.866 2.8882 0.06 0.9823 0.34374 1,1- 1CH2+1CCl2 4 3 Dichloroe thane CCL3 80.838 21.302 1.3126 0.015 0.98907 0.15162 1,1,1- 1CH2+1CCL 1 8 trichloroe 3 thane CCL4 97.1 26.563 0.3216 0 0.38951 0.19943 Carbon 1CCl4 8 3 Tetrachlo ride ACCL 38.873 9.7296 0.7866 0.0644 0 0.73826 Chlorobe 5ACH+1ACC 83 nzene L CNO2 57.426 11.863 7.1015 0 0.37882 1.24394 1- 2CH2+1CNO 3 9 nitroprop 2 ane ACNO2 39.273 7.6195 5.9638 0.0544 0.15697 0.99299 Nitrobenz 5ACH+1ACN 9 83 ene O2 CS2 60.6 23.446 0.0655 0 0.14524 0.08124 Carbon 1CS2 7 5 Disulfide I 37.113 17.782 1.1124 0 0.3021 0.33191 Diiodome 1CH2+2I 5 3 thane BR 33.27 8.9712 1.1085 0.0276 0 0.68579 Bromobe 6ACH+1Br

49 9 9 nzene DMSO 71.3 18.527 12.726 0 0 6.98793 DMSO 1DMSO 6 31 CLCC 21.447 6.7376 0.2631 0 0.20711 0 Trichloro 1CdbC+ 4 ethylene 3CLCC DMF 62.767 17.535 5.7932 0 0.2209 6.15195 N,N- 6CH2+1DMF 3 7 dibutylfor amide COO 24.785 6.6418 3.0088 0 0.09942 1.53409 Diethyl 4CH2+6ACH 8 Phthalate +2COO NMP 100.6 26.076 11.974 0 0.76756 6.11831 N- 1NMP 5 23 formylmo rpholine OCCO 59.052 13.343 5.3137 0 1.17597 5.25289 2- 2CH2+1OCC H 6 ethyoxyet OH hanol S(CO)2 57.052 17.012 14.091 0 0.41984 4.17372 Sulfolane 2CH2+1S(CO 8 59 )2 ACN 39.573 5.6535 5.9503 0.0544 0 2.31679 Benzonitr 5ACH+1ACN 4 83 ile PO4 115.514 24.736 8.1823 0 0 8.25838 Dibuylph 8ACH+1PO4 5 3 ospate NMF 59.1 14.290 4.7023 0 1.96186 5.35074 N- 1NMF 5 7 methylfor mamide M- 63.708 16.838 4.7196 0 0.70593 6.60618 N,N- 1CH2+1Aceta acetami 8 3 dimethyla mide de cetamide

50 To test the accuracy of this new UNIFAC-GC and Abraham-MOSCED LSER (AM LSER), we collected all the activity coefficient infinite dilution data which MOSCED was parameterized for and correlated it using UNIFAC-GC, original GC, AM LSER and MOSCED itself. The results and figure are provided in the table below. As seen from figure 1, MOSCED itself is in excellent agreement with experiment data, while other methods such as GC and UNIFAC GC are in good agreement. As seen from the table 8, MOSCED only as solvent and solute has the lowest error and a very high correlation. But as we go from MOSCED only to MOSCED as solvent and GC- UNIFAC as solute, the error increases slightly and much more if its only GC-UNIFAC as both solvent and solute. The same trend can be observed from original GC as well, which suggests that if MOSCED parameters are available, it’s always best to use the original MOSCED parameters, however in absence of parameters, it is still reasonable to use GC methods as solute properties. Also, as mentioned earlier, the error does increase going from original GC to GC- UNIFAC for both cases. As for LSER only, it has the highest stats, but we have to keep in mind that all these data for LSER were correlated using only seven different constants as compared to GC methods. And as seen from the table, MOSCED combined with LSER does better than GC- UNIFAC which indicates a good correlation for the LSER parameters.

Table 8 : Stats in correlating activity coefficient at infinite dilution method.

Method Pearson Correlation AAE RMSE MOSCED only 0.98 0.11 0.15 MOSCED(solvent)-GC- 0.94 0.19 0.28 UNIFAC(solute) GC UNIFAC (solute & solvent both) 0.91 0.25 0.36 MOSCED(solvent)-Original GC(solute) 0.95 0.16 0.24 Original GC(Solvent & solute both) 0.94 0.211 0.29 MOSCED(Solvent) & lSER(Solute) 0.92 0.23 0.34 LSER(Solvent & Solute) 0.83 0.36 0.51

Figure 7 : Activity Coefficient at Infinite Dilution Predicted for the original test.

Application: Activity Coefficient at Infinite Dilution Method. The current most widely used models to predict activity coefficient at infinite dilution method are UNIFAC [22], MOD-UNIFAC [23], which are analytical method, and COSMO-SAC [24], a quantum mechanical calculation method. To test the reliability of these methods, R.P Gerber .et.al [25] compile 2236 binary mixture activity coefficient infinite dilution method which do not form hydrogen bonds using different sources[26][27][28][29][30][31][32][33].They found MOD-UNIFAC performance the best with a mean absolute error of 0.12 ln-units against 0.22 COSMO-SAC method. But for multi-functional group they found COSMO-SAC performing well against MOD-UNIFAC because MOD-UNIFAC being a group contribution method doesn’t properly take in account for multi-functional interactions. Using this database, we decided to use MOSCED and its methods to see how well MOSCED does in comparison against MOD-UNIFAC and COSMO-SAC. Since all the

52 compounds present in the non-hydrogen bonding database isn’t present in the original MOSCED list, so we combined MOSCED with each method to fill in the gap when compounds were missing.

Table 9 : Activity Coefficient at Infinite Dilution Stats for Non-Hydrogen Bonding Set

Method Ln-units AAE Remarks MOD-UNIFAC 0.12 COSMO-SAC 0.22 MOSCED&LSER 0.09 MOSCED&UNIFAC- 0.13 Triacetin molecule couldn’t be predicted by GC unifac-gc, so used LSER. MOSCED& Original 0.13 Triacetin molecule couldn’t be predicted by GC& UNIFAC-GC unifac-gc or original gc, so used LSER. MOSCED&SMD 0.19 MOSCED&SM8 0.13

Figure 8: Activity Coefficient at Infinite Dilution for Non-Hydrogen bonding set using different method.

As seen from figure 8, LSER does the best as compared to other methods for predicting infinite dilution for non-hydrogen bonding set and better than COSMO-SAC and UNIFAC as seen from table 9. All these results just show the strength of LSER method, which uses just seven constants to predict properties for any organic compound. One reason why LSER does so well as compared to other method might be because of the non-hydrogen bonding set which have relative low gamma and simple molecular interaction as compared to complex hydrogen bonding interaction. The paper also presents cases where COMO-SAC does better than UNIFAC such as cases where UNIFAC fails to lack isomers and behaviors with multifunctional molecules. To demonstrate this scenario, the paper picks three molecules which are: tri-ester(triacetin), cyclic ester(G-Butyrolactone) and a cyclic ether(tetrahydropyran). Although the paper mentions they collected 141 data for these three systems, the total number data reported in the supporting information tally’s to 121 different data.

Table 10: Stats for multifunctional molecule using different methods.

Method Ln-units AAE Remarks MOD-UNIFAC 0.44 141 data points COSMO-SAC 0.20 141 data points MOSCED&LSER 0.32 121 data points MOSCED&SMD 0.79 121 data points MOSCED&SM8 0.72 121 data points Stats provided from table 10 strengthens the case that LSER& MOSCED can be used to compute properties for bigger multifunctional molecules as well or when functional groups have complex multiple interactions.

3.5 Conclusion: In this work, we showed two new methods to expand MOSCED database that allows coverage of a wide variety of organic compounds. All the LSER parameters were taken from Abraham LSER database, which is a free database that contains more than 3700 compounds. Each MOSCED parameter including volume took a unique correlation with provided accurate activity coefficient and the lowest error for non-hydrogen bonding stats. The other method is a group contribution method based on UNIFAC groups which allowed us to cover wide variety of compounds using a small number of functional groups. Although the qualitative results performed poor when used as a solute and solvent, it could be used as a quick screening tool for selecting solvents by looking at solvent parameters or be used as solute if MOSCED parameters are missing.

3.6 References:

1. Michael J Lazzaroni, David Bush, Charles A Eckert, Timothy C. Frank, Sumnesh Gupta, James D Olson; Ind Eng Chem Res 2005, 44, 4075-4083.

55 2. Thomas E R , Eckert C A; Ind Eng Chem Process Dev. 1984, 23,194-209. 3. Pratik Dhakal , Sydnee N.Roese, Erin .M.Stalcup, Andrew.S.Paluch; Fluid Phase Equilbria 2018, 470, 232-240. 4. Mortimer J.Kamlet and R.W.Taft; J.Am.Chem.Soc., 1976, 98(2), pp 377-383. 5. Kamlet , M.J ; Doherty,R.M; Abraham, M.H; Carr, P.W; Doherty, R.F; Taft,R.W. J.Phys.Chem, 1987, 91,1996-2004. 6. Kamlet , M.J ; Doherty,R.M; Abraham, M.H; Mackay, D; Carr, P.W; Doherty, R.F; Taft,R.W. Environ.Sci.Technol.1988,22,503-509. 7. Kamlet , M.J ; Doherty,R.M; Abraham,M.H ; Taft,R.W. Environ.Sci.Technol.1986,20,690-695. 8. M.H.Abraham. Chromatographia Vol 23.No. 4,April 1987. 9. J.C.Mc Gowan , J Appl.Chem.Biotechnol,.28,599 (1978). 10. J.C.Mc Gowan, P.Ahmad , A.Mellors,Canad.J.Pharm.Sci., 14,72(1979). 11. J.C.Mc Gowan , J.Appl.Chem.Biotechnol,.34A,38 (1984). 12. Michael H.Abraham, Adam Ibrahim, Andreas M.Zissimos; J.Chrom.A, 1037 (2004), 29- 47. 13. www.ufz.de/lserd/ 14. Storn R; Pirce K, J.Global Optim , 1977, 11,341-359. 15. Eaton J .W ; Bateman, D; Hauberg S. GNU Octave Version 3.01 Manual,ISBN 1441413006. 16. D.David Lawson, J.D Ingham; Nature.Vol.223, August 9, 1969. 17. Syamsul B.Abdullah, Z.Man, L.Ismail, M.I.Abdul Mutalib; Advances Materials Research; ISSN : 1662-8985, Vol 917, pp 44-55; 2014 Trans Tech Publication, Switzerland. 18. Pratik Dhakal , Sydnee N.Roese, Erin .M.Stalcup, Andrew.S.Paluch; Fluid Phase Equilbria 2018, 470, 232-240 19. Jorge Marrero, Rafiqual Gani; Fluid Phase Equilbria 183-184(2001) 183-208. 20. Wittig R.Lohmann J, Gmehling J; Ind.Eng.Chem.Res , 42(1), 183-188, 2003 21. www.ddbst.com 22. Aage Fredenslund , Jurgen Gmehling, Peter Rasmussen, Elsevier Scientfic , NY, 1979.

56 23. Jurgen Gmehling, Jldlng Li,Martin Schller ; Ind.Eng.Chem.Res, 1993, (32),1 pp 178-193. 24. Andzelm J, Kolmel C and Klamt A; The Journal of Chemical Physics, 103,(21),9312- 9321(1995) 25. R.P Gerber , R.P.Soares; Brazilian Journal of Chemical Engineering Vol.30, No .01, pp 1-11, January -March, 2013. 26. Alicia Bermudez , Gloria Foco, Susana B.Bottlni ; J.Chem.Eng.Data 45,6,1105-1107. 27. Ceclla B Castells, David I Elkens, Peter W .Carr ; J.Chem.Eng.Data 45,2,369-375 28. Dallas A.J, Carr.P.W ; The Journal of Physical Chemistry, 98 , (18) ,4927-4939 (1994). 29. Lin S T, Sandler S I; Ind.Eng.Chem.Res, 41(5),899-913(2002). 30. Georgios M Kontogeorls, Phillis Coutslkos ; Ind.Eng.Chem.Res, 44,9,3374-3375. 31. Wang, S,.Sandler , S I , C-C; Ind.Eng.Chem.Res , 46,(22),7275-7288(2007). 32. Thomas E.R, Newman B.A , Long.T.C , Wood,D,A, Eckert C,A ; Journal of Chemical & Engineering Data, 27(4), 399-405(1982).

4. Expansion of MOSCED to Ionic Liquids for Efficient Early Stage Chemical Process Design: Application such as selecting Entrainers, breaking Azeotropic Vapor Liquid Equilibria.

4.1 Introduction

Room temperature ionic liquids are gaining widespread attention as an environmentally friendly and effective solvent for various chemical separation processes. Due to its molecular structure, Ionic liquids exhibit unique behavior such as negligible vapor pressure, high thermal stability, high selectivity and more. And these properties are extremely important in the chemical industry for environment concerns, safety of people handling solvents and chemical process efficiency. Ionic liquids are entirely composed of ions, where the cations are mainly organic such as imidazole, pyridinum, quaternary ammonium, tetra-alkyl -phosphonium and the anions are mainly in-organic molecule such as halide, acetate, alkyl-sulfate, borate, trifuloromethanesulfonate and so on. Due to a wide variety of possible cations and anions, ILs are often called “designer solvents” because properties such as melting point, hydrophobicity, viscosity, solubility are determined by the choice of cations and anions. Ils have many potential uses such as capture of carbon dioxide from combustion flue- gas[1], entrainers in extractive distillation to break azeotropes[2][3][4], liquid -liquid extraction of aromatic hydrocarbons[5], electrolytes in batteries[6], heat transfer fluids[7], fuel cells[8], and novel reaction media[9]. Separation of systems that form an azeotropic mixture can be a real challenge for the chemical industry due to higher energy consumption and numerous refinery processes. As a result, a popular technique to separate such system is through extractive distillation method where, an entrainer or solvent is added to the mixture to change the volatility of the system. Choosing the right entrainer however requires various thermodynamic information such as the difference in affinity of the solvent between the solutes in the mixture. Additionally, selecting the right solvent is limited because of most organic solvents being volatile which leads to significant loss in the atmosphere, while solid salts lead to corrosion of pipelines [10]. Therefore, Ionic Liquids have started to become the popular choice of entrainers for the separation of non-ideal

58 systems due to nonvolatility which allows easy recycle of solvent, efficient removal of solvent from the pure product and less damaging to machinery. An IL paper by Joan F. Brennecke et .al[3] showed that they were able to break the azeotrope formed between ethyl acetate and ethanol using only 2.5% mol of [emim][MeSO3] or [emim][MeSO4] effectively. Another Il paper by Q.Li et.al showed that the azeotrope disappears between Tetrahydrofuran and Methanol mixture by adding 0.20 mole fraction of [EMIM][BF4][11]. Although extractive distillation is the common choice of separation method in the chemical industry for separating mixtures, a major downside of this method is the high energy consumption that leads to tremendous cost for running the system. As a result, liquid-liquid extraction (LLE), which is based on the immiscibility of two liquid phases has started to become a cost-effective method of separation. Additionally, LLE is an excellent choice of method for separating mixtures that have close boiling points such as aromatic and hydrocarbons system which is a major separation issue for the fuel industry. Sulfolane[12][13], N- methylpyrrolidone(NMP)[14][15], ethylene glycols[16][17] and propylene carbonate[18] are common solvents used for such separation process. However, these solvents have a low regeneration rate and are expensive on a large scale, which is why ILs have been started to use as replacement for conventional solvents in LLE separations. Several studies have shown that Ils have a high selectivity and distribution coefficient as compared to common solvents [5][19][20], which indicates Ils as suitable solvents for LLE extractions.

All this application mentioned above does make Ils as a perfect solvent for most chemical separation purpose. So, if Ils were to be commercial solvents in the industries, several important properties such as toxicity, melting point, flammability and thermodynamic properties need to be properly understood, but a major problem is that there are more than 103 different Ils that are commercially available as of now, and chemist claim they can synthesize 1014 Ils [21][22][23]. Obtaining all these data experimentally and then classifying them however would be impossible. As a result, predictive methods that can quickly predict properties for such enormous amount of Ils could be an extremely cost-effective method of choosing the right Il for a specific problem. MOSCED (Modified Separation of Cohesive Energy Density) is a solubility parameter ∞ method model that allows prediction of activity coefficient at infinite dilution (푦푖푗 ), which can

59 be then used to predict several important thermodynamic properties such as Vapor Liquid Equilibria, Liquid-Liquid Equilibria, Henry’s Constant, Solvation Free Energy and more [24][25][26][27]. In addition to quantitative prediction, MOSCED can also be used as a qualitative tool to understand the intermolecular interaction at molecular level. This is particularly useful in early stage process design, where we want to keep the cost as minimum as possible, so cases such as quick solvent selection or classifying large number of compounds based on inter molecular interactions. MOSCED takes in account for three major molecular interactions, which are dispersion interaction, polarity interaction, and hydrogen donating - accepting interactions. Based on this one can theoretically look at the solutes MOSCED parameters and then select the appropriate solvent parameters. For example, to extract solute 1 from solute 2, selecting solvent parameters close to solute 1 or selecting a higher difference in hydrogen bonding term between solute 1 and solvent will result a low infinite dilution value for solute 1 in the solvent (since the MOSCED equation is the difference in interaction parameters between solute and solvent) as compared to solute 2 in the solvent. Let’s look at an example in the case of separating aromatic compounds from hydrocarbons using LLE. To do that one needs to select a list of compounds that has a high selectivity towards aromatic compounds over hydrocarbons. Hexane infinitely dilute in Dimethyl Sulfide Oxide (DMSO) at 298 Kelvin has a value of 68.94, while Benzene infinitely dilute in DMSO at 298 K has a value of 2.24, so DMSO has a selectivity ratio for aromatic over hydrocarbon of 30.778, which indicates DMSO as a good solvent for this mixture. Now MOSCED not only allows easy solvent selection based on parameters, but it also allows to choose, classify and generalize for numerous solvents based on the same physical properties. Looking at DMSO molecular structure, it has a double bonded oxygen connected to the sulfur atom, which means this molecule has a high hydrogen accepting characteristics that results a beta or hydrogen accepting value of 26.17. Based on this information, one could intuitively divide molecules based on such properties and classify huge number of molecules based on hydrogen donating ability, hydrogen accepting ability and polar ability. Thus, all of this makes MOSCED a perfect predictive tool for dealing with Ils on a quantitative and qualitative purpose. The revised MOSCED paper by Michael J Lazzaroni et.al

60 had included only two Ils, 130 organic compounds and water in the solvent list[28].So this paper is primarily focused on Il expansion using data regression and understand the molecular interaction of Ils using MOSCED .And the reason Il expansion through MOSCED is extremely important because as shown in our Group Contribution (GC) Paper[25] ,if there are enough molecule in the database, we could then formulate IL GC , which could be extremely powerful for theoretically designing Ils based on one’s need, given the massive number of Ils that could be synthesize. In this paper we will focus on expanding MOSCED parameters for imidazolium Ils which are the most common well studied and stable Ils.1 alkyl-3methyl imidazolium Ils are an association of imidazolium cations and anions through hydrogen bonds as shown in the figure (1). Systematically studying these Ils would then allow us to shed light on the molecular interaction and thermodynamic behaviors through MOSCED and examine how varying alkyl chain length on cation and changing anion effects the Il properties.

Figure 9: 1-Ethyl 3-methylimidazolium Ethyl Sulfate (Source: www.Sigmaaldrich.com)

4.2 Methodology Data Collection

61 ∞ Regressing MOSCED parameters requires activity coefficient at infinitely dilute (푦푖푗 ) data and the solutes present in the MOSCED database. If both are available, then one could regress solvent MOSCED parameters by fitting the equation. We surveyed the literature and we found a paper on Il that uses Machine Learning method to calculate activity coefficient at infinite dilution for Ils [29]. Additionally, this paper has activity coefficient at infinite dilution data for 188 Ils with more than 6826 data points for 10 different Il families. The paper also classifies data ∞ into acceptable and rejected based on trends and slope of ln 푦푖푗 vs 1/T. Thus, allowing us to easily select the correct experiment data for regression. Lastly, the paper provides stats for all the Ils family, which could be used as a benchmark on how well MOSCED does as compared to such advanced method. As for the validity of the regressed MOSCED parameters, two general rules were set. Firstly, there should be enough number of data covering wide varieties of solutes for regression and, secondly the hydrogen bonding parameter of the regressed IL was compared to Tom Welton et.al paper which uses experimental technique to measure hydrogen bonding interaction of the IL to see if the same trend was observed using MOSCED [30]. Regression

Parameters for the Ils were regressed by minimizing the objective function (Obj) as shown in equation (1):

푛 ∞ ∞ 2 푂퐵퐽 = ∑푗=1(푦푟푒푓 − 푦푝푟푒푑) equation 1 , which is the square difference between the experiment value and predicted value. During the regression, q is set to 0.9 due to Imidazole compound having an aromatic compound, while lambda, tau, alpha and beta were treated as adjustable parameters. In some cases when the volume of Il could not be found, the volume was treated as an adjustable parameter along with other four parameters. (Ils whose volume were regressed are denoted by a * in the parameter list in the result section). The objective function was minimized by using the differential evolution global optimization method [31] as implemented in GNU Octave [32].

62 Quantifying Errors

As done in the paper [29], the stats for three different Machine Learning Algorithm are given where, the root mean square error (RMSE) and average absolute deviation (AARD) of ∞ natural logarithmic 푦푖푗 were calculated. Among the three method, the lowest error in stats were picked and compared to MOSCED stats.

∞ ∞ 2 푅푀푆퐸. = √∑(푙푛훾푟푒푓 − 푙푛훾푝푟푒푑) /푁 equation 2

|푦∞ −푦∞ | 푁 푟푒푓 푝푟푒푑 퐴퐴푅퐷 = ∑푖−1 ∞ ∗ 100% equation 3 푦푟푒푓

4.3 Computational Methods

Ternary Vapor-Liquid Equilibrium Modelling

In this study we will investigate ternary vapor-liquid equilibrium prediction using activity coefficient model at infinite concentration through WILSON [33] and NRTL [33] because MOSCED only predicts activity coefficient at the infinite dilution limit. Assuming the vapor phase at equilibrium is an ideal gas at low pressure and the Poynting correction is negligible, we have modified Raoult’s law as shown in equation (5) Modified raoult’s law equation. 푠푎푡 푥푖훾푖(푥푖, 푇, 푝)푝푖 = 푦푖푝 equation 4

where xi is the liquid mole fraction of component i, yi is the vapor mole fraction of 푠푎푡 component i, 푦푖 is the activity of component i, 푝푖 is the vapor pressure of component i and P is the system pressure. And as shown by Schreiber and Eckert[34] , and our earlier MOSCED paper[24][25][26][27], infinite dilution data can be used to parameterize excess Gibbs free energy model to predict activity coefficient of a component at any given concentration. In our application of MOSCED paper [24], we had shown that MOSCED combined with WILSON equation had the lowest error as compared to NRTL and TK-WILSON, so we decided to use WILSON as the primary choice for predicting activity for ternary vapor liquid equilibria.

63 However, to get activity coefficient from WILSON and NRTL equation, we need to know two binary interaction parameters (BIPs) for each component in a multicomponent system. Wilson Equation for multicomponent can be seen below.

푣푗 휆푖푗−휆푖푖 훬푖푗 ≡ exp (− ) equation 5 푣푖 푅푇

푣푖 휆푗푖 − 휆푗푗 훬푗푖 ≡ exp (− ) 푣푗 푅푇

푚 푚 푥푖훬푖푘 푙푛훾푘 = −푙푛(∑푗=1 푥푗훬푘푗) + 1 − ∑푖=1 푚 equation 6 ∑푗=1 푥푖훬푖푗

At the infinite dilution limit, BIPs can be calculated using the following equation 8 and 9

∞ 푙푛훾1 = − ln(훬12) − 훬21 + 1 equation 7 ∞ 푙푛훾2 = − ln(훬21) − 훬12 + 1 equation 8

∞ ∞ ∞ ∞ ∞ ∞ Where 푙푛훾12, 푙푛훾21, 푙푛훾13, 푙푛훾31, 푙푛훾23, 푙푛훾32 can be calculated using MOSCED and solve for three pairs of 훬푖푗 푎푛푑 훬푗푖

As for NRTL equation, to calculate activity for multicomponent system, the equation takes the following form. 푔 −푔 휏 = 푗푖 푖푖 equation 9 푗푖 푅푇

퐺푗푖 = exp(−훼푗푖휏푗푖) 훼푗푖 = 훼푖푗 equation 10

Where, 훼푗푖 is related to non-randomness of the mixture and its mostly varies 0.2 to 0.47.

푚 푚 ∑푗=1 휏푗푖퐺푗푖푥푗 푚 푥푗퐺푖푗 ∑푟=1 푥푟휏푟푗퐺푟푗 푙푛훾푖 = 푚 + ∑푗=1 푚 (휏푖푗 − 푚 ) equation 11 ∑푙=1 퐺푙푖푥푙 ∑푙=1 퐺푙푗푥푙 ∑푙=1 퐺푙푗푥푙

And at the infinite dilution limit, BIPs can be calculated using the following equation. ∞ 푙푛훾1 = 휏21 + 휏12퐺12 equation 12

64 ∞ 푙푛훾2 = 휏12 + 휏21퐺21 equation 13

Where, 휏21 and 휏12 are adjustable parameters. For all the vapor liquid calculation, the vapor pressure of a component was calculated using Antoine Coefficient taken from ‘Yaws Handbook of Antoine Coefficients [37]. As for Ils, the vapor pressure was set to zero due to negligible vapor pressure. During TXY (fixed Pressure) ∞ VLE calculation, six sets of 푙푛훾푖푗 was calculated using MOSCED for more than 300 different ∞ temperature points using equation (4) to fit an energy dependent correlation. And these 푙푛훾푖푗 were then used to parameterize BIPs for the multicomponent system using eq (8) (9) (13) (14). ∞ The objective function used for fitting was the sum squared difference in MOSCED 푙푛훾푖푗 and ∞ 푙푛훾푖푗 using BIPs. Once those BIPs are known, interaction energy term was calculated using eq (6,10). And since we want to calculate BIPS at any given temperature required, a linear correlation of the energy term was fit using the equation ( aij = ao+ a1*T) for 600 temperatures. This equation now allows us to calculate interaction energy for a given system at any temperature, which could be then used to calculate BIPs using equation. Once the BIPs are known at a specified temperature, we can then calculate activity using eq (7) (12). And to measure how well we do in predicting activity and temperature of the system, the experimental liquid mole fraction of the system xi was specified, while temperature and activity were calculated at the mole fraction. ∞ As for PXY VLE systems, 푙푛훾푖푗 was calculated at that given fixed temperature, which was then used to calculate BIPs at that temperature using equation (8) (9) (13) (14). Once the BIPs were known, activities of the component were calculated using eq. (7) (12).

Selectivity Coefficient and Distribution Coefficient

For the selection of appropriate entrainers, it is important to know the selectivity and distribution coefficient at the infinite dilution, which can be calculated using equation shown below. Distribution Coefficient.

∞ 1 퐷1 = ∞ equation 14 훾1 65 ∞ 1 퐷2 = ∞ equation 15 훾2 Selectivity.

∞ ∞ ∞ 퐷1 훾2 푆1/2 = ∞ = ∞ equation 16 퐷2 훾1 4.4 Result and Discussion

MOSCED Parameters

A total of 33 Ils were parameter were regressed using MOSCED and all their standard names are provided in table (1). The Ils regressed covers three family 1 alkyl-3methyl imidazolium which are 1 ethyl-3methyl imidazolium [EMIM], 1 butyl-3methyl imidazolium [BMIM] and 1 alkyl- ∞ 3methyl imidazolium [HMIM]. The stats for correlation between 푙푛훾푖푗 using MOSCED parameters and experiment data, reference data using Least Squares Support Vector Machine (LSVVM) and experiment data is also provided in table (11) . Although the errors in correlating the data is higher than the machine learning algorithm [29], MOSCED does provide qualitative insight on a molecular level that could help in selecting the right solvent as an entrainers for

Figure 10:Correlation of Activity Coefficient Data

∞ mixtures. As seen from figure (10), the values of 푙푛훾푖푗 correlated by MOSCED are in good ∞ agreement with experiment data. Most of those outliers in the graph are 푙푛훾푖푗 of alkanes in Ils which do not have a favorable interaction with the IL and MOSCED seems to over predict slightly for most of them.

Figure 4. 2 Activity Coefficient at Infinite Dilution Predicted vs Experiment

Table 11: MOSCED parameters for the Ionic Liquids with its standard anion name, where cation [EMIM] stands for 1 ethyl-3methyl imidazolium [EMIM], 1 butyl-3methyl imidazolium [BMIM] and 1 alkyl-3methyl imidazolium [HMIM]. Lambda, tau, alpha, beta is in units of (J/cm3)1/2 and molar volume(v) is in cm3/mol.

Ionic Liquid Anion Standard Name v Λ Tau Q alpha beta

[EMIM][C2SO4] 190.6 16.29 12.36 0.9 3.24 30.80 ethyl sulfate 4

[EMIM][C8SO4] 291.9 16.40 6.69 0.9 1.43 26.64 octyl sulfate 8

[EMIM][C2O2O1 2-(2- 251.0 16.75 13.13 0.9 2.40 31.05 SO4] methoxyethoxy)ethyl 1 sulfate

[EMIM][CSO3] 165.5 16.39 15.42 0.9 1.89 43.57 Methanesulfonate 5 [EMIM][FAP] trifluorotris(pentafluoroe 324.6 15.00 11.46 0.9 6.87 2.47 thyl)-λ 5 -phosphanuide 1

[EMIM][NTF2] bis(trifluoromethylsulfon 256.4 16.55 7.95 0.9 15.18 8.69 yl)azanide 2 [EMIM][OTF] Trifluoromethanesulfona 188.5 16.15 13.88 0.9 0.18 5.28 te 7

67 [EMIM][TCB] 217.2 17.01 10.22 0.9 14.72 5.28 Tetracyanoboranuide 9 [EMIM][TFA] 173.1 16.69 11.56 0.9 2.90 40.94 Trifluoroacetate 1

[EMIM][NO3] 154.0 15.73 14.32 0.9 4.20 30.91 Nitrate 3 [BMIM][DMP] 227.5 16.52 7.69 0.9 3.61 47.54 dimethyl phosphate 4 [BMIM][Cl] 161.4 17.05 13.52 0.9 3.55 49.00 Chloride 9

[BMIM][CSO3] 203.6 16.82 12.78 0.9 4.36 38.23 Methanesulfonate 4 [BMIM][TOS] 4-methylbenzene-1- 264.2 17.42 11.18 0.9 2.18 39.72 sulfonate 1

[BMIM][NO3] 173.5 16.36 12.89 0.9 1.13 28.61 Nitrate 2

[BMIM][C2O2O1 2-(2- 287.9 16.44 12.72 0.9 1.17 28.90

SO4] methoxyethoxy)ethyl 2 sulfate

[BMIM][CSO4] methyl sulfate 206.7 17.28 5.9 0.9 7.92 31.07

[BMIM][C8SO4] 325.4 15.55 4.48 0.9 3.55 29.19 octyl sulfate 6 [BMIM][OTF] Trifluoromethanesulfona 220.7 16.41 10.64 0.9 3.77 20.90 te 3 [BMIM][SCN] 183.9 17.96 13.03 0.9 2.23 19.18 Thiocyanate 4

[BMIM][BF4] 187.5 16.18 13.04 0.9 2.23 19.18 Tetrafluoroborate 7

[BMIM][PF6] 207.0 16.21 12.03 0.9 5.54 7.04 Hexafluorophosphate 9

68 [BMIM][BOB] 1,4,6,9-tetraoxa-5- 251.5 11.66 10.18 0.9 1.60 9.48 boraspiro[4,4]nonan-5- 9 uide

[BMIM][C(CN)3 218.1 16.50 9.14 0.9 15.13 7.93 ] Tricyanomethide 6

[BMIM][NTF2] bis(trifluoromethylsulfon 290.8 16.77 8.98 0.9 8.58 3.46 yl)azanide 2

[BMIM][SbF6] hexafluoroantimonate(V) 221.3 16.66 10.98 0.9 10.57 3.35 1 [HMIM][FAP] trifluorotris(pentafluoroe 393.6 15.60 8.96 0.9 6.15 2.37 thyl)-λ 5 -phosphanuide 0 [HMIM][NO3] 205.0 17.29 10.16 0.9 2.12 28.46 Nitrate 8

[HMIM][NTF2] bis(trifluoromethylsulfon 324.8 15.88 8.09 0.9 6.78 4.95 yl)azanide 5

[HMIM][PF6] 240.2 20.34 7.52 0.9 1.76 12.97 Hexafluorophosphate 2 [HMIM][TCB] 282.1 16.17 8.77 0.9 10.20 5.78 Tetracyanoboranuide 6 [HMIM][TFA] 242.9 17.06 6.47 0.9 3.20 37.97 Trifluoroacetate 9 [HMIM][OTF] Trifluoromethanesulfona 254.6 14.38 9.47 0.9 20.21 3.73 te 4

Table 12: Stats for all the Ils RMSE in log gamma, AARD in gamma, NO of data points by MOSCED and * indicates LSSVM method. Average error is given at the end of sheet and total no of data points used for correlation

Ionic Liquid RMSE in AARD in No of RMSE AARD No of

69 log gamma gamma data in log in data points gamma* gamma* points*

[EMIM][C2SO4] 0.29644 24.145 77 0.24 18.6 113

[EMIM][C8SO4] 0.15639 12.568 80 0.174 9.85 115

[EMIM][C2O2O1SO4] 0.233 19.253 84 0.090 7.07 112

[EMIM][MeSO3] 0.633 32.88 184 0.112 8.83 259 [EMIM][FAP] 0.229 19.426 234 0.14 9.69 390

[EMIM][NTF2] 0.517 47.57 146 0.147 11.3 229 [EMIM][OTF] 0.143 11.441 45 0.082 6.82 72 [EMIM][TCB] 0.238 20.63 192 0.102 7.13 242 [EMIM][TFA] 0.238 19.79 137 0.087 6.96 184

[EMIM][NO3] 0.4417 28.49 120 0.322 27.22 145 [BMIM][DMP] 0.171 12.715 112 0.181 13.2 228 [BMIM][Cl] 0.433 25.527 128 0.171 13.4 229

[BMIM][CSO3] 0.449 24.873 128 0.254 14.9 228 [BMIM][TOS] 0.157 12.455 157 0.103 8.26 278

[BMIM][NO3] 0.257 21.545 119 0.132 10.9 150

[BMIM][C2O2O1SO4] 0.207 16.176 36 0.153 12.4 48

[BMIM][CSO4] 0.252 20.208 124 0.247 20.5 164

[BMIM][C8SO4] 0.197 16.19 38 0.0975 7.49 50 [BMIM][OTF] 0.258 21.757 337 0.132 10.9 477 [BMIM][SCN] 0.417 37.571 160 0.112 8.83 259

[BMIM][BF4] 0.329 29.548 157 0.262 18.8 278

[BMIM][PF6] 0.196 16.081 125 0.201 16.7 191 [BMIM][BOB] 0.295 25.145 80 0.157 11.6 115

[BMIM][C(CN)3] 0.275 24.438 156 0.084 6.77 209

[BMIM][NTF2] 0.352 29.854 64 0.156 10.9 271

[BMIM][SbF6] 0.211 16.41 57 0.084 7.15 81 [HMIM][FAP] 0.268 23.156 93 0.245 14.9 138 [HMIM][NO3] 0.172 14.149 100 0.146 12.4 150

70 [HMIM][NTF2] 0.197 16.255 110 0.156 10.9 369

[HMIM][PF6] 0.365 29.383 118 0.285 20.5 176 [HMIM][TCB] 0.452 29.191 237 0.109 8.05 362 [HMIM][TFA] 0.252 20.704 116 0.299 22.8 158 [HMIM][OTF] 0.409 30.778 102 0.258 19.4 150 Average Error 0.293 22.736 4153 0.167 12.572 6620

Joan.F.Berneckee.et.al [2] in their paper reported on how the IL studied in their paper were based on activity coefficient at infinite dilution data. Infinite dilution Activity coefficient in Ethyl acetate in [EMIM][MeSo3] vs infinite dilution activity coefficient in ethanol was found to be a big difference, which is why they suggested this IL could be an effective entrainer because the IL has a higher affinity for ethanol than azeotrope. And these phenomena can be also explained through MOSCED through its parameters and cross interaction term which are the difference of product of the hydrogen bonding term between the Il and the solute as shown in table (13).

Table 13 : MOSCED hydrogen bonding parameters and the cross-interactions term

COMPOUND ALPHA BETA ETHYL ACETATE(1) 0 7.25 ETHANOL(2) 12.58 13.29 [EMIM][MESO3](3) 1.89 43.57 In our earlier paper [24], we showed on how cross interaction of the association parameters can be used to describe the strength of the interaction and the deviation from Raoults’ Law. As seen from the table, the cross term for [EMIM[MESo3] and ethanol is much more negative than [EMIM][MeSo3] and ethyl acetate, because ethanol has a higher alpha, while ethyl acetate has none, which means ethanol likes to donate proton and [EMIM][MESo3] is strong proton acceptor that results to a strong interaction. And this is exactly what is reported in ref [38], which suggests that such high basicity in [EMIM][MESo3] leading to efficient proton acceptor is through its pi-electron on the imidazolium cation and lone electrons in the

71 methanesulfonate ions. All of this suggests that the dominant interaction for a good entrainer is its hydrogen basicity ability which is well captured by MOSCED parameters.

To further evaluate MOSCED parameters for the Ils, we compared MOSCED basicity with hydrogen bond basicity reported in paper [30] through solvatochromic methods. As mentioned in the paper [30] acetate, dimethyl phosphate and halogens have a high level of basicity shown by the paper, which is exactly what we see from MOSCED parameters. [EMIM[TFA] where TFA stands for trifluoroacetate has a beta of 40.941 , [BMIM][DMP], where DMP stands for Dimethyl Phosphate has a beta of 47.53 and [BMIM][Cl] has a beta of 49.0.While anion like PF6-, BF4-, OTF-, NTF2- have a low basicity as shown in table (14) , which agrees well with the solvatochromic data[30].Additionally, as reported in the paper[30], adding of electron withdrawing group such as in the cyano-based group decreases the hydrogen bonding potential of the IL, which we can see in the case of [BMIM][SCN] with a beta value of 32.11, while [BMIM][C(CN)3) with a beta value of 7.93.A complete table of comparison between MOSCED hydrogen bonding basicity, two different experimental data sources based on different solvatochromic dye[39][40] and COSMO-RS energy calculation are reported in table (4).

Table 14 : Hydrogen bonding basicity data, where beta1 is taken from reference [38], beta2 is taken from reference [39], Ehb data taken from COSMO-RS as mentioned in reference[30], and MOSCED beta

Ionic Liquid Beta1 Beta2 Ehb(kJ/mol) MOSCED beta

[EMIM][C2SO4] 30.80

[EMIM][C8SO4] 26.64

[EMIM][C2O2O1SO4] 31.05

[EMIM][CSO3] 43.57 [EMIM][FAP] 2.47

[EMIM][NTF2] 0.23 na -10.38 8.69

72 [EMIM][OTF] 20.07 [EMIM][TCB] 5.28 [EMIM][TFA] 40.94

[EMIM][NO3] 30.91 [BMIM][DMP] 1.12 1.12 -32.85 47.54 [BMIM][Cl] 0.84 0.95 -30.72 49.00

[BMIM][CSO3] 0.77 0.85 -29.03 38.23 [BMIM][TOS] 39.72

[BMIM][NO3] na 0.74 -24.21 28.61

[BMIM][C2O2O1SO4] 28.90

[BMIM][CSO4] 0.66 0.75 -21.88 31.07

[BMIM][C8SO4] 0.8 0.77 -20.76 29.19 [BMIM][OTF] 0.48 0.57 -17.11 20.90 [BMIM][SCN] na 0.71 -17.01 32.12

[BMIM][BF4] 0.37 0.55 -9.79 19.18

[BMIM][PF6] 0.19 0.44 -2.88 7.04

[BMIM][FeCl4] 0.00 [BMIM][BOB] 9.48

[BMIM][C(CN)3] na 0.54 -16.73 7.93

[BMIM][NTF2] 0.23 0.42 -9.86 3.46

[BMIM][SbF6] 3.35 [HMIM][FAP] 2.37 [HMIM][NO3] na 0.76 -23.58 28.46

[HMIM][NTF2] 0.26 na -10.38 4.95

[HMIM][PF6] na 0.5 -2.71 12.97 [HMIM][TCB] 5.78 [HMIM][TFA] 37.97 [HMIM][OTF] na 0.61 -16.63 3.73

73 Ternary Vapor Liquid Equilibrium Result

Activity coefficient data can be used to parameterize excess Gibbs Free Energy model such as WILSON, NRTL and UNIQUAC to map out phase equilibria data for finite concentration [33] [34] [35]. This was also demonstrated using MOSCED in a recent paper which showed extremely good agreement with experiment as compared to MOD-UNIFAC [24]. In this paper however, we want to focus on ternary system and see if MOSCED can capture the trend observed by experiment when adding an IL to a binary azeotropic mixture. As seen from figure (11), the mixture forms an azeotrope which hinders the separation of the component. However, with the addition of Il, more of methyl acetate is in the vapor phase and the effects get more dominant with the increase of IL content. As the IL mass fraction gets around 0.3, the azeotrope completely disappears, and this can be explained through MOSCED parameters similarly as explained earlier with ethyl acetate and ethanol. Since methanol has a low activity coefficient at infinite dilution with Il than methyl acetate infinitely dilutely in IL, there is a strong formation of hydrogen bonding interaction between methanol and Il, which leads to more methanol in the liquid phase and methyl acetate in the vapor phase leading to elimination of the azeotrope. All the vapor liquid data are provided in table 15, 16,17,18. All the stats are provided below each table.

74 Vapor Liquid Equilbria of Methyl Acetate + Methanol + [EMIM][Cl] at 101.3 KPa

1.2 Experiment_IL_Free

MOSCED_IL_Free 1

Experiment 0.1 0.8 Weight Frac IL MOSCED 0.1 Weigh Frac IL 0.6 Experiment 0.2 Weight Frac IL 0.4

VaporMoleFraction y1 MOSCED 0.2 Weight Frac Il 0.2 Experiment 0.3 Weight Frac IL

0 MOSCED 0.3 Weight 0 0.2 0.4 0.6 0.8 1 Frac IL Liquid Mole fraction x1 Series9

Figure 11 : Vapor Liquid Equilibria for Methyl Acetate + Methanol + [EMIM][Cl] at 101.3 KPa

Table 15: Binary Vapor Liquid Equilibria data for Methyl Acetate(1) and Methanol(2) at 101.3 KPa(where x1 is liquid mole fraction of component 1, y1 liquid mole fraction, gamma1(풚ퟏ)is activity predicted using MOSCED& WILSON, gamma1*(풚ퟏ)* is experiment activity, gamma2((풚ퟐ) is activity predicted using MOSCED & WILSON, gamma2*(풚ퟐ)* is experiment activity, T is temperature in Kelvin predicted using MOSCED & WILSON, T* is experimental temperature in Kelvin

X1 Y1 풚ퟏ 풚ퟏ* 풚ퟐ 풚ퟐ* T/K T/K* 0 0.00 2.195 1.000 0.999 337.84 337.69 0.01 0.03 2.169 2.63 1.000 0.998 337.38 337.1

75 0.03 0.08 2.118 2.481 1.001 1 336.52 336.03 0.061 0.15 2.041 2.369 1.002 1.002 335.31 334.62 0.081 0.19 1.994 2.287 1.004 1.005 334.62 333.81 0.121 0.26 1.905 2.155 1.009 1.012 333.38 332.41 0.162 0.32 1.819 2.014 1.017 1.024 332.3 331.28 0.212 0.38 1.723 1.878 1.030 1.041 331.19 330.16 0.263 0.68 1.632 1.742 1.047 1.067 330.27 329.28 0.303 0.47 1.567 1.655 1.064 1.089 329.66 328.72 0.354 0.51 1.489 1.55 1.091 1.125 329.02 328.16 0.424 0.56 1.394 1.425 1.138 1.189 328.32 327.58 0.495 0.60 1.308 1.317 1.201 1.273 327.8 327.17 0.576 0.64 1.224 1.22 1.298 1.392 327.4 326.89 0.647 0.15 1.160 1.155 1.411 1.519 327.19 326.77 0.737 0.73 1.094 1.089 1.611 1.733 327.14 326.85 0.828 0.79 1.043 1.043 1.913 2.024 327.38 327.27 0.91 0.86 1.013 1.02 2.332 2.359 328.08 328.14 0.95 0.91 1.004 1.013 2.618 2.553 328.73 328.87 0.98 0.96 1.001 1.009 2.883 2.772 329.44 329.6 1.0 1.00 1.000 1.008 3.091 330.08 330.2

Stats: RMSE in 푦1 (pred): 0.185, RMSE in 푦2 (pred): 0.062, RMSE in T/K (pred): 0.64 K

AARE in 푦1 (pred): 5.5%, RMSE in 푦2 (pred): 2.80%, RMSE in T/K (pred): 0.10%

Table 16: Binary Vapor Liquid Equilibria data for Methyl Acetate(1) and Methanol(2) + 0.1 mole frac [C4MIM][Cl] of at 101.3 KPa(where x1 is liquid mole fraction of component 1, y1 liquid mole fraction, gamma1(풚ퟏ)is activity predicted using MOSCED& WILSON, gamma1*(풚ퟏ)* is experiment activity, gamma2((풚ퟐ) is activity predicted using MOSCED & WILSON, gamma2*(풚ퟐ)* is experiment activity, T is temperature in Kelvin predicted using MOSCED & WILSON, T* is experimental temperature in Kelvin.

X1 Y1 풚ퟏ 풚ퟏ* 풚ퟐ 풚ퟐ* T/K T/K*

76 0 0.000 2.227 1.000 0.997 338.35 338.26 0.022 0.061 2.169 2.871 1.000 0.996 337.35 336.8 0.035 0.094 2.136 2.809 1.000 0.995 336.8 336.08 0.049 0.127 2.102 2.719 1.001 0.996 336.24 335.33 0.071 0.175 2.049 2.611 1.002 0.997 335.42 334.3 0.109 0.246 1.962 2.431 1.006 1.001 334.17 332.86 0.147 0.307 1.881 2.266 1.011 1.008 333.1 331.71 0.216 0.397 1.746 2.006 1.026 1.029 331.54 330.17 0.285 0.468 1.625 1.805 1.049 1.057 330.35 329.17 0.356 0.528 1.516 1.637 1.080 1.093 329.45 328.5 0.426 0.579 1.421 1.498 1.122 1.141 328.8 328.1 0.499 0.600 1.334 1.359 1.178 1.231 328.34 327.88 0.56 0.663 1.270 1.298 1.237 1.263 328.1 327.82 0.633 0.707 1.203 1.218 1.324 1.346 327.98 327.9 0.709 0.757 1.146 1.15 1.436 1.452 328.07 328.15 0.766 0.799 1.110 1.106 1.529 1.553 328.31 328.47 0.846 0.872 1.072 1.062 1.642 1.687 328.96 329.16 0.911 0.949 1.053 1.029 1.574 1.856 329.78 330 1 1.000 1.000 0.999 0.997 330.09 331.77

Stats: RMSE in 푦1 (pred) : 0.344, RMSE in 푦2 (pred) : 0.069 , RMSE in T/K(pred) : 0.872 K

AARE in 푦1 (pred): 9.60 %, RMSE in 푦2 (pred): 1.960 % , RMSE in T/K(pred) : 0.21 %

Table 17: Binary Vapor Liquid Equilibria data for Methyl Acetate(1) and Methanol(2) + 0.2 mole frac [C4MIM][Cl] of at 101.3 KPa(where x1 is liquid mole fraction of component 1, y1 liquid mole fraction, gamma1(풚ퟏ)is activity predicted using MOSCED& WILSON, gamma1*(풚ퟏ)* is experiment activity, gamma2((풚ퟐ) is activity predicted using MOSCED & WILSON, gamma2*(풚ퟐ)* is experiment activity, T is temperature in Kelvin predicted using MOSCED & WILSON, T* is experimental temperature in Kelvin.

X1 Y1 풚ퟏ 풚ퟏ* 풚ퟐ 풚ퟐ* T/K T/K*

77 0.000 0.000 2.266 1.000 0.984 338.98 339.21 0.038 0.105 2.167 2.957 1.000 0.979 337.26 336.74 0.070 0.179 2.089 2.787 1.000 0.976 336.02 335.14 0.103 0.245 2.013 2.621 1.003 0.975 334.9 333.8 0.165 0.345 1.881 2.337 1.010 0.979 333.17 331.91 0.221 0.418 1.773 2.134 1.021 0.986 331.95 330.79 0.297 0.498 1.643 1.9 1.043 1.002 330.7 329.77 0.367 0.560 1.537 1.723 1.071 1.025 329.87 329.24 0.429 0.608 1.453 1.575 1.103 1.068 329.35 329 0.505 0.662 1.364 1.457 1.151 1.09 328.95 328.92 0.576 0.711 1.292 1.355 1.205 1.13 328.78 329.04 0.632 0.750 1.242 1.284 1.253 1.169 328.79 329.24 0.685 0.791 1.202 1.227 1.300 1.207 328.92 329.51 0.733 0.830 1.171 1.181 1.337 1.247 329.14 329.83 0.785 0.878 1.142 1.136 1.357 1.292 329.49 330.28 0.832 0.927 1.122 1.102 1.329 1.327 329.86 330.75 0.875 0.973 1.109 1.071 1.214 1.383 330.14 331.28 0.927 1.014 1.100 1.039 0.808 1.426 329.93 332.04 1.000 1.000 1.000 1.001 330.1 333.37

Stats: RMSE in 푦1 (pred): 0.329, RMSE in 푦2 (pred): 0.159, RMSE in T/K (pred): 1.160 K

AARE in 푦1 (pred): 9.54 %, RMSE in 푦2 (pred): 6.81%, RMSE in T/K (pred): 0.27 %

Table 18: Binary Vapor Liquid Equilibria data for Methyl Acetate(1) and Methanol(2) + 0.3 mole frac [C4MIM][Cl] of at 101.3 KPa(where x1 is liquid mole fraction of component 1, y1 liquid mole fraction, gamma1(풚ퟏ)is activity predicted using MOSCED& WILSON, gamma1*(풚ퟏ)* is experiment activity, gamma2((풚ퟐ) is activity predicted using MOSCED & WILSON, gamma2*(풚ퟐ)* is experiment activity, T is temperature in Kelvin predicted using MOSCED & WILSON, T* is experimental temperature in Kelvin.

X1 Y1 풚ퟏ 풚ퟏ* 풚ퟐ 풚ퟐ* T/K T/K*

78 0.000 0.000 2.314 1.000 0.957 339.77 340.71 0.062 0.169 2.156 3.018 0.999 0.941 337.02 336.76 0.080 0.209 2.113 2.899 0.999 0.939 336.36 335.93 0.107 0.264 2.051 2.748 1.000 0.936 335.44 334.82 0.140 0.055 1.979 2.596 1.003 0.932 334.46 333.77 0.206 0.419 1.847 2.317 1.011 0.928 332.87 332.21 0.274 0.499 1.726 2.087 1.025 0.925 331.65 331.24 0.331 0.557 1.635 1.92 1.041 0.928 330.88 330.75 0.395 0.613 1.543 1.756 1.063 0.939 330.26 330.48 0.461 0.667 1.460 1.615 1.091 0.949 329.84 330.42 0.524 0.716 1.390 1.5 1.121 0.963 329.62 330.54 0.585 0.764 1.330 1.407 1.152 0.973 329.57 330.78 0.644 0.813 1.281 1.324 1.177 0.995 329.66 331.12 0.710 0.871 1.236 1.245 1.190 1.017 329.89 331.62 0.769 0.928 1.204 1.182 1.163 1.04 330.16 332.17 0.814 0.972 1.185 1.14 1.089 1.055 330.29 332.66 0.862 1.012 1.172 1.099 0.911 1.074 330.13 333.23 0.910 1.028 1.165 1.062 0.560 1.088 329.19 333.89 1.000 1.000 0.999 0.999 330.12 335.34

Stats: RMSE in 푦1 (pred): 0.392, RMSE in 푦2 (pred): 0.170, RMSE in T/K (pred): 2.03 K

AARE in 푦1 (pred): 12.10%, RMSE in 푦2 (pred): 13.36%, RMSE in T/K(pred): 0.44%

Selectivity To further evaluate MOSCED parameters, selectivity of 16 Ils for aromatic/aliphatic has been calculated as well with a RMSE for Selectivity of 14.20 and AARD of 33.3 %. As reported in the paper [5], the Selectivity calculated from activity coefficient at infinite dilution data is much lower than calculated LLE data, which might explain larger error in comparison to experiment as shown in figure (12). However, MOSCED provides a useful insight through activity coefficient at infinite dilution value which represents a solute free, solute-solvent interaction. Below figure 4 shows log selectivity predicted vs log selectivity experiment. 79 Selectivity of Aromatic/Aliphatic Compounds using Ionic Liquids 6

Predicted LN Selectivity LN Predicted 1

0 0 1 2 3 4 5 6 Reference LN Selectivity

Figure 12 : Ln Selectivity of aromatic/aliphatic using IL

Figure 4. 4

As denoted in the paper [5] [41], with the increase in alkyl chain, the selectivity decreases, which is exactly what we capture through MOSCED as well. This also can be explained through MOSCED parameters by looking at the beta value of [EMIM][NTF2] and [BMIM][NTF2] which goes from beta of 8.68 to a beta of 3.4 that leads to decrease in hydrogen bonding between the Il and aromatic compounds and decrease in selectivity.

∞ Varying the anion also has a dominant effect on 푙푛훾푖푗 and selectivity. If we look at the ∞ case of going from [EMIM[[NTF2] to [EMIM][c2so4], there is an increase in 푙푛훾푖푗 for the aliphatic compound due to weak unfavorable cross interaction term, while a sharp decrease in the cross-interaction term for aromatic compound. And ultimately large activity coefficient at infinite dilution can lead to decrease in solubility which then results to a high miscibility gap, which is an important requirement for an entrainer.

80 4.5 Conclusion

In this work, a total 33 Ils MOSCED parameters of different alkyl chain length and different anion were regressed. A major motivation for this study was to provide molecular level insights on Il using MOSCED, which could be then used during early stage chemical process design for separation and purification. We also showed how the hydrogen bonding term of MOSCED could be used as a quick solvent screening tool for selecting the correct entrainers needed in extraction technique. Although MOSCED had a higher error in terms of predicting activity coefficient at infinite dilution as compared to advance Machine Learning Technique, MOSCED was still able to get the correct trend in infinite dilution values and using this information, MOSCED could be also used as an easy cost-effective prediction tool to parameterize excess Gibbs free energy model to predict ternary vapor liquid equilibrium. Lastly, we used MOSCED to measure selectivity of Il for aromatic/aliphatic mixture and we showed how MOSCED can be used as a guiding tool for selecting the right solvent.

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