Ionic Liquids¶

6.1: Using the ADF COSMO-RS ionic liquid database¶

Ionic liquids (ILs), usually consisting of a large organic cation and a small inorganic polyatomic anion, have attracted considerable attention in recent years due to their unique thermophysical properties. The low vapor pressure and high conductivity of these molten salts combined with highly tunable properties, have resulted in highly diverse applications across many different fields in chemistry, materials science (battery electrolytes), chemical engineering (gas sorption and purification), and many more.

To calculate thermodynamic properties of ionic liquids with COSMO-RS, the IL may be described either as a single ion pair or as discrete cations and anions. The latter method will be mainly used here. The COSMO-RS ionic liquid database ADFCRS-IL-2014 contains 80 cations and 56 anions. This ADFCRS-IL-2014 database consists of ADF COSMO result (.coskf) files, from standard ADF quantum mechanical calculations, as described in tutorial 1: COSMO result files. The user can create new anions and cations using that same approach and add them to the List of Added Compounds.

The ADFCRS-IL-2014 database is part of the ADFCRS-2018 COSMO-RS database. Install the ADFCRS-2018 database if it is not yet installed, see tutorial 4: The COSMO-RS compound database.

SCM gratefully acknowledges Prof. Zhigang Lei’s research group (State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, China) for providing the ionic liquid database, the corresponding tutorial, and the reparameterization of COSMO-RS for ionic liquids (ADF Lei 2018).

6.2: Ionic liquid volumes and densities¶

Ionic liquid densities may be estimated from the molecular volume and molar mass (MW) of the constituent cations and anions. The COSMO volume is stored in the coskf file and is displayed, together with the MW, when a compound is selected in the COSMO-RS GUI.

Click on the search button in the compounds field

Select IL_cation_1-butyl-3-methyl-imidazolium

Click OK

Volumes and molar mass of other cations and anions can be similarly found. Data for a few compounds are listed below.

The molecular liquid density could be approximately calculated as (V in ų and MW in g/mol) using Avogadro’s number:

density = (MW_cation + MW_anion )/[0.6022*(V_cation + V_anion )]

As can be seen from this table, the calculated densities are systematically overestimated by approximately 15%. Thus, the COSMO volumes underestimate the volume of a single compound, if they are used for estimating the liquid densities.

6.3: Activity coefficient calculation¶

The activity coefficient of a compound i solvated in an ionic liquid is an important thermodynamic property. The cation and anion, which have been treated separately, will be used in equal amounts to ensure an electroneutral mixture in the COSMO-RS calculation.

In other applications cation-anion pair have been treated as one molecule, however, in the COSMO-RS calculations below we will treat the cation and anion as two separate molecules. This has consequences for the value of the activity coefficients.

For example, for a 1:1 IL (i.e., [A]⁺ [B]^- ), the activity coefficient at a finite concentration of solute i in the binary mixture (IL + solute) can be calculated by

γ_i ^bin = (γ_i ^tern x_i ^tern )/x_i ^bin = γ_i ^tern /(1+x_IL ^bin )

where the superscript “tern” represents the hypothetical ternary system comprising cation, anion and solute i, with

x_cation ^tern = x_anion ^tern

x_cation ^tern + x_anion ^tern + x_i ^tern = 1

and the superscript “bin” represents the binary mixture comprising solute and IL, with

x_IL ^bin + x_i ^bin = 1

Accordingly, the activity coefficient of a solute i in the binary mixture (IL + solute) at infinite dilution is simplified as

γ_i ^bin = 0.5 γ_i ^tern     (at infinite dilution)

Thus in this case we should scale the activity coefficient at infinite dilution γ_i ^tern , which is directly obtained from the COSMO-RS calculation, with a factor of 0.5.

Similarly, for a ternary system comprising component i, component j and an ionic liquid, the activity coefficient at finite concentration of component i can be calculated by

γ_i ^tern = γ_i ^quart /(1+x_IL ^tern )

where the superscript “quart” represents the hypothetical quaternary system comprised of cation, anion, solute i and solute j, with:

x_cation ^quart = x_anion ^quart

x_cation ^quart + x_anion ^quart + x_i ^quart + x_j ^quart = 1

and the superscript “tern” represents the ternary mixture comprising solute i, j, and IL, with

x_IL ^tern + x_i ^tern + x_j ^tern = 1

Select Properties → Activity coefficients

Select ‘2 components’ in the popup menu next to Solvent

Select ‘IL_cation_1-ethyl-3-methyl-imidazolium’ for the first component in Solvent

Enter 0.5 for the Mole fraction of the first component

Select ‘IL_anion_tetracyanoborate’ for the second component in Solvent

Enter 0.5 for the Mole fraction of the second component

Enter ‘308.15’ for ‘Temperature Kelvin’

Check the ‘+’ button to add ‘Hexane’, ‘Heptane’, ‘Octane’, and ‘Decane’

Press ‘Run’

If one does not supply a density of the solvent in the input, the program calculates the density of the solvent by dividing the mass of a molecule with its COSMO volume. Note that the calculated activity coefficients do not depend on this density. The result of the calculation is given in the form of a table.

Note that for a comparison to experimental numbers, the calculated activity coefficients have to be scaled with 0.5, as was discussed before. In the next figure the results of the calculated activity coefficients at different temperatures are compared to experiment.

In this figure activity coefficients at infinite dilution of n-alkenes in [EMIM]⁺ [TCB]^- are shown for different temperatures ranging from 298 K to 358 K. The scattered points are experimental data from Ref.[633]. The points that are connected with a line are calculated numbers with ADF COSMO-RS. For example, for Hexane, the calculated values T = 308.15 K are: 1000/308.15 = 3.245, ln(0.5*63.8579) = 3.46.

6.4: Henry’s law constants¶

In this tutorial, we will calculate Henry’s law constants for CO₂ in different ionic liquids. Henry’s law constant reflects the solubility of a gas in a solvent, and one way to define it is

where H_i is the ratio between the partial vapor pressure of a compound i in the gas phase and its molar fraction in the liquid phase, \(\gamma_i^\infty\) is the the activity coefficient of the compound at infinite dilution, and P_i ^S is the saturated pure compound vapor pressure of the gas.

The familiar Antoine and Wagner equations can be used to calculate the vapor pressure below the critical temperature T_c , if one knows the coefficients. Above T_c , they can be extrapolated as a hypothetical vapor pressure. If the experimental saturated vapor pressures of a gas is not available, then it can be estimated by COSMO-RS.

The saturated vapor pressure of CO₂ at 298.15 K can be calculated by the following Antoine equation:

ln P_CO2 ^S (MPa) = 12.3312 - 4759.46/(T(K)+156.462)

The saturated vapor pressure of CO₂ at 298.15 K is 6.436 MPa (= 64.36 bar) according to this equation. The Antoine equation can also be written as:

\({}^{10}\)log P_CO2 ^S (bar) = 6.35537 - 2067.0/(T(K)+156.462)

The activity coefficients of infinitely diluted carbon dioxide in [HMIM]⁺ [Tf2N]^- will now be calculated.

Select Compounds → List of Added Compounds

Search on the left side ‘Carbon dioxide’ and click on it

Enter 6.35537 for the Antoine coefficient A on the right side

Enter 2067.0 for the Antoine coefficient B

Enter 156.462 for the Antoine coefficient C

Select Properties → Activity coefficients

Select ‘2 components’ in the popup menu next to Solvent

Select ‘IL_cation_1-hexyl-3-methyl-imidazolium’ for the first component in Solvent

Enter 0.5 for the Mole fraction of the first component

Select ‘IL_anion_bis(trifluoromethylsulfonyl)amide’ for the second component in Solvent

Enter 0.5 for the Mole fraction of the second component

Enter ‘298.15’ for ‘Temperature Kelvin’

Check the ‘+’ button to add ‘Carbon dioxide’ (Remove the alkanes if they are still present)

Press ‘Run’

The results of the activity coefficients.

As discussed before, we should scale the COSMO-RS calculated activity coefficient at infinite dilution \(\gamma^\infty\) with a factor of 0.5. Henry’s law coefficient is \(\gamma^\infty\) times the saturated vapor pressure of CO₂ at 298.15 K (64.36 bar). For CO₂ in [HMIM]⁺ [Tf2N]^- the calculated H = 0.5*1.0148*64.36 = 32.7 bar. Applying the same calculations for more ionic liquids gives these results:

There are many different definitions of Henry’s law constant. Henry’s constant as calculated directly by COSMO-RS, k_H (mol/(L atm)), is defined as the ratio between the liquid phase concentration of a compound and its partial vapor pressure in the gas phase. The relationship between k_H and H is:

H = k_H,inv ^px = 1/(k_H V_solvent )

where V_solvent is the molar volume of the ionic liquid. If no densities for the cation, anion, or solvent are given, COSMO-RS will use the COSMO volume for calculating the molar volume of the ionic liquid, which is 0.2735 L/mol (=(241.00+213.17)*0.6022/1000) for [HMIM]⁺ [Tf2N]^- , if the usual convention is followed, that a pair of a cation and an anion is treated as one molecule. Thus in this case H = 1.01325/(0.1134 * 0.2735) = 32.7 bar, where a conversion factor from atm to bar is included.

Note that k_H does not depend on whether one treats a cation and an anion as separate molecules, or if a pair of a cation and an anion is treated as one molecule. H = k_H,inv ^px does depend on this definition.

6.5: Gas solubility and selectivity in ionic liquids¶

In this example the solubility of carbon dioxide in ionic liquids is calculated and compared to experimental data.

In the ADF COSMO-RS calculation, an ionic liquid molecule is described as a discrete cation and anion. Thus, the system of gas and ionic liquid will be treated as a hypothetical ternary mixture (“tern”) consisting of gas, cation, and anion. For a 1:1 ionic liquid, the solubility of gas x_gas ^tern in the hypothetical ternary system can be calculated by

x_gas ^tern = n_gas /(n_gas + n_cation +n_anion ) = n_gas /(n_gas + 2n_IL )

where x_gas ^tern is the molar fraction of the gas in the hypothetical ternary system, and n_gas , n_cation , n_anion , and n_IL are the molar amounts of gas, cation, anion, and IL in the liquid phase, respectively. For the real gas and IL binary system, the gas solubility x (molar fraction of the gas in the IL) is defined as:

x = n_gas /(n_gas + n_IL )

Combining the previous equations yields:

x = 2 x_gas ^tern /(x_gas ^tern + 1)

First we use the experimental Antoine coefficients for CO₂ .

(Skip this part if you have just done COSMO-RS tutorial 6.4)

Select Compounds → List of Added Compounds

Search on the left side ‘Carbon dioxide’ and click on it

Enter 6.35537 for the Antoine coefficient A on the right side

Enter 2067.0 for the Antoine coefficient B

Enter 156.462 for the Antoine coefficient C

Next we calculate CO₂ solubilities.

Select Properties → Solubility in Mixture

Select ‘2 components’ in the popup menu next to Solvent

Select ‘IL_cation_1-hexyl-3-methyl-imidazolium’ for the first component in Solvent

Enter 0.5 for the Mole fraction of the first component

Select ‘IL_anion_bis(trifluoromethylsulfonyl)amide’ for the second component in Solvent

Enter 0.5 for the Mole fraction of the second component

Enter ‘8’ for ‘Temperature: number of steps’

Enter ‘282.0’ for ‘Temperature from’

Enter ‘322.8’ for ‘Temperature to’

Change the popup menu next to Solutes to ‘Gas’

Use ‘MPa’ units for the pressure

Enter ‘2.0’ for the partial vapor pressure

Check the ‘+’ button to add ‘Carbon dioxide’

Press ‘Run’

From the results we will use the calculated mole fractions at 282.0 K, 297.3 K, and 322.8 K.

Do the same calculation for a number of vapor pressures of Carbon dioxide, namely 0.5 MPa, 1.0 MPa, and 1.5 MPa. Remember that we need to convert the calculated solubilities x_gas ^tern to the solubility x in the binary system, consisting of gas and IL, with x = 2 x_gas ^tern /(x_gas ^tern + 1):

In this example we also calculated the solubity of carbon dioxide at relatively high presures. In this case, for more accurate results, we also need to take the nonideal behavior of the gas into account, the gas fugacity.

f_gas = P_gas \(\Phi\) (T,P)

where f_gas is the gas fugacity at the system temperature and pressure, and \(\Phi\) (T,P) is the fugacity coefficiency of the gas. We will approximate the fugacity coefficients with:

Note that these values are only approximate, and certainly not applicable for higher pressures. We can use the same solubilities as calculated before but plot them agains fugacity instead of pressure.

The results can be compared with experimental values fromRef.[651].

For low pressures one can estimate gas solubility using Henry’s law constants:

For low pressures \(\Phi\) (T,P) will be close to 1. Calculating Henry’s law constants has been described in COSMO-RS Tutorial 6.4, and following this procedure for CO₂ in [HMIM][Tf₂ N], results in H = 2.242 MPa at T = 282 K, H = 3.204 MPa at T = 297.3 K, and H=5.5222 MPa at T = 322.8 K.

Gas selectivity in ionic liquids can be defined as

S_i/j = H_i /H_j

where S_i/j is the selectivity between gas i and j in ionic liquids; H_i and H_j are Henry’s law constants of gas i and j, which can be calculated using the methods as described in the COSMO-RS Tutorial 6.4.

6.6: VLE for systems containing ionic liquids¶

In this example a vapor-liquid diagram of Acetone in [EMIM][Tf₂ N] at 353.15 K is calculated and compared to experiment. The experimental saturated pure compound vapor pressure is used for Acetone.

Select Compounds → List of Added Compounds

Search on the left side ‘Acetone’ and click on it

Enter ‘2.1516’ in the ‘Pure compound vapor pressure’ field

Enter ‘353.15’ in the ‘at temperature’ field

Select Properties → Solvents s1 - s2 Composition Line

Select ‘3 components’ in the popup menu next to Solvents

Select ‘Acetone’ for the first component in Solvents

Select ‘IL_cation_1-ethyl-3-methyl-imidazolium’ for the second component in Solvent

Select ‘IL_anion_bis(trifluoromethylsulfonyl)amide’ for the third component in Solvent

Enter ‘1.0’ for the mole fraction of compound 1 of solvent s1

Enter ‘0.0’ for the mole fraction of compound 1 of solvent s2

Enter ‘0.0’ for the mole fraction of compound 2 of solvent s1

Enter ‘0.5’ for the mole fraction of compound 2 of solvent s2

Enter ‘0.0’ for the mole fraction of compound 3 of solvent s1

Enter ‘0.5’ for the mole fraction of compound 3 of solvent s2

Enter ‘20’ for ‘Number of mixtures’

Select ‘Isotherm’ from the Isotherm, isobar, flash point popup menu

Use ‘Kelvin’ as units for the temperature

Enter ‘353.15’ for ‘Temperature’

Press ‘Run’

Remember that, before we compare to experiment, we need to convert the calculated molar fractions x_i ^tern from the hypothetical ternary system to the molar fractions x_i ^bin in the binary acetone-IL system with:

x_i ^bin = 2 x_i ^tern /(x_i ^tern + 1)

x_i ^tern = x_i ^bin /(2 - x_i ^bin )

Comparing the calculated and experimental vapor pressure of acetone in [EMIM][Tf2N] in a graph:

References

661. M. Döker, J. Gmehling Measurement and prediction of vapor–liquid equilibria of ternary systems containing ionic liquids, Fluid Phase Equilibria 227 (2005), 255