Ionic Liquids¶

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 the tutorial: 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 the tutorial: 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).

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.

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.

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. To be able to compare to experimental activity coefficients in which the cation-anion pair is treated as one compound, we will also make one compound. However, in the calculation this compound only has the dissociated form.

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.

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(30.219) = 3.41. Note that the calculated numbers in this figure are calculated with an older version of COSMO-RS. These will not change much if you use a newer COSMO-RS version.

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.

The results of the activity coefficients.

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 = 0.5065*64.36 = 32.6 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/(0.1136 * 0.2735) = 32.6 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.

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.

First we use the experimental Antoine coefficients for CO₂.

Next we make the ionic liquid as one compound and calculate CO₂ solubilities.

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

In this example we also calculated the solubility of carbon dioxide at relatively high pressures. In such cases, 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 against fugacity instead of pressure.

The results can be compared with experimental values from Ref.[651]. Note that the calculated numbers in this figure are calculated with an older version of COSMO-RS. These will not change much if you use a newer COSMO-RS version.

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 = 2.24 MPa at T = 282 K, H = 3.20 MPa at T = 297.3 K, and H = 5.51 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.

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.

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