A Simple Guiding Principle for the Temperature Dependence of the Solubility of Light Gases in Imidazolium-based Ionic Liquids Derived from Molecular Simulations

TL;DR

This study uses molecular simulations to reveal a universal temperature dependence pattern for the solubility of light gases in imidazolium-based ionic liquids, introducing a simple analytical model called the "solvation funnel" model.

Contribution

It introduces the "solvation funnel" model, linking solvation free energy and temperature dependence, based on extensive molecular dynamics simulations and analysis of solvation entropy-enthalpy compensation.

Findings

Solvation free energy and its temperature derivatives are closely related.

The "solvation funnel" model accurately predicts solubility trends for light gases.

The model aligns well with experimental data, especially for hydrogen.

Abstract

We have determined the temperature dependence of the solvation behavior of a large collection of light gases in imidazolium-based Ionic Liquids (ILs) with the help of extensive molecular dynamics simulations. The solubility of molecular hydrogen, oxygen, nitrogen, methane, krypton, argon, neon and carbon dioxide in the imidazolium based ILs of type 1-n-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C$_n$mim][NTf$_2$]) with varying chain lengths $n\!=\!2,4,6,8$ are computed for a temperature range between $300\,\mbox{K}$ and $500\,\mbox{K}$ at $1\,\mbox{bar}$. By applying Widom's particle insertion technique and Bennet's overlapping distribution method, we are able to determine the temperature dependent solvation free energies for those selected light gases in simulated imidazolium based ILs with high statistical accuracy. Our simulations show that the magnitude of the solvation free energy of a gas molecule at a chosen reference temperature and its temperature-derivatives are intimately related with respect to oneanother. We conclude that this "universal" behavior is rooted in a solvation entropy-enthalpy compensation effect, which seems to be a defining feature of the solvation of small molecules in Ionic Liquids. We argue that this feature is based on a hypothesized funnel-like shape of the free energy landscape of a solvated gas molecule. The observations lead to simple analytical relations, determining the temperature dependence of the solubility data based on the absolute solubility at a certain reference temperature, which we call "solvation funnel" model. By comparing our results with available experimental data from many sources, we can show that the "solvation funnel" model is particularly helpful for providing reliable estimates for the solvation behavior of very light gases, such as hydrogen, where conflicting experimental data exist.