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Chemical Modelling Applications and Theory Volume 9
A Review of Recent Literature
By M. Springborg
The Royal Society of ChemistryCopyright © 2012 The Royal Society of Chemistry
All rights reserved.
Uncovering molecular secrets of ionic liquids
Ionic liquids offer high-potential solutions to an amazingly broad range of applications. The large number of cations and anions which can be combined to a low melting salt suggests the feasibility to design a required liquid for every task. The variety of possible ionic liquids even outnumbers traditional solvents in chemistry. Unfortunately, little is known about general properties of ionic liquids except the obvious fact that they consist solely of ions. It is the human and scientific nature that always finds its way to characterize the unknown or find ways to overcome challenges. One such challenge is the distillation of ionic liquids which was originally thought impossible due to the low volatility of known ionic liquids. However, ionic liquids can be distilled.
The history of ionic liquids goes back nearly one hundred years. As early as 1914, Paul Walden reported the first systematic study of ionic liquids. However, the scope of ionic liquids was recognized barely until the development of air and water stable imidazolium-based ionic liquids in 1992. Since then, the interest in these compounds has increased greatly leading to manifold applications of these compounds in natural sciences and industry. For example, ionic liquids are used in battery, solar cell, fuel cell, and lubricant applications. Nevertheless, even fundamental properties of ionic liquids are far from being understood.
Due to the technical progress and the developments in theoretical chemistry over the last 20 years, computational methods have become a powerful tool in chemistry because various approaches can be employed for an investigation at the molecular scale. Observed macroscopic properties can be assigned to functional parts of a molecule which facilitates a more task-related design of new compounds. Still, the interplay of nuclei and electrons is too complex for feasible black box methods of systems larger than a few atoms. Therefore, a computational chemist should always choose an approach carefully and verify how the necessary approximations influence the results.
Ionic liquids are a special challenge for computational chemistry. Due to the important role of cooperativity, the investigation of large systems is necessary to obtain reliable results. Unfortunately, only for medium sized systems are there any computational approaches available which possess the required flexibility of electronic structure for an accurate ab initio description of cooperativity. Additionally, not only cooperativity, but also dispersion forces make the choice of a reliable approach for ionic liquids a challenging task. Nevertheless, carefully selected computational approaches allow predictions for ionic liquids, which can be confirmed by experiments if possible. One example is the nanoscale segregation of polar and nonpolar domains (also called microheterogeneity) in ionic liquids. These domains were found in corse-grained model and in fully atomistic model molecular dynamics simulations before they were reported by X-ray diffraction or Raman-induced Kerr effect spectroscopy studies as well. Not only the prediction of the liquid structure but also the calculation of thermodynamic data, like the gaseous enthalpy of formation, is feasible. These two discussed examples exemplify that carefully selected computational approaches are a powerful tool for the investigation of ionic liquids.
2 Choice of a suited computational method
The investigation of large systems is necessary for ionic liquids due to the important role of cooperativity. Additionally, commonly used ionic liquids consist of inorganic anions and organic cations with alkyl side chains and aromatic moieties. Both functional groups of the cation are well-known for a significant contribution of dispersion forces to equilibrium structure and interaction energy. Long alkyl chains of ionic liquids result in nanoscale segregation, in which the nonpolar domains are dominated by dispersion forces. Furthermore, π-π-stacking of aromatic cations was also observed. Even the interplay of counter ions is influenced significantly by dispersion forces. Thus, reliable computational approaches for an investigation of ionic liquids do not need only a proper description of electrostatic and induction forces, also an accurate description of dispersion forces is needed.
Ab initio correlated or so-called post Hartree–Fock methods provide a proper description of dispersion forces. Unfortunately, these methods are computationally limited to systems with few atoms. Only few CCSD(T) calculations of very small ionic liquid systems were reported so far. Second-order Møller–Plesset perturbation theory (MP2) might be also a suitable ab initio method to study ionic liquids. Recent developments have made this approach available for systems with hundreds of atoms. However, calculations of medium sized ionic liquid systems need still enormous computational resources. Thus, MP2 and similar approaches seem to be limited to static quantum chemical calculations and are still too expensive for ab initio molecular dynamics simulations over an appropriate system size and time frame.
A feasible compromise of accurate forces and available system size might be Kohn–Sham density functional theory (KS-DFT). Several approaches, especially for general gradient approximation (GGA) functionals, are known to reduce the computational cost much lower than for conventional correlation methods. Unfortunately, KS-DFT accounts for electrostatic, exchange and induction forces very well, but fails for the description of dispersion forces. Del Pópolo et al. have attributed observed large errors in calculated equilibrium volumes of ionic liquid crystal structures to the limitations of KS-DFT in dealing with dispersion interactions. Several possible solutions were proposed to correct this shortcoming of Kohn–Sham density functional theory. Most computational investigations of ionic liquids still use traditional exchange-correlation functionals, e.g. B3LYP, without a dispersion correction. However, two studies have shown that energy and structure obtained with traditional functionals deviates to MP2 references similar like Hartree-Fock calculations. Zahn and Kirchner reported that the empirical dispersion correction proposed by Grimme in 2006 reduces the deviation to the reference values significantly. An empirical dispersion correction by a dispersion corrected atom-center dispersion potential (DCACP) was also recommended. Both approaches increase the computational time marginally and the deviance is within the error of the MP2 reference method. Similar results were obtained also by Izgorodina et al. Additionally, this study recommended three recently developed functionals (M05-2X, KMLYP, and M05) for the investigation of ionic liquids. Furthermore, a study reported good matching ionic liquid crystal structure volumes if the non-empirical dispersion correction of Dion et al. is employed. Non-local van der Waals density functionals as well as the third version of Grimme's empirical dispersion correction gave excellent results for ionic liquids, too. The study of Grimme, Hujo, and Kirchner shows also that the self interaction error of KS-DFT is only important at large ion distances. Thus, various feasible dispersion corrected KS-DFT approaches are available for reliable investigations of ionic liquid systems.
Ab initio molecular dynamics simulations might be the best approach to study middle-sized ionic liquid systems because dispersion corrected KS-DFT approaches give excellent results, and cooperativity is also considered. A recent study has shown that electronic properties like the dipole moment are strongly localized properties of ionic liquids. Furthermore, Lynden-Bell observed strong electrostatic screening between solute charges at distances comparable to the radius of the first solvation shell. Therefore, the feasible system size of ab initio molecular dynamics simulations is sufficient to study many body effects or solvent-solute interactions. Numerous ab initio molecular dynamics simulations were published in the last years which provide a molecular view on ionic liquids. As mentioned above, these simulations are limited to medium system size and short timescales as well. Ionic liquids are often high viscous liquids which results in slow dynamic processes on the molecular scale. Additionally, ab initio molecular dynamics simulations need large amounts of computational resources. Therefore, classical molecular dynamics simulations with a well parametrized force field could be a suited alternative or even better choice to study certain properties of ionic liquids.
Especially for imidazolium based ionic liquids, several force fields can be found in the literature. The first force field of Hanke, Price, and Lynden-Bell was developed to reproduce experimental crystal structures. Unfortunately, a comparison of the reported liquid structure to later published ab initio molecular dynamics simulations show large deviations. For example, the preferred position of the chloride anion in the study of Hanke et al. is above and below the imidazolium plane and nearly no anion can be found in front of the most acidic hydrogen atom of the imidazolium ring. The force field proposed by Morrow and Maginn in 2002 was developed using a combination of ab initio calculations and the CHARMM22 force field. Most interestingly, the magnitude of used ion charges was less than one which is in agreement with later published results of large ion clusters. Also, the agreement between experimental and computed values of the volume expansivity, isothermal compressibility and molar volumes were good for this ab initio parametrized force field. The model of Liu, Huang, and Wang published 2004 is based on the AMBER force field in which missing parameters were taken from static quantum chemistry calculations. Additionally, parameters were adjusted to match vibrational frequencies. Furthermore, the van-der-Waals diameter of the most acidic proton of the imidazolium ring was optimized. A good agreement between experimental and calculated density was obtained for several ionic liquids. Also, the obtained liquid structure matches the results from later published ab initio molecular dynamics simulations. In 2004, Canongia Lopes et al. proposed a force field for several imidazolium based ionic liquids, too. Missing parameters, like torsion energy profiles and charge distribution, were obtained from static quantum chemical calculations. Crystallographic data and density of fourteen ionic liquids were reproduced well with this force field. Later, Canongia Lopes and Pádua published extensions of their force field, which provides parameters for the triflate, bistriflymide, dicyanamide, alkylsulfonate, and alkylsulfate anions as well as for phosphonium, pyridinium, trialkylimidazolium, and alkoxycarbonylimidazolium cations. Thus, their force field facilitate to study a broad range of commonly used ionic liquids. In 2007, Köddermann, Paschek, and Ludwig published a revised version of the force field of Canongia Lopes and Pádua for imidazolium based ionic liquids, in which the Lennard-Jones parameters were adjusted to reproduce experimental measurements. The finally obtained model for imidazolium bistriflymide ionic liquids shows improved results for self-diffusion coefficients. Additionally, a good agreement of experimental and calculated heats of vaporization, shear viscosity, and NMR rotational correlation times was found. Bhargava and Balasubramanian reported also a refined model for imidazolium ionic liquids, based on the force field of Canongia Lopes and Pádua. They changed Lennard-Jones parameters of few atoms and scaled the charges of the ions by 0.8 which is close to the value found in large ion clusters. A similar reparametrization was reported by Zhao et al. as well. These refined models show an improved agreement of the liquid structure compared to ab initio molecular dynamics simulations. Especially, the hydrogen bond structure could be reproduced very well. Additionally, diffusion coefficients and surface tension show a good agreement to experimental measurements. An investigation of Youngs and Hardacre showed that the best agreement of classical molecular dynamics simulations and ab initio molecular dynamics simulations is achieved if the partial charges obtained from isolated ions are scaled between 0.7 and 0.8 in the force field models. Thus, the charge scaling seems to be a good choice to consider charge transfer between cation and anion and avoid more time consuming polarisable force fields. Already in 2004 Yan et al. investigated the influence of polarisability by comparing a nonpolarisable with a polarisable force field. A faster dynamics and better agreement to experimental values was observed for the polarisable model. Similar results were reported for various polarisable force field models. These results highlight that the too slow dynamics of most nonpolarisable force fields might be a result of neglecting polarisation and charge transfer between the ions. Of special interest of the polarisable models might be the the quantum chemistry-based polarisable force field of Borodin because it is available for various ionic liquids and gives good results for liquid structure, ion self- diffusion coefficients, conductivity, and viscosity. We will come back to this point in the following chapter.
In summary, various approaches were developed and validated for ionic liquids over the last years. It was shown that dispersion corrected KS-DFT approaches allow reliable results for ionic liquids. Recently, a comparison of trajectories obtained from ab initio molecular dynamics simulations with and without a dispersion correction revealed that the dynamics of the system is more accurately described for the dispersion corrected one, which highlights the necessity of dispersion corrected approaches in ab initio molecular dynamics simulations. Polarisable force fields were developed which allow the investigation of various ionic liquids. Cheaper nonpolarisable force fields are also available for a broad range of ionic liquids. However, the latter force fields tend to show too slow dynamical properties due to the negligence of polarisability. A feasible correction for them might be the usage of reduced total ion charges, which were observed in large scale ionic liquid cluster calculations, too.
3 Functionalizing ionic liquids for a low melting point or low viscosity
One focus of computational investigations is the characterization of molecular features contributing to a low viscosity or a low melting point of ionic liquids. A low melting point increases the usable temperature window of the liquid while a high viscosity influences several properties undesirably, such as electrical conductivity or even reaction rates. Most ionic liquids consist of inorganic anions and organic cations. Unfortunately, the cations are commonly too complex to identify easily molecular features contributing to a low melting point. Thus, investigations with simple model systems might be reasonable to characterize general molecular features contributing to desired macroscopic properties.
Two excellent studies of Spohr and Patey employ simple spherical model systems to characterize the influence of ion size disparity and charge asymmetry on macroscopic properties, like viscosity and electrical conductivity. Their first study, published 2008, showed that the electrical conductivity increases from an ion size disparity from 1:1 to 2:1 (cation: anion). The conductivity is then nearly unaffected up to a size ratio of 3:1. Larger size disparities decrease the electrical conductivity such that the size ratios 1:1 and 5:1 have nearly the same conductivities. This behavior was traced back to the competing impact of ion diffusion (increasing) and ion density (decreasing). Additionally, the influence of ion size disparity on shear viscosity is strongest up to a size ratio of 3:1 then decreases and seems to reach a limiting value at a size disparity of 5:1. Spohr and Patey reported that charge asymmetry increases electrical conductivity and decreases viscosity. However, this trend is reversed if charge asymmetry exceeds a critical value. The sharp decrease of conductivity and rapid increase of viscosity was attributed to the formation of directional long living ion pairs. This result seems to be in contradiction to the concepts proposed by Ludwig and our groups who suggested that strong, directional charge asymmetry induced by hydrogen bonds fluidize ionic liquids. However, while Spohr and Patey did not consider a particular class of ionic liquids and neglected the possibility of hydrogen bonding, the conclusions of Fumino et al. and of our investigations are based solely on the observation of ionic liquids with diverse imidazolium cations. These cations form hydrogen bonds with anions. Furthermore, classical molecular dynamics studies reported a short time correlated motion of cations and anions for imidazolium ionic liquids but the existence of long living ion pairs was excluded. Overall, the travelled distance of most ion associates is smaller than the ion-ion distance. Therefore, no significant displacement is reached before they dissociate. In classical molecular dynamics simulations of molten salts solely short time correlated motions of ions were found, too. The deviation from the Nernst-Einstein relation of ionic liquids and molten salts was attributed to the short time correlated movement. Furthermore, stable ion aggregates could be excluded for imidazolium and pyrrolidinium ionic liquids based on dielectric spectroscopy measurements. Thus, the term "ion association" seems to be more suitable for most ionic liquids because distinct ion pairs could not be observed. Therefore, ionic liquids are discussed also as extremely dissociating solvents because no preferential Coulombic attraction between any particular cation-anion combination can be observed due to the large number of undistinguishable neighbors. Distinct long-living ion pairs might only exist in ionic liquids which consist of highly asymmetric ions, like in the model systems of Spohr and Patey.
Excerpted from Chemical Modelling Applications and Theory Volume 9 by M. Springborg. Copyright © 2012 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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