A Classical Density Functional Theory of Ionic Liquids

Abstract

Classical Density Functional Theory of Ionic Liquids 3 Other approachesILs are fascinating from a theoretical standpoint. In order to treat ILs, a theory must account for both electrostatic and steric correlations. Attempts to develop such a theory have appeared in the literature. These include the lattice based model by Kornyshev and co-workers (Fedorov et al. , 2008;Kornyshev , 2007). In another lattice approach by Lauw and coworkers (Lauw et al. , 2009), both cations and anions were modelled by a star-like architecture, with each monomer subject to an independently specified dielectric response. Under certain circumstances, these models were able to qualitatively reproduce the so-called "camel-shaped" differential capacitance, C D , profile observed in imidazolium ILs at carbon electrodes (Islam et al. , 2009;Lockett et al. , 2008a). This behaviour is an indication of subtle structuring effects at charged surfaces and is a stern test for theory. Although camel-shaped C D profiles are predicted, qualitative discrepancy against experimental results remains. This is not surprising since these crude theories lack a proper description of electrostatic correlations despite accounting for steric contributions. Charge-charge correlations have been shown to be important in interfacial phenomena of highly coupled electrostatic fluids. As with dispersion forces, ionic correlations are always attractive and lower the total energy. Thus, we expect that they will also play a role in establishing the camel shape of the C D . That this is the case, is seen from both simulations (Lamperski & Zydor , 2007;Vatamanu et al. , 2010) (Fedorov et al. , 2010;Trulsson et al. , 2010), play an important role in determining their properties. In this work, we will use a model for ILs wherein the molecular ions interact via dispersion, as well as electrostatic, forces and the cation has an oligomeric structure consistent with imidazolium ions. This model has also been adopted by us in previous recent publications (Forsman et al. , 2011;Trulsson et al. , 2010), and employs the methods of polymer free energy density functional theory (DFT) (Woodward , 1991). The result will be a simple, albeit approximate DFT for ILs. We have already introduced the salient features of the theory in a previous publication (Forsman et al. , 2011). Here, we will present a much more thorough treatment, emphasizing the relation to theories of simpler fluids. We will also extend the scope of the study with some emphasis on temperature dependence and the effects of ion-specific adsorption. The IL-DFT that we will discuss here is an off-lattice theory, whose accuracy can be straightforwardly tested against computer simulations of the same molecular model. We will begin with a discussion of relevant earlier work, in order to introduce the essential mechanistic components that will be combined in our density functional theory for ionic liquids. Classical density functional theory (DFT) of simple fluidsThe ideal gas law is known and used by most physicists and chemist...

Classical density functional theory & simulations on a coarse-grained model of aromatic ionic liquids

“…On the other hand, surface depletion of the RTIL at the neutral electrode can cause the differential capacitance to decrease at low potentials as well. [4][5][6][7] This can be offset if the neutral electrode surface has a high affinity to the RTIL. These effects combine to generate a (now characteristic) 'camel-shaped' differential capacitance curve.…”

“…6 In that work we used a simple CG model of the RTIL, which facilitated our semi-analytical approach. While our theory was also successful in producing novel differential capacitance behaviour, comparisons with Monte Carlo simulations of the same CG model highlighted some discrepancies.…”

“…6 In common with that model, it consists of simple bonded beads containing partial charges and interacting via Lennard-Jones forces. While this general model can be optimized to fit a range of RTILs we will focus on a cation structure which roughly matches the homologous series of 1-alkyl-3-methyl imidazoliums , CnM IM + , where n denotes the length of the alkyl chain.…”

Classical Density Functional Study on Interfacial Structure and Differential Capacitance of Ionic Liquids near Charged Surfaces

“…On the other hand, steric hindrance due to large molecular structure is quite strong and causes RTILs to remain fluid rather than to crystallize. 3 This strong interplay between steric exclusion and electrostatic interactions brings many desirable properties to RTILs including low melting point, negligible vapor pressure and high electrochemical stability. These coupled with a large variety of cations and anions to choose from, make RTILs a vigorous research area at the moment.…”

Capillary Condensation of Ionic Liquid Solutions in Porous Electrodes

“…In this article, we shall use a classical density functional theory (DFT) to carry out a theoretical study, which will focus on capillary condensation of RTIL+solvent mixtures in model pores with slit-like geometries. A classical DFT for ionic liquids was recently reported by us to study oligimeric ionic liquids at interfaces [22]. Other approaches using the primitive model for electrolytes have also been reported in the literature [23].…”