A classical density functional theory for the asymmetric restricted primitive model of ionic liquids

Effect of surface roughness on partition of ionic liquids in nanopores by a perturbed-chain SAFT density functional theory

In this work, the distribution and partition behavior of ionic liquids (ILs) in nanopores with rough surfaces are investigated by a two-dimensional (2D) classical density functional theory (DFT) model. The model is consistent with the equation of state (EoS) that combines the perturbed-chain statistical associating fluid theory (PC-SAFT) and the mean spherical approximation (MSA) theory for bulk fluid. Its performance is verified by comparing the theoretical predictions to the results from molecular simulations. The fast Fourier transform (FFT) and a hybrid iteration method of Picard iteration and Anderson mixing are used to efficiently obtain the solution of density profile for the sizeable 2D system. The molecular parameters for IL-ions are obtained by fitting to experimental densities of bulk ILs. The model is applied to study the structure and partition of the ILs in nanopores. The results show that the peak of the density profile of counterions near a rough surface is much higher than that near a smooth surface. The adsorption of counterion and removal of coions are enhanced by surface roughness. Thus the nanopore with rough surfaces can store more charge. At low absolute surface potential, the partition coefficient for ions on rough surfaces is lower than that on smooth surfaces. At high absolute surface potential, increasing surface roughness leads to an increase in partition coefficient for counterions and a decrease in partition coefficient for coions.

Boundary-Monte Carlo Method for Neutral and Charged Confined Fluids

In this work, we describe a new Monte Carlo (MC) simulation method to investigate highly coupled fluids in confined geometries at a constant chemical potential. This method is based on so-called multi-scale Hamiltonian methods, wherein the chemical potential is determined using a more amenable Hamiltonian for a fluid in an "outer" region, which facilitates standard methods, such as grand canonical MC simulations or Widom's particle insertion method. The (inner region) fluid of interest is placed in diffusive contact with the simpler outer fluid via a boundary zone wherein the Hamiltonian is transformed. The current method utilizes an ideal fluid for the outer regions, which allows for implicit rather than explicit simulations. Only the boundary and inner region need explicit consideration; hence, the nomenclature used is boundary-Monte Carlo. We illustrate the utility of the method for simple neutral and charged fluids in cylindrical and planar pores. In the latter case, we use a dense room-temperature ionic liquid model and illustrate how the boundary zone establishes a proper Donnan equilibrium between inner and outer fluids in the presence of charged planar electrodes. Thus, the method allows direct calculation of properties such as the differential capacitance, without the need for additional difficult calculations of the requisite Donnan potential.

Structural transitions at electrodes, immersed in simple ionic liquid models

We used a recently developed classical Density Functional Theory (DFT) method to study the structures, phase transitions, and electrochemical behaviours of two coarse-grained ionic fluid models, in the presence of a perfectly conducting model electrode. Common to both is that the charge of the cationic component is able to approach the electrode interface more closely than the anion charge. This means that the cations are specifically attracted to the electrode, due to surface polarization effects. Hence, for a positively charged electrode, there is competition at the surface between cations and anions, where the latter are attracted by the positive electrode charge. This generates demixing, for a range of positive voltages, where the two phases are structurally quite different. The surface charge density is also different between the two phases, even at the same potential. The DFT formulation contains an approximate treatment of ion correlations, and surface polarization, where the latter is modelled via screened image interactions. Using a mean-field DFT, where ion correlations are neglected, causes the phase transition to vanish for both models, but there is still a dramatic drop in the differential capacitance as proximal cations are replaced by anions, for increasing surface potentials. While these findings were obtained for relatively crude coarse-grained models, we argue that the findings can also be relevant in "real" systems, where we note that many ionic liquids are composed of a spherically symmetric anion, and a cation that is asymmetric both from a steric and a charge distribution point of view.

Density functional theory of confined ionic liquids: the influence of power-law attractions on molecule distributions and surface forces

Interaction energies and density profiles for two model ionic liquids, [C₄mim⁺][BF₄⁻] and [C₄mim⁺][TFSI⁻], confined between charged planar walls are studied within a density functional theory framework. The results of these simulations are also compared with results assuming a simpler linear hexamer–monomer, cation–anion system. We focus attention on the effect on the atom site distributions and the surface forces of an additional, specific attractive potential between oppositely charged molecules. We consider both short- and long-ranged attractive potentials in order to span the degree to which the ionic counterions associate. Independent of its strength, we interpret the results found with the short-ranged potential to be a manifestation of limited molecular association. In contrast, depending on its strength, the results found with the long-ranged potential suggest a much stronger and possibly longer ranged associations of ionic groups. Both potentials are found to influence the behavior of the surface force at small separations, while the long-ranged attractive potential has the greater influence of the two on the long-ranged behavior of the surface force.

Interaction energies and density profiles for two model ionic liquids, [C₄mim⁺][BF₄⁻] and [C₄mim⁺][TFSI⁻], confined between charged planar walls are studied within a density functional theory framework.

Local Grand Canonical Monte Carlo Simulation Method for Confined Fluids

We describe a new local grand canonical Monte Carlo method to treat fluids in pores in chemical equilibrium with a reference bulk. The method is applied to Lennard-Jones particles in pores of different geometry and is shown to be much more accurate and efficient than other techniques such as traditional grand canonical simulations or Widom's particle insertion method. It utilizes a penalty potential to create a gas phase, which is in equilibrium with a more dense liquid component in the pore. Grand canonical Monte Carlo moves are employed in the gas phase, and the system then maintains chemical equilibrium by "diffusion" of particles. This creates an interface, which means that the confined fluid needs to occupy a large enough volume so that this is not an issue. We also applied the method to confined charged fluids and show how it can be used to determine local electrostatic potentials in the confined fluid, which are properly referenced to the bulk. This precludes the need to determine the Donnan potential (which controls electrochemical equilibrium) explicitly. Prior approaches have used explicit bulk simulations to measure this potential difference, which are significantly costly from a computational point of view. One outcome of our analysis is that pores of finite cross-section create a potential difference with the bulk via a small but nonzero linear charge density, which diminishes as ∼1/ln(L), where L is the pore length.

General theory of charge regulation and surface differential capacitance

A generalization of the mean-field approach will be derived that will take into account the ion-ion as well as ion-surface non-electrostatic effects on an equal footing, being based on the bulk and surface equations of state in the absence of electrostatic interactions. This approach will be applied to the analysis of a single planar surface with dissociable sites with several models of the specific ion-surface non-electrostatic interactions, providing a general thermodynamic insight into the characteristics of the surface differential capacitance. The ion-surface interactions and ion-ion packing considerations at the surface will be shown to be more relevant than the bulk packing constraints for ions vicinal to the surface, as well as to set in prior to the conditions where the bulk packing constraints would become relevant.