Cracking Ion Pairs in the electrical double layer of ionic liquids

Here we investigate a limiting case of the theory for aggregation and gelation in the electrical double layer (EDL) of ionic liquids (ILs). The limiting case investigated only accounts for ion pairs, ignoring the possibility of larger clusters and a percolating ionic network. This simplification, permits analytical solutions for the properties of the EDL. The resulting equations demonstrate the competition between the free energy of an association and the electrostatic potential in the EDL. For small electrostatic potentials and large negative free energies of associations, ion pairs dominate in the EDL. Whereas, for electrostatic potential energies larger than the free energy of an association, electric-field-induced cracking of ion pairs occurs. The differential capacitance for this consistent ion pairing theory has a propensity to have a “double hump camel” shape. We compare this theory against previous free ion approaches, which do not consistently treat the reversible associations in the EDL

Theory of the Double Layer in Water-in-Salt Electrolytes.

One challenge in developing the next generation of lithium-ion batteries is the replacement of organic electrolytes, which are flammable and most often contain toxic and thermally unstable lithium salts, with safer, environmentally friendly alternatives. Recently developed water-in-salt electrolytes (WiSEs), which are nonflammable, nontoxic, and also have enhanced electrochemical stability, are promising alternatives. In this work, we develop a simple modified Poisson-Fermi theory for WiSEs, which demonstrates the fine interplay between electrosorption, solvation, and ion correlations. The phenomenological parameters are extracted from molecular dynamics simulations, also performed here. The theory reproduces the WiSEs' electrical double-layer structure with remarkable accuracy

Atomistic Hartree theory of twisted double bilayer graphene near the magic angle

Twisted double bilayer graphene (tDBLG) is a moiré material that has recently generated significant interest because of the observation of correlated phases near the magic angle. We carry out atomistic Hartree theory calculations to study the role of electron–electron interactions in the normal state of tDBLG. In contrast to twisted bilayer graphene, we find that such interactions do not result in significant doping-dependent deformations of the electronic band structure of tDBLG. However, interactions play an important role for the electronic structure in the presence of a perpendicular electric field as they screen the external field. Finally, we analyze the contribution of the Hartree potential to the crystal field, i.e. the on-site energy difference between the inner and outer layers. We find that the on-site energy obtained from Hartree theory has the same sign, but a smaller magnitude compared to previous studies in which the on-site energy was determined by fitting tight-binding results to ab initio density-functional theory (DFT) band structures. To understand this quantitative difference, we analyze the ab initio Kohn–Sham potential obtained from DFT and find that a subtle interplay of electron–electron and electron–ion interactions determines the magnitude of the on-site potential

Gelation, clustering, and crowding in the electrical double layer of ionic liquids.

Understanding the bulk and interfacial properties of super-concentrated electrolytes, such as ionic liquids (ILs), has attracted significant attention lately for their promising applications in supercapacitors and batteries. Recently, McEldrew et al. [J. Phys. Chem. B 125, 2677 (2021)] developed a theory for reversible ion associations in bulk ILs, which accounted for the formation of all possible (Cayley tree) clusters and a percolating ionic network (gel). Here, we adopt and develop this approach to understand the associations of ILs in the electrical double layer at electrified interfaces. With increasing charge of the electrode, the theory predicts a transition from a regime dominated by a gelled or clustered state to a crowding regime dominated by free ions. This transition from gelation to crowding is conceptually similar to the overscreening to crowding transition

Interfacial layering in the electric double layer of ionic liquids

Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly interacting environment, leading to the formation of discrete layers of charges at interfaces and spin-glass structure in the bulk. Here, we propose a simple theory that captures the coupling between steric and electrostatic forces in ionic liquids. The theory predicts the formation of discrete layers of charge at charged interfaces. Further from the interface, or at low polarization of the electrode, the model outputs slowly decaying oscillations in the charge density with a wavelength of a single ion diameter, as shown by analysis of the gradient expansion. The gradient expansion suggests a new structure for partial differential equations describing the electrostatic potential at charged interfaces. We find quantitative agreement between the theory and molecular simulations in the differential capacitance and concentration profiles

Water in the electrical double layer of ionic liquids on graphene

The performance of electrochemical devices using ionic liquids (ILs) as electrolytes can be impaired by water uptake. This work investigates the influence of water on the behavior of hydrophilic and hydrophobic ILs─with ethylsulfate and tris(perfluoroalkyl)trifluorophosphate or bis(trifluoromethyl sulfonyl)imide (TFSI) anions, respectively─on electrified graphene, a promising electrode material. The results show that water uptake slightly reduces the IL electrochemical stability and significantly influences graphene's potential of zero charge, which is justified by the extent of anion depletion from the surface. Experiments confirm the dominant contribution of graphene's quantum capacitance (CQ) to the total interfacial capacitance (Cint) near the PZC, as expected from theory. Combining theory and experiments reveals that the hydrophilic IL efficiently screens surface charge and exhibits the largest double layer capacitance (CIL ∼ 80 μF cm-2), so that CQ governs the charge stored. The hydrophobic ILs are less efficient in charge screening and thus exhibit a smaller capacitance (CIL ∼ 6-9 μF cm-2), which governs Cint already at small potentials. An increase in the total interfacial capacitance is observed at positive voltages for humid TFSI-ILs relative to dry ones, consistent with the presence of a satellite peak. Short-range surface forces reveal the change of the interfacial layering with potential and water uptake owing to reorientation of counterions, counterion binding, co-ion repulsion, and water enrichment. These results are consistent with the charge being mainly stored in a ∼2 nm-thick double layer, which implies that ILs behave as highly concentrated electrolytes. This knowledge will advance the design of IL-graphene-based electrochemical devices

Underscreening, overscreening and double-layer capacitance

There have recently been reports of extraordinarily long screening lengths in concentrated electrolytes and which vary non-monotonically with ion concentration. There were several attempts to explain these puzzling observations. In this communication we further explore possibilities to rationalise those results. Our analysis does not yet close the problem, but it highlights conflicting consequences of the models designed to reproduce those observations

Theory of polymer-electrolyte-composite electroactuator sensors with flat or volume-filling electrodes

In reverse actuation, a voltage/electrical-current signal can be generated from applying a mechanical force to an electroactuator. Such processes are of interest in touch sensing and soft robotics applications. We develop a classical density functional theory of reverse actuation for polymer-electrolyte-composite electroactuators, which treats mobile cations in the same spirit as forward actuation (curving in response to applied voltage). The proposed framework is applied to electroactuators with micro-structured porous electrodes (with cylindrical or slit pores) and flat electrodes, the dynamic response of which has to be modelled differently. Open- and short-circuit operation modes are investigated separately. A detailed analysis of the proposed theory indicates the preferred architectures for sensing, depending on the operation regimes

Mean-field theory of electrical double layer in ionic liquids with account of short-range correlations

We develop the theory of the electrical double layer in ionic liquids as proposed earlier by Kornyshev (2007). In the free energy function we keep the so called ‘short-range correlation terms’ which were omitted there. With some simplifying assumptions, we arrive at a modified expression for differential capacitance, which makes differential capacitance curves less sharply depending on electrode potential and having smaller values at extrema than in the previous theory. This brings the results closer to typical experimental observations, and makes it appealing to use this formalism for treatment of experimental data. Implications on Debye length and the extent of ion paring in ionic liquids are then briefly discussed

On the temperature dependence of the double layer capacitance of ionic liquids.

The temperature dependence of room temperature ionic liquids differential capacitance is studied here with both theoretical and computational methods. On the theory front, the lattice-gas mean-field theory of ionic liquids is further generalised to account for ‘ion pairing’ and ‘neutral aggregate’ formation. An anomalous temperature dependence of linear response capacitance was found, similar to that reported in earlier work. The theory also predicted that differential capacitance curves transform from a camel to bell shape with increasing temperature. Molecular dynamics simulations verified the expected transition in shape of differential capacitance curves with temperature and the dependence of linear response capacitance on temperature. Further investigation into charge density distributions revealed an ordered structure, reminiscent of oriented ion pairs and neutral aggregates, extending far enough from the electrode to control the capacitance-voltage response. It was found that these structures were dismantled with increasing temperature, as predicted by the mean-field theory