Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior

Multicritical bifurcation and first-order phase transitions in a three-dimensional Blume-Capel antiferromagnet

We present a detailed study by Monte Carlo simulations and finite-size scaling analysis of the phase diagram and ordered bulk phases for the three-dimensional Blume-Capel antiferromagnet in the space of temperature and magnetic and crystal fields (or two chemical potentials in an equivalent lattice-gas model with two particle species and vacancies). The phase diagram consists of surfaces of second- and first-order transitions that enclose a "volume" of ordered phases in the phase space. At relatively high temperatures, these surfaces join smoothly along a line of tricritical points, and at zero magnetic field we obtain good agreement with known values for tricritical exponent ratios [Y. Deng and H. W. J. Blöte, Phys. Rev. E 70, 046111 (2004)10.1103/PhysRevE.70.046111]. In limited field regions at lower temperatures (symmetric under reversal of the magnetic field), the tricritical line for this three-dimensional model bifurcates into lines of critical endpoints and critical points, connected by a surface of weak first-order transitions inside the region of ordered phases. This phenomenon is not seen in the two-dimensional version of the same model. We confirm the location of the bifurcation as previously reported [Y.-L. Wang and J. D. Kimel, J. Appl. Phys. 69, 6176 (1991)0021-897910.1063/1.348797], and we identify the phases separated by this first-order surface as antiferromagnetically (three-dimensional checker-board) ordered with different vacancy densities. We visualize the phases by real-space snapshots and by structure factors in the three-dimensional space of wave vectors.

Theory and Simulations of Ionic Liquids in Nanoconfinement

Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

Ionic liquids in conducting nanoslits: how important is the range of the screened electrostatic interactions?

Analytical models for capacitive energy storage in nanopores attract growing interest as they can provide in-depth analytical insights into charging mechanisms. So far, such approaches have been limited to models with nearest-neighbor interactions. This assumption is seemingly justified due to a strong screening of inter-ionic interactions in narrow conducting pores. However, how important is the extent of these interactions? Does it affect the energy storage and phase behavior of confined ionic liquids? Herein, we address these questions using a two-dimensional lattice model with next-nearest and further neighbor interactions developed to describe ionic liquids in conducting slit confinements. With simulations and analytical calculations, we find that next-nearest interactions enhance capacitance and stored energy densities and may considerably affect the phase behavior. In particular, in some range of voltages, we reveal the emergence of large-scale mesophases that have not been reported before but may play an important role in energy storage.

Capacitive energy storage in single-file pores: Exactly solvable models and simulations

Understanding charge storage in low-dimensional electrodes is crucial for developing novel ecologically friendly devices for capacitive energy storage and conversion and water desalination. Exactly solvable models allow in-depth analyses and essential physical insights into the charging mechanisms. So far, however, such analytical approaches have been mainly limited to lattice models. Herein, we develop a versatile, exactly solvable, one-dimensional off-lattice model for charging single-file pores. Unlike the lattice model, this model shows an excellent quantitative agreement with three-dimensional Monte Carlo simulations. With analytical calculations and simulations, we show that the differential capacitance can be bell-shaped (one peak), camel-shaped (two peaks), or have four peaks. Transformations between these capacitance shapes can be induced by changing pore ionophilicity, by changing cation-anion size asymmetry, or by adding solvent. We find that the camel-shaped capacitance, characteristic of dilute electrolytes, appears for strongly ionophilic pores with high ion densities, which we relate to charging mechanisms specific to narrow pores. We also derive a large-voltage asymptotic expression for the capacitance, showing that the capacitance decays to zero as the inverse square of the voltage, C ∼ u^-2. This dependence follows from hard-core interactions and is not captured by the lattice model.

Superionic Liquids in Conducting Nanoslits: Insights from Theory and Simulations

Mapping the theory of charging supercapacitors with nanostructured electrodes on known lattice models of statistical physics is an interesting task, aimed at revealing generic features of capacitive energy storage in such systems. The main advantage of this approach is the possibility to obtain analytical solutions that allow new physical insights to be more easily developed. But how general the predictions of such theories could be? How sensitive are they to the choice of the lattice? Herein, we address these questions in relation to our previous description of such systems using the Bethe-lattice approach and Monte Carlo simulations. Remarkably, we find a surprisingly good agreement between the analytical theory and simulations. In addition, we reveal a striking correlation between the ability to store energy and ion ordering inside a pore, suggesting that such ordering can be beneficial for energy storage.

Grand canonical simulations of ions between charged conducting surfaces using exact 3D Ewald summations

We present a useful methodology to simulate ionic fluids confined by two charged and perfectly conducting surfaces. Electrostatic interactions are treated using a modified 3D Ewald sum, which accounts for all image charges across the conductors, as well as the 2D periodicity, parallel to the surfaces. The energy expression is exact, and the method is trivial to implement in existing Ewald codes. We furthermore invoke a grand canonical scheme that utilizes a bias potential, that regulates the surface charge density. The applied bias potential also enables us to calculate individual chemical potentials of the ions. Finally, we argue that our approach leads to a pedagogically appealing description of the Donnan potential, and what it measures in these systems.