Figure 6.

Lattice model for slit confinements. (a) Ions on a square lattice in a quasi 2D slit confinement. The model given by eq 23 predicts the existence of ordered and disordered phases. The disordered phase consist of a homogeneous mixture of ions and voids, while the ordered phase has cation and anions located on two sublattices (say A and B). J is the coupling constant describing the interaction between the ions. (b) Bethe lattice with coordination number q = 4, corresponding to the square lattice, has been used to calculate the charging properties analytically.^40,43,77 (c) Charge on sublattices A and B, (d) capacitance, and (e) stored energy density as functions of the voltage. The symbols are the results of Monte Carlo simulations and the lines denote the Bethe-lattice solution. An ionic liquid with βJ = 2 (red lines and triangles) is in the ordered state at low voltages and experiences a first-order transition to the disordered state at βeu ≈ 8 (red vertical line). An ionic liquid with βJ = 0.2 (black lines and circles) is in the disordered state at all voltages. Adapted with permission from ref (43). Copyright 2021 American Chemical Society under CC-BY (https://creativecommons.org/licenses/by/2.0/).