Unusual properties of the electric double layer in an extremely narrow nanotube. A grand canonical Monte Carlo and classical DFT study

On Capacitance and Energy Storage of Supercapacitor with Dielectric Constant Discontinuity

“…The former is analytically available from textbook of statistical thermodynamics, and the latter originates from internal interactions within the system, and its acquirement has to resort to approximations. In the present calculations, we use the density functional approximations tested in literatures [ 77 , 78 , 79 , 80 ]. In detail, the hard sphere repulsion coming from the internal inter-ion short-range interaction is treated by a well confirmed fundamental measure functional, the long-range inter-ion electrostatic interaction is dealt with by mean field approximation, and the interplay between the hard sphere repulsion and electrostatic interaction is calculated by a second order functional perturbation expansion whose expansion coefficient is exactly the bulk second order direct correlation function based on a mean spherical approximation closure to the Ornstein-Zernike integral equation.…”

“…In detail, the hard sphere repulsion coming from the internal inter-ion short-range interaction is treated by a well confirmed fundamental measure functional, the long-range inter-ion electrostatic interaction is dealt with by mean field approximation, and the interplay between the hard sphere repulsion and electrostatic interaction is calculated by a second order functional perturbation expansion whose expansion coefficient is exactly the bulk second order direct correlation function based on a mean spherical approximation closure to the Ornstein-Zernike integral equation. Relevant details are recorded in literatures [ 77 , 78 , 79 , 80 ] and not repeated here. Particularly, literature [ 80 ] indicates that the electrical capacitance properties of extreme nanoscale SC can still be predicted rather reliably even the prediction of density distribution becomes worse under the extreme condition.…”

“…Relevant details are recorded in literatures [ 77 , 78 , 79 , 80 ] and not repeated here. Particularly, literature [ 80 ] indicates that the electrical capacitance properties of extreme nanoscale SC can still be predicted rather reliably even the prediction of density distribution becomes worse under the extreme condition.…”

Capacitive Behavior of Aqueous Electrical Double Layer Based on Dipole Dimer Water Model

“…In fact, the limitation of the narrow electrochemical window can be overcome in highly concentrated aqueous electrolytes, also known as water-in-salt (WiS) electrolytes [ 8 , 9 , 10 , 11 , 12 , 13 ], which have been shown to significantly widen the electrochemical stability window to over 3.0 V, via interface modification [ 14 , 15 ], or the development of chemically stable, high surface area carbon structures [ 16 , 17 , 18 ]. As a result, aqueous electrolytes are still popular in the study of EDLCs [ 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ].…”

“…In theoretical studies, simpler coarse-grained models are used, but essential features can be captured. Usually, the aqueous electrolyte solution is modeled by so-called primitive model (PM) [ 20 , 22 , 50 , 51 , 52 ], in which a water solvent is considered as a structureless continuum and shows its existence only through a high dielectric constant completely neglecting its hard core; some researches [ 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 ] pick up the hard core missed in the PM and use an appropriately high dielectric constant to reflect the electric dipole moment of the water molecule (such a model is called the solvent primitive model abbreviated as SPM). There are studies [ 61 , 62 ] that consider a semi-primitive model where the solvent is represented by hard spheres with a Yukawa attraction and a dielectric permittivity is also introduced to reflect the electrostatic shielding effect of water molecules; in a very recent study [ 63 ], one Lennard–Jones (LJ) sphere with a higher energy parameter is used to model the water molecule to reflect its strong polarity, both the LJ energy and size parameters are determined by reproducing the two experimentally measured a and b parameters in the van der Waals equation of the state of water.…”