A statistical mechanics study on relationship between nanopore size and energy storage in supercapacitors

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

“…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.…”

“…The aim of the present work is to reproduce the experimentally observed capacitive behaviors of the aqueous EDLC with help from the classical density functional theory (CDFT) in which the water is modeled by a more realistic dipole dimer hard sphere model and the salt ions are approximated by charged hard spheres as in the PM. Compared with a large number of reports on the aqueous EDLC capacitance behaviors based on the PM [ 20 , 22 , 50 , 51 , 52 , 68 ] and SPM [ 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 ], the report of capacitance behaviors of the EDLC based on the dipole dimer hard sphere model for water is almost blank (instead of the EDLC capacitance behaviors, the literature [ 67 ] only reports the electrical double layer structure). So, the present report is necessary and urgent.…”

On Capacitance and Energy Storage of Supercapacitor with Dielectric Constant Discontinuity

“…One of the most significant changes caused by the low value is that both the value and the value reduce greatly with the low value dropping. Generally speaking, previous studies indicate repeatedly [ 73 , 74 ] that the value falls within order of magnitude of for the normal aqueous value, such as , whereas for the low value, as considered presently, such as , the value falls within order of magnitude of . i.e., the value goes down two orders of magnitude for approximately equal electrode potential.…”

“…i.e., the value goes down two orders of magnitude for approximately equal electrode potential. Corresponding to this, the value at voltage of 2 V reduces to one twentieth of the value corresponding to [ 73 ]. We will explore the relevant action mechanisms by analyzing the ion adsorption inside the pore and the space electrical potential distribution.…”

“…In the present work, the electrolyte solution is modeled by the primitive model (PM), and the solution relative dielectric constant is kept fixed at 10.0, this value is far smaller than that of bulk water. This is another novel point of the present work as a considerable part of the works for the SC [ 16 , 70 , 71 , 72 , 73 ] employing aqueous electrolyte solution uses the value corresponding to that of the bulk water. This is necessary because as the device size becomes smaller and smaller, amount of solvent adsorption near the interface tends to decrease [ 74 ]; moreover, correlation of the electric dipole perpendicular to the surface also decreases.…”