Impacts of solvent electric dipole and ion valency on energy storage in ultrananoporous supercapacitor: An ising model study

Abstract

A four-state BEG model is constructed to investigate effects of electric dipole of solvent molecule and ion valency on differential capacitance Cd and energy storage Eof the supercapacitor based on electrical double layer inside an ultranano-cylindrical pore about the size of the ions and solvent. In the model, existence of voids is permitted, solvent molecule is modelled as neutral hard sphere with an electrical dipole moment and ions are described by the primitive model; all electrostatic interactions between cation, anion, and polarized charges on the solvent molecule are limited to the nearest neighbor interactions. The present investigation is limited to weak solvent-solvent electrostatic interaction in comparison to that of the solvent-ion and ion-ion. New effects are found and summarized as follows. (i) There appears a zero Cd and zero E platform around the zero surface potential, which widens with the increase of the solvent transfer energy w0 and moves to positive surface potential side with replacement of the monovalent cation by bivalent cation. (ii) The saturated surface potential |Usat|, beyond which Cd reduces to zero and E reaches its saturation value Esat, is positively correlated with the w0 value. The correlation strength reduces with the counter-ion valence. (iii) For appropriate positive w0 value, both |Usat| and Esat always increase with the solvent polarized charge valence b and dipole length l whether the electrolyte type is +1: 1 or +2: 1; whereas for negative w0 value, the value and l value effects are very small and graphically unobservable. (iv) Presence of bivalent counter-ions causes an increase of the Cd peak strength and Esat value, whereas the presence of bivalent co-ion almost does not bring graphically observed effect. (v) Within the ranges of the b and l values considered, the energy storage is raised by increasing the solvent electrical dipole moment (whether by increasing b valueb or l value) without paying for the cost of high surface potential applied.