Ultrananoporous supercapacitor with ionic liquid comprised of two-site cation: an Ising model study (II)

Abstract

Abstract A four-state one-dimension discrete spin model with the nearest neighbor and partial next nearest neighbor lattice interactions is proposed for describing electrical double layer formed by ionic liquid in cylindrical pore that can accommodate only one row of particles. The model, in which cation is modeled as a dimer formed by two hard spheres (HSs): one is positively charged with diameter d + , while the other is neutral with diameter d + 0 , and anion is modeled by charged HS with diameter d − , is designed to investigate effects of pore diameter d c y l i n , ion transfer free energy, ion size and electrical valence on behaviors of specific differential capacitance C d and specific energy storage E and its saturation value E s a t . Relevant Kramers–Wannier transfer matrix is 16 × 16 , which gives system partition function by numerically solving maximum real root of the relevant characteristic equation. Main findings are briefly described below. (i) The ion valence has little effect on the E s a t value, but does reduce the threshold voltage strength U s a t , beyond which the energy storage reaches E s a t . However, the ion valence (whether co- or counter-ion) raises both the E s a t and U s a t values as the relevant ion size decreases enough. (ii) Decreasing of the d c y l i n value weakly reduces the U s a t value, but raises the C d peak height and the E s a t value obviously; correlation between the d c y l i n value and E s a t value becomes stronger with the ions getting more pore hostile. (iii) With the counter-ion or co-ion charged site size decreasing, both the E s a t value and U s a t value rise. However, the effect of the co-ion charged site size is weakened as the co-ion gets more pore hostile, and the cation neutral site size influences on the E s a t value less than the cation charged site size does. (iv) Pore friendly co-ion or pore hostile counter-ion always helps in raising the E s a t value; the two have significant synergistic effect with the co-ion pore friendliness playing more important role than the counter-ion pore hostility.