Ising model study on effects of solvent electric dipole on ultrananoporous supercapacitor

Abstract

A three-state one-dimensional Ising model is used to investigate effects of solvent electric dipole on specific differential capacitance Cd and energy storage per unit area E in shallow cylindrical pore. Maximum real root of the 16×16 Kramers-Wannier transfer matrix and the system partition function are obtained numerically. The present method is rather general in that it covers symmetry and asymmetry cases of both ion size and ion valence, but the solvent electric dipole effects are analyzed only in the cases of charge symmetry and asymmetry. Main findings are briefly described below. (i) High solvent pore affinity raises the saturation energy storage but at the cost of simultaneously raising the threshold surface potential strength. Encouragingly, the presence of high valence ion can raise the saturation energy storage to the same extent or to an even greater extent and in the meantime, threshold surface potential strength remains basically unchanged. (ii) For 2:1 type electrolyte, the Cd curves always present camel-shaped whether the solvent pore affinity is moderate (w0=6kBT) or even higher (w0=12kBT), and the solvent electric dipole moment is high or low. However, for 1:1 type electrolyte, the Cd curves can take bell-shaped as the solvent electric dipole moment is lower and the solvent pore affinity is moderate (w0=6kBT). (iii) Both the l parameter and b parameter have similar effects in influencing the Cd and .. profiles; what counts most is the value of the solvent electric dipole moment. (iv) Presence of the bivalent co-ion in the coexistence bulk causes two effects. First, the threshold surface potential strength reduces, and the supercapacitor reaches its saturation energy storage at a lower potential strength applied. Second, the pattern of growth of E with the surface potential strength is modified, the E rapidly reaches its saturation value once the threshold surface potential strength is reached; whereas in the absence of the bivalent co-ion, the E saturation value is reached more gently.