Theoretical approach to ion penetration into pores with pore fractal characteristics during double-layer charging/discharging on a porous carbon electrode

The effects of pore fractal characteristics on the kinetics of double-layer charging/discharging on a porous carbon electrode were investigated by using theoretical calculations of potentiostatic current transients (PCTs) and cyclic voltammograms (CVs). Prior to theoretical calculation, it was experimentally evidenced that pore fractality is clearly possessed by the porous carbon electrode. From the analyses of the PCTs and the CVs theoretically calculated at various values of pore fractal dimension d(F,pore), inner cutoff length r(min), and outer cutoff length r(max) of the pore fractality, it was found that as d(F,pore) increased, the absolute values of the derivatives of the logarithmic PCTs decreased to 0.5, and the current decayed more slowly with time. The rate capability gamma decreases with increasing d(F,pore) over the whole scan-rate range, which leads to the lower power density. As rmin increased, the current decayed more rapidly in the later stage of the PCT, which is mainly limited by the smaller pores. On the other hand, as rmax increased, the current decayed more rapidly in the earlier stage of the PCT, which is mainly determined by the larger pores. Moreover, the larger values of r(min) and r(max) enhance the rate capability gamma as well, but they reduce the double-layer capacitance. The beneficial contribution of the larger pores to the power density competes with the detrimental contribution of those pores to the energy density.