Charging Dynamics and Optimization of Nanoporous Supercapacitors

An improved mean-field model used earlier (J. Phys.: Condens. Matter 2011, 23, 022201) to explain the anomalous increase of capacitance in nanoporous supercapacitors is extended to the study of charging dynamics. We find that charging of initially empty (i.e., ionic liquid-phobic) pores proceeds in a front-like way, while charging of filled (i.e., ionophilic) pores is diffusive; in both cases, however, the accumulated charge grows as a square root of time. We also discuss two-step complementary optimization of porous electrodes for supercapacitors. In a first step, the optimal pore width is chosen to maximize the stored energy density; in a second step, the optimal pore depth/length (that is, electrode's thickness) is chosen to satisfy the requirement on charging times. In addition, the use of nanoporous channels in a multilayered configuration is suggested to decrease the volume and to increase the capacitance, stored energy, and power density of a supercapacitor.