Complex Impedance with Transmission Line Model and Complex Capacitance Analysis of Ion Transport and Accumulation in Hierarchical Core-Shell Porous Carbons

The transmission line model (TLM) and complex capacitance analysis were applied to study the electrochemical capacitive performance and ion transport behaviors in 3D hierarchical carbon networks with hollow core and mesoporous shell (HCMS) structure. The shell thickness ( S ) was stepwise increased from S = 0 to 100 nm while the diameters of hollow core and mesopores were kept constant. The electrochemical impedance spectra (EIS) were fitted with a 5-level transmission line model (TLM). TLM demonstrated that major capacitance was contributed from the second to the fourth level, which can be associated to the mesoporous shell region in the HCMS texture. Complex capacitance analysis provides additional information, particularly in the low frequency range. The relaxation time constants determined from the peak frequency of the imaginary part C '' ( ω) increase with S but are larger than the values determined by TLM analysis. Decomposition of complex power into active and reactive components reveals dependence on frequency and shell thickness. These results revealed that the HCMS carbons with thicker shells can provide larger specific capacitance but lower rate capability. The mesoporous shell thickness in the HCMS carbons can be tuned to fulfill separate demands of energy and power for advanced electrochemical capacitors.