Effect of simple cubic, face-centered cubic, and body-centered cubic-electrodes on the electric double layer capacitance of supercapacitors

Abstract

The continuum theory has been used to analyze the polarization, ion crowding, and electrostatic forces of the electric double layer in the electrode materials having simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) morphologies. The study manifests the effect of thickness of electrodes, electrode's particle size, and porosity on electric double-layer specific capacitance (EDLC). Electrochemical interference and the specific capacitance depend on the packing factor. The larger particle size decreases the specific capacitance, but porosity increases due to more surface area. Due to symmetry, SC, BCC, and FCC morphologies have 1, 3, and 5 spheres in a unit cell. The number of unit cells is varied from 1 to 100 in model 1 to analyze the effect of electrode thickness. Model 2 has three unit cells to understand the effect of porosity, and only pore lengths are varied. The critical thickness of the electrodes is the integer multiples of 1.71 µm in all the morphologies. The Stern layer-specific capacitance is 167.6 µF cm-2 in all cases. The EDLC in BCC is around 5.6-7.6 µF cm-2 in the steady state that is intermediate between SC and FCC morphologies. The more dense packing of carbon particles in a unit cell increases the energy storage capabilities of electrodes. The average electrode permittivity slightly decreases due to the combined effect of the high electric field, status of polarization, and electrode particle size. The least optical transmission of electrodes is 98.35%.

Effect of Mixed Morphology (Simple Cubic, Face-Centered Cubic, and Body-Centered Cubic)-Based Electrodes on the Electric Double Layer Capacitance of Supercapacitors

“…Energy potentials show a band-like structure that increases with the number of electrode particles interfaced with the electrolyte, like 1 for SC, 2 for BCC, and 3 for FCC. 23,24 This is similar to the fringes or pattern formation in optical interference theory after a repeated increase in the number of photons is visualized. The maximum positive interfacial potential behaves like a wavelet for energy storage and information processing.…”

“…The field-dependent permittivity decreases due to the higher electric field and polarization, which restricts the movement of electrolyte ions. 23,24 The increasing order of the average electrolyte permittivity is 61 in FCC mixed morphologies 3,4 < 62.4 in BCC mixed morphologies 1,2 < 64.37 in SC mixed morphologies 5,6 as shown in Figure 6b,d,f. The steady electrolyte permittivity is around 60, 62, and 64.3 in FCC, BCC, and SC morphologies.…”

“…Figure 3a,c,e,g shows maximum interfacial potential, and Figure 3b,d,f represents the corresponding minimum of diffuse layer potential varying with the electrode thickness in the range 50 nm to around 0.04 mm in mixed morphologies compared with SC, BCC and FCC, respectively. 23,24 EDLC is based on charge separation at the electrode−electrolyte interface. 59 Materials with extensive convex surfaces will lead to maximized capacitance compared to concave surfaces.…”

“…3D contour plots representing mean electric potential have already been reported. 23,24 The Stern layer specific capacitance is determined to be 167.6 μF cm −2 in each morphology from eq 8. The permittivity is in the reverse order of magnitude of the maximum interfacial electric field, as shown in Figure 6b,d,f.…”

“…31,32 The results of SC models have been compared with ordered FCC and BCC morphology-based electrodes. 24 The present article aims to further the study to analyze the effect of disordered electrodes in a supercapacitor. It is done to understand the basic underlying phenomenon associated with the formation of EDL under different conditions in supercapacitors utilizing equilibrium conditions.…”