A coupled plasma-assisted growth and electrochemical modelling framework for predicting the supercapacitor performance of vertically oriented graphene nanosheets

A coupled plasma-assisted growth and electrochemical modelling framework is developed to establish a quantitative relationship between plasma-enhanced chemical vapor deposition (PECVD) operating conditions, vertically oriented graphene nanosheet (VGNS) morphology, and supercapacitor performance. Plasma characteristics obtained from a two-dimensional axisymmetric COMSOL model are coupled with a reduced-order growth model to determine the evolution of nanosheet height, thickness, and electrochemically accessible surface area under different chamber pressures and RF powers. Plasma-induced defect generation and electrochemically active-site formation are further incorporated into the electrochemical model to evaluate the individual contributions of electric double-layer capacitance (EDLC) and pseudocapacitance. The results show that decreasing the chamber pressure and increasing the RF power promote the growth of taller VGNS with a larger electrochemically accessible surface area while simultaneously increasing the density of electrochemically active sites. Consequently, the projected capacitance increases under more energetic plasma conditions, with EDLC remaining the dominant charge-storage mechanism and pseudocapacitance providing an additional contribution through plasma-induced surface activation. The model predicts a maximum projected capacitance of 196 µF cm⁻², which is in good agreement with reported experimental values for plasma-grown VGNS electrodes. The proposed framework provides a physically consistent basis for understanding the coupled effects of plasma processing, graphene growth, and electrochemical behaviour, and offers a practical computational tool for optimizing PECVD conditions for VGNS-based supercapacitor electrodes.