Insights on the rate performance of polyaniline supercapacitors by integrated mathematical modeling and machine learning

Abstract

The specific capacitance of supercapacitors (SCs) decreases as the applied current increases during the charge–discharge process. The rate of capacitance reduction is influenced by a combination of factors, including the synthesis approach, structural properties of the electrode material, electrode fabrication protocol, and operational conditions. However, decoupling the impacts of these interconnected parameters and determining the individual contribution of each factor to the rate performance of supercapacitor (SC) materials, such as polyaniline (PANI), remains unclear. In this work, a machine learning (ML) approach is employed as an alternative to experimental approaches to elucidate the impacts of structural, fabrication, and operational features on the rate performance of PANI-based SCs. Mathematical parametrization of the rate performance of PANI using different model selection criteria was performed, with the exponential decay (ED) function showing the highest accuracy. The gradient boosting machine (GBM) model properly predicted the rate performance parameters, achieving an R² value of 0.91 for the decay rate. The SHapley Additive exPlanations (SHAP) interpretation technique revealed that binder- and carbon-free electrodes or electrolytes that typically have a potential window (PW) 1 volt or higher, enhance capacitance at low current densities (CDs). A carbon-free electrode with a higher binder ratio (BR) and lower levels of PANI accelerates the decay rate. Additionally, increasing the start and end CDs is favorable for minimizing the decay rate. Electrolytes with typical PW of 0.5 or 0.7 volts, higher CD operational conditions, a lower active material ratio (AMR), a higher carbon ratio (CR), and electrodes with large specific surface areas (SSA) contribute to achieving high capacitance at elevated CDs. This study demonstrates the robust capabilities of ML in elucidating the underlying complex mechanisms affecting rate performance and provides valuable insights for designing high-rate performance PANI-based SCs. We anticipate our study to be a starting point for investigating the rate behavior of other SC electrode materials using data-driven approaches.