Python-Based Automated Response Surface Methodology: Computational Replication and Validation Framework for Supercapattery Materials Optimization

Response Surface Methodology (RSM) combined with Central Composite Design (CCD) represents a powerful statistical approach for materials optimization in energy storage systems [1,2]. RSM has been extensively applied in materials science to efficiently explore design spaces and identify optimal synthesis conditions, reducing experimental burden while maintaining rigor [2]. This study presents a complete computational framework for replicating, validating, and extending RSM-based optimization of NiCo₂S₄–graphene supercapattery materials through automated Python implementation, demonstrating the feasibility of reproducible computational design methodologies.

We replicated the optimization study [1] using a 20-experiment CCD with a five-level three-factor design. Independent variables were graphene/NCS ratio (0.6–7.4%), hydrothermal time (4.6–11.4 hours), and S/Ni molar ratio (3.3–6.7). Specific capacitance served as the response variable. A quadratic polynomial model was developed using multiple linear regression, with automated analysis including ANOVA calculations, Pareto analysis (α = 0.05), Shapiro–Wilk normality testing, and response surface mapping implemented in Python.

The quadratic model achieved R² = 0.9716 and adjusted R² = 0.9460, explaining 97.16% of variance. The G/NCS ratio emerged as the dominant factor (57.19% contribution, p < 0.0001), with significant synergistic interactions for G/NCS×S/Ni (p = 0.0068) and time×S/Ni (p = 0.0057). Residuals demonstrated normal distribution (Shapiro–Wilk p = 0.8531). The optimal predictions were G/NCS = 6.0% and time = 10.0 h, S/Ni = 6.0, yielding 2263 F/g with 2.32% deviation from the original experimental results.

This automated Python framework validates RSM methodology through independent replication with 97.68% agreement with the original study [1]. The computational approach significantly reduces time investment while maintaining statistical validity, supporting industry adoption of data-driven design methodologies in energy storage materials. The complete Python code is provided as open-source supplementary material, enabling transparency, reproducibility, and broader methodological accessibility for future materials optimization research.

References
[1] Hong, Z.-Y. et al. Response Surface Methodology Optimization in High-Performance Solid-State Supercapattery Cells Using NiCo₂S₄–Graphene Hybrids. Molecules 2022, 27, 6867.
[2] Pandey, V.K. et al. A Response Surface Methodology Optimization Approach to Architect Low-Cost Activated Carbon-Based Ternary Composite for Supercapacitor Application with Enhanced Electrochemical Performance. Synth. Metals 2025, 311, 117844.