Interpretable Machine Learning on a Small, High-Quality Experimental Dataset Reveals Structure–Property Trade-Offs in Carbon Anodes for Sodium-Ion Batteries

Abstract

Carbon-based anodes are promising candidates for sodium-ion batteries due to their structural tunability and cost-effective precursors; however, their electrochemical performance is governed by complex and often non-linear interactions among pore structure, defect chemistry, and structural ordering. In this work, a series of carbon materials derived from pitch, phenolic resin, and biomass precursors were synthesized under controlled carbonization and activation conditions to generate a diverse microstructural space. Comprehensive physicochemical characterization including specific surface area (SSA), pore size distribution, defect degree (ID/IG), nitrogen content, interlayer spacing (d₀₀₂), and tap density was performed to establish correlations with electrochemical behavior. Electrochemical evaluation in sodium half-cells reveals a clear trade-off between reversible capacity, rate capability, and initial Coulombic efficiency (ICE). Materials with higher SSA exhibit enhanced capacity and rate performance due to improved electrolyte accessibility and ion transport, but at the expense of reduced ICE, associated with increased surface reactivity and solid–electrolyte interphase formation. Conversely, denser carbons with lower SSA and higher tap density show improved ICE and cycling stability but limited capacity. To elucidate these structure–property relationships, interpretable machine learning was employed as a complementary analytical framework. The analysis identifies SSA as the dominant descriptor, followed by ICE and interlayer spacing (d₀₀₂), revealing that electrochemical performance is governed by a non-linear interplay between surface-driven storage mechanisms and structural stability. Partial dependence analysis further demonstrates a saturation behavior of capacity at high SSA, while Pareto analysis confirms a fundamentally constrained trade-off between capacity and efficiency. These findings provide experimentally grounded and quantitatively supported design insights, highlighting that optimal performance arises not from maximizing a single parameter, but from balancing surface development, electrochemical reactivity, and structural compactness within a constrained design space.