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Density-dependent sodium-storage mechanisms in hard carbon materials

Alexis Front, Tapio Ala-Nissila, Miguel A. Caro

TL;DR

This work addresses the unclear sodium-storage mechanisms in hard carbon (HC) anodes due to HC's complex microstructure. It introduces a multiscale framework that combines grand-canonical Monte Carlo simulations with a Δ-learning Gaussian Approximation Potential (GAP) to model Na–C interactions across HC densities from $0.7$ to $1.9$ g cm$^{-3}$. The findings show that storage occurs via three mechanisms—adsorption, intercalation, and pore filling—with their relative importance governed by density; low-density HC favors pore filling and high capacities near zero voltage, while high-density HC yields safer voltages with lower capacity, and intermediate density ($1.3-1.6$ g cm$^{-3}$) offers the best balance (~$400$ mAh g$^{-1}$) with minimal expansion. This density-engineering insight provides a rational design principle to optimize HC-based SIB anodes for improved energy density and cycling stability.

Abstract

Understanding the sodium-storage mechanism in hard carbon (HC) anodes is crucial for advancing sodium-ion battery (SIB) technology. However, the intrinsic complexity of HC microstructures and their interactions with sodium remains poorly understood. We present a multiscale methodology that integrates grand-canonical Monte Carlo (GCMC) simulations with a machine-learning interatomic potential based on the Gaussian approximation potential (GAP) framework to investigate sodium insertion mechanisms in hard carbons with densities ranging from 0.7 to 1.9 g cm$^{-3}$. Structural and thermodynamic analyses reveal that increasing carbon density reduces pore size and accessibility, thereby modulating the relative contributions of adsorption, intercalation, and pore filling to the overall storage capacity. Low-density carbons favor pore-filling, achieving extremely high capacities at near-zero voltages, whereas high-density carbons primarily store sodium through adsorption and intercalation, leading to lower but more stable capacities. Intermediate-density carbons ($1.3-1.6$ g cm$^{-3}$) provide the most balanced performance, combining moderate capacity ($\approx 400$ mAh g$^{-1}$), safe operating voltages, and minimal volume expansion ($<10$\%). These findings establish a direct correlation between carbon density and electrochemical behavior, providing atomic-scale insight into how hard carbon morphology governs sodium-storage. The proposed framework offers a rational design principle for optimizing HC-based SIB anodes toward high energy density and long-term cycling stability.

Density-dependent sodium-storage mechanisms in hard carbon materials

TL;DR

This work addresses the unclear sodium-storage mechanisms in hard carbon (HC) anodes due to HC's complex microstructure. It introduces a multiscale framework that combines grand-canonical Monte Carlo simulations with a Δ-learning Gaussian Approximation Potential (GAP) to model Na–C interactions across HC densities from to g cm. The findings show that storage occurs via three mechanisms—adsorption, intercalation, and pore filling—with their relative importance governed by density; low-density HC favors pore filling and high capacities near zero voltage, while high-density HC yields safer voltages with lower capacity, and intermediate density ( g cm) offers the best balance (~ mAh g) with minimal expansion. This density-engineering insight provides a rational design principle to optimize HC-based SIB anodes for improved energy density and cycling stability.

Abstract

Understanding the sodium-storage mechanism in hard carbon (HC) anodes is crucial for advancing sodium-ion battery (SIB) technology. However, the intrinsic complexity of HC microstructures and their interactions with sodium remains poorly understood. We present a multiscale methodology that integrates grand-canonical Monte Carlo (GCMC) simulations with a machine-learning interatomic potential based on the Gaussian approximation potential (GAP) framework to investigate sodium insertion mechanisms in hard carbons with densities ranging from 0.7 to 1.9 g cm. Structural and thermodynamic analyses reveal that increasing carbon density reduces pore size and accessibility, thereby modulating the relative contributions of adsorption, intercalation, and pore filling to the overall storage capacity. Low-density carbons favor pore-filling, achieving extremely high capacities at near-zero voltages, whereas high-density carbons primarily store sodium through adsorption and intercalation, leading to lower but more stable capacities. Intermediate-density carbons ( g cm) provide the most balanced performance, combining moderate capacity ( mAh g), safe operating voltages, and minimal volume expansion (\%). These findings establish a direct correlation between carbon density and electrochemical behavior, providing atomic-scale insight into how hard carbon morphology governs sodium-storage. The proposed framework offers a rational design principle for optimizing HC-based SIB anodes toward high energy density and long-term cycling stability.

Paper Structure

This paper contains 8 sections, 6 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Machine-learning interatomic potentials
  4. Hard carbon generation
  5. Hybrid Monte Carlo/molecular dynamics atomistic simulations
  6. Results and discussion
  7. Electrochemical properties
  8. Summary and conclusions

Figures (5)

  • Figure 1: Overview of the structures in the database. The initial database contains dimers, defected graphite, nanoporous carbon and C$_{60}$ structures. At each iteration, graphite and nanoporous carbon structures are added to the database to improve the accuracy of the model. Carbon and sodium atoms are in grey and green, respectively.
  • Figure 2: 3D snapshots of the five hard carbon samples of different densities. (a) Ring-size distributions, (b) bond-angle distributions, and (c) pore-size distributions.
  • Figure 3: (a) Sodium concentration and (b) dimensional change as a function of MC steps for the five hard carbon samples at 300 K. Each green line corresponds to a given chemical potential. Note the different vertical scales of the $\rho = 0.7$ g cm$^{-3}$ sample as compared to the other ones.
  • Figure 4: Potential as a function of specific capacity at a given chemical potential: (a) $-1.00$ eV, (b)$-1.24$ eV, (c) $-1.50$ eV. Each line represents a different density. Insets show details of the voltage inflection.
  • Figure 5: Contributions of adsorption, intercalation, and pore filling to sodium storage in hard carbon across a density range of 0.7–1.9 g cm$^{-3}$. (a) Voltage curves showing potential versus specific capacity. (b) Cumulative storage capacity of adsorption, intercalation, and pore filling as a function of specific capacity. Snapshots in (c–e) illustrate adsorption, intercalation, and pore-filling sites, respectively. The lower panel (f) shows all three classes of storage sites together. Simulations were performed at 300 K with a chemical potential of $\mu=-1.24$ eV. All snapshots correspond to configurations at the maximum specific capacity. Color coding: orange = adsorption, blue = intercalation, green = pore-filling, and grey = carbon.