Machine learning-assisted design of cathode materials for lithium–sulfur batteries derived from a metal–organic framework

Abstract

Designing cathode materials is crucial for developing advanced Li–S batteries, but conventional trial-and-error methods are time- and resource-intensive. This study employs machine learning (ML) with feature analysis, data augmentation, and backward prediction using particle swarm optimization (PSO) for rapid discovery and inverse design of cathode materials. The predictive model with XGBoost achieved high accuracy with a determination coefficient (R² = 0.8345) and a mean absolute error (MAE = 4.48%) in estimating capacity retention. The PSO-based backward prediction identified titanium (Ti) and 2-methylimidazole (2-MeIM) as optimal MOF precursors. A Ti/2-MeIM MOF is synthesized in the form of Ti/Zn-ZIF via post synthetic exchange, and subsequent carbonization yields Ti-derivative embedded nitrogen-doped carbon (NC–Ti) as a sulfur host material (S@NC–Ti). S@NC–Ti demonstrated average capacity retentions of 62.3%, 72.1%, and 65.3% at 0.1 C, 0.5 C, and 1.0 C, respectively, aligning with ML predictions. Furthermore, forward prediction successfully anticipated a capacity retention of 75.16% for the Ti/Zn bimetallic ZIF, a carbon precursor, at 1.5 C with a 65 wt% sulfur–carbon ratio, matching the experimental result of 84.13% within a 12% error margin. This study highlights the potential of ML-driven approaches in accelerating cathode material development for Li–S batteries.

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New concepts

This work presents an empirical data-driven inverse design strategy via machine learning (ML), in which targeted capacity retention of lithium–sulfur (Li–S) batteries guides the composition of metal–organic frameworks (MOFs) used as carbon-based precursors for cathodes. While prior ML-assisted material design approaches rely on synthetic data that may not fully reflect experimental complexity, our model captures MOF composition-capacity retention correlations aligning with physicochemical trends observed in empirical datasets. Experimental validation of MOF compositions identified through backward prediction closes the design loop, demonstrating the rationality of performance-oriented cathode optimization for Li–S batteries. Data augmentation mitigates experimental data scarcity by adding Gaussian noise to the feature space—a technique that expands the dataset with slight deviations while preserving the original data characteristics, thereby improving the model's generalization. Among predicted candidates, a MOF with Ti and 2-methylimidazole combination—the most frequently occurring metal–ligand pair—was synthesized and carbonized into a Ti-derivative–containing N-doped carbon. When applied to sulfur cathodes, experimental capacity retention fell within 12% of the predicted value, confirming the predictive reliability of our performance-tailored method in practice. This work offers a generalizable framework for data-driven compositional engineering in complex electrochemical systems, leveraging real-world performance constraints.

1. Introduction

Despite extensive efforts in energy storage system (ESS) development, the growing demand for advanced ESS necessitates breakthrough innovation.^1,2 With machine learning (ML) emerging as a new paradigm in materials chemistry, research approaches have shifted from traditional trial-and-error methods to ML-driven strategies for faster progress in ESS research.^3–6 ML, with its superior prediction accuracy and computational efficiency, shows great promise in various aspects of ESS research, including fault detection,⁷ lifetime prediction,⁸ aging analysis,⁹ property classification,¹⁰ and material design for diverse ESS (e.g., Li-ion batteries,^11,12 Na-ion batteries,¹³ supercapacitors,^14,15 and fuel cells^16,17).

ML has been widely utilized in ESS design to improve performance such as energy density and stability by predicting complex processes and rapidly identifying materials.^18–20 For example, Liow et al. used ML with particle swarm optimization (PSO) to design a cathode for Li-ion batteries with a target specific initial capacity (e.g., 150, 175, and 200 mAh g⁻¹), which was subsequently validated experimentally.¹⁸ A crystal graph convolutional neural network based ML model was employed to screen binary alloy anodes for metal-based batteries (e.g., Li, Na, K, Zn, Mg, Ca, and Al) by evaluating formation energy, potential, and specific capacity from a large materials database.¹⁹ Furthermore, Wang et al. used a data-driven ML approach to identify oxygen-rich porous carbon as an active material for aqueous supercapacitors from previously reported works.²⁰

Among various ESS, Li–S batteries are promising candidates for secondary battery systems owing to their high energy density (2600 Wh kg⁻¹), abundant sulfur supply, and cost-effectiveness.^21,22 However, Li–S batteries still face severe challenges such as shuttle effects, sluggish sulfur redox reactions (SRR), and Li anode corrosion caused by complex reaction chemistry. As efforts to overcome these challenges increase, ML has been increasingly used to accelerate material screening, cell component design, and optimization of operating conditions for enhanced Li–S battery systems.^23–25 In particular, ML-driven cathode development has garnered considerable attention, as an improved cathode mitigates the shuttle effects, enables high active material loading, and enhances electrode stability. Notably, achieving high cycling retention by alleviating the shuttle effects is a pivotal goal in cathode material design for Li–S batteries, since shuttle effects cause irreversible capacity loss due to self-discharge, low coulombic efficiency, and the formation of unstable and dendritic lithium–metal anodes, hindering long-term battery performance and commercialization. To address this, ML has been employed to reduce shuttle effects, assisting the cathode material discovery. For example, Zhang et al. utilized transfer learning based on the 2DMatPedia database to rapidly identify 14 promising AB₂-type sulfur host structures to reduce shuttle effects.²⁶ Lujie et al. combined ML with density functional theory (DFT) in a three-step protocol to design anchoring materials (AMs) for lithium sulfide (Li₂S) adsorption: evaluating Li₂S anchoring properties, selecting 44 types of two-dimensional AMs, and analyzing their geometrical characteristics for Li₂S anchoring effects.²⁷

Although ML accelerates cathode material discovery and design, experimental validation is essential to ensure its practical applicability. Zhiyuan et al. integrated DFT calculations with an ML framework consisting of filter, wrapper, and embedded modules to identify key factors influencing the catalytic activity of high-efficiency DAC-based multi-site catalysts, achieving an initial specific energy of 436 Wh kg⁻¹ in a Fe–Co DASC cathode pouch cell.²⁸ Similarly, Han et al. used binary descriptors based on band match and lattice mismatch indices to design NiSe₂ as a catalyst for sulfur host materials using ML, confirming that Li–S batteries with NiSe₂ maintain high gravimetric energy even under harsh conditions (e.g., high sulfur loading or at low temperature of −20 °C).²⁹

In this work, we employed ML to expedite cathode material design for Li–S batteries, where metal–organic framework (MOF)-derived porous or hollow carbon structures were chosen as cathode materials for their superior electrical conductivity, structural stability, and design flexibility.^30,31 As cathode precursors, MOFs provide tuneable pore structures and they enhance electrochemical activity through the carbonization of metal and ligand components.^32,33 First, we constructed datasets incorporating MOF composition (metal and ligand type), synthesis and carbonization conditions for MOF-derived carbon (i.e., synthesis and carbonization time and temperature), weight ratio of sulfur to carbon, and C-rate as input features, with cycling retention after 100 cycles as the output feature. Second, ML identified the relationship between input and output features using SHapley Additive exPlanations (SHAP) explainer to select key input features crucial for output features. The limited data size was expanded to 1040 by adding feature-specific Gaussian noise to each datapoint, while maintaining patterns and dataset properties. An eXtreme gradient boosting (XGBoost)-based predictive model, trained on 80% of augmented dataset, achieved superior predictive accuracy (coefficient of determination >0.92), and demonstrated strong generalization (coefficient of determination difference between training and testing datasets = 0.0042). Subsequently, ML performed backward prediction to inversely design a MOF precursor for cathode materials, integrating titanium (Ti) and 2-methylimidazole (2-MeIM). To validate the prediction, a MOF comprising Ti and 2-MeIM was synthesized via post-synthetic exchange (PSE) by converting zinc (Zn) in ZIF-8 to Ti (Ti/Zn-ZIF), followed by carbonization to form hollow nitrogen-doped carbon with Ti-derivatives (NC–Ti) as a sulfur host (S@NC–Ti). S@NC–Ti demonstrated lower polarization, higher electrical conductivity, and enhanced SRR kinetics than S@NC and S@C owing to evenly distributed Ti-derivatives within the carbon matrix. For cycling performance, S@NC–Ti exhibited average capacity retentions of 62.3%, 72.1%, and 65.3% after 100 cycles at 0.1 C, 0.5 C, and 1.0 C, respectively. Furthermore, S@NC–Ti exhibited a capacity retention of 84.13% under the condition of a 65 wt% sulfur–carbon ratio at 1.5 C. This result falls within a 12% error margin of the forward prediction result, which was derived by combining the backward-predicted conditions (ligand, S-wt, and C-rate) with the experimentally applied bimetallic ZIF (Ti and Zn for metal). This study provides a basis for rational cathode material design for Li–S batteries.

2. Results and discussion

2.1. Framework for machine learning-assisted design of a MOF-derived carbon host

In this study, ML was used to elucidate the relationship between MOF—a precursor of porous or hollow carbon for sulfur host materials—and capacity retention of Li–S batteries, followed by inverse design of the MOF through backward prediction. This strategy involves five steps: (1) constructing datasets from peer-reviewed studies, focusing on the MOF-derived carbon cathode of Li–S batteries, and reporting long-term cycle retention; (2) engineering features via feature ranking (SHAP importance) with expertise (domain knowledge) and data augmentation; (3) applying the augmented dataset to decision tree-based models and selecting the most accurate and generalizable predictor; (4) performing backward prediction through particle swarm optimization (PSO) to inversely design MOF precursors for carbon-based cathodes; and (5) experimentally verifying the electrochemical performance of the designed MOF-derived carbon cathode (Fig. 1).

Fig. 1 Scheme of machine-learning (ML)-assisted inverse design process of the metal–organic framework (MOF) for the cathode of the Li–S battery and its experimental validation.

2.2. Construction of dataset and feature engineering

The ML dataset from previous studies on MOF-derived carbon cathodes for Li–S batteries contained 65 experimental data points and 9 variables. These included variables of MOF components (types of metal and ligand, denoted as metal and ligand), synthesis and carbonization conditions of time and temperature (S-temp, S-time, C-temp, and C-time), weight ratio of sulfur to carbon (S-wt), charge/discharge rate (C-rate), and capacity retention after 100 cycles (tetention), reflecting cathode properties, electrochemical conditions, and performance of Li–S batteries. Metal, ligand, S-time, S-temp, C-time, C-temp, S-wt, and C-rate were used as input features, while retention served as the output. Table S1 (ESI†) provides a detailed rationale for selecting these features.

While each input feature contributes to retention prediction, high feature dimensionality can cause overfitting, computational inefficiency, and decreased predictive accuracy.^34,35 To address this issue, we employed SHAP values with domain knowledge to guide data-driven feature importance evaluation. Also, Categorical Boosting (CatBoost), which effectively processes both nominal (e.g., metal and ligand) and numerical features (e.g., S-wt, C-rate, S-Time, S-Temp, C-Time, and C-Temp), was used to derive SHAP values for our dataset. Importantly, SHAP global importance scores were averaged across ten independently shuffled datasets. As shown in Fig. S1 (ESI†), the global SHAP importance values categorized the eight input features into a high-SHAP group—comprising C-rate (4.78 ± 0.30), metal (4.62 ± 0.48), and S-wt (2.13 ± 0.16)—and a mid-SHAP group, which included C-Temp (1.32 ± 0.14), ligand (1.12 ± 0.20), S-Time (0.95 ± 0.18), S-Temp (0.77 ± 0.14), and C-Time (0.64 ± 0.12). The SHAP decision plot (Fig. S2, ESI†) visually implies that all features contribute in a multivariate and interdependent manner, which may reflect the complex interactions governing Li–S battery chemistry. However, such multivariate contribution does not necessarily imply equal importance in predictive modelling; hence, we applied a dual-filter feature selection framework to refine the input space and alleviate redundancy. In this framework, each input feature was evaluated using two complementary criteria: (i) statistical importance derived from SHAP values and (ii) mechanistic relevance determined by domain knowledge. SHAP offered a data-driven evaluation of feature importance related to capacity retention, while domain knowledge complemented this by ensuring that selected features were mechanistically relevant to the design objective and Li–S battery systems. Accordingly, features with high SHAP importance were preliminarily retained and confirmed to be chemically consistent with known electrochemical behaviors. Specifically, the C-rate regulates electrochemical reaction rates during battery operation, affecting capacity retention.³⁶ During carbonization, metal in MOFs transforms into various metal-derivatives, enhancing cycling performance of Li–S batteries by absorbing LiPS and facilitating SRR.³⁷ Optimizing S-wt also influences both discharge capacity and capacity retention.^38,39 Among the mid-SHAP group features, only ligand was retained due to its pivotal role in both the predictive modelling objective and its mechanistic relevance to capacity retention in Li–S batteries.⁴⁰ Ligand is not only one of the key components in MOF formation but also serves as a precursor for the cathode material after carbonization. In addition, the identity of ligands determines the pore structure, specific surface area, heteroatom doping, and electrical conductivity of the MOF-derived carbon, all of which are closely related to LiPS confinement and redox kinetics—key factors that contribute to the capacity retention of Li–S batteries.^41,42

To further support SHAP-driven and domain-informed feature selections, we conducted visual analysis using scatter and box plots. Selected features exhibited clear associations with retention, such as an optimal region for S-wt or distinct distributional differences across different categorial variables (e.g., metal and ligand types). On the other hand, time- and temperature-related features exhibited either localized patterns confined to sparsely sampled regions or insignificant trends, both of which limit their reliability and generalizability across the dataset (see Fig. S3 for detailed information, ESI†). Additionally, time- and temperature-related features showed a low correlation with retention and exhibited correlation-based redundancy with metal and ligand (see Fig. S4 for detailed information, ESI†). Such a low correlation and correlational redundancy may introduce model instability or reduce interpretive clarity, thereby supporting the rationale for exclusion of time- and temperature-related features. Accordingly, four features (i.e., C-rate, metal, S-wt, and ligand) were retained as important features based on both SHAP importance and domain relevance. Among retained features, the C-rate was further examined due to its highest SHAP value and role as an operating condition, unlike other features referring to material properties. As shown in SHAP decision plots (Fig. S5, ESI†), the SHAP values for a given C-rate vary substantially (ranging approximately from −6 to +6) depending on the categorical types or values of other features, indicating that the model does not learn a nonlinear dependence on the C-rate. Rather, the C-rate acts as a conditional variable whose influence is modulated through interactions with material descriptors. Therefore, this dual-filter feature selection framework—combining SHAP-based importance grouping with domain-guided interpretation—yielded a reduced yet robust feature set (C-rate, metal, S-wt, and ligand) that balances statistical significance with functional relevance. Refined input space not only improved model interpretability but also laid the groundwork for the subsequent predictive modelling and validation, the results of which are detailed in Section 2.4.

2.3. Data augmentation

Reducing dataset dimensionality with key features for retention enhanced ML interpretability, but the small sample size (65 data points) hindered robust predictive model construction, necessitating data augmentation. In order to prevent data leakage, the original dataset was first split into training (80%) and testing (20%) subsets. Data augmentation was then applied exclusively to the training set, while the testing set remained untouched and used solely for performance evaluation. Before augmentation, metal and ligand features were one-hot encoded by converting nominal data into binary vectors (e.g., Co → [1, 0, 0, …], Ti → [0, 1, 0, …], and Zn → [0, 0, 1, …]). The augmented dataset requires not only to preserve the informational characteristics of the original dataset but also to introduce variability to maintain learning objectives and enhance generalization capability.⁴³ Nonetheless, this variability must be carefully calibrated; excessive noise reduces model performance, while insufficient noise offers limited learning benefit. To evaluate the effect of noise scale in data augmentation, we systematically varied the noise ratio—defined as the standard deviation of added noise to that of each continuous input feature variables, across a range from 0.01 to 1.00, and assessed model performance using mean absolute error (MAE) and coefficient of determination (R²) metrics with a surrogate gradient boosting model. As shown in Table S2 (ESI†), optimal performance was observed within the noise ratio range of 0.03 to 0.05, which improved both MAE and R², indicating that moderate augmentation can enhance model robustness by meaningfully expanding the training space while still adhering to the original data distribution. When the noise ratio was too small (e.g., 0.01), the augmented samples were nearly indistinguishable from the original data, offering minimal diversity and limited benefit to model training. Conversely, at high noise ratios (e.g., ≥0.50), MAE increased substantially while R² dropped below 0.4, indicating a breakdown in model performance. Based on these findings, we adopted a noise ratio of 0.05 for data augmentation with lowest MAE (5.72%) and second-highest R² (0.7526) throughout this study. To validate that the selected augmentation strategy balances statistical consistency with the variability required for generalization, data points distribution within individual features and inter-feature relationships were analyzed. Since metal and ligand—represented as binary vectors to preserve categorical properties—were directly duplicated without introducing variation, they were excluded from the structural and comparative analysis. The original and augmented datasets exhibited high distributional similarity with slight variations, as indicated by low Wasserstein distance values (0.2760, 0.0179, and 0.4002 for S-wt, C-rate, and retention, respectively), similar cumulative probability functions, and probability densities (Fig. S6, ESI†). Beyond individual data point distribution, maintaining feature correlations in the augmented dataset is essential to preserving the learning objectives. We assessed feature correlations using principal component analysis (PCA), representing feature correlations as principal components (PCs) to extract key data patterns. PC1 captures primary variance and reflects feature correlations, while PC2, orthogonal to PC1, reveals inter-feature relationships. Together, PC1 and PC2 provide a comprehensive explanation of feature correlations. The PCs of the augmented data (orange circles) closely align with those of the original data (blue stars) (Fig. 2). Explained variance analysis (EVA) further validates this similarity, PC1 and PC2 values of [0.8131, 0.1822] for the original data and [0.8129, 0.1825] for the augmented data. The minimal EVA difference (<0.0003 difference) confirms that augmentation preserved the variance structure among features.

Fig. 2 Comparison of the principal component distributions between the original (blue stars) and augmented (orange circles) dataset.

2.4. Forward and backward prediction

A predictive model was trained on the augmented dataset using decision-tree-based ML algorithms, including decision tree regressor (DTR), random forest regressor (RFR), gradient boosting regressor (GBR), and eXtreme gradient boosting (XGBoost), which effectively handle nonlinear and complex Li–S battery systems. The hyperparameters of each algorithm were optimized by 10-fold cross-validation with grid search on 80% of the augmented data (training set). The predictive performance of the optimized models was then evaluated on the remaining 20% (testing set) using the R². Fig. 3 shows that XGBoost had the highest R² of 0.8345 and lowest MAE of 4.48%, indicating superior predictive performance and generalization capability. Accordingly, XGBoost was selected as the most suitable algorithm for the inverse design of MOFs. The selected model was then used to compare the performance (R² and MAE) of the selected-feature set against that of the full-feature model, thereby evaluating the effectiveness of the feature selection strategy described in Section 2.2. To ensure a fair comparison of model performance across different feature subsets, it is a common practice in feature selection studies to evaluate models under identical training conditions.⁴⁴ Thus, both models were trained and evaluated under identical conditions (i.e., hyperparameter and initialization), differing only in the number of input features. The selected-feature model achieved a higher R² (0.8345 vs. 0.6212) and a lower MAE (4.48% vs. 8.07%) compared to the full-feature model (Fig. S7, ESI†), which may be attributed to the elimination of redundant or noisy features that could introduce overfitting or reduce generalization. This result confirms that dimensionality reduction through SHAP- and domain-informed selection improves predictive accuracy while enhancing model interpretability.

Fig. 3 Prediction performance of (a) decision tree regressor (DTR), (b) random forest regressor (RFR), (c) gradient boosting regressor (GBR), and (d) eXtreme gradient boosting (XGBoost) algorithm.

Subsequently, we performed backward prediction using the particle swarm optimization (PSO) integrated with an XGBoost-based predictive model to inversely design advanced MOFs for cathode materials. The target output—capacity retention above 68.5% after 100 cycles—was determined based on the average retention value of the dataset, ensuring reliable backward prediction aligned with the state-of-the-art MOF-derived carbon for sulfur cathodes while allowing room for capacity retention enhancement. During PSO, particles explored the solution space to estimate input feature values (i.e., metal, ligand, S-wt, and C-rate), which were then fed into XGBoost to predict the output value (i.e., capacity retention after 100 cycles). Input spaces were constrained within the training data range, and categorical variables were represented via one-hot encoding (see Section 4.2 for details). The expected output was evaluated to ensure that it exceeded 68.5%. PSO then iteratively adjusted inferred input features using feedback from XGBoost to refine solutions. Backward prediction yielded 500 possible MOF designs (Table S3, ESI†), providing a data-driven set of candidates predicted to satisfy the retention target. Compared to retention statistics of the original dataset (mean = 68.50%, variance = 16.85), those of PSO-derived designs exhibited higher predicted retention (mean = 78.66%) with reduced variance (8.11%). These results indicate that the ML-guided optimization strategy effectively identifies input feature combinations with higher predicted retention, providing a rational basis for experimental prioritization. In addition, PSO-derived candidates revealed distinct design patterns. Specifically, consistently high predicted retention across a wide range of C-rates (0.05–2.0 C) suggests that the model favored input combinations capable of sustaining capacity retention under varying cycling conditions. S-wt showed a concentrated distribution within the 60–80 wt% range, reflecting the known optimization window that balances sufficient sulfur loading with mitigation of the polysulfide shuttle effect (Fig. S8 (a)–(d), ESI†). For the categorial variables, the one-hot encoded metal and ligand features demonstrated selective sampling behavior, where specific categories were associated with higher (e.g., Fe, or terephthalic acid) or stable (e.g., Ti, or 2-MeIM) predicted retention than others (Fig. S8(e)–(h), ESI†). This selective behavior indicates the model's ability to distinguish the impact of individual distinct categories on retention performance, despite categorical features being encoded without explicit chemical descriptors. Such patterns may reflect underlying chemical effect—such as conductivity, redox activity, and polysulfide confinement—associated with metal–ligand combinations, sulfur content, and C-rate, even though these properties were not explicitly included in the input features. The indicative alignment between predicted design patterns and domain-relevant features likely emerged through the combined mechanism of: (i) the model's learning of input–output correlations from the training dataset, (ii) model-guided global exploration with PSO as evidenced by a PCA projection, and (iii) repeated convergence toward high-performance input combinations (Fig. S9, ESI†). Taken together, our backward prediction strategy integrated both broad design space exploration and locally optimized solution refinement, enabling data-driven discovery of MOF candidates for carbon-based sulfur cathode.

To gain insights into MOF precursors for carbon-based cathode materials in Li–S batteries from the backward prediction results, metal–ligand combinations were ranked by their frequency of co-occurrence among the 500 PSO-derived candidate input sets, and the most frequently appearing combination was subsequently selected for experimental validation. The highest-ranked MOF combination, titanium (Ti) and 2-methylimidazole (2-MeIM), appeared in 41 predictions (8.2%). Notably, previous studies showed Ti transforms into Ti-derivatives, such as TiO₂ and TiN, during carbonization, enhancing the electrochemical activity of Li–S batteries by facilitating LiPS adsorption and improving charge transport.^45,46 Nitrogen-doped porous or hollow carbon structures derived from 2-MeIM enhance conductivity and stability, improving electrochemical performance.⁴⁷ The highest-ranked metal and ligand combination had average values of 71.31 wt% (±10.75 wt%), 1.10 C (±0.46 C), and 73.53% (±2.74%) for S-wt, C-rate, and retention, respectively. Within these ranges, commonly used experimental values —65 wt% for S-wt and 1.5 C for C-rate—were selected for experimental validation. This approach reduces the resources required to test all 41 S-wt and C-rate combinations while providing practical feasibility guidelines. The impact of those conditions on retention was assessed through additional forward predictions and experiments, detailed in Section 2.6.

2.5. Synthesis and characterization of Ti/Zn-ZIF and NC–Ti

Guided by backward prediction, Ti and 2-MeIM-based MOF was synthesized via post-synthetic exchange (PSE) of ZIF-8, a common method for obtaining titanium-based MOFs (Fig. 4).^48,49 Although a recent study reported a direct one-pot synthesis of the Ti–Zn-MeIM MOF,⁵⁰ PSE was chosen to preserve the parent ZIF structure⁵¹ and ensure compatibility with transition metal incorporation strategies.⁵² First, ZIF-8 was synthesized following a reported method⁵³ and dispersed in DMF with TiCl₄. Cation exchange from Zn to Ti was driven by the Kirkendall-like effect due to differences in diffusion rates between Zn and Ti ions. Additionally, the strong Lewis acidity of TiCl₄ disrupted Zn–N coordination in ZIF-8 and promoted Zn ion leaching, resulting in a hollow-structured Ti/Zn-ZIF.⁵⁴ During carbonization, Zn was removed through evaporation, yielding a hollow-structured nitrogen-doped carbon with uniformly dispersed Ti-derivatives (NC–Ti), which was further applied to Li–S battery cathodes.

Fig. 4 Schematic illustration of synthesis of Ti/Zn-ZIF, NC–Ti, and S@NC–Ti.

Scanning electron microscopy (SEM), and transmission electron microscopy (TEM) images show its rhombic dodecahedron morphology with an average edge length of 150 nm (Fig. S3a, ESI† and Fig. 5(a), (b)). In contrast, Ti/Zn-ZIF shows a hollow-structured rhombic dodecahedron morphology with a shell arising from the cation exchange between Zn in ZIF-8 and Ti from TiCl₄ (Fig. S3b, ESI† and Fig. 5(c), (d)). Powder X-ray diffraction (PXRD) analysis confirms that Ti/Zn-ZIF retains the crystal framework of ZIF-8 (Fig. S4, ESI†) during the hollow structure formation by cation exchange. The Brunauer–Emmett–Teller (BET) method was used to characterize the specific surface area and pore structure (Fig. S5a and b, ESI†). The N₂ isotherm of Ti/Zn-ZIF displays both micropores and mesopores, similar to ZIF-8, except for the hollow structure indicated by a hysteresis loop under high relative pressure (P/P₀ > 0.5). Ti/Zn-ZIF has a specific surface area of 971.99 m² g⁻¹, which is lower than 1575 m² g⁻¹ for ZIF-8, resulting from the partial dissolution of its porous structures during PSE. Simultaneously, the average pore volume slightly increased from 2.14 cm³ g⁻¹ for ZIF-8 to 2.44 cm³ g⁻¹ for Ti/Zn-ZIF due to the hollow structure of Ti/Zn-ZIF. Compositional properties of Ti/Zn-ZIF were analyzed by energy dispersive X-ray spectroscopy (EDS) with TEM and X-ray photoelectron spectroscopy (XPS). EDS mapping confirms uniform distribution of N, Zn, Ti, and Cl in the shell of Ti/Zn-ZIF (Fig. 5(e)). The high-resolution XPS spectrum provides detailed information on the chemical environment of Ti in the Ti/Zn-ZIF shell, revealing two characteristic Ti 2p peaks. Fig. 5(f) shows that Ti exhibits two peaks at 457.9 eV for Ti 2p_3/2 and 463.7 eV for Ti 2p_1/2 lower than that of conventional titanium dioxide (459.5 eV and 465.2 eV for Ti 2p_3/2 and Ti 2p_1/2, respectively).⁵⁵ This shift to lower binding energies suggests increased electron density around Ti, resulting from its coordination with N atoms in 2-MeIM, where N donates a lone pair of electrons to Ti.⁵⁶

Fig. 5 Images of (a) transmission electron microscopy (TEM) and (b) high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) of ZIF-8. Images of (c) TEM and (d) HRTEM of Ti/Zn-ZIF. (e) (i) HAADF-STEM image of Ti/Zn-ZIF and elemental mapping of (ii) N, (iii) Zn, (iv) Ti, and (v) Cl in Ti/Zn-ZIF. (g) High-resolution X-ray photoelectron spectroscopy (XPS) spectra of Ti 2p in Ti/Zn-ZIF.

High-temperature carbonization of Ti/Zn-ZIF produced NC–Ti as a cathode material for Li–S batteries. NC–Ti has a large BET surface area (582.02 m² g⁻¹) and high average pore volume (3.26 cm³ g⁻¹), forming a well-developed meso-micro pore structure (Fig. S5c, ESI†). The PXRD and Raman spectroscopy of NC–Ti reveal the structural characteristics of the carbon shell. The PXRD pattern of NC–Ti shows only (002) and (100)/(101) diffraction peaks, indicating graphitic carbon while the Raman spectra display typical D/G bands confirming amorphous or nanocrystalline carbon (Fig. S6, ESI†). The SEM image in Fig. S7a (ESI†) shows that NC–Ti retains a slightly shrunken rhombic dodecahedron morphology with hollow structure, similar to Ti/Zn-ZIF. The TEM image confirmed the inner hollow structure of NC–Ti (Fig. 6(a)). These structural characteristics offer advantages such as high sulfur loading capacity, adaptability to volume changes during charge/discharge, improved electrolyte penetration, and enhanced Li⁺ ion diffusion.⁵⁷ The HAADF-STEM image reveals that numerous Ti-derivative nanoclusters exist and Ti single atoms (Ti–SAs) as bright spots are randomly distributed throughout the carbon shell without agglomeration (Fig. 6(b) and (c)). EDS mapping confirms uniform N and Ti distribution, traces of Cl, and complete Zn removal during the carbonization (Fig. 6(d)–(g)).

Fig. 6 Images of (a) TEM, and (b) and (c) HAADF-STEM with different magnifications. Elemental mappings of NC–Ti for (d) N, (e) Zn, (f) Ti, and (g) Cl, respectively.

The chemical environments of Ti, N, and O in NC–Ti were further investigated by XPS analysis. The high-resolution Ti 2p spectrum deconvoluted Ti 2p_3/2 and Ti 2p_1/2 peaks into Ti³⁺ and Ti⁴⁺ oxidation states, indicating Ti–N and Ti–O bonding.⁵⁸ The N 1s spectrum deconvolutes into four components: pyridinic N (398.25 eV), metal–N (398.8 eV), pyrrolic N (399.86 eV), and graphitic N (400.71 eV), with the metal–N peak confirming the presence of Ti–N bonding and supporting the existence of Ti–SA. The O 1s spectrum exhibits peaks at 533.31 eV, 531.74 eV, and 530.2 eV, corresponding to adsorbed H₂O (H₂Oads), C=O species, and O²⁻, respectively. The O²⁻ peak indicates fully oxidized Ti species, possibly TiO₂. The absence of detectable TiO₂ nanoclusters in the XRD and Raman analyses likely results from their small size and low crystallinity, which may stem from limited carbonization time. TEM and XPS results suggest the coexistence of TiO₂ nanoparticles and Ti–SA in NC–Ti, where TiO₂ strongly adsorbs LiPS,⁵⁹ while Ti–SA catalyzes conversion of LiPS,⁵⁸ thereby improving capacity retention of the Li–S battery.

2.6. Battery test and experimental validation

After synthesizing NC–Ti, sulfur was incorporated via melt diffusion to fabricate a sulfur cathode for a Li–S battery (S@NC–Ti). For comparison, sulfur was similarly loaded into NC (nitrogen-doped carbon derived from ZIF-8) and C (Super P), yielding S@NC and S@C. Thermogravimetric analysis (TGA) confirmed a sulfur content of approximately 65 wt% for all samples (Fig. S8, ESI†). Fig. S9a–c (ESI†) show the cyclic voltammetry (CV) profiles of S@C, S@NC, and S@NC–Ti for the first three cycles at a scan rate of 0.1 mV s⁻¹, showing two pairs of reduction–oxidation (redox) peaks. Two distinct cathodic peaks at approximately 2.3 V and 2.1 V correspond to the conversion of S₈ to long-chain lithium polysulfides (S₈ → Li₂S_x; 4 < x < 8) and their subsequent reduction to solid lithium sulfide (Li₂S₂/Li₂S). The overlapping anodic peaks at 2.4–2.5 V correspond to the oxidation of Li₂S₂/Li₂S back to S₈.⁶⁰ S@NC–Ti exhibited the sharpest peaks and highest peak currents compared to S@NC and S@C, indicating enhanced sulfur redox kinetics in S@NC–Ti (Fig. 7(a)). The consistent CV profiles across three cycles further confirm the reversibility and electrochemical stability of S@NC–Ti. Galvanostatic discharge–charge profiles also support the superior electrochemical properties of S@NC–Ti (Fig. 7(b)). Compared to S@NC and S@C, S@NC–Ti delivers a higher initial specific capacity of 840 mAh g⁻¹ with significantly reduced polarization, consistent with the CV results. The rate performance further supports the superior electrochemical properties of S@NC–Ti. The rate performances of S@NC–Ti are 862.04 mAh g⁻¹, 663.31 mAh g⁻¹, 500.22 mAh g⁻¹, 345.99 mAh g⁻¹, and 208.89 mAh g⁻¹ at 0.1, 0.2, 0.5, 1.0, and 2.0 C, respectively, showing superior recovery to 656.96 mAh g⁻¹ after the current density was returned to 0.2 C (Fig. 7(c)). Moreover, the S@NC–Ti cathode exhibited higher capacity retention of 65% after 100 cycles at 0.1 C, compared with S@NC (57%) and S@C (47%) (Fig. 7(d)). In addition, S@NC–Ti exhibited initial capacities of 710.25 mAh g⁻¹ and 492.37 mAh g⁻¹ at higher current densities of 0.5 C and 1.0 C, with retention rates of 70% and 65%, respectively, after 100 cycles (Fig. 7(e)). The overall high electrochemical performance of S@NC–Ti is attributed to the synergistic contribution of suppressed shuttle effects at elevated C-rates and enhanced adsorption/catalytic conversion of Ti-derivatives in the cathode; at higher current densities, shortened reaction time limits the diffusion of lithium polysulfide (LiPS) into electrolyte mitigating the shuttle effect, while the uniformly distributed TiO₂ nanoparticles and atomically dispersed Ti–SA embedded in a carbon matrix serve as robust anchoring sites for LiPS and efficient electrocatalysts lowering the energy barrier for sulfur redox reactions.^58,59 Notably, S@NC–Ti meets the capacity retention criteria of the backward prediction at various C-rates. The average cycle retentions from three experiments per C-rate of 0.1 C, 0.5 C, and 1.0 C are 62.3%, 72.1%, and 65.3%, respectively, all of which fall within both the 10% error margin of the target retention threshold (>68.5%) and the predicted mean-variance range from backward prediction results. These findings confirm the reliability of our predictive model in identifying optimal MOF composition that contributes to cycling retention trends of MOF-derived porous carbon-based sulfur cathodes.

Fig. 7 (a) The merged plot of the cyclic voltammetry (CV) profile at a scan rate of 0.1 mV s⁻¹ for S@C, S@NC, and S@NC–Ti. (b) The galvanostatic discharge–charge profiles of S@NC–Ti, S@NC, and S@C at 0.1 C. (c) Rate performance from 0.1 to 2 C of S@NC–Ti, S@NC, and S@C. The cycling performances of (d) S@NC–Ti, S@NC, and S@C at 0.1 C and (e) S@NC–Ti at 0.5 C and 1 C. (f) Experimental validation of capacity retention at predicted retention values under 65 wt% of S-wt and 1.5 C of C-rate.

The metal–ligand combination suggested by the model through backward prediction was partially adjusted based on domain knowledge and experimentally implemented as a Ti/Zn–ZIF structure, which still retained the Ti–2-MeIM framework. The NC–Ti electrode fabricated through carbonization exhibited good agreement with the predicted retention target, with a deviation of less than approximately 10%. The superior electrochemical performance of NC–Ti can be attributed to the contributions of TiO₂, Ti–SA, and nitrogen-doped porous carbon structures formed during the carbonization process, which provides LiPS adsorption site, facilitates LiPS conversion reaction, and enhances conductivity, respectively. The quantitative agreement between the predicted and experimental retention values suggests that our model may have indirectly captured the underlying physicochemical mechanisms influencing performance through the relationship between output (i.e., retention) and composition-based input variables, such as the types of metals and ligands. Although the domain-guided synthesis enabled implementation of the Ti–2-MeIM framework, it was necessary to verify whether this composition resided within the model's learned design space—ensuring that it represented not an exception, but a generalizable case supported by the model. Accordingly, we conducted forward predictions and experimental validation, maintaining Ti and Zn as MOF precursor metals, and 2-MeIM as a ligand. Values of S-wt and C-rate were selected based on the average and standard deviation derived from the backward prediction results: 65 wt% for S-wt and 1.5 C for C-rate. The forward prediction result met the output criteria for backward predictions (Table 2), and experimentally verified. As shown in Fig. 7(f), S@NC–Ti exhibited a capacity retention of 84.13% after 100 cycles at 1.5C with 65 wt% sulfur loading, starting from an initial capacity of 509.85 mAh g⁻¹ and retaining 428.95 mAh g⁻¹. This result not only satisfied the backward prediction criteria but also matched the forward prediction result within a 12% error margin, confirming the robustness of our ML model in both forward and backward predictions. The agreement between the predicted and experimental retention values can be attributed to the model's ability to generalize to unseen combinations. Notably, the implemented Ti/Zn-ZIF was not included in the original dataset, yet the model generated consistent predictions by leveraging patterns learned from a diverse set of metal and ligand combinations in the augmented training set. Building on this, we conducted an additional experimental validation to enhance the clarity and credibility of our predictive model; metal–ligand combination of Ti and 2,5-dihydroxyterephthalic acid (H₄-dobdc) was selected, which ranked sixth in predictive frequency (Table 1). The Ti–H₄-dobdc combination was not included in our original dataset and, to the best of our knowledge, its application as a cathode material for Li–S batteries has not been reported. Thus, we synthesized a carbonized Ti–H₄-dobdc MOF and applied it as a sulfur cathode for a Li–S battery. Electrochemical testing confirmed a capacity retention of 77.84% after 100 cycles, successfully meeting the performance target of the backward prediction (Fig. S17, ESI†). To further assess the model's predictive capability, we re-entered the Ti–H₄-dobdc pair into the forward prediction model. The sulfur content (S-wt) and C-rate were set to 65 wt% and 1.5 C, respectively—values representative of the statistical distribution of PSO-derived results, falling within one standard deviation of their respective means. The model predicted a capacity retention of 77.74%, while the experimentally measured retention was 77.84% with a prediction error of only 0.12%, demonstrating the practical validity of the model-generated candidates. Our closed-loop validation process—comprising inverse design, candidate selection, experimental evaluation, and forward prediction across multiple validation points—reinforces the predictive robustness and generalizability of the model within a chemically plausible design space.

Table 1 Predictive frequency ranking of metal–ligand combinations from 500 backward prediction results

Ranking	Metal	Ligand	Count
1	Ti	2-Methylimidazole	41 (8.2%)
2	Fe	Terephthalic acid	39 (7.8%)
3	Fe	2-Methylimidazole	38 (7.6%)
4	Fe	2,5-Dihydroxyterephthalic acid	36 (7.2%)
5	Fe	2-Aminoterephthalic acid	35 (7.0%)
6	Ti	2,5-Dihydroxyterephthalic acid	34 (6.8%)
7	Fe	Trimesic acid	33 (6.6%)
8	Co	2,5-Dihydroxyterephthalic acid	31 (6.2%)
9	Ti	Terephthalic acid	28 (5.6%)
10	Co	Terephthalic acid	22 (4.4%)

---

Table 2 Comparison of the capacity retention after 100 cycles between ML forward prediction (pred. retention) and experimental validation (Exp. retention)

Metal	Ligand	S-wt^a	C-rate	Pred. retention^b (12% error margin)	Exp. retention^c
a Sulfur loading amount in host material expressed as weight percentage. b Prediction capacity retention after 100 cycles using machine learning with input features obtained from real experimental conditions (metal) and those predicted through backward prediction (ligand, S-wt and C-rate). c Measurement of capacity retention after 100 cycles.
Ti/Zn	2-Methylimidazole	65 wt%	1.5 C	75.16% (66.14–84.18%)	84.13%
Ti	2,5-Dihydroxyterephthalic acid	65 wt%	1.5 C	77.74% (68.41–87.07%)	77.84%

---

Finally, we demonstrated that augmenting the dataset enhances the reliable inverse design of MOF for carbon materials used as Li–S battery cathodes. Built solely on experimental data without predefined physiochemical guidance, the augmented dataset retained the original structural information while introducing slight variations for generalization. The ML algorithm trained on the augmented dataset exhibited high predictive accuracy and successfully identified MOF precursors that met the backward prediction retention criteria. Nevertheless, further advancements could be suggested to our ML prediction for designing practical and high-performance cathodes for Li–S batteries. For example, a dual-output ML model predicting both retention and initial capacity would support the design of high-performance cathode materials for Li–S batteries. Adding input features related to the N/P ratio and electrolyte composition enables ML to capture complex electrochemical interactions during cycling, thereby enhancing capacity retention prediction. Furthermore, incorporating physiochemical guides such as density functional theory or molecular dynamics into the ML pipeline or experimental validation process could provide mechanistic insights into electrochemical reactions during battery operation and improve the overall cathode design framework.

3. Conclusions

This study employed an inverse design approach using ML backward prediction to develop MOF-derived cathode precursors for Li–S batteries, followed by experimental validation. Key performance-impacting features were selected through feature analysis and domain knowledge, and data augmentation was applied to alleviate accuracy loss from data insufficiency. The augmented data preserved the original dataset characteristics, and the XGBoost-based predictive model trained on the augmented dataset achieved high predictive accuracy with a determinant coefficient of 0.8435 and a mean absolute error of 4.48%. Using PSO-driven backward prediction, MOF components that achieved >68.5% capacity retention after 100 cycles were identified. For experimental validation, Ti/Zn-ZIF was synthesized via PSE and carbonized to obtain Ti/Zn-ZIF-derived N-doped hollow carbon (NC–Ti) with uniformly dispersed TiO₂ nanoparticles and Ti–SA. As a sulfur host for the Li–S battery cathode, S@NC–Ti promoted LiPS adsorption and facilitated conversion reactions, achieving an initial capacity of 862.04 mAh g⁻¹ and a retention rate of 62.3% after 100 cycles at 0.1 C. Furthermore, S@NC–Ti delivered capacity retentions of 72.1% and 65.3% after 100 cycles at 0.5 C and 1.0 C, validating rationality of our ML model. Moreover, the forward-predicted capacity retention of S@NC–Ti with a 65 wt% sulfur-carbon weight ratio at 1.5 C matched the experimental capacity retention of 84.13%, falling within a 12% error margin. This study underscores the potential of ML in designing cathode materials for advanced Li–S batteries and highlights the multidisciplinary research between computer science and materials chemistry.

4. Experimental

4.1. Materials

2-Methylimidazole (2-MeIM; Sigma Aldrich), zinc nitrate hexahydrate (Zn(NO₃)₂·6H₂O; Sigma Aldrich), titanium(IV) chloride tetrahydrofuran complex (TiCl₄·2THF; Sigma Aldrich), anhydrous methyl alcohol (MeOH; Sigma Aldrich), N,N-dimethylformamide (DMF; Aldrich, 99.8%), nitric acid (SAMCHUN, 68–70%), sulfur (Sigma Aldrich), lithium bis(trifluoromethyl sulfonyl)imide (LiTFSI; Sigma Aldrich), lithium nitrate (LiNO₃; Sigma Aldrich), 1,3-dioxolane (DOL; Sigma Aldrich), 1,2-dimethoxymethane (DME; Sigma Aldrich), and polyvinylidene fluoride (PVDF; Beyond Battery) were purchased and used without further purification.

4.2. Machine-learning process

The dataset was compiled from published scientific literature in ACS, Elsevier, the Royal Society of Chemistry, Wiley, Springer, Nature Research, MDPI, and the Electrochemical Society. Only studies where MOFs were synthesized, carbonized, and used as sulfur host were included, while those using other substrates or materials were excluded. Manually collected from previous studies, the dataset was organized based on the chemical composition of MOFs (i.e., metal and ligand types, denoted as metal and ligand, respectively), synthesis and carbonization conditions (time and temperature, denoted as S-time, S-temp, C-time, and C-temp), sulfur loading fraction (weight percent of sulfur in host materials denoted as S-wt), and measurement conditions (current rate denoted as C-rate).

Key features were identified using SHapley Additive exPlanations (SHAP) based on a CatBoost algorithm, which can handle both categorical features (e.g., metal and ligand) and numerical features (e.g., S-Time, S-Temp, C-Time, C-Temp, S-wt, C-rate and retention). Since CatBoost employs target-based encoding for categorical features—an approach inherently sensitive to the order of input data, we repeated the entire procedure (i.e., dataset shuffling, model training, and SHAP computation) ten times to mitigate order-dependent bias in feature importance estimation. Global feature importance was then determined by averaging the absolute SHAP values across ten runs, with standard deviation reported to indicate consistency.

Nominal data in metal and ligand were converted into binary vectors via one-hot encoding by eliminating potential order assumptions and preserving their discrete characteristics, improving ML interpretability. Data augmentation was performed by introducing additive Gaussian noise with varying standard deviations set to 5% of the standard deviation of the original data: 0.389% for S-wt, 0.0376C for C-rate, and 0.843% for retention. The intrinsic nominal properties of the one-hot encoded features were preserved by duplicating metal and ligand data without modification. The reliability of the augmented data was assessed using metrics such as Wasserstein distance (WD), cumulative probability function (CPF), and probability density plot for datapoint distribution, and principal component analysis (PCA) for inter-feature correlations.

XGBoost was selected for forward prediction. The original dataset was first split into 80% training and 20% test sets before augmentation was applied. Noise was then added only to the training set to generate the augmented training dataset, while the test set was kept in its original form. This approach ensured that the test set contained truly unseen data points, allowing for a more accurate assessment of the model's generalization performance. The hyperparameters of XGBoost were optimized using grid search with 10-fold cross-validation, and predictive performance were evaluated on the remaining test set by coefficient of determination (R²) and mean absolute errors (MAE).

Backward prediction was performed using PSO with a swarm size of 30 and a maximum 200 iterations. During PSO, particles explored the input space defined by four variables: metal, ligand, sulfur weight ratio to MOF-derived carbon (S-wt), and C-rate. The exploration input space boundaries were strictly constrained within the ranges observed in the augmented training dataset. For the continuous variables, S-wt ranged from 49.19 to 90.04 wt% and C-rate ranged from 0.05 to 2.01 C. For the categorical variables, metal and ligand were one-hot encoded into binary vectors, with each feature constrained to binary values (0 or 1). The metal and ligand feature sets contained 11 and 5 distinct chemical identities, respectively. The metal set included Co, Ti, Zn, Al, Ni, Fe, and In, as well as heterometallic combinations such as Fe/Zn, Co/Zn, Co/Fe, and Co/Ni. The ligand set included terephthalic acid, 2-aminoterephthalic acid, trimesic acid, 2,5-dihydroxyterephthalic acid, and 2-methylimidazole.

4.3. Synthesis of ZIF-8

Zn (NO₃)₂·6H₂O (1.189 g, 4 mmol) and 2-MeIM (1.313 g, 16 mmol) were dissolved in 40 mL of MeOH, denoted as solution A and solution B, respectively. Solution B was added to solution A, and the mixed solution was stirred at room temperature for 8 hours, followed by aging for 16 hours. The synthesized powder was repeatedly washed with anhydrous methanol by centrifugation and dried under a vacuum overnight at a temperature of 60 °C.

4.4. Synthesis of Ti/Zn-ZIF

To carry out post-synthetic exchange for obtaining Ti/Zn-ZIF, ZIF-8 particles (100 mg) were dispersed in 40 mL of DMF. Then, 11.7 mg of TiCl₄ was added to the ZIF-8 dispersion and stirred for 4 hours at room temperature with the Zn : Ti molar ratio of 10 : 1. All processes were conducted under an argon (Ar)-filled glove box (KK-011AS, Korea Kiyon). Ti/Zn-ZIF was washed several times with MeOH by centrifugation and dried under vacuum overnight at a temperature of 60 °C.

4.5. Synthesis of NC–Ti and NC

NC–Ti was obtained by carbonizing Ti/Zn-ZIF in a tube furnace at 900 °C for 2 hours with a heating rate of 5 °C min⁻¹ under an Ar atmosphere. The carbonized sample was dispersed in 0.2 M nitric acid at 70 °C for 2 hours to eliminate the residual byproducts. The product was collected, washed with deionized water by centrifugation, and dried under vacuum overnight at 60 °C. This product is referred to as NC–Ti. The comparison sample, NC, was prepared by carbonizing ZIF-8 instead of Ti/Zn-ZIF using the same process as for NC–Ti.

4.6. Synthesis of S@NC–Ti, S@NC, and S@C

Sulfur was loaded into NC–Ti and NC via a typical melt-diffusion method. The carbonized samples (NC–Ti and NC) were mixed with S powder in a weight ratio of 3.5 : 6.5 by mortar grinding and placed into a ceramic boat. The mixture was heated to 155 °C for 24 hours, and final products were referred to as S@NC–Ti and S@NC, respectively. For comparison, the same process was applied to Super P (S@C).

4.7. Material characterization

Scanning electron microscopy (FE-SEM; JSM-7100F, JEOL) and transmission electron microscopy (FE-TEM; JEM-2100F, JEOL) equipped with energy dispersive spectroscopy (EDS) were used to characterize the morphology and composition of the as-prepared samples. Crystal structures of the as-prepared samples were measured by powder X-ray diffraction (PXRD; smartLAB, Rigaku) with Cu-K_β radiation (λ = 1.3923 Å) in the range of 2θ = 5–80°. The surface area and pore structure were confirmed via an automatic analyzer (Autosorb-iQ 2ST/MP, Quantachrome). X-ray photoelectron spectroscopy (XPS; K-ALPHA, Thermo Fisher Scientific) with Mg-K_α radiation (hν = 1253.6 eV) apparatus was used to analyze surface chemistry and composition of the samples. The mass loading of sulfur was determined by thermogravimetric analysis (TGA; Q50, TA Instruments) operated at a heating rate of 10 °C min⁻¹ from 30 °C to 800 °C under N₂ flow.

4.8. Cell preparation

The 70 wt% sulfur-loaded samples (S@NC–Ti, S@NC, and S@C), 20 wt% Super P, and 10 wt% PVDF were mixed in 1-methyl-2-pyrrolidinone (NMP) by mortar grinding into a homogeneous black ink. The black ink was coated on aluminum foil via doctor blading and dried at 60 °C for 24 hours in a box furnace to obtain the sulfur electrode. The coated Al foil was punched into discs with a diameter of 1.2 cm. Coin cells (CR 2032) were assembled in an Ar filled glove box with the punched sulfur electrode as the cathode, lithium foil as the anode (0.1 t, Wellcos), Cellgard 2400 as a separator, a gasket, two spacer disks (0.8 t, Wellcos), a wave spring, and 1.0 M LiTFSI with 2.0 wt% LiNO₃ in DOL and DME (1 : 1, v/v) as an electrolyte. The areal sulfur mass loading on the electrode was in the range from 1.5 to 2.0 mg cm⁻², and the electrolyte to sulfur ratio was fixed to 20 μL mg⁻¹.

4.9. Electrochemical measurements

All electrochemical measurements of the above batteries were performed by a battery cycler (WBCS3000Le, WonA Tech) in the potential window from 1.7 to 2.8 V. Values of specific capacity were calculated based on the mass of loaded sulfur. All experiments were conducted at room temperature and the operating temperature was controlled by a humid-temperature chamber (LH-TP-100, LK Lab Korea).

Author contributions

S. Oh: conceptualization, methodology, software, validation, investigation, writing – original draft, writing – review and editing. K. Choi: conceptualization, methodology, software, writing – review and editing. J. Park: validation, writing – review and editing. G. Kim: investigation, writing – review and editing. S. Yoon: funding acquisition, investigation, writing – review and editing. D. Kim: conceptualization, writing – review and editing. S. Lee: writing – review and editing. J. Kim: supervision, methodology, funding acquisition, writing – review and editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the ESI.†

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (no. RS-2025-00523354).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5mh00635j

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