During discharge, the sulfur cathode successively generates a series of sulfur-containing species via the SRR. Figure 1A depicts the optimized molecular structures of S₈ and Li₂S_n (n = 1, 2, 4, 6, 8) clusters, which are in good agreement with the previous reports^[49]. As the sulfur index n increases, Li₂S_n evolves from short-chain motifs into intricate three-dimensional clusters. The long-chain LiPSs (Li₂S₈, Li₂S₆ and Li₂S₄) exhibit elongated S-S bond lengths and diminished bond energies, which facilitate their dissolution in the electrolyte and contribute to the shuttle effect.

To investigate the line-defect graphene as cathode materials for Li-S batteries, we construct three common-used line-defect graphene: double-pentagon-double-heptagon graphene (d5d7G), triple-pentagon-triple-heptagon graphene (t5t7G), and pentagon-octagon-pentagon graphene (585G) as shown in Figure 1B-D. A 6 × 11 × 1 graphene supercell is built to mitigate the interference from excessive defect density^[38]. All the line-defect graphene (d5d7G, t5t7G, and 585G) originate from double-vacancy reconstruction. The d5d7G and t5t7G motifs are reconstructed from these divacancies via a Stone-Wales (STW) transformation, where a single carbon-carbon bond is rotated 90°^[50,51]. The 585G is formed by grain boundary reconstruction through removal of a carbon dimer, a ^1/2a (a = graphene lattice constant) relative lattice shift and subsequent relaxation into a low strain pentagon-octagon-pentagon array. The observed grain boundary structure is consistent with those formed during the graphene epitaxial growth^[51].

To evaluate the stability of the line-defect graphene, the formation energy per unit length E_c(α) is calculated using the following equation^[52]:

(2) $$ E_{\mathrm{c}(\alpha)}=\left(E_{\mathrm{T}(\alpha)}-N_{\alpha} \times E_{\mathrm{gr}}\right) / d_{\alpha} $$

where α indicates the nature of the line-defect: d5d7G, t5t7G, and 585G, and the E_T(α) is the total energy of a graphene plane containing an α-type line-defect in the supercells. N_α, E_gr, and d_α correspond to the number of the C atoms of the defective graphene in the supercells, the energy of one C atom in the pristine graphene, and the cell parameter in the direction of the defect extension in the supercells, respectively. The E_c(α) of d5d7G, t5t7G, and 585G are 0.82 eV Å^-1, 0.79 eV Å^-1, and 0.97 eV Å^-1, respectively. Although the 585G possesses the highest formation energy, it has been successfully synthesized in experiments^[53]. The lower E_c(α) of the other defects suggest that they are also synthetically feasible. It is reported that the t5t7G is a topological structure obtained through laser irradiation exhibiting excellent stability^[38], which is consistent with our theoretical prediction. Experimental studies have demonstrated that well-defined graphene line defects can be successfully synthesized and manipulated through increasingly mature fabrication strategies^[54,55], while line-defect-rich graphene structures have also been integrated into rechargeable battery electrodes and exhibited promising electrochemical performance^[56,57]. Combined with the favorable formation energies by DFT conclusion in this work, these findings support the structural feasibility and practical relevance of line-defect graphene as sulfur-host materials.

To further validate the thermal stability, we perform AIMD simulations of these line-defect graphene at a temperature of 500 K. As shown in Figure 2, after a 2,000 fs time interval, these structures exhibit almost no significant changes when compared to their initial structures. The relatively minor energy fluctuations of the line-defect graphene demonstrate their structural integrity at high temperatures.

As shown in Figure 3A-D, to explore the effect of line defects on the electronic structure of graphene, we calculate the PDOS of the intrinsic/defective graphene. Compared with those of the pristine graphene, the electron states around the Fermi level are enhanced in the line-defect graphene, especially in the 585G. The increased electronic-state occupation near the Fermi level indicates a stronger metallic character and a higher density of electronically accessible states, which can facilitate electron transport and accelerate interfacial charge-transfer processes during the electrochemical reactions, thereby potentially improving the electronic conductivity of the electrode. In the Figure 3E-H, due to its non-polar nature, the pristine graphene exhibits a symmetric distribution of electron gain and loss among carbon atoms. In contrast, the line defects break the intrinsic lattice symmetry, leading to a substantial redistribution of Bader charges along the defect zones. This symmetry-breaking induces an extended local polarization across the defect region rather than isolated polar spots, which may facilitate the adsorption of S₈ and LiPSs^[39].

The adsorption strength of S₈ and LiPSs on cathode materials is crucial in mitigating the shuttle effect. The adsorption structures of S₈ and LiPSs on the intrinsic and the line-defect graphene are relaxed and illustrated in Figure 4. The S₈ molecules adsorb parallel to both pristine and line-defect graphene surfaces. Similarly, the short-chain LiPSs (Li₂S, Li₂S₂) adsorb with the Li-Li axis parallel to the cathode surface. In contrast, the long-chain LiPSs (Li₂S₄, Li₂S₆, and Li₂S₈) adsorb with the Li-Li axis perpendicular to the cathode surface, except that the Li-Li axis of Li₂S₄ tends to align parallel to the substrate in t5t7G. From a top-view perspective, S₈ and LiPSs are preferentially adsorbed directly above the center of the defects in the line-defect graphene. There is a large octagon defect in the 585G, and S₈ and LiPSs preferentially adsorb atop the octagon defect.

Subsequently, we calculate the adsorption energy E_a for the line-defect graphene to the isolated S₈ and LiPSs by the following equation^[58]:

(3) $$ E_{\mathrm{a}}=E_{\mathrm{t}} -E_{\mathrm{LD}} - E_{\mathrm{PS}} $$

where E_t, E_LD, and E_PS represent the energy of the adsorbed system, the free-standing line-defect graphene, and the isolated S₈ and LiPSs, respectively. A more negative adsorption energy indicates stronger binding and a more stable structure after adsorption. Figure 5 depicts the adsorption energies of the stable structures, with corresponding values listed in Supplementary Table 1. The adsorption energies are weakest with the range from -0.45 eV to -0.88 eV for S₈ and LiPSs in the pristine graphene. Both d5d7G and t5t7G show moderate adsorption enhancement, with adsorption energies ranging from -0.84 eV to -1.72 eV and -0.89 eV to -1.74 eV, respectively. Notably, 585G exhibits the strongest adsorption among all samples, with values between -0.89 eV and -1.86 eV. Meanwhile, the adsorption energy of Li₂S on 585G is distinctly higher than that on d5d7G and t5t7G. Notably, the adsorption energies from Li₂S₄ to Li₂S are significantly enhanced in the line-defect graphene relative to the pristine graphene. Compared to the pristine graphene, the line-defect graphene exhibits polarity due to the extended local polarization induced by symmetry-breaking, which enhances the electronic interaction with the polysulfides. Meanwhile, the adsorption energies are generally higher than those reported for representative point-defect graphene systems in previous studies (-0.58 eV to -1.06 eV)^[28,59], indicating that the line-defect graphene provides stronger polysulfide anchoring capability. In contrast to the point-defect graphene, the line-defect graphene provides a continuous and high-density array of active sites, which significantly enhances the polysulfides adsorption and effectively suppresses the shuttle effect. Among them, the t5t7G and the 585G, with relatively large and concentrated defect structures, show prominent adsorption advantages.

Li₂S adsorption constitutes the first step of the entire nucleation process and significantly influences subsequent Li₂S nucleation and growth^‌[60,61]. Owing to the similar bonding character of Li₂S and other LiPSs, a substrate that strongly binds Li₂S usually exhibits high affinity toward other LiPSs as well^[62]. Therefore, we choose Li₂S as a representative model to further investigate the interaction between LiPSs and these materials. In the Supplementary Figure 1, to further elucidate the macroscopic crystallization behavior of Li₂S and evaluate whether it induces active-site passivation, AIMD simulations were performed using a (Li₂S)₅ cluster at 500 K for 10,000 fs. Characteristically, even when the (Li₂S)₅ cluster was initially positioned away from the line defect, the molecules spontaneously rearranged and anchored onto the 585G framework during the dynamic relaxation. More importantly, the optimized snapshot exhibits a distinct 2D surface-spreading growth mode, where Li₂S species wet the flat 1D periodic atomic boundary uniformly, instead of rolling up into spherical 3D insulating clusters as typically observed on pristine graphene^[29]. This prominent structural alignment confirms that the 585G serves as a low-barrier, continuous catalytic highway that may enable orderly Li₂S film deposition without blocking the active electrochemical interfaces.

Furthermore, we systematically analyzed the average variations in Li-S bond lengths and Li-S-Li bond angles, as well as the charge transfer upon Li₂S adsorption, as listed in Supplementary Table 2. For the weakest adsorption in the pristine graphene, the charge transfer (-0.31 e) is minimal, the Li-S bond-length change (0.01 Å) is negligible, and the bond-angle variation (1.60°) is slight. The line-defect graphene exhibit significantly enhanced Li-S bond-length changes, bond-angle variations, charge transfer numbers and adsorption energies. Among them, the 585G with large-sized octagonal defects exhibits the highest adsorption energy, corresponding to the largest charge transfer number (-0.99 e), as well as the maximum bond-length change (0.24 Å) and bond-angle variation (13.80°)‌. The large-sized defect structure of the 585G provides a favorable environment for the electron interactions.

Supplementary Figure 2 further illustrates the positive relationship among adsorption energy, charge transfer, and Li-S bond/angle distortion. Upon adsorption, the greater Li-S bond/angle distortion corresponds to the higher adsorption energy and the larger charge transfer. This arises because the stronger binding stretches the Li-S bond, pulls the sulfur closer to the defective active sites, and thereby increases mutual charge transfer. Thus, the amount of charge transfer between Li₂S and the defective substrate can serve as a descriptor for the adsorption strength of the host material. By calculating the charge density difference ∆ρ after Li₂S adsorption, thus providing insight into the interaction mechanism between polysulfides and the substrates. As shown in Supplementary Figure 3, the yellow and cyan parts represent the charge accumulation and loss, respectively. In the line-defect graphene, charge accumulates between S and the defect-site C while depleting between Li and S, evidencing that Li₂S adsorption is governed by S-C chemical bonding, which endows it with strong adsorption capability.

To gain deeper insight into the interaction between the line-defect graphene and polysulfides, the PDOS for Li₂S₄ adsorbed on the four systems are further analyzed as a representative model system [Figure 6]. Compared with the pristine graphene, there are pronounced electronic-state occupation near the Fermi level in the line-defect graphene, indicating their high electrochemical activity and conductivity, which is advantageous for the reversible charge/discharge reactions. What’s more, little appreciable overlap exists between the C_2p orbital and the Li_2s/S_2p orbitals around the Fermi level in the pristine graphene and d5d7G, reflecting a weak chemical interaction. Meanwhile, the Li_2s states remain relatively localized in these two systems, indicating limited orbital coupling and interfacial charge redistribution involving Li species. An obvious hybridization between C_2p and S_2p orbitals occurs in the 585G around the Fermi level, while it also occurs in the t5t7G at -0.5 eV to -1 eV. The orbital hybridization between C_2p and S_2p is highest in the 585G, which is consistent with the strongest adsorption. In addition, the enhanced overlap between the delocalized C_2p states and Li_2s states in the 585G suggests strengthened interfacial orbital coupling and charge-transfer interaction involving Li species, which further contributes to the improved adsorption and catalytic conversion behavior.

The conversion of polysulfides during the discharge process are crucial for the battery performance. We explore the role of line defects in graphene in the kinetics of LiPSs conversion through the Gibbs free energy barrier analysis. Figure 7 presents the Gibbs free energy barriers for the complete discharge process, which involves the reduction of S₈ to Li₂S. The Gibbs free energy barriers for the reaction steps from S₈ to Li₂S₂ is negative, signifying the spontaneous reactions. The Gibbs free energy barriers for converting solid-phase Li₂S₂ to Li₂S are positive, identifying this conversion as the rate-limiting stage, in agreement with the previous studies^[63]. The barriers of the rate-limiting step for the pristine graphene, d5d7G, t5t7G, and 585G are 2.59, 2.46, 2.40, and 2.35 eV, respectively. Among them, the 585G exhibits the lowest energy barrier in the final step, demonstrating the highest catalytic efficiency and combining superior adsorption performance with catalytic advantages. Compared to the pristine graphene, the introduction of line defects lowers the barrier of the rate-limiting step for the Li-S battery. This indicates that line defects can not only effectively trap polysulfides, but also enhance the catalytic conversion performance of graphene.

Catalytic activity is closely correlated with the band center position; systematically investigating the p-band centers of different line defects is key to uncovering the origin of their activity differences. To this end, we calculate the p-band centers of the pristine graphene and three line-defect graphene by analyzing their C_2p orbital density of states [Supplementary Figure 4]. The p-band center of the pristine graphene is -1.77 eV. Introduction of the line defects modifies the electronic structure, which shifts the p-band center upward to the Fermi level. The p-band center of d5d7G, t5t7G, and 585G are -1.18 eV, -1.16 eV, and -1.10 eV, respectively. Notably, the 585G exhibits the highest p-band center, which aligns well with its superior adsorption and catalytic performance Consistent with the established theory, a p-band center closer to the Fermi level corresponds to higher energy of bonding-state electrons, which facilitates electron exchange^[64,65].

To further probe the role of the p-band center in catalytic activity of these systems, we examine its correlation with the Gibbs free energy barrier during the discharge progress as depicted in Figure 8. A distinct trend is observed: a higher p-band center (closer to the Fermi level) correlates with a lower Gibbs free energy barrier for both the solid-solid conversion from Li₂S₂ to Li₂S and the overall discharge reaction (from S₈ to Li₂S). A higher p-band center closer to the Fermi level indicates that the carbon p orbitals possess stronger electronic activity and are more readily involved in interfacial charge transfer during the sulfur-conversion reactions. Such enhanced electronic coupling can strengthen the orbital hybridization between the defected graphene and sulfur species, thereby facilitating electron-transfer kinetics and reducing the Gibbs free energy barrier of the catalytic conversion process. This supports the use of the p-band center as an effective descriptor for connecting defect geometry with catalytic efficacy. Insights from p-band center analysis thus offer a promising avenue for predicting and optimizing the catalytic behavior of related materials.

To elucidate the reaction kinetics in Li-S batteries, we investigate Li⁺ diffusion on the four material surfaces. As illustrated in Supplementary Figure 5, multiple diffusion paths are selected for each material to ensure the simulation accuracy, with the corresponding diffusion barriers listed in Figure 9. The diffusion barrier is highly path-dependent. For the pristine graphene, the Li⁺ diffusion barrier is 0.31 eV, comparable to the value reported in the previous study^[66]. For the line-defect graphenes, the barrier varies due to differences in the line-defect structures and the electronic structure. For the d5d7G, the lowest diffusion barrier is 0.24 eV for the diffusion from the five-membered ring to the five-membered ring corresponding to the path 1. For the t5t7G, the lowest diffusion barrier is 0.31 eV for the diffusion from the five-membered ring to the seven-membered ring corresponding to the path 2. Meanwhile, for the 585G, the lowest diffusion barrier is 0.28 eV for the diffusion from the five-membered ring to the five-membered ring corresponding to the path 2. Compared with the reported point-defect graphene systems (0.69 eV)^[66], the present line-defect graphene also exhibits relatively low Li⁺ diffusion barriers, suggesting favorable catalytic conversion kinetics. The line defects in graphene eliminate the issue of Li atoms being trapped at vacancies and unable to hop to adjacent sites. Furthermore, the abundance and continuity of defect sites enable sustained Li⁺ diffusion with low overall barriers, resulting in markedly smoother ion transport.

All results in this work are obtained via first-principles calculations. It should be noted that our theoretical simulations only focus on the electrode material itself, while a practical lithium-sulfur battery consists of electrodes, electrolyte and other components. Theoretical simulations confirm the high thermodynamic stability of line-defect graphene. This material can retain stable structures throughout adsorption and catalysis, thereby benefiting its long-term cycling stability. In fact, previous experimental studies have demonstrated that line-defect graphene can be synthesized in a controllable manner^[54-57]. Therefore, the electrochemical performance of the line-defect graphene can be further verified by assembling full batteries in follow-up experimental investigations.