We evaluated the confinement effects on promoting electrochemical oxygen reduction reactions (ORRs) inside the channel of FeN₄-embedded carbon nanotubes (CNTs) via density functional theory calculations. A curvature-activity relationship was constructed through energy decomposition analysis and scaling relation fitting. Originating from the bending of the carbon skeleton, the Fe atom migrates from the N₄ plane, leading to formally inequivalent dsp^2+x hybridization and surface-dependent structural distortion. A larger distortion energy and a weaker orbital interaction jointly destabilize the intermediates of ORR inside the tubes and depress the overpotential in comparison to that on graphene and the convex side of CNTs. The closed cavity of CNT also affects the interactions between adsorbates and water molecules in the confined space. A modest tube FeN₄/(6,6)CNT achieves a low-lying overpotential by balancing the energy penalty attributed to the negatively curved surface and the stabilizing effect resulting from the adsorbate-solvent hydrogen bonding network.

我们通过密度泛函理论计算评估了 FeN ₄ 嵌入碳纳米管 (CNT) 通道内对促进电化学氧还原反应 (ORR) 的限制效应。通过能量分解分析和尺度关系拟合构建了曲率-活度关系。由于碳骨架的弯曲，Fe 原子从 N ₄ 平面迁移，导致形式上不等价的 dsp ^2+x 杂化和表面相关的结构畸变。与石墨烯和碳纳米管凸面相比，较大的畸变能和较弱的轨道相互作用共同破坏了管内 ORR 中间体的稳定性，并降低了过电势。碳纳米管的封闭空腔也会影响有限空间内吸附物和水分子之间的相互作用。适度的管 FeN ₄ /(6,6)CNT 通过平衡负曲面造成的能量损失和吸附物-溶剂氢键网络产生的稳定效应，实现了较低的过电势。