The large inherent flexibility and highly modular nature of metal–organic frameworks (MOFs) make them ideal candidates for the study of negative thermal expansion (NTE). Among diverse organic ligands, the biphenyl unit, which can unrestrictedly rotate along its C–C single bond, can largely enhance the structural flexibility. Herein, we explored the thermal expansion behaviors of four indium biphenyl tetracarboxylates (BPTCs). Owing to the different dihedral angles of BPTC ligands and coordination mode of In³⁺, they show distinct topologies: InOF-1 (nti), InOF-2 (unc), InOF-12 (pts) and InOF-13 (nou). Intriguingly, it is found that the thermal expansion is highly dependent on the specific topology. The MOFs featuring mononuclear nodes show normal positive thermal expansion (PTE), and the magnitudes of coefficients follow the trend of InOF-2 < InOF-12 < InOF-13, inversely related to averaged molecular volumes. In contrast, the InOF-1, composed of a 1D chain of corner-shared InO₆ octahedrons, shows pronounced NTE. Detailed high-resolution synchrotron powder X-ray diffraction and lattice dynamic analyses shed light on the fact that NTE in the InOF-1 is a synergy effect of the spring-like distortion of the inorganic 1D helical chain and twisting of the BPTC ligands. The present work shows how the topological arrangement of building blocks governs the thermal expansion behaviors.

中文翻译：

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联苯四甲酸基金属有机框架：拓扑相关热膨胀的案例

金属有机框架（MOF）固有的巨大灵活性和高度模块化性质使其成为负热膨胀（NTE）研究的理想候选者。在多种有机配体中，联苯单元可以沿着C-C单键不受限制地旋转，可以大大增强结构的灵活性。在此，我们探讨了四种联苯四甲酸铟（BPTC）的热膨胀行为。由于BPTC配体的二面角不同和In ³⁺的配位方式不同，它们表现出不同的拓扑结构：InOF-1 ( nti )、InOF-2 ( unc )、InOF-12 ( pts ) 和 InOF-13 ( nou )。有趣的是，我们发现热膨胀高度依赖于特定的拓扑结构。具有单核节点的MOF表现出正常的正热膨胀（PTE），系数的大小遵循InOF-2 < InOF-12 < InOF-13的趋势，与平均分子体积成反比。相比之下，InOF-1由共享角的InO ₆八面体的一维链组成，表现出明显的NTE。详细的高分辨率同步加速器粉末X射线衍射和晶格动力学分析揭示了InOF-1中的NTE是无机一维螺旋链的弹簧状扭曲和BPTC配体扭曲的协同效应的事实。目前的工作展示了构建块的拓扑排列如何控制热膨胀行为。