Biphenyl tetracarboxylic acid-based metal–organic frameworks: a case of topology-dependent thermal expansion

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.