Homology analysis revealed a hidden correlation between the charge-transport properties and the three-dimensional (3D) phase connectivities of metal/oxide nanocomposites. A group of Pt/CeO2 nanostructured composites with different nanotextures ranging from fibrous networks to lamellae were synthesized and identified by electron tomography. The pre-exponential factor of the ionic conductivity of each nanocomposite showed a linear correlation with one of the homological invariants corresponding to the three-dimensional (3D) connectivity of the ion-conductive CeO2 phase, i.e., 3D-β0. The other descriptor for ionic transport, namely, the activation energy, could not be rationally attributed to any of the Betti numbers but mainly correlated with the local crystallinity at the Pt/CeO2 interface. These findings are helpful in the design of electrolytes or electrodes with high oxygen ionic conductivities for application in solid-oxide fuel cells. Moreover, the homological approach proposed in this work can be extended to different nanocomposites, opening up an unexplored pathway for the rational design of nanocomposites based on the homological linkages between their 3D nanotextures and their resulting functionalities.
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