Sub-Unit-Cell Logic Governs Transport in TPMS Architectures

Next-generation energy, thermal, and chemical systems require architectures capable of highly efficient transport across multiple length scales. Triply periodic minimal surfaces (TPMS), first conceptualized in 1865, offer inherently scalable geometries with exceptional transport potential, yet mechanistic links between topology and performance have remained elusive. Here we introduce a sub-unit-cell conduit framework that governs transport in TPMS architectures. By integrating crystallographic symmetry analysis with Voronoi tessellation, we show that each TPMS can be resolved into a network of identical intrinsic conduits oriented in different directions, with geometry and connectivity uniquely determined by topology. This framework reveals that transport efficiency is determined primarily by two conduit-scale descriptors-conduit uniformity and conduit spatial density-while conduit surface area and connectivity play secondary roles. Building on these insights, we derive predictive descriptors and a performance quotient that link local conduit geometry to TPMS transport behavior independent of scale and operating conditions. The model identifies Fischer-Koch as a leading topology, which we validate using additively manufactured copper Fischer-Koch TPMS heat exchangers fabricated via green-laser powder bed fusion. Experiments reveal up to a 156-fold improvement in heat-exchange efficiency (quantified by the j/f ratio) for the copper Fischer-Koch TPMS, compared with a conventional baseline, aligning closely with model predictions. This sub-unit-cell conduit approach provides a generalizable mechanistic basis for the rational design of high-performance TPMS-architected materials across diverse transport applications.