Microstructure-informed multiscale modeling of piezoresistivity in graphene foam

Graphene foam (GF) has gained increasing attention as a next-generation strain sensing material, combining multidirectional mechanical deformability with highly interconnected conductive pathways. Understanding how its hierarchical microstructure governs piezoresistive response is essential for developing GF-based stretchable strain sensors with superior performance. Here, we present a microstructure-informed multiscale simulation framework that elucidates how the atomic-scale features of GF propagate through hierarchical levels to dictate the macroscopic piezoresistive behavior of GF-based strain sensors. The complex three-dimensional GF architecture is represented as an interconnected network of polycrystalline graphene cell walls. At the atomic scale, density functional theory (DFT) calculations reveal that grain boundaries with higher structural asymmetry exhibit stronger resistance modulation but reduced mechanical stability under strain. At the island scale, an Ohmic scaling law incorporates DFT-derived transport properties to describe the piezoresistive behavior of polycrystalline graphene islands, showing that smaller grain sizes amplify strain-induced resistance changes. At the cell wall scale, Monte Carlo resistor-network simulations identify the characteristic island size, rather than grain size, as the dominant parameter controlling strain sensitivity, where reduced island size enhances tunneling modulation and significantly increases the gauge factor. To examine this prediction experimentally, controllable pre-stretching is applied to tune the island structure within the graphene cell walls of GF. Optical characterization and electromechanical measurements confirm that increasing pre-stretch strain reduces the effective island size and enhances the gauge factor, consistent with the model prediction. This work establishes a predictive framework for microstructural engineering of GF-based strain sensors.