3D Graph Theory Analysis Unveils the Role of Structure‐Dependent Contact Resistances in Conductive Polymer Composites

Metallic filler particles form continuous paths in nonconductive elastomers and provide electrical conduction. The resulting conductive polymer composites (CPCs) are useful as flexible and stretchable conductors or strain sensors. Percolation theory accurately describes the changes in conductivity close to a critical loading φ _C but fails to predict conductivities above this transition. Here, we show that graph theory (GT) metrics can be used to correlate network structure and macroscopic electrical conductivity above φ _C . We used FIB‐SEM tomography to reconstruct (31.5 μm) ³ large CPC volumes with 2.5‐μm‐diameter silver spheres at loadings between 27 and 52 vol%. We find linear correlations between the number of nodes and edges and the average graph degree, length, efficiency, and current‐flow betweenness with the conductivity of CPCs. We formulate a simple model that describes the increase in conductivity above φ _C in terms of network morphology. Kirchhoff circuit analysis reveals that the change in network topology alone cannot explain the experimentally observed conductivity. We show that the average particle–particle contact resistance scales reciprocally with degree. This suggests that the filler loading affects contact areas or tunneling widths, providing a link between mechanical and electrical network properties.