Scale-free network framework for cross-scale formation of particle networks in mixing-processed composite materials

The particle dispersion structures formed during mixing strongly influence the functional properties of composite materials. However, it remains challenging for conventional simulation approaches to simultaneously describe large-scale particle systems and the nonequilibrium structural characteristics generated during mixing. The particle network formation in mixing-processed composite materials was modeled in this study using a static structure-generation approach based on a spatially constrained scale-free network framework with preferential attachment. The proposed model reproduced the scale-free cluster-size distributions and multifractal structural characteristics. These features are consistent with the self-organized structural characteristics reported for polymer-based composites formed by nonequilibrium mixing processes. Furthermore, the simulations captured the crossover from microscale cluster enlargement to macroscale network formation with increasing particle volume fraction and clarified its relationship with percolation behavior. These results demonstrate that the model parameters controlling the aggregation progression and connection range strongly influence the percolation threshold. This model provides a unified framework for describing particle network formation in nonequilibrium mixing processes and offers useful insights for process design aimed at controlling particle network structures in composite materials.