Percolation Mechanisms in Transient Polymer Networks across Dilute and Semidilute Regimes

Abstract

Percolation in transient polymer networks remains poorly understood because reversible cross-links continuously reorganize the network structure. In this study, we investigated percolation in transient polymer networks by independently controlling network connectivity and polymer concentration in a well-defined Tetra-PEG slime model system. Using diffusing-wave spectroscopy (DWS) microrheology, the Winter–Chambon criterion was identified at high frequencies (>102 rad s–1), despite the system being macroscopically a viscoelastic liquid. In the dilute regime, the critical connectivity required for percolation decreases with decreasing polymer concentration, accompanied by an increase in the fractal dimension of the percolating clusters. While lattice-based percolation models describe the behavior near the overlap concentration, they fail in the dilute regime, for which a reaction-limited particle–cluster aggregation mechanism enabled by reversible cross-links provides a better explanation of network formation. These results reveal that percolation in transient networks follows a mechanism that is fundamentally different from that in permanently cross-linked gels.