Intermediate Phase in Calcium-Silicate-Hydrates: Mechanical, Structural, Rigidity, and Stress Signatures

Topological constraint theory (TCT) classifies disordered networks as flexible, stressed-rigid, or isostatic based on the balance between the number of topological constraints and degrees of freedom. In contrast with the predictions from a mean-field enumeration of the constraints, the isostatic state-wherein the network is rigid but free of stress-has been suggested to be achieved within a range of compositions, the intermediate phase, rather than at a fixed threshold. However, our understanding of the nature and potential structural signatures of the intermediate phase remains elusive. Here, based on molecular dynamics simulations of calcium-silicate-hydrate systems with varying compositions, we seek for some mechanical and structural signatures of the intermediate phase. We show that this system exhibits a composition-driven rigidity transition. We find that the fracture toughness, fracture energy, mechanical reversibility, and creep compliance exhibit an anomalous behavior within a compositional window at the vicinity of the isostatic threshold. These features are argued to constitute a mechanical signature of an intermediate phase. Notably, we identify a clear structural signature of the intermediate phase in the medium-range order of this system, which is indicative of an optimal space-filling tendency. Based on these simulations, we demonstrate that the intermediate phase observed in this system arises from a bifurcation between the rigidity and stress transitions. These features might be revealed to be generic to isostatic disordered networks.