Dynamic and stress signatures of the rigid intermediate phase in glass-forming liquids

We study the evolution of enthalpic changes across the glass transition of model sodium silicate glasses (Na₂O)_x(SiO₂)_100-x, focusing on the detection of a flexible-rigid transition and a possible reversibility window in relationship with dynamic properties. We show that the hysteresis resulting from enthalpic relaxation during a numerical cooling-heating cycle is minimized for 12% ≤ x ≤ 20% Na₂O, which echoes with the experimental observation. The key result is the identification of the physical features driving this anomalous behavior. The intermediate-flexible boundary is associated with a dynamic onset with increasing depolymerization that enhances the growing atomic motion with a reduced internal stress, whereas the intermediate-stressed rigid boundary exhibits a substantial increase in the temperature at which the relaxation is maximum. These results suggest an essentially dynamic origin for the intermediate phase observed in network glass-forming liquids.