Cross-Hierarchical Analysis of Self-Oscillating Polymer Materials Through Activation Energy

In chemically driven soft materials, polymer architecture can shape how chemical reactions are transduced into material-level dynamic behavior. However, the relationship between polymer architecture and the resulting dynamics remains insufficiently understood. Here, using Arrhenius analysis, we perform a cross-hierarchical comparison of the temperature dependence of Belousov-Zhabotinsky (BZ) reaction-driven oscillatory dynamics across three structurally related systems: molecular Ru(bpy)₃Cl₂, a linear self-oscillating polymer (SOP), and a self-oscillating microgel (SOMG). In these systems, Ru(bpy)₃ complex is present in solution as a molecular catalyst or covalently incorporated into either a linear polymer or a crosslinked microgel network. The resulting apparent activation energies E_{a, app} are used to quantify the overall temperature dependence of their oscillatory dynamics. In the SOP, the redox and coacervation/dissolution oscillations exhibit similar E_{a, app} values, indicating that periodic liquid-liquid phase separation had only a limited effect on the overall temperature dependence. In contrast, in the SOMG, the flocculation/dispersion oscillation exhibits a substantially higher E_{a, app} than the redox oscillation. Moreover, the relative order of E_{a, app} between the SOP and SOMG is reversed between the redox and structural oscillatory modes. These results indicate that E_{a, app} is modulated by both the underlying polymer architecture and the architecture-dependent structural dynamics accompanying BZ-driven oscillations.