Mapping the Dynamics of Thermal Frontal Polymerization: Instabilities in the Presence of Heat Losses

Free-radical frontal polymerization exhibits complex dynamical behaviors that directly impact the quality and reliability of the resulting polymeric materials. In this study, we investigate how thermal parameters, kinetic parameters, and system size govern the stability and propagation of thermal fronts in two-dimensional (2D) geometries. By constructing phase diagrams, we classify front behavior into regimes of steady propagation, oscillatory dynamics (single- and double-period), chaotic-like behavior, and quenching. These diagrams reveal a hierarchical sequence of transitions showing that fronts destabilize when heat loss increases or the initial temperature decreases. Damped oscillations commonly arise as transient responses that bridge distinct dynamical regimes. In addition, system thickness acts as an additional control parameter in 2D: thin layers are prone to quenching due to surface heat losses, whereas thicker layers suppress instabilities and stabilize propagation. We uncover a new pathway where increasing heat loss first destabilizes the front and further increase leads to its restabilization, a behavior absent in one-dimensional (1D) models. This mechanism underlines how dimensionality fundamentally shapes the dynamics of frontal polymerization.