Critical Role of Layer Thickness in Frontal Polymerization.

Thermal frontal polymerization (FP) is a chemical process during which a cold monomer-initiator mixture is converted into a hot polymer as a polymerization front propagates in the system due to the interplay between heat diffusion and the exothermicity of the reaction. The theoretical description of FP generally focuses on one-dimensional (1D) reaction-diffusion (RD) models where the effect of heat losses is encoded into an effective parameter in the heat equation. We show here the limits of such 1D models to describe FP under nonadiabatic conditions. To do so, the propagation of a polymerization front is analyzed both analytically and numerically in a rectangular two-dimensional (2D) layer. The layer thickness is shown to control the dynamics of the front and to determine its very existence. We find that for given heat losses, a minimum thickness is required for front propagation as recently observed in FP experiments of 2D thin films on wood. Moreover, when the thickness exceeds a critical value, the front is observed to survive independently of the rate of heat losses. This result cannot be predicted with 1D models where front extinction is always possible. A scaling analysis is proposed to highlight the physical interpretation of such a front survival. The influence of dimensionality on thermal instabilities is also analyzed, with a focus on the differences with the 1D predictions.