Critical Role of Layer Thickness in Frontal Polymerization

Abstract

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.

Frontal Polymerizations: From Chemical Perspectives to Macroscopic Properties and Applications

“…For thicker layers, the reaction outcompetes thermal cooling. Similar to the layer thickness study by Tiani et al, 105 instabilities in thin-film geometries with thermally insulating substrates were recently reported by Gao et al 124 The existence of convective and thermal instabilities has significant repercussions for FP chemistries and FP-derived materials. 112 In certain structural applications that require homogeneous features, for example, these non-uniform propagation motifs induce hot-spots that may negatively affect the properties of the final polymer.…”

“…where h is the heat transfer coefficient (W m -2 K -1 ), and P (m) and S (m 2 ) are the perimeter and surface area of the domain cross-section, respectively. [103][104][105] Combining eqs 7-9, a final 1-D expression of heat conservation describes the evolution of temperature with time inside a control volume: As discussed in Section 2.3.3, ideal FP systems only exhibit large temperature changes in close proximity to the reaction zone (i.e., small Lθ and Lα on the scale of 0.1 to 1 mm). The final governing equation (11) illustrates several key physical properties that modulate effective front propagation.…”

“…∇T, where 𝒖 ⃗ ⃗ is the fluid velocity (m s -1 ), and a recent report highlighted that spatial patterning in reaction-diffusion processes is highly impacted by the introduction of an intentional fluid-flow. 123 Most recently, Tiani et al 105 and Gao et al 124 numerically studied the effect of reaction thickness on FP. In the absence of thermal cooling at the boundary (i.e., inside an insulator), a uniform planar front exists.…”

Frontal Polymerization of Thin Layers on a Thermally Insulating Substrate

“…However, at the interface, the higher of unstable fronts have a nonmonotonic dependence on d r due to the thermal spikes. The effect of the layer thickness on front velocity and temperature is similar when FP is subjected to convective heat loss …”

“…Therefore, leveraging the competition between the heat generated by the reaction and the thermal transport enables the tuning of key features that influence the efficiency and feasibility of FP, that is, the front shape, velocity, and temperature. , Moreover, thermochemical instabilities emerge at a critical reaction–thermal transport power balance, − potentially resulting in polymeric parts with complex geometries and heterogeneous properties . A recent numerical study has reported that the resin layer thickness controls the front dynamics and determines its existence subject to convective heat loss . Nevertheless, a quantitative relationship between front propagation, resin amount, and substrate effects is still lacking.…”