Mathematical modeling of frontal polymerization

Abstract

Frontal polymerization is way to convert liquid resin into a solid material with a self-propagating reaction. The reaction spreads like a flame from the heat of the reaction that diffuses into neighboring regions, starting more reaction. The frontal velocity has been accurately modeled for free-radical polymerization systems. The dynamics of fronts have been studied theoretically and experimentally. If the viscosity of the initial medium is low, then fronts can become unstable due to buoyancy-driven convection. A fascinating aspect of frontal polymerization is that fronts often do not propagate as a plane waves but exhibit complex modes such as “spin modes” and chaos. The kinetics of the polymerization significantly affects the onset of these modes. Multifunctional acrylates exhibit more complex dynamics than monoacrylates. Using multifunctional acrylates and inorganic fillers, 3P LLC created “cure-on demand” systems that do not require mixing before use, have a long shelf life and can be hardened in seconds to minutes. We consider two commercial products using frontal polymerization. The first is a wood filler that can be applied to a damaged section of wood and hardened in a few seconds by the application of heat to the surface. The second product is QuickCure Clay (QCC). QCC has an unlimited working time during which it can be sculpted. QCC is then cured by heating part of the object to 100 °C, setting off the propagating curing front. The modeling of frontal polymerization helped guide the development of these products.

Microstructural study of epoxy-based thermosets prepared by “classical” and cationic frontal polymerization

“…This was also revealed in the mathematic modeling of frontal polymerization on acrylates. 22 In the case of the time derivative of the temperature prole for photo and thermal RICFP (Fig. S7 †), the extent of the separation, or the overlap, of the temperature proles, which indicate the existence of thermal waves.…”

“…We also examined the microstructural changes in the radial and angular proles, which support the nding that the frontal reaction forms non-planar spin modes that propagate spirally with the helical path. 21,22 Experimental section…”

A Review on Modeling Cure Kinetics and Mechanisms of Photopolymerization

“…The main shortcoming of photopolymerization lies in the limited penetration depth, caused by decreasing light intensity along the height of the formulation to be cured, which greatly limits the application potential of photopolymerization to thin films and adhesive applications [ 27 , 43 ]. Layers with a typical thickness between 5 and 200 or, at the very most, a few millimeters thickness can be polymerized [ 1 , 44 ].…”

“…The presence of fibers as a reinforcing phase may even contribute to this shortcoming by further reducing the transmission of light [ 45 , 46 ]. Therefore, photopolymerization can be effectively used for curing thin samples, but it is not suitable for curing thick samples, especially those containing carbon fibers or other opaque materials [ 43 ]. According to Decker [ 1 ], photoinitiation has proven to be well suited to induce frontal polymerization, which is highly beneficial to curing thick specimens.…”

Mathematical Modeling of Polyphosphazenes

“…Many researchers synthesized polymeric materials and they used for applications for mathematical modeling [21][22][23][24][25][26][27][28][29][30].…”