Frontal Polymerization of Dicyclopentadiene: A Numerical Study

A Mechanism-Based Reaction-Diffusion Model for Accelerated Discovery of Thermoset Resins Frontally Polymerized by Olefin Metathesis

Frontal ring-opening metathesis polymerization (FROMP) involves a self-perpetuating exothermic reaction, which enables the rapid and energy-efficient manufacturing of thermoset polymers and composites. Current state-of-the-art reaction-diffusion FROMP models rely on a phenomenological description of the olefin metathesis kinetics, limiting their ability to model the governing thermo-chemical FROMP processes. Furthermore, the existing models are unable to predict the variations in FROMP kinetics with changes in the resin composition and as a result are of limited utility toward accelerated discovery of new resin formulations. In this work, we formulate a chemically meaningful model grounded in the established mechanism of ring-opening metathesis polymerization (ROMP). Our study aims to validate the hypothesis that the ROMP mechanism, applicable to monomer-initiator solutions below 100 °C, remains valid under the nonideal conditions encountered in FROMP, including ambient to >200 °C temperatures, sharp temperature gradients, and neat monomer environments. Through extensive simulations, we demonstrate that our mechanism-based model accurately predicts the FROMP behavior across various resin compositions, including polymerization front velocities and thermal characteristics (e.g., Tmax). Additionally, we introduce a semi-inverse workflow that predicts FROMP behavior from a single experimental data point. Notably, the physiochemical parameters utilized in our model can be obtained through DFT calculations and minimal experiments, highlighting the model's potential for rapid screening of new FROMP chemistries in pursuit of thermoset polymers with superior thermo-chemo-mechanical properties.

Polymer Patterning by Laser-Induced Multipoint Initiation of Frontal Polymerization

Frontal polymerization (FP) is an approach for thermosetting plastics at a lower energy cost than an autoclave. The potential to generate simultaneous propagation of multiple polymerization fronts has been discussed as an exciting possibility. However, FP initiated at more than two points simultaneously has not been demonstrated. Multipoint initiation could enable both large-scale material fabrication and unique pattern generation. Here, the authors present laser-patterned photothermal heating as a method for simultaneous initiation of FP at multiple locations in a 2-D sample. Carbon black particles are mixed into liquid resin (dicyclopentadiene) to enhance absorption of light from a Ti:sapphire laser (800 nm) focused on a sample. The laser is time-shared by rapid steering among initiation points, generating polymerization using up to seven simultaneous points of initiation. This process results in the formation of both symmetric and asymmetric seam patterns resulting from the collision of fronts. The authors also present and validate a theoretical framework for predicting the seam patterns formed by front collisions. This framework allows the design of novel patterns via an inverse solution for determining the initiation points required to form a desired pattern. Future applications of this approach could enable rapid, energy-efficient manufacturing of novel composite-like patterned materials.

Numerical Simulation of Polyacrylamide Hydrogel Prepared via Thermally Initiated Frontal Polymerization

Traditional polymer curing techniques present challenges such as a slow processing speed, high energy consumption, and considerable initial investment. Frontal polymerization (FP), a novel approach, transforms monomers into fully cured polymers through a self-sustaining exothermic reaction, which enhances speed, efficiency, and safety. This study focuses on acrylamide hydrogels, synthesized via FP, which hold significant potential for biomedical applications and 3D printing. Heat conduction is critical in FP, particularly due to its influence on the temperature distribution and reaction rate mechanisms, which affect the final properties of polymers. Therefore, a comprehensive analysis of heat conduction and chemical reactions during FP is presented through the establishment of mathematical models and numerical methods. Existing research on FP hydrogel synthesis primarily explores chemical modifications, with limited studies on numerical modeling. By utilizing Differential Scanning Calorimetry (DSC) data on the curing kinetics of polymerizable deep eutectic solvents (DES), this paper employs Malek's model selection method to establish an autocatalytic reaction model for FP synthesis. In addition, the finite element method is used to solve the reaction-diffusion model, examining the temperature evolution and curing degree during synthesis. The results affirm the nth-order autocatalytic model's accuracy in studying acrylamide monomer curing kinetics. Additionally, factors such as trigger temperature and solution initial temperature were found to influence the FP reaction's frontal propagation speed. The model's predictions on acrylamide hydrogel synthesis align with experimental data, filling the gap in numerical modeling for hydrogel FP synthesis and offering insights for future research on numerical models and temperature control in the FP synthesis of high-performance hydrogels.

Unraveling Reactivity Differences: Room-Temperature Ring-Opening Metathesis Polymerization (ROMP) versus Frontal ROMP

In this study, we explore the distinct reactivity patterns between frontal ring-opening metathesis polymerization (FROMP) and room-temperature solventless ring-opening metathesis polymerization (ROMP). Despite their shared mechanism, we find that FROMP is less sensitive to inhibitor concentration than room-temperature ROMP. By increasing the initiator-to-monomer ratio for a fixed inhibitor/initiator quantity, we find reduction in the ROMP background reactivity at room temperature (i.e., increased resin pot life). At elevated temperatures where inhibitor dissociation prevails, accelerated frontal polymerization rates are observed because of the concentrated presence of the initiator. Surprisingly, the strategy of employing higher initiator loading enhances both pot life and front speeds, which leads to FROMP rates exceeding prior reported values by over 5 times. This counterintuitive behavior is attributed to an increase in the proximity of the inhibitor to the initiator within the bulk resin and to whether the temperature favors coordination or dissociation of the inhibitor. A rapid method was developed for assessing resin pot life, and a straightforward model for active initiator behavior was established. Modified resin systems enabled direct ink writing of robust thermoset structures at rates much faster than previously possible.

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. In this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

Review on Frontal Polymerization Behavior for Thermosetting Resins: Materials, Modeling and Application

The traditional curing methods for thermosetting resins are energy-inefficient and environmentally unfriendly. Frontal polymerization (FP) is a self-sustaining process relying on the exothermic heat of polymerization. During FP, the external energy input (such as UV light input or heating) is only required at the initial stage to trigger a localized reaction front. FP is regarded as the rapid and energy-efficient manufacturing of polymers. The precise control of FP is essential for several manufacturing technologies, such as 3D printing, depending on the materials and the coupling of thermal transfer and polymerization. In this review, recent progress on the materials, modeling, and application of FP for thermosetting resins are presented. First, the effects of resin formulations and mixed fillers on FP behavior are discussed. Then, the basic mathematical model and reaction-thermal transfer model of FP are introduced. After that, recent developments in FP-based manufacturing applications are introduced in detail. Finally, this review outlines a roadmap for future research in this field.

Frontal Polymerizations: From Chemical Perspectives to Macroscopic Properties and Applications

The synthesis and processing of most thermoplastics and thermoset polymeric materials rely on energy-inefficient and environmentally burdensome manufacturing methods. Frontal polymerization is an attractive, scalable alternative due to its exploitation of polymerization heat that is generally wasted and unutilized. The only external energy needed for frontal polymerization is an initial thermal (or photo) stimulus that locally ignites the reaction. The subsequent reaction exothermicity provides local heating; the transport of this thermal energy to neighboring monomers in either a liquid or gel-like state results in a self-perpetuating reaction zone that provides fully cured thermosets and thermoplastics. Propagation of this polymerization front continues through the unreacted monomer media until either all reactants are consumed or sufficient heat loss stalls further reaction. Several different polymerization mechanisms support frontal processes, including free-radical, cat- or anionic, amine-cure epoxides, and ring-opening metathesis polymerization. The choice of monomer, initiator/catalyst, and additives dictates how fast the polymer front traverses the reactant medium, as well as the maximum temperature achievable. Numerous applications of frontally generated materials exist, ranging from porous substrate reinforcement to fabrication of patterned composites. In this review, we examine in detail the physical and chemical phenomena that govern frontal polymerization, as well as outline the existing applications.

Frontal polymerization-triggered simultaneous ring-opening metathesis polymerization and cross metathesis affords anisotropic macroporous dicyclopentadiene cellulose nanocrystal foam

Multifunctionality and effectiveness of macroporous solid foams in extreme environments have captivated the attention of both academia and industries. The most recent rapid, energy-efficient strategy to manufacture solid foams with directionality is the frontal polymerization (FP) of dicyclopentadiene (DCPD). However, there still remains the need for a time efficient one-pot approach to induce anisotropic macroporosity in DCPD foams. Here we show a rapid production of cellular solids by frontally polymerizing a mixture of DCPD monomer and allyl-functionalized cellulose nanocrystals (ACs). Our results demonstrate a clear correlation between increasing % allylation and AC wt%, and the formed pore architectures. Especially, we show enhanced front velocity (v_f) and reduced reaction initiation time (t_init) by introducing an optimal amount of 2 wt% AC. Conclusively, the small- and wide-angle X-ray scattering (SAXS, WAXS) analyses reveal that the incorporation of 2 wt% AC affects the crystal structure of FP-mediated DCPD/AC foams and enhances their oxidation resistance.

Switching Frontal Polymerization Mechanisms: FROMP and FRaP

Two frontal polymerization (FP) mechanisms, frontal ring-opening metathesis polymerization (FROMP) of dicyclopentadiene and frontal radical polymerization (FRaP) of benzyl acrylate and hexanediol diacrylate, were combined for rapid manufacturing of welded thermoset materials. Leveraging the immiscibility of the two different FP resins, welded thermosets and gradient foams of varying composition were achieved by switching of FP mechanisms. The adhesion strength of the welded thermoset materials differed depending on the originating mechanism. Finally, welded thermoset foams of varying porosity and homogeneity were generated through initiation from the bottom of the two resins.

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.

Anisotropic frontal polymerization in a model resin-copper composite

This work investigates experimentally and numerically frontal polymerization in a thermally anisotropic system with parallel copper strips embedded in 1,6-hexanediol diacrylate resin. Both experiments and multiphysics finite element analyses reveal that the front propagation in the thermally anisotropic system is orientation-dependent, leading to variations in the front shape and the front velocity due to the different front-metal strip interaction mechanisms along and across the metal strips. The parameters entering the cure kinetics model used in this work are chosen to capture the key characteristics of the polymerization front, i.e., the front temperature and velocity. Numerical parametric analyses demonstrate that the front velocity in the directions parallel and perpendicular to the metal strips increases as the system size decreases and approaches the analytical prediction for homogenized systems. A two-dimensional homogenized model for anisotropic frontal polymerization in the metal-resin system is proposed.

Controllable Frontal Polymerization and Spontaneous Patterning Enabled by Phase-Changing Particles

Frontal polymerization provides a rapid, economic, and environmentally friendly methodology to manufacture thermoset polymers and composites. Despite its efficiency and reduced environmental impact, the manufacturing method is underutilized due to the limited fundamental understanding of its dynamic control. This work reports the control and patterning of the front propagation in a dicyclopentadiene resin by immersion of phase-changing polycaprolactone particles. Predictive and designed patterning is enabled by multiphysical numerical analyses, which reveal that the interplay between endothermic phase transition, exothermic chemical reaction, and heat exchange govern the temperature, velocity, and propagation path of the front via two different interaction regimes. To pattern the front, one can vary the size and spacing between the particles and increase the number of propagating fronts, resulting in tunable physical patterns formed due to front separation and merging near the particles. Both single- and double-frontal polymerization experiments in an open mold are performed. The results confirm the front-particle interaction mechanisms and the shapes of the patterns explored numerically. The present study offers a fundamental understanding of frontal polymerization in the presence of heat-absorbing second-phase materials and proposes a potential one-step manufacturing method for precisely patterned polymeric and composite materials without masks, molds, or printers.

Manipulating Frontal Polymerization and Instabilities with Phase-Changing Microparticles

Recently presented as a rapid and eco-friendly manufacturing method for thermoset polymers and composites, frontal polymerization (FP) experiences thermo-chemical instabilities under certain conditions, leading to visible patterns and spatially dependent material properties. Through numerical analyses and experiments, we demonstrate how the front velocity, temperature, and instability in the frontal polymerization of cyclooctadiene are affected by the presence of poly(caprolactone) microparticles homogeneously mixed with the resin. The phase transformation associated with the melting of the microparticles absorbs some of the exothermic reaction energy generated by the FP, reduces the amplitude and order of the thermal instabilities, and suppresses the front velocity and temperatures. Experimental measurements validate predictions of the dependence of the front velocity and temperature on the microparticle volume fraction provided by the proposed homogenized reaction-diffusion model.

Rapid frontal polymerization achieved with thermally conductive metal strips

Frontal polymerization, which involves a self-propagating polymerizing reaction front, has been considered as a rapid, energy-efficient, and environmentally friendly methodology to manufacture lightweight, high-performance thermoset polymers, and composites. Previous work has reported that the introduction of thermally conductive elements can enhance the front velocity. As follow-up research, the present work investigates this problem more systemically using both numerical and experimental approaches by investigating the front shape, front width, and heat exchange when aluminum and cooper metal strips are embedded in the resin. The study reveals that the enhancement in the front velocity is mainly due to a preheating effect associated with the conductive element. Moreover, the numerical parametric study for the system size shows that the front speed increases as the system size decreases, ultimately approaching a prediction provided by a homogenized model for polymer-metal composites.

Rapid synchronized fabrication of vascularized thermosets and composites

Bioinspired vascular networks transport heat and mass in hydrogels, microfluidic devices, self-healing and self-cooling structures, filters, and flow batteries. Lengthy, multistep fabrication processes involving solvents, external heat, and vacuum hinder large-scale application of vascular networks in structural materials. Here, we report the rapid (seconds to minutes), scalable, and synchronized fabrication of vascular thermosets and fiber-reinforced composites under ambient conditions. The exothermic frontal polymerization (FP) of a liquid or gelled resin facilitates coordinated depolymerization of an embedded sacrificial template to create host structures with high-fidelity interconnected microchannels. The chemical energy released during matrix polymerization eliminates the need for a sustained external heat source and greatly reduces external energy consumption for processing. Programming the rate of depolymerization of the sacrificial thermoplastic to match the kinetics of FP has the potential to significantly expedite the fabrication of vascular structures with extended lifetimes, microreactors, and imaging phantoms for understanding capillary flow in biological systems.

Bioinspired vascular networks transport heat and mass in multifunctional materials but lengthy multistep fabrication processes hinder large-scale application of structural vascular materials. Here, the authors report rapid, scalable, and synchronized fabrication of vascular thermosets and fiberreinforced composites under ambient conditions.

Spontaneous Patterning during Frontal Polymerization

Complex patterns integral to the structure and function of biological materials arise spontaneously during morphogenesis. In contrast, functional patterns in synthetic materials are typically created through multistep manufacturing processes, limiting accessibility to spatially varying materials systems. Here, we harness rapid reaction-thermal transport during frontal polymerization to drive the emergence of spatially varying patterns during the synthesis of engineering polymers. Tuning of the reaction kinetics and thermal transport enables internal feedback control over thermal gradients to spontaneously pattern morphological, chemical, optical, and mechanical properties of structural materials. We achieve patterned regions with two orders of magnitude change in modulus in poly(cyclooctadiene) and 20 °C change in glass transition temperature in poly(dicyclopentadiene). Our results suggest a facile route to patterned structural materials with complex microstructures without the need for masks, molds, or printers utilized in conventional manufacturing. Moreover, we envision that more sophisticated control of reaction-transport driven fronts may enable spontaneous growth of structures and patterns in synthetic materials, inaccessible by traditional manufacturing approaches.

Rapid Synthesis of Elastomers and Thermosets with Tunable Thermomechanical Properties

Rapid, solvent-free synthesis of poly(1,4-butadiene) in ambient conditions is demonstrated by frontal ring-opening metathesis polymerization (FROMP) of 1,5-cyclooctadiene (COD). Furthermore, cross-linked copolymers with a wide range of tunable properties are readily prepared by FROMP of mixtures of COD and dicyclopentadiene (DCPD). Specifically, glass transition temperature and tensile modulus are varied from -90 to 114 °C and 3.1 MPa to 1.9 GPa, respectively, by controlling the comonomer ratio. Copolymers with subambient glass transition temperature exhibit robust elastomeric behavior, with the ability to repeatedly recover from large elastic deformations. As a demonstration of the capability of this manufacturing strategy, gradient materials are fabricated in less than a minute with spatially controlled properties for multistage shape memory actuation. This simple yet powerful manufacturing strategy enables rapid synthesis of copolymers ranging from elastomers to thermosets with precise control over thermomechanical properties.

Traveling-waves of metal-containing monomer polymerization without diffusion and heat-transfer

The new approach for modeling kinetics of complex spatial self-propagating traveling-wave reactions is proposed. This approach is intended to replace well-known reaction–diffusion equations and self-propagating high-temperature synthesis (SHS) as methods for mathematical modeling of spatial propagation of chemical reactions. A chemical kinetic model for frontal polymerization of metal-containing monomers under this approach is suggested.