Comprehensive model predicts complex dynamics in free-radical photopolymerization

(Nanowerk Spotlight) The ability to rapidly transform liquid monomers into solid polymers using light has been a transformative technology for over half a century. This process, known as photopolymerization, enables the fast fabrication of coatings, adhesives, dental fillings, and intricate 3D printed structures on demand.
In photopolymerization, light-sensitive compounds called photoinitiators absorb photons and generate reactive chemical species known as free radicals. These free radicals then rapidly string together monomers into long polymer chains, causing the liquid to solidify into a hardened plastic material.
Despite its widespread use, precisely predicting and controlling the complex chemical and physical changes that occur during photopolymerization has been a longstanding challenge. The strong coupling between light absorption, heat generation, molecular diffusion, and chemical reaction kinetics leads to sharp gradients in material properties that evolve in time and space. Existing mathematical models have often neglected key aspects of this dynamic interplay, limiting their predictive power and generality.
Now, researchers Adam Dobson and Christopher Bowman from the University of Colorado have developed a comprehensive computational framework that captures photopolymerization's intricacies with unprecedented fidelity. Their model unifies decades of theoretical and experimental insights into a cohesive multiphysics simulation platform. By explicitly accounting for the effects of oxygen inhibition, light attenuation, heat transfer, component mobility, and the differing reactivities of short and long polymer chains, the model can predict the complete spatio-temporal evolution of the polymerizing system.
The team reports their findings in Advanced Functional Materials ("A Comprehensive, Multidimensional First-Principles Model for Free-Radical Photopolymerizations in Bulk and Thin Films").
Complexities of Modeling Free-Radical Photopolymerization
Complexities of Modeling Free-Radical Photopolymerization. A) Schematic showing selected gradients on the macroscale and localized microscale that affect polymerization kinetics and final material properties. B) Polymerization rate as a function of conversion 25 µm from the top surface of the sample shows an increase in polymerization rate (Rp) with increasing light intensity. The maximum polymerization rate scales with I00.54 for higher intensities but with I01.1 for lower intensities. C) Simulated conversion profiles after 60 s exposure shows dramatic gradients in the degree of cure due to factors such as oxygen inhibition, species diffusion, and heat transfer. Simulations presume an optically thin, 100 μm film of 1,6-hexanediol diacrylate with 0.01 M Irgacure 819, weakly convecting (h = 10 W m−2 K−1) surface thermal boundary condition, and constant surface oxygen concentration cured with 405 nm light at intensities of 1 (black), 3 (yellow), 5 (blue), 10 (gray), or 20 (green) mW cm−2. (Reprinted with permission by Wiley-VCH Verlag)
One of the key innovations is the model's ability to accommodate the dramatic shift in reaction kinetics that occurs as the polymer network forms. Initially, when monomers and short polymer chains are highly mobile, polymerization is fast as free radicals can readily propagate and terminate. However, as the crosslinked network grows, the diffusion of reactive species becomes increasingly constrained.
The model captures this transition by dynamically adjusting the rate constants for propagation and termination based on the evolving "free volume" available for molecular motion. This free volume is estimated using the thermal expansion coefficients and glass transition temperatures of each reacting species. The inclusion of such composition and conversion-dependent mobilities allows the model to seamlessly span the entire range of radical kinetics, from early-stage gel formation to late vitrification, a capability that sets it apart from previous models.
To validate their approach, the researchers compared model predictions with experimental measurements of the polymerization kinetics of 1,6-hexanediol diacrylate, a widely used monomer, over a range of photoinitiator concentrations and light intensities. The Dobson-Bowman model accurately captured the complete conversion profiles across all intensities after fitting just a lower and medium rate case.
In contrast, simpler chain-length independent models could only fit a single curing condition. For example, at the highest light intensity of 50 mW/cm2, the model predicted a final conversion within 2% of the experimentally observed value, demonstrating its robustness in handling diverse reaction conditions.
The model also sheds light on the crucial role of oxygen inhibition in shaping the polymerization kinetics, especially near the illuminated surface. By constantly replenishing dissolved oxygen, the uncured liquid layer in contact with air can severely deplete free radicals and limit the polymerization rate.
The model quantitatively predicts the thickness of this inhibition zone and its dependence on light intensity, showing excellent agreement with established analytical scaling laws. For instance, the model predicts that doubling the light intensity reduces the inhibition layer thickness by nearly 30%, closely matching the square root dependence expected from theory. These insights provide a rational basis for designing curing protocols and resin formulations that mitigate the detrimental effects of oxygen.
Another key advance is the seamless integration of heat generation and transport into the modeling framework. The model rigorously accounts for the heat released by the exothermic polymerization reactions, the temperature rise due to light absorption, and the conductive and convective transfer of this thermal energy.
Simulations reveal that apparently modest changes in the thermal boundary conditions can dramatically influence the polymerization kinetics. Even in thin films, using insulated vs conducting substrates alters the reaction exotherm, which in turn affects the diffusion, the onset of autoacceleration, the limiting conversion, and the depth of cure. For example, the model predicts that an insulating boundary can increase the ultimate conversion by up to 20% compared to a conductive boundary, while simultaneously reducing the depth of cure by half.
The model even predicts the self-propagating reaction fronts that can arise in thicker layers due to the coupling between thermal diffusion and initiator decomposition.
Perhaps most impressively, the model's predictive power extends beyond one-dimensional profiles into full three-dimensional structures. By incorporating a spatially varying light intensity profile, the researchers simulated the polymerization of a cylindrical volume element, or "voxel", under conditions relevant to stereolithographic 3D printing. The model captured the complex interplay between lateral diffusion of oxygen from the surrounding uncured resin and the attenuation of light with depth.
Notably, the illumination time alone was insufficient to predict the dimensions of the cured voxel. Instead, the polymerization kinetics depended strongly on the peak light intensity, with higher intensities leading to greater curing depths but reduced voxel widths due to increased oxygen inhibition.
These findings highlight the need for physics-based models to optimize the print speed, resolution and mechanical integrity of photopolymer additive manufacturing.
The Dobson-Bowman model represents a major step towards predictive, first-principles based engineering of photopolymer reactivity and structure. By faithfully capturing the dynamic interplay between light, heat, mass transport, reaction kinetics, and network formation, the model provides researchers with a powerful tool to rationally design photoinitiators, monomers, and processing conditions for a wide range of applications. Its ability to predict full spatio-temporal property evolution in arbitrary 3D geometries opens new avenues for the computational optimization of stereolithography, holography, dentistry, and coatings.
With further refinements to include effects like polymerization shrinkage, photobleaching, and mechanical property development, integrated multiphysics models will accelerate the development of faster, higher resolution, and more robust photopolymer additive manufacturing. More broadly, this work showcases the power of combining physical insights, mathematical models, and experimental data to unravel the complexities of reactive polymer processing.
Michael Berger By – Michael is author of three books by the Royal Society of Chemistry:
Nano-Society: Pushing the Boundaries of Technology,
Nanotechnology: The Future is Tiny, and
Nanoengineering: The Skills and Tools Making Technology Invisible
Copyright © Nanowerk LLC

Become a Spotlight guest author! Join our large and growing group of guest contributors. Have you just published a scientific paper or have other exciting developments to share with the nanotechnology community? Here is how to publish on