Stereolithography (SLA) Fundamentals
SLA 3D printing remains a prominent tool to fabricate complex structures for rapid prototyping and manufacturing, decades past its invention in 1983. However, extension to cytocompatible hydrogel biomaterials for regenerative medicine requires a greater understanding of how transport phenomenon such as diffusion and swelling limit fabrication fidelity. For exampleChuck Hull introduced the use of a strong photo-absorber to control the penetration depth of the laser and thus the layer thickness. Less well documented is that the transverse feature size depends both on the optical spot size and the reaction and diffusion kinetics of the exposed resin.
A significant portion of this thesis is dedicated to understanding and harnessing these kinetics, specifically in low solids content, high diffusivity resins. Similarly, hydrogels introduce postgelation swelling that can significantly distort printed structures during or after printing.
This chapter introduces the fundamental principles and components of SLA systems including photopolymerization, diffusion, and Beer-Lambert absorption. The trade-offs between different system design components are considered, including resolution and minimum feature size, illumination and wavelength, depth of focus, and choice of programmable mask. With these principles, a custom SLA system is designed and characterized.
Photopolymerization and Diffusion
The transport and reaction kinetics during photopolymerization affect photopattern fidelity, total printing time, and the ability to photopattern mechanical property variations. Polymerization is the mechanism by which small molecules, monomers, are linked together to form larger molecules, oligomers, that eventually become a solid polymer. The most common initiation mechanism for SLA is free-radical polymerization. The reaction proceeds by first initiation, in which radicals are generated by photolysis of a photoinitiator, then propagation, in which these monomer radicals react with additional monomers to create propagating polymer radicals and finally termination, in which propagating polymer radicals terminate.
The process of initiation begins when an initiator (?), absorbs a photon (ℎ? = , where ℎ is Plank’s constant and ? is the radiation frequency) and cleaves to form reactive species (?•) that can then diffuse and react with monomer (?) to produce a reactive monomer species, as described by the following equations,
? + ℎ? → 2?•
?• + ? → ? − ? • → (
•) . (1)
These combined processes govern the rate of primary and propagating radical generation. Unreacted monomers species (M) can readily diffuse and react with the propagating polymer radicals (•) to produce a new, larger radical species (•),
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which is generally called propagation. As this process continues, the oligomers produced continue to grow in molecular weight, increasing the material viscosity. In the multifunctional monomers that will be used here, sufficient crosslinks eventually form such that the network spans the printed volume and the molecular weight becomes effectively infinite. At this phase transition, the high viscosity oligomers become a low modulus solid swollen with the remaining monomer, unattached oligomers and water; in other words, a gel. Controlling this gelation is the central goal of SLA. Further conversion of stiff monomers at high solids content can lead to a second phase transition from a rubbery solid to a vitrified glass reducing chemical transport and suppressing continued reactions.
Finally, termination is the mechanism that consumes radicals, reducing radical concentrations, and can occur via three different avenues: recombination, disproportionation, and/or occlusion, as depicted below,
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Recombination occurs when two radical oligomers and/or polymers combine to a single molecule and the radicals terminate one another. Disproportionation occurs when one radical oligomer abstracts the radical from a second oligomer, terminating both oligomers without forming a covalent bond between them. Finally in some cases, the radical species are unable to interact with another species because they are physically confined, as indicated by the curly brackets, and result in trapped radical species, which is called occlusion.
Rate equations such as these are sufficient when the intensity is spatially uniform. In patterned exposure of a liquid or gel material, however, concentration and chemical potential gradients lead to diffusion of liquid components. This in turn causes swelling of the solid network. Diffusion-driven concentration change as a function of time can be understood using Fick’s second law, written in one dimension as,
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where ? is the diffusion coefficient. ? may vary in space, ?, and time, ?, particularly due to local monomer, ?, conversion. However, in the case of low solids content hydrogels (~5-20 wt%), ? is approximately a constant because the distance between crosslinks in the polymer, or mesh size, is much greater than the hydrodynamic radius of the diffusing species (~10-100X). Expanding this work to incorporate reaction kinetics contributing to the changing species -concentration gives,
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where ? is rate at which a species is consumed, where, in the case of photopolymerization it represents the rate of polymerization, ?F. At steady state, the rate of radical species generation is equivalent to the rate of termination and the concentration of radical species is therefore constant given, again, that ? is monomer concentration. Combining this assumption with constant diffusion, the species consumption becomes
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This relationship governs the spatial distribution of polymer in an SLA system, the goal of which is to create a layer of polymer that is a close approximation of the photopattern design, producing high-fidelity features. However, photopolymerization and subsequent diffusion of species do not naturally result in a polymer distribution that is a close copy of the optical dose. To understand the relationship between reaction-diffusion kinetics and feature fidelity, consider two limiting cases: (1) polymerization occurs much more rapidly than diffusion and (2) the polymerization rate is much lower than the diffusion rate.
When the rate of reaction is much faster than diffusion, radical species react before they can diffuse outside of the illuminated region. This is the ideal printing environment for SLA because it ensures high-fidelity. This is the reason why most SLA printing materials have much higher viscosity and lower diffusivity than the hydrogel precursors considered here. Since high viscosity is not possible in the high solvent conditions used here, instead this work shows that a highly reactive monomer can overcome the high diffusion transport rate. Additionally, high illumination intensity can increase reaction rate, however this is often limited by light source availability and cytocompatibility.
Conversely, when the diffusion rate is comparable to or much faster than the reaction rate, species can move into and out of the photo pattern during the reaction. This transport blurs the edges of the patterned material in at least two ways: diffusion of monomer into the pattern and diffusion of radical species out. These processes, not optical diffraction, typically limit the resolution (the minimum distance between features) and critical dimension (the minimum isolated feature size) of the SLA process. This work is particularly concerned with patterning hydrated gels for cellular biology applications, and therefore the viscosity of the precursor solution is similar to water with diffusion rates for small molecules that are correspondingly quite fast in comparison to traditional SLA resins (~100 μ/s vs. 0.01 μ/s, respectively). Therefore, high-fidelity hydrogel features are only attainable if the reaction rate can be is increased with respect to the rapid diffusion rate. Unfortunately, the reaction rate in hydrogels is reduced relative to traditional SLA resins because of high water content and thus low monomer concentration dictated by cytocompatibility. Initiator concentrations in cytocompatible gels are similarly limited in order to constrain the radical concentration. Thus, the only means to increase the reaction rate are by choosing high-reactivity species and/or by increasing the illumination within a range of cytocompatible intensities.
Beer-Lambert Absorption
SLA 3D printing confines polymerization to a 2D layer by adding a strong absorber. It is generally preferred that this absorber not photo-bleach because minimum layer thickness is constrained by maximum achievable absorbance and also because bleaching would needlessly complicate the printing process. Without bleaching, this absorption causes exponential decay of intensity with depth according to the Beer-Lambert law as
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where IL (mW c) is the incident intensity, ? is the molar concentration of a light-absorbing species, and ? (L c) is the molar absorptivity of species . Assuming that the steady state propagation rate scales as and that conversion increases linearly with exposure time at the low conversion levels typical prior to gelation, the “effective dose” to reach gelation can be written
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The thickness of a layer defined by the material conversion reaching the gel point at a depth ? = can be determined by combining these two equations as
9
where ? is the effective dose at the illuminated surface of the material. In the SLA literature, the sublinear dependence of conversion on intensity is typically ignored and the material response is assumed to be reciprocal, or ? ≡ 1. This derivation shows that the “working curve” derived by experimentally determining the parameters of Equation (9) can be applied even in the case of sublinear material response with appropriate definition of an effective depth of penetration and effective dose ? ≡ ?. The primary point of this discussion is that the available printer intensity (), desired print time per layer (t), desired layer depth (), the gel conversion fraction and the linearity of the intensity response (m) are coupled by Equation 9 and must be jointly optimized.