On the evolution of cured voxel in bulk photopolymerization upon focused Gaussian laser exposure

Abstract

Unconstrained depth photopolymerization is emerging as a promising technique for fabrication of several polymer microstructures such as self propagating waveguides, 3D freeform structures by bulk lithography, and polymer nanoparticles by flash exposure. Experimental observations reveal governing physics beyond Beer Lambert's law and scattering effects. This paper seeks to model unconstrained depth photopolymerization using classical nonlinear Schrödinger equation coupled with transient diffusion phenomenon. The beam propagation part of the proposed model considers scattering effects induced due to spatial variation of the refractive index as a function of the beam intensity. The critical curing energy model is used to further predict profile of polymerized voxel. Profiles of photopolymerized voxel simulated using proposed model are compared with the corresponding experimental results for several cases of exposure dose and duration. The comparison shows close match leading to conclusion that the experimentally observed deviation from Beer Lambert's law is indeed due to combined effect of diffusion of photoinitiator and scattering of light because of change in the refractive index.

New stereolithographic resin providing functional surfaces for biocompatible three-dimensional printing

“…The origins of these filament structures are still unknown, but it can be assumed that self-focusing may be a reason for this effect. 20 , 21 Photopolymerization-induced refractive index variation is a well-known effect. 22 – 24 Thus, the liquid and later the polymer works as an optical lens during the irradiation.…”

The upcoming 3D-printing revolution in microfluidics

“…Partial differential equations describing (1) the DMD pixel or laser source light intensity profile 86,87 , (2) the penetration of UV into the liquid monomer solution (Beer-Lambert law) 14,88 , (3) the chemical kinetics related to polymer chain initiation, propagation and termination 89 , (4) the thermodynamics of chemical bond formation during polymerization 14 , and (5) the diffusion of the photo-initiator and radicals through the partially polymerized resin 14,88 need to be solved to get a good a priori estimate of the expected resolution. The depth of curing assumes particular importance when building the roof of microchannels, since light penetration into the void of the channels can partially cure the resin, making it hard to remove after printing.…”

“…Simulations and finite element modeling (FEM) has been used to model the complex process of photo-polymerization and estimate the exposure parameters for achieving the highest possible z-resolution. Partial differential equations describing (1) the DMD pixel or laser source light intensity profile, 86,87 (2) the penetration of UV into the liquid monomer solution (Beer-Lambert law), 14,88 (3) the chemical kinetics related to polymer chain initiation, propagation and termination, 89 (4) the thermodynamics of chemical bond formation during polymerization, 14 and (5) the diffusion of the photo-initiator and radicals through the partially polymerized resin 14,88 need to be solved to get a good a priori estimate of the expected resolution. The depth of curing assumes particular importance when building the roof of microchannels, since light penetration into the void of the channels can partially cure the resin, making it hard to 90 Nordin and colleagues have systematically studied the minimal (non-transparent) channel dimensions that can be reliably printed with SL (60 μm (h) × 108 μm (w)) 77 (Fig.…”

3D printing of optical components via free-radical frontal polymerization

“…In an attempt to quantify the uncertainty, we measure the standard deviation of the cure depth from the idealistic fitting of equation 2. It was also noted by [12] and [7] that self-focusing of the polymers can alter the curing characteristics due to a gradient refractive index, but we do not anticipate that this effect is prominent with the scale of our samples being in the several mm range. It can also be minimized by using a lower curing intensity.…”

“…As mentioned at the end of section 2.5, the approach of using a Jacobs working curve only applies for a specific set of dose conditions. This has been noted by several studies ( [7,12]) without comprehensive analysis. We will now provide an overview of current work in the field which approaches the issue from a kinetic analysis standpoint.…”