Correlation between Critical Energy, Penetration Depth, and Photopolymerization Kinetics in Aluminum–Phosphate–Silicate Hybrid Materials for Vat Photopolymerization

The photopolymerization of aluminum–phosphate–silicate resins obtained from the hybrid sol–gel route for Vat photopolymerization (VPP) process was investigated. The printing parameters derived from Jacob’s work curve model, critical energy (E_c) and penetration depth (D_p), were determined as a function of laser power and MPTMS (silicate) concentration for materials with stoichiometry Si_(x)-(Al + P)_(1–x), 0 ≤ x ≤ 0.7. The kinetics of photopolymerization was further explored using steady- and unsteady-state photo-DSC experiments. The oxygen inhibition and primary termination had similar contributions to the polymerization process for all compositions, while the propagation and bimolecular termination constants increased with MPTMS concentration. These experimental results were used to test the validity of the E_c ∝ k_t^1/2/k_p and D_p ∝ ϵ relationship derived from a photochemical model for VPP assuming steady-state kinetics. Both E_c ∝ (k_t^1/2/k_p) and D_p ∝ ϵ may be used to predict critical energy and penetration values for an arbitrary resin without calculating its work curve function, according to our study.