Interpreting Critical Exposure and Penetration Depth in Vat Photopolymerization

Critical exposure, Ec, and penetration depth, Dp, are widely used to characterize photopolymerizable resins and select exposure conditions in stereolithography, digital light processing and masked stereolithography. Their compact representation in the Jacobs working curve is useful, but it can encourage an interpretation that is physically broader than the measurement supports. An experimentally fitted Ec is not necessarily the dose of the first molecular initiation event, while a fitted Dp is not necessarily an invariant optical attenuation length. Both values depend on formulation, wavelength, irradiance, exposure time, specimen preparation, oxygen history, cleaning, dimensional metrology and the criterion used to identify cured material. Interlaboratory results demonstrate that procedural variability can dominate the reported values even when the same resin is tested.

This review proposes a layered interpretation connecting incident and absorbed light, formation of initiating reactive species, inhibitor consumption, functional-group conversion, gelation, dimensional survival and layer-by-layer exposure history. It distinguishes the quantum yield of initiating-species formation from the efficiency with which a liquid formulation becomes a dimensionally persistent solid. Functionality, reactive-group equivalent weight, viscosity, molecular mobility, backbone structure, photobleaching, absorption and scattering are treated as coupled variables rather than independent predictors. The analysis is extended to thin layers, retained resin and enclosed microfluidic channels, where repeated sub-threshold exposures can produce delayed gelation outside the intended geometry. A verification framework is proposed that combines working curves with chemical conversion, rheological or mechanical gelation, spatial test artifacts and channel-retention measurements. The objective is not to replace Ec and Dp, but to define what they measure, what they omit and how they can be used without confusing cure speed with dimensional fidelity.