Mathematical Model for Surface-Initiated Photopolymerization of Poly(ethylene glycol) Diacrylate

A general mathematical model has been developed to describe the surface initiated photopolymerization of PEG‐DA forming crosslinked hydrogel membranes upon the surface of a substrate. Such membranes are formed by photopolymerizing a PEG‐DA prepolymer solution by initiation with eosin‐Y‐functionalized surfaces and TEA using VP as accelerator. Experimental measurements of the thickness of hydrogel membranes compare well with the model. The model is developed by using the pseudo‐kinetic approach and the method of moments, and is capable of predicting the crosslink density and thickness of the hydrogel membrane. Parametric sensitivity of the effects of PEG‐DA, VP and coinitiator TEA concentration towards the crosslink density and the thickness of the hydrogel is also investigated. The results obtained for different PEG‐DA and VP concentrations suggest that the concentration ratio of these two monomers is a key parameter in controlling the gel thickness and permeability. This model can also be applied to systems where drugs, proteins or cells are encapsulated through surface initiated photopolymerization to predict the growth and crosslink density profiles of the encapsulating membrane. In a previous study we have experimentally demonstrated that these membranes could be made to attach covalently to the surface of the underlying substrate. Comparison of experimental measurements and model simulation of PEG‐DA hydrogel membrane thickness versus laser duration at high PEG‐DA concentrations.