Model simulations on network formation and swelling as obtained from cross-linking co-polymerization reactions

Cross-linking co-polymerization was studied in the presence of di-, tri- or tetra-functional cross-linkers using the Bond Fluctuation Model (BFM). Network formation was analyzed for varying cross-linker reaction rates, cross-linker composition and number fraction, cross-linker functionality and time dependent initiator release. Additionally, the effect of inhomogeneous radical release and radical aging was examined. For all simulations we observe an auto-acceleration of reaction kinetics similar to the “Trommsdorff-Norrish effect” (or “gel effect”) independent of the degree of cross-linking. While kinetics does not follow mean field models, the resulting structure can still be described using mean field arguments. In particular, the weight distribution of “chains” that result from reactions of one radical and the number distribution of cross-linkable sites on these chains are approximated by Poisson distributions. Delayed release of initiators causes a pronounced broadening of these distributions that can be modeled by a partitioning of the reaction bath into compartments with different initiator density and instant initiation. The network structure is analyzed and the weight fractions of the active material and gel, and the average strand length within the active material are determined. We discuss the impact of the different variables onto the network structure and how this structure can be optimized concerning low amounts of soluble material or a high volume fraction of active chains. The a-thermal swelling data of most networks agrees with the prediction of the Flory-Rehner model. An additional non-affine contribution to the equilibrium degree of swelling is observed for networks with a low density of active cross-links.

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