Random graph modeling of three-dimensional copolymerization of acrylates

The polymerization of multifunctional acrylates is commonly used to form three-dimensional networks. During network formation, reaction conditions change drastically due to increasing diffusion limitations and the liquid-to-solid phase transition, posing significant modeling challenges. We developed a two-level mathematical model for 3D radical copolymerization. The monomer-level model predicts the possible configurations in which individual monomer units are incorporated into the network. This connectivity information is then used to deduce polymer properties through a polymer-level model based on random graphs (RG). This model is applied to the terpolymerization of N-butyl acrylate (NBA), 1,6-hexanediol diacrylate (HDDA), and trimethylolpropane triacrylate (TMPTA), utilizing kinetic data from previous studies. Because it is necessary to track configurations of reactive groups and various types of bonds formed on the monomer units, as well as all possible ways such configurations may be formed, the monomer model itself has a significant combinatorial complexity. To address this, we employ an automated procedure known as Automated Reaction Network Generation (ARNG), inspired by computational linguistics. In addition to standard features predictable by RG models, such as polymer size distributions, gel points, and gel fractions, we extend the approach to include bivariate distributions to obtain size/mass and size/number of radicals distributions. This enhanced information provides deeper insights into the structural changes during acrylate network formation, particularly at low monomer conversions.