Geometry-based cross-linking algorithm for modeling resorcinol resins through united-atom molecular dynamics simulations

The addition-condensation polymerization (ACP) of resorcinol with formaldehyde and the electrochemical polymerization (ECP) of resorcinol were desirable to improve the performances of resins. To achieve computational design, a new geometry-based cross-linking modeling algorithm for three-dimensional (3D) cross-linked network structures of resorcinol resins was developed for molecular dynamics (MD) simulations using a united-atom model. The ACP and ECP of resorcinol were successfully modeled using one algorithm by changing the parameters of the reaction rate constants of methylene, ether, and biphenyl bond formations. Furthermore, reaction judgment was performed under a reaction probability function comprising the Gaussian functions based on the interatomic distance of the reaction candidate atom pairs and interior angles regarding the spatial arrangement of two resorcinol rings. This geometry-based cross-linking algorithm successfully generated strainless 3D cross-linked network structures of the ACP and ECP resorcinol resins without the formation of highly bent unstable structures, such as U-shaped biphenyls. The MD simulation results indicated that the cross-linking of the ACP resin comprising methylene linkages proceeded with a network structure formation mechanism similar to that of phenolic resins, where the cross-linked network structure was determined at the gel point and the reactions after the gel point were to fix and freeze the network structure. For the ECP resins comprising ether and biphenyl linkages, the molar ratio of ether to biphenyl bonds affected the elastic property of the resins, and the incorporation of rigid biphenyl structures into ether-linkage networks increased the elastic modulus. Moreover, an increase in rigidity was observed as a decrease in the Poisson's ratio.