In a Polymers paper, we developed a Monte Carlo model to describe the formation of branched polymers via step-growth polymerization. We also introduced an approximation scheme that makes it possible to compute the molecular weight distribution from the Flory-Stockmayer theory. The simulation results are compared to the prediction of the theory, which shows that the theory only applies for systems well below the gel point. However, our Monte Carlo model enables a quick calculation of the molecular weight distribution for a wide range of polymerizing systems, be they below, around, or above the gel point, stoichiometric or nonstoichiometric, full reacted or only partially reacted.

In a Macromolecules paper, we developed a coarse-grained model for a branched polyetherimide derived from two backbone monomers [4,4'-bisphenol A dianhydride (BPADA) and m-phenylenediamine (MPD)], a chain terminator [phthalic anhydride (PA)], and a branching agent [tris[4-(4-aminophenoxy)phenyl] ethane (TAPE)]. We demonstrated how the "force matching theory" developed by Voth, Andersen, Noid, and coworkers can be used to systematically construct a library-like, expandable coarse-grained model for a polymer and how the coarse-grained model can be rendered transferable by adding a correction term to the coarse-grained force field that enables density matching between the coarse-grained model and the all-atom model or experiment. The underlying physics is revealed as the correlation between the thermal expansion coefficient of a polymer and its mechanical properties.

In a J. Polym. Sci. paper, we explored three different approaches to either compute the glass transition temperature (Tg) for a polyimide via all-atom molecular dynamics (MD) simulations or predict Tg via a mathematical model generated by using machine-learning algorithms to analyze existing data collected from literature. Our simulations reveal that Tg can be determined from examining the diffusion coefficient of simple gas molecules in a polyimide as a function of temperature and the results are comparable to those derived from data on polymer density versus temperature and actually closer to the available experimental data. Furthermore, the predictive model of Tg derived with machine-learning algorithms can be used to estimate Tg successfully within an uncertainty of about 20 degrees, even for polyimides yet to be synthesized experimentally.