Cost‐efficient modeling of distributed molar mass and topological variations in graft copolymer synthesis by upgrading the method of moments

Cost-efficient deterministic method of moments solvers, as widely used to calculate average characteristics of chemical processes driven by population variations (e.g., average chain lengths), can be a posteriori extended with approximated solutions delivering distributed properties (e.g., chain length distributions). However, these solutions are rarely verified, specifically for complex systems with many population members and strong coupling, as is the case for industrially relevant free-radical-induced grafting (FRIG) toward graft copolymer (GC) synthesis with monomer unit dependent reactions. FRIG, as studied in the present work with polybutadiene at low styrene conversions, is an important chemical process, for example, the production of compatibilizers and high-impact materials. Deterministic model validation is uniquely performed by benchmarking the low to medium molar mass (MM) results (29 topologies) in the log-molar mass distribution with detailed matrix-based kinetic Monte Carlo simulation output, inherently capable of mapping distributions. The GC product is identified to be a heterogeneous mixture in MM, chemical composition, and molecular topology at any styrene conversion. The molecular structural evolution during GC synthesis is further theoretically related to both one-dimensional size-exclusion chromatography (1D-SEC) and two-dimensional liquid chromatography (2D-LC) analysis. It is shown that conventional SEC-even in the absence of broadening-is insufficient for GC separation, mainly due to the unavoidable coelution of topologically different GC species. In any case, the parallel running of advanced modeling tools allows for detailed molecular interpretation.