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

Abstract

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.

Analytical and numerical simulations of depolymerization based on discrete model: A chain‐end scission scenario

“…27 Using MoM-based model, the computation time can be second scale. 39 It should be noted here that the concentration of dimer (P 2 ) is included in the current kinetic model. As such, an issue raised in the previous work 22 remains, namely the standard MoM is inappropriate for use in the case of depolymerization of dimer (P 2 ), which is attributed to that the variable of P 2 cannot be simply obtained from the moments of CLD.…”

Digital Strategies to Improve Product Quality and Production Efficiency of Fluorinated Polymers: 1. Development of Kinetic Model and Experimental Verification for Fluorinated Ethylene Propylene Copolymerization

“…In theory, there are an infinite number of molar balance differential equations. In order to obtain the average molecular weight of the polymer, the method of moment is employed in this work. − The moments of radical and dead polymer chains are defined as follows: and . Applying the mass balance principle, we have the following equations for all the species involved in the FEP polymerization system:…”

Kinetic modeling of simultaneous polycondensation and free radical polymerization for polyurethane/poly(methyl methacrylate) interpenetrating polymer network

“…With the development of computer simulation, kinetic models have been widely used in modeling chain-growth polymerization such as free radical polymerization, [21][22][23][24][25][26][27] free radical-induced grafting and cross-linking, [28][29][30][31][32][33] and step-growth polymerization. [34][35][36][37] Unfortunately, few broadly applicable kinetic models to reveal competitive hybrid independent mechanisms are available in IPN synthesis.…”