Comparison of estimation methods for reactivity ratios in copolymerizations using in‐situ 1 H ‐ NMR spectroscopy and particle swarm optimization

In copolymerization, chemical composition (CC) strongly influences rheological and end‐use properties. CC is commonly analyzed using the Mayo–Lewis equation (MLE) and derived models, where monomer reactivity ratios (RRs) are key parameters. Common RR estimation methodologies include the Meyer–Lowry equations (MeLE), Skeist's equations—based on residual monomer composition ( f vs. X ) and copolymer composition ( F vs. X ) versus conversion—and monomer balance equations (MOBE). However, a rigorous comparison of these methodologies has not been previously reported. In this work, these methods were applied to estimate RRs for three methacrylate‐based systems: methyl methacrylate (MMA)/vinyl acetate (VAc), MMA/2‐(dimethylamino)ethyl methacrylate (DEAEMA), and DEAEMA/styrene (Sty). Copolymerization kinetics and CC were determined in situ via 1 H‐NMR spectroscopy. A particle swarm optimization (PSO) algorithm was implemented alongside these methodologies and compared with the Levenberg–Marquardt optimization (LMO) algorithm. Results showed that estimated RRs for MMA/DEAEMA and Sty/DEAEMA were largely insensitive to the methodology, depending instead on intrinsic system characteristics. Conversely, the MMA/VAc system exhibited more pronounced deviations, highlighting that methodological choices matter depending on the system. While all data were satisfactorily described by the dynamic approach, the versus X formulation yielded the lowest Akaike information criterion (AIC) and Bayesian information criterion (BIC) values. Finally, both optimization algorithms produced identical RR estimates, confirming the numerical strategy did not significantly affect parameter estimation.