From Flory Theory to Real Systems: Decoding Polymerization Deviations in Poly(β-amino ester)s (PAEs)

Step-growth polymerizations of linear poly(β-amino ester)s (LPAEs) often show substantial deviations from classical Flory theory, particularly under practical reaction conditions involving different solvents, temperatures, and concentrations. This work establishes a unified mathematical framework, offering a practical route to predict polymer structures beyond the limits of Flory theory. First, using the model system of 1,4-butanediol diacrylate (BDA) and 5-amino-1-pentanol (AP), we systematically quantify these deviations through combined experiments, Monte Carlo (MC) simulations, molecular dynamics (MD) simulations, and machine-learning (ML) analysis. Experimental kinetic traces of number-average molecular weight (M¯n), weight-average molecular weight (M¯w), and dispersity (D̵) reveal pronounced condition-dependent departures from ideal Flory predictions on A2 + B2 system. MC simulations and Random Forest models confirm that the intrinsic difference between the primary- and secondary-amine reactivities (k1 ≠ k2) contributes minimally to the overall molecular-weight evolution. Instead, MD simulations show that spatial constraints─chain crowding, intermolecular attraction, and reduced mobility─dominate the late-stage polymerization behavior. Then, to bridge experimental observations with theory, symbolic regression was used to derive a general correction function f(P,θ), where θ is a continuous descriptor encoding solvent, temperature, and concentration effects. The resulting analytical expression accurately reconstructs experimental M¯w −PA curves across 15 distinct reaction conditions. Feature-importance analysis further identifies solvent effects (particularly DMSO) and temperature as the primary determinants of θ.