Extrapolative Prediction of Propagation Rate Coefficient in Free-Radical Polymerization Based on kp (T, NI)-QSPR Model

Abstract

This work assesses the extrapolation performance of the kp (T, NI)-QSPR model for free-radical polymerization. Although QSPR models often achieve high interpolation accuracy, their reliability for predicting beyond the training domain, a situation common in monomer reactivity exploration, remains a critical challenge. To address this, prediction set is classified into interpolation and extrapolation categories using descriptor visualization. Extrapolation validation (EV) is employed to evaluate model reliability, defining an extrapolation degree (ED) to quantify how far test samples lie outside the training domain. Results demonstrate that the model achieves excellent interpolation accuracy but shows limited reliability when descriptors fall beyond the training set range. Descriptors suitable for forward or backward extrapolation are identified, with backward extrapolation yielding relatively better predictions for certain monomers. Uneven descriptor distributions are revealed as the primary cause of high ED and reduced extrapolation performance. This work provides a practical framework for assessing the applicability domain of the kp (T, NI)-QSPR model. More importantly, the established EV approach provides a transferable framework for applicability domain assessment and offers critical guidance for improving extrapolation robustness, thereby laying a foundation for extending such predictive methods to other temperature-dependent kinetic parameters in free-radical polymerization.