# A Theory-Guided Machine Learning and Molecular Dynamics Approach for Characterizing Fast-Curing Polyurethane Systems

## TL;DR

This paper presents a new method combining machine learning and simulations to study how fast-curing polyurethane materials harden and change properties during the process.

## Contribution

A novel framework integrating theory-guided machine learning and molecular dynamics to characterize fast-curing polyurethane systems.

## Key findings

- The KS model accurately predicted conversion and curing rates with R2 > 0.99.
- Gelation occurred at DoC ≈ 0.53, with Tg determined via DSC and rheology.
- MD simulations and Gaussian process regression captured Tg evolution with λ ≈ 0.29.

## Abstract

Fast-curing polyurethane (PU) systems are attractive for high-throughput manufacturing, but quantifying cure kinetics, gelation, and cure-dependent glass transition temperature (Tg) is difficult, especially at a low degree of cure (DoC). Here, a fast-reacting BASF PU formulation was studied using non-isothermal differential scanning calorimetry (DSC) at multiple heating rates, rheometry at 50 °C, and molecular dynamics (MD) simulations to extend Tgα in the low-DoC regime. DSC provided reaction enthalpy and conversion histories, and Kamal–Sourour (KS) parameters were identified by robust nonlinear fitting, reproducing conversion and curing rate profiles (R2 > 0.99 and >0.95). Rheology indicated gelation between 475 and 625 s (DoC ≈ 0.53), and DSC-based Tg at uncured, gelation, and fully cured states, established the experimental Tg trend. MD (LAMMPS) with topological crosslinking and NPT thermal scans extracted Tg from density–temperature slopes at selected DoC points. Experimental and MD Tg data were fused with Gaussian process regression constrained by the DiBenedetto relationship (5-fold cross-validation), giving λ ≈ 0.29 and confidence intervals. This framework links kinetics, gelation, and Tg evolution for fast-curing PU and identifies the low-DoC region as the main source of uncertainty.