A constitutive model for soft semi-crystalline polymers undergoing intra-chain and inter-chain crystallization towards excellent strength
The semi-crystalline strategy has emerged as a sustainable and reversible route to reinforce soft polymers, yet their complex microstructure precludes accurate characterization by classical statistical-chain theories. In this work an extended deformable freely rotating chain (dFRC) model is proposed that explicitly discriminates between intra-chain and inter-chain crystallization and couples the conformational entropy of amorphous chains with crystalline constraints. The crystalline phase in soft semi-crystalline polymers is believed to follow the mathematical law of grasshopper jumping folding and exhibit the characteristic of freely rotation, but the amorphous part is highly deformable, thus extending the classical FRC model. Parametric studies reveal that intra-chain crystallization (compact chain folding) shortens the end-to-end distance and increases apparent stiffness, whereas inter-chain crystallization (chain alignment) extends the end-to-end distance and promotes strain hardening. The model contains only three composite parameters—chain deformation ability, chain stiffness and thermal deformation—all of which are physically measurable. The dFRC framework therefore provides a concise yet physically rigorous platform for designing soft semi-crystalline networks with programmable strength and toughness.