Application of catastrophe theory to thermal shrinkage behavior of cold-drawn crystalline polymer solids

This study investigates the thermal shrinkage behavior of cold-drawn or necked crystalline polymer solids through a mathematical framework of catastrophe theory. While polymers necked by uniaxial stretching exhibit irreversible macroscopic plastic deformation, they demonstrate significant shape-memory recoverability upon thermal treatment. A phenomenological approach based on the van der Waals equation was used to model the phase transitions and mechanical properties observed during necking and thermal recovery. Our findings suggest that thermal shrinkage is driven not solely by elastic recovery but by cooperative rearrangements of cluster blocks composed of lamellar crystals through thermodynamic affinity, analogous to martensitic transformations in metals. Experimental results confirm that thermal shrinkage behavior is consistent with theoretical predictions, offering insights into the recoverable deformation mechanism. This work provides a foundation for developing molecular theories to explain thermal shrinkage behavior in typical plastic materials.