# Rigidity Percolation Dictates Rheological Hysteresis Regime in Polypropylene during Crystallization and Melting

## TL;DR

This study shows how the rigidity of polypropylene changes during crystallization and melting, revealing two distinct hysteresis regimes linked to percolation thresholds.

## Contribution

The paper introduces a new framework linking rigidity percolation to rheological hysteresis in polypropylene using simultaneous rheology and Raman spectroscopy.

## Key findings

- Polypropylene exhibits different rheological behavior during crystallization and melting at the same crystallinity due to thermal pathway.
- Hysteresis onset aligns with the percolation threshold calculated by the GEM model.
- Two hysteresis regimes are identified: one with limited hysteresis before percolation and one with large hysteresis after percolation.

## Abstract

Understanding structure–property relationships
during polymer
crystallization and melting has been limited by challenges in the
simultaneous measurement of crystallinity and rheological properties.
Consequently, rheological models overlook the fundamental asymmetry
between crystallization and melting processes. Here, we use simultaneous
rheology and Raman spectroscopy to directly measure rheological behavior
as a function of crystallinity. We find that polypropylene’s
rheological behavior can differ significantly between crystallization
and melting at identical crystallinity values depending on thermal
pathway. Using a generalized effective medium (GEM) model, we show
that the onset of hysteresis aligns with the calculated percolation
threshold. We quantify hysteresis through a normalized hysteresis
parameter ΔG̃ and show that the maximum
value of ΔG̃ occurs at the percolation
threshold calculated by the GEM model for systems that have achieved
complete space filling. Finally, we identify two hysteresis regimes:
one prior to percolation with limited hysteresis and one after percolation
with large hysteresis values. Mechanically, these regimes reflect
the structural differences between the semicrystalline components
and pure melt state: the former represents a suspension of “softening
spheres” while the latter constitutes a softening network.