Dynamic Correlation Analysis between Stress-Strain Curve and Polymer Film Structure Using Persistent Homology

Area of Science:

• Materials Science
• Computational Chemistry
• Polymer Physics

Background:

• Understanding the relationship between polymer structure and mechanical properties is crucial for materials design.
• Molecular dynamics (MD) simulations offer insights into polymer behavior, but correlating structural features with macroscopic properties remains challenging.

Purpose of the Study:

• To develop and validate a computational framework combining coarse-grained molecular dynamics (CG-MD) and persistent homology (PH) with principal component analysis (PCA).
• To correlate specific structural features, particularly ring structures, with the stress-strain behavior of polymer films.

Main Methods:

• Coarse-grained molecular dynamics (CG-MD) simulations were performed on polymer films under uniaxial tension.
• Persistent homology (PH) analysis was applied to the simulation data to identify topological features (ring structures).
• Principal component analysis (PCA) was used to analyze persistence diagrams generated by PH, correlating them with stress-strain curves.

Main Results:

• The first principal component of the persistence diagram showed strong agreement with the stress-strain curves.
• Inverse analysis revealed that smaller ring structures (≤10 CG beads) significantly influence the principal component, linked to poly(ethylene oxide) helical structures.
• The PH + PCA approach successfully predicted stress-strain curves for polymers with varying interactions and bond lengths, explaining yield stress variations through ring distribution.

Conclusions:

• Persistent homology analysis coupled with PCA provides a robust method for linking polymer film structure (ring distribution) to mechanical properties (stress-strain behavior).
• This integrated approach offers a versatile framework for analyzing complex polymer systems without prior structural assumptions.
• The findings highlight the importance of specific ring structures in dictating polymer film mechanical responses.