The document presents a workflow for analyzing x-ray scattering datasets of polyethylene to derive processing linkages between microstructure and properties. Principal component analysis was used to reduce the dimensionality of the x-ray scattering data, and a transfer function model was applied to predict microstructural trajectories and establish processing linkages for different polyethylene samples subjected to varying conditions. Future work is proposed to further extract spatial statistics from the data and reconstruct microstructures to establish stronger linkages between structure and properties.

1. 1
Structure - Processing Linkages
in
Polyethylene
David Brough
Abhiram Kannan
Final Presentation
ME 8883

2. Outline
‣ Motivation & Objective
‣ X Ray Scattering Datasets of Polyethylene
‣ Workflow
‣ Results and Discussions
‣ Future Work
‣ Summary
‣ Acknowledgements

3. Motivation
Jancar, J. et al. Current issues in research on structure - property relationships in polymer nanocomposites.
Polymer 51, 3321–3343 (2010)
Hierarchical structural assembly of a material influences the
properties on the macroscopic scale

4. Motivation & Objective
Processing
Condition a
Processing
Condition b
Microstructure
Set a
Microstructure
Set b
Properties
Set a
Properties
Set b
PE
Temperature
Pressure
Isotropic vs Anisotropic
Homogeneous vs Heterogeneous
Yield
Strength
Polyethylene (PE)

5. X Ray Scattering Data of PE
Small Angle X Ray Scattering (SAXS) data is related to spatial
statistics
200 µm x 200 µm
Lamella
Inter
Crystalline
Amorphous
~10 nm
X Rays

6. Play
Film sample is strained continuously while being probed by X rays
X Ray Scattering Data of PE
X Rays

7. Bulk Density Processing Condition Film Thickness (µm)
0.912 gms/cc
1 20 30 75
2 20 30 75
0.923 gms/cc
1 20 30 75
2 20 30 75
Workflow
spatial
statistics
dimensionality
reduction
processing
linkage
SAXS
Data
Principal
Components
Analysis (PCA)
Transfer
Function
Model (TFM)

8. Principal Components Analysis
• 3200 .tif images across 12 samples (~250 per sample)
• Log intensity scaled by mean to account for thickness effects
• Scaled images fed to PCA Algorithm
• Outputs of PCA Algorithm visualized in D3
Compare :-
1. Effects of Processing Conditions
2. Effects of Density
3. Effects of Thickness

9. Transfer Function Model Linkage
• For sample 6,10 each Principal Component is fit to a Transfer
Function model of order (2,1,5)
• Using obtained coefficients, predictions for the remaining
samples are made
• Comparison of Predicted and True Low Dimensional
Trajectories.
Model Equation:-
Xt = a1Xt−1 + a2 Xt−2 + b0εt + b1εt−1 + b2εt−2 + b3εt−3 + b4εt−4 + b5εt−5 + Err

10. Summary
• Dimensionality Reduction of time resolved data by PCA
• Objective comparison between strain derived microstructures of
PE
• Minimization of User Bias incurred from traditional analysis
protocols
• Applied method for deriving processing linkages via Transfer
Function Model might hold potential

11. Future Work
• Extraction of spatial statistics by via transformation of SAXS
data
• Reconstruction of 2 Phase Crystalline - Amorphous
Microstructures
• Extend Transfer Function Model to incorporate Stress Values
• Property Linkage with Crystallinity, Orientation etc.
• Additional Length Scales (~0.1 nm) from Wide Angle Scattering
Data (WAXS)

12. Acknowledgements
• Dr. Surya Kalidindi (GT)
• Dr. Hamid Garmestani (GT)
• Dr.Tony Fast (GT)
• Dr. David Bucknall (GT)
• Dr. David Fiscus (ExxonMobil)