Using SAXS images of polyethylene samples, structure processing linkages were created.

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)