1. Quantitative structure property relationships of nanotube structural and mechanical propertiesTammie L Borders1,Andrew Rusinko III1, KJ Cho2, and Alexandre F Fonseca2.(1) Department of Chemistry, University of North Texas, 1155 Union Circle, #305070, Denton, TX 76203, (2) Department of Physics, University of Texas at Dallas, Richardson, TX 75080

2. Motivation - Carbon nanotube (CNT) reinforced composites • Goals • Improve load transfer at critical interfaces • CNT-polymer • CNT intra-wall • Investigate interface failure mechanisms • Consider realistic variations (i.e., defects, functionalization, etc) • Problem  large parameter space • Solution  informatics methodologies Courtesy of KJ Cho, UTD

3. Outline • Data preparation • Carbon nanotube test case matrix • MD methodology, calculations and results • Descriptors • Multivariate model generation • Partial least squares (PLS) • Vacancy only test set • Complete test set • Model validation • Y-scrambling • Training set – random 20% • Future work • Conclusion

4. Carbon nanotube test case matrix- Data preparation

5. Carbon nanotube test case matrix- Data preparation 54 test cases

6. Carbon nanotube test case matrix- Data preparation Define Vacancies (n10m0 zig-zag) Single vacancy Double horizontal Double vertical • Potential descriptors • Surface area • Orientation of maximum width • Number carbons with coordination number 2 • Number of missing carbons Tolvanen, A., J. Kotakoski, et al. (2007). "Relative abundance of single and double vacancies in irradiated single-walled carbon nanotubes." Applied Physics Letters91(17): 173109-3.

7. MD methodology- Data preparation • Structure preparation • Perfect CNTs – Nanotube Modeler & UTD scripts • Defects & methyl groups – Python scripts • MD potential: AIREBO • Initial relaxation (50 – 100 ps) • Apply axial tension • Quasi-static stretching technique • Add 0.1 A to each end • Freeze coordinates of C’s on end (z only for chiral) • Relax structure (15 – 40 ps) • Repeat 24 times (5 A stretch, ~ 5% strain for 100A) • Output – energy of relaxed structure

8. MD calculations & results- Data preparation • Output: Young’s modulus (GPa) • Elastic (region 1  2) • Calculation method 1 • Elastic energy  y = ax2 + bx + c • Calculation method 2 • Stress / strain  y = ax Thickness = 3.35 Å Area = 2rt

9. MD calculations & results- Data preparation

10. Descriptors- Data preparation • Variable that “encodes” information • 25 descriptors • % type defect • % total defects • Radius • Chiral angle • Angle of defect maximum width • Energy of formation (requires initial relaxation run) • Surface area of defects

11. Descriptors- Data preparation

12. Partial least squares (PLS)- Model generation • Combination of principal component analysis (PCA) and multiple regression • Project to Latent Structures • Concept • Reduce dimensionality of original data set • Forms set of latent variables (linear combination of original) • No loss of essential data • Advantages: • Works well for large number of variables • Ability to handle multi-collinearity • Latent vectors are directly related to the response • Disadvantages: • Can be computationally slow • Interpretation of parameters is difficult

13. Multivariate models – all cases, PLS- Model generation • r2 = 0.9245 • Std error = 23 GPa • Variables • Chiral angle • Num double defects • Num methyl groups • Normal angle • Total surface • Total defect surface • Surface ratio

14. Y-scrambling – all cases- Model validation • r2 = 0.218 • Std error = 75 GPa

15. Test set – 20%- Model validation • Training set • r2 = 0.9245 • Std error = 23 GPa • Test set • 0.9256 • Std error = 22 GPa

16. Multivariate models – vacancies, PLS- Model generation • r2 = 0.939 • Std error = 18 GPa • Variables • Chiral angle • Num double defects • Num missing C’s • Num perfect C’s • Surface ratio

17. Y-scrambling – vacancies- Model validation • r2 = 0.264 • Std error = 63 GPa

18. Future • Descriptors • Electron density distributions, connectivity matrices, eigenvalues • Analysis & cross-correlation • Investigate other nanotube properties (i.e., intra-wall) • Plastic behavior (i.e., critical stress) • Sensitivity analysis in continuum model • Full model validation & definition of domain • Experimental data (common database?)

19. Conclusion • Motivation – improve CNT reinforced composites • Data preparation • MD analysis of axial tension to calculate Young’s modulus • Descriptors • Model generation • Partial least squares (PLS) • PLS for all cases • PLS for vacancy only cases • Model validation • Y-scrambling • Future studies

20. Thanks!!

21. MD methodology- Data preparation • Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) • REBO – covalent bonding • New terms: torsion, dispersion, non-bonded repulsion, adaptive LJ terms (2008) • Varying chemical environments & hybridizations Appropriate for defects Stuart, S. J., A. B. Tutein, et al. (2000). "A reactive potential for hydrocarbons with intermolecular interactions." Journal of Chemical Physics112(14): 6472-6486.

22. MD calculations & results- Data preparation • Use 0 – 3% strain • gnuplot, scipy / numpy

23. Feature / descriptor analysis- Model generation All 54 cases – methyls, vacancies, perfect • Num methyls • Num carbons • Radius • Total surface area • Num single defects • Num double defects • Number missing C’s • L/D • Num 2Coord C’s • Total defect surface • Chiral angle http://reccr.chem.rpi.edu/Software/modeling/index.html

24. Feature / descriptor analysis- Model generation 36 vacancy test cases • Radius • Num carbons • Num double defects • L/D • Total surface area • Num single defects • Num missing carbons • Total defect surface • Num 2Coord C’s • Defect to total surface • Chiral angle http://reccr.chem.rpi.edu/Software/modeling/index.html