Developing Descriptors to Predict Mechanical Properties of Nanotubes Dr. Tammie L. Borders May 16, 2013

Outline (1) Problem description Methodologies  Informatics flow  Selecting descriptors CNT surfaces  Derive critical descriptors for mechanical properties  Modular extension of QSPR to two types of defects Comparison to experimental results  Investigating load transfer mechanisms in multi-walled CNTs  Prediction of monolayer graphene mechanical properties Future Work Conclusion 2

3 Problem description - Carbon nanotube (CNT) reinforced composites Goals  Improve load transfer at interfaces CNT-polymer CNT intra-wall  Maintain intrinsic properties of CNTs  Consider realistic variations (i.e., defects, functionalization, etc) Problem  large parameter space Solution  informatics methodologies Informatics-molecular dynamics approach to explore large problem space; Refinement with experimental data provides quantitative accuracy

4 Problem description - Carbon nanotube (CNT) reinforced composites (1) Goals  Improve load transfer at interfaces CNT-polymer CNT intra-wall  Maintain intrinsic properties of CNTs  Consider realistic variations (i.e., defects, functionalization, etc) Problem  large parameter space Solution  informatics methodologies Informatics-molecular dynamics approach to explore large problem space; Refinement with experimental data provides quantitative accuracy 1) Surface morphology – stiffness / strength 2) Intra-wall bonding – load transfer

Outline (2) Problem description Methodologies  Informatics flow  Selecting descriptors CNT surfaces  Derive critical descriptors for mechanical properties  Modular extension of QSPR to two types of defects Comparison to experimental results  Investigating load transfer mechanisms in multi-walled CNTs  Prediction of monolayer graphene mechanical properties Future work Conclusion 5

Informatics flow MEASUREMENTS Process parameters Characterization DatabasesMEASUREMENTS Process parameters Characterization Databases THEORY Atomic calculations Mesoscale calculations Continuum calculationsTHEORY Atomic calculations Mesoscale calculations Continuum calculations CORRELATIONS Clustering Feature selection Data mining & analysisCORRELATIONS Clustering Feature selection Data mining & analysis KNOWLEDGE Process-structure- property relationships Materials discovery Hidden data trendsKNOWLEDGE Process-structure- property relationships Materials discovery Hidden data trends 6

Selecting descriptors - Borrowing for pharmaceutics Most descriptors to date – for small drug like molecules First approach – simple constitutional, topological, physicochemical Properties of interest  Pharma – activity, toxicity (ADME-T)  Materials – mechanical, electrical, thermal, lifecycle behavior / mechanisms Scales of interest  Pharma – molecular  Materials – molecular  macro 7

Selecting descriptors - The process Data Collection & Pre-processing Determine Descriptors  Initial guess Clustering  Principal Component Analysis Loadings Plot Feature Selection  Principal Component Analysis  Star Plots  Partial Least Squares Multivariate Analysis  Partial Least Squares Validation  Y-scrambling Can we improve model interpretability? Accuracy?  Descriptor set next guess 8 Selecting Descriptors is a Human-in-the-Loop, Iterative Process with the Goal of Simultaneously Improving Model Interpretability and Accuracy Initial Guess (20)

Selecting descriptors - Clustering & feature selection 9 Star Plots Identifies descriptor stable / robustness; Provides measure of strength / correlation PCA Loadings Plot Identifies clusters, important descriptors PC1 & PC2 account for 69% of variance

Selecting descriptors - Multivariate analysis and validation 10 PLS Regression Model Provides interpretability, accuracy Y-Scrambling Measure of model robustness

Outline (3) Problem description Methodologies  Informatics flow  Selecting descriptors CNT surfaces  Derive critical descriptors for mechanical properties  Modular extension of QSPR to two types of defects Comparison to experimental results  Investigating load transfer mechanisms in multi-walled CNTs  Prediction of monolayer graphene mechanical properties Future work Conclusion 11

12 CNT surfaces – descriptors DescriptorsDefinition Theoretical Radius (Å)Theoretical radius of perfect nanotube % Methyl GroupsPercentage of surface functionalized methyl groups # Missing C’s (C M )Number of missing due to a vacancy defect # Methyl Groups (M N )Number of methyl functional groups M N / C T Ratio of methyl groups to total number of carbons C M / C T Ratio of missing carbons to total number of carbons # Single DefectsNumber of single defect types # Non-sp 2 C’s (C N2 )Number of non-sp 2 hybridized carbons C N2 / C T Ratio of non-sp 2 hybridized carbons to total number of carbons Surface Area (S P )Total surface area of nanotube (uses average radius) Defect Surface Area (S D )Surface area of defects S D / S P Ratio of defect area to total surface area Chiral AngleChiral angle Started with ~20 Descriptors, Massaged & Down-selected to 2 & 3

Young’s modulus – vacancy defect Critical descriptors  C N2 / C T – captures size and type of defect  Chiral angle Accurate & interpretable QSPRs  20-descriptor & 2-descriptor model have similar accuracy  2-descriptor interpretability improved 13 Two Critical Descriptors - C N2 / C T & chiral angle

Young’s modulus – vacancy & methyl defects 14 ‘Modularly extend’ to more than one type of defect (f(x,y) = ax + by +…) Identify critical descriptors  C N2 / C T – captures changes to CNT surface structure  Chiral angle  M N / C T – captures intrinsic properties of functional group Loadings plot clear indicate methyl group is new cluster PLS R 2 values ~ same for vacancy & vacancy / methyl studies Easy to add new groups - no need to start from scratch Easy to use higher fidelity calculations - for specific groups only

Outline (4) Problem description Methodologies  Informatics Flow  Selecting Descriptors CNT surfaces  Derive critical descriptors for mechanical properties  Modular extension of QSPR to two types of defects Comparison to experimental results  Investigating load transfer mechanisms in multi-walled CNTs  Prediction of monolayer graphene mechanical properties Future Work Conclusion 15

Investigating load transfer mechanisms in multi-walled carbon nanotubes Observation  Load transfer increase of 2.4 (maximum is 3)  Inner CNT ~95% area of outer CNT (assume area is equal) Plausible explanations  Assume all walls participate equally & load transfer is simultaneous  YM 4 = 90% of YM 0 ;  C N2 / C T predicts ~0% (off by 100x)  Assume walls do not participate equally (1.0, 0.8, 0.6) & load transfer is not simultaneous (Assume) no decrement to Young’s modulus (Observation / assumption) Inner walls do not participate until ~2% strain  1050 GPA (0-2% strain for 1 wall) GPA (2-4% strain for 3 walls) = 941 GPA 16

Monolayer graphene mechanical properties Our equation:  (Young’s Modulus) = -2,225 C N2 / C T M N / C T Elastic moduli (E 2D ) = volumetric Young’s modulus * thickness Experimental  Monolayer graphene: 342 N/m N/m  Monolayer graphene oxide: N/m Computational  Monolayer graphene: 382 N/m  Monolayer graphene oxide: 212 N/m Using our equation to predict graphene oxide  40% sp 3 bonding with oxygen / carbon ratio of 1:5 C N2 / C T ~ 0.4 and M N / C T ~ 1/6 Use methyl descriptor as approximation for epoxide & hydroxyl groups  Predicts E 2D of 150 N/m 17

Outline (5) Problem description Methodologies  Informatics Flow  Selecting Descriptors CNT surfaces  Derive critical descriptors for mechanical properties  Modular extension of QSPR to two types of defects Comparison to experimental results  Investigating load transfer mechanisms in multi-walled CNTs  Prediction of monolayer graphene mechanical properties Future work Conclusion 18

Future work New descriptors  Experimental  Length scales  Higher fidelity, other types  Other functional groups Complex systems  Quantify load transfer in multi-walled CNTs  Optimize two interfacial transfers (CNT-polymer, inter-wall)  Optimize interfacial stress transfer & dispersions 19

Conclusion Critical descriptors for mechanical properties  C N2 / C T – captures changes to CNT surface structure  M N / C T – captures intrinsic properties of functional group  Chiral angle – effect at smaller radii; (not discussed) should be negligible for larger radii New types of defects can be successfully modeled as new descriptors  (CURRENT) Evaluation of complex systems require large, complex simulations  (NEW) Information in descriptors; easy to add experimental / higher fidelity ONLY to descriptors that need it  (NEW) Complex systems can ‘modularized’ Piece-wise simple systems or f(x,y) = ax + by +… Computational models  Good for qualitative explanations  Potential direct link between computational-experimental (Raman spectroscopy) Using descriptors – creates straightforward method to update with experimental data (quantitative accuracy) 20

Thank you! Questions? 21