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

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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

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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

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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

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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

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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

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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

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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)

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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

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

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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

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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

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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

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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

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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

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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 ; 0.0002622 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) + 832 GPA (2-4% strain for 3 walls) = 941 GPA 16

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Monolayer graphene mechanical properties Our equation: (Young’s Modulus) = -2,225 C N2 / C T + 1975 M N / C T Elastic moduli (E 2D ) = volumetric Young’s modulus * thickness Experimental Monolayer graphene: 342 N/m +- 30 N/m Monolayer graphene oxide: 145.3 +- 16.3 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

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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

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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

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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

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Thank you! Questions? 21

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