Developing Descriptors to Predict Mechanical Properties of Nanotubes

Dr. Tammie L. BordersMay 16, 2013

2

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

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 / strength2) Intra-wall bonding – load transfer

5

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

6

Informatics flow

MEASUREMENTS• Process parameters• Characterization• Databases

THEORY• Atomic calculations• Mesoscale calculations• Continuum calculations

CORRELATIONS• Clustering• Feature selection• Data mining & analysis

KNOWLEDGE• Process-structure- property relationships• Materials discovery• Hidden data trends

7

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

8

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

Selecting Descriptors is a Human-in-the-Loop, Iterative Process with the Goal of Simultaneously Improving Model Interpretability and Accuracy

Initial Guess (20)

9

Selecting descriptors- Clustering & feature selection

Star PlotsIdentifies descriptor stable / robustness;

Provides measure of strength / correlation

PCA Loadings PlotIdentifies clusters, important descriptors

PC1 & PC2 account for 69% of variance

10

Selecting descriptors- Multivariate analysis and validation

PLS Regression ModelProvides interpretability, accuracy

Y-ScramblingMeasure of model robustness

11

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

12

CNT surfaces – descriptors Descriptors Definition

Theoretical Radius (Å) Theoretical radius of perfect nanotube

% Methyl Groups Percentage of surface functionalized methyl groups

# Missing C’s (CM) Number of missing due to a vacancy defect

# Methyl Groups (MN) Number of methyl functional groups

MN / CT Ratio of methyl groups to total number of carbons

CM / CT Ratio of missing carbons to total number of carbons

# Single Defects Number of single defect types

# Non-sp2 C’s (CN2) Number of non-sp2 hybridized carbons

CN2 / CT

Ratio of non-sp2 hybridized carbons to total number of carbons

Surface Area (SP) Total surface area of nanotube (uses average radius)

Defect Surface Area (SD) Surface area of defects

SD / SP Ratio of defect area to total surface area

Chiral Angle Chiral angle

Started with ~20 Descriptors, Massaged & Down-selected to 2 & 3

13

Young’s modulus – vacancy defect

Critical descriptors CN2 / CT – captures size and type of

defect Chiral angle

Accurate & interpretable QSPRs 20-descriptor & 2-descriptor model

have similar accuracy 2-descriptor interpretability improved

Test Set R2Train R2

Test Descriptors

3A 2-21 Å

0.95 0.76

Surface Area (SP)

Chiral Angle

CN2 / CT

% Double Defects

3B 2-21 Å

0.94 0.85

Theoretical radius

Chiral Angle

CN2 / CT

Test set R2Train Descriptors, Individual Coefficients

Chiral Angle Individual R2

Measure of Defects

Individual R2

3C 2-21 Å 0.92 Chiral Angle

0.25 CN2 / CT 0.66

Two Critical Descriptors - CN2 / CT & 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 CN2 / CT – captures changes to CNT

surface structure Chiral angle MN / CT – captures intrinsic

properties of functional group Loadings plot clear indicate methyl

group is new cluster PLS R2 values ~ same for vacancy &

vacancy / methyl studies

Easy to add new groups - no need to start from scratchEasy to use higher fidelity calculations - for specific groups only

Model R2Train R2

Test Descriptors

20-descriptor QSPR 0.95 0.89

Surface Area (SP)

Chiral Angle

# Single Defects % Double Defects

CN2 / CT

% Methyl

3-descriptor QSPR 0.92 0.93

Chiral Angle

CN2 / CT

MN / CT

15

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

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

YM4 = 90% of YM0; 0.0002622 CN2 / CT 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

Sample Gauge Length (nm)

Inner Diameter

(nm)

Outer Diameter

(nm)

Broken shells

Total Shells

CN2 / CT (All single

vacancies)

CN2 / CT

(All methyl groups)

Young’s Modulus

(GPa)

Load transfer increase

1 1,852 - 14.72 1 12 - - 990

2 2,024 - 15.71 1 17 - - 1,049

3 2,105 - 25.97 1 2 or 3 - - 1,105

4 1,035 37.44 39.48 3 18 0.0002622 0.0000874 932 2.4 / 3

ollAF

Y

Monolayer graphene mechanical properties

Our equation: (Young’s Modulus) = -2,225 CN2 / CT + 1975 MN / CT

Elastic moduli (E2D) = 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% sp3 bonding with oxygen / carbon ratio of 1:5

CN2 / CT ~ 0.4 and MN / CT ~ 1/6 Use methyl descriptor as approximation for epoxide & hydroxyl groups

Predicts E2D of 150 N/m

17

18

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

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 CN2 / CT – captures changes to CNT surface structure

MN / CT – 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