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Minority Leaders SensorsProgram Review

Presented byDimitris C. Lagoudas

Gary D. Seidel

Micromechanics Modeling of the Electrical Conductivity of Carbon Nanotube-Epoxy

Nanocomposites

25 – 28 February 2008

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Project Outline

• Project Members• Problem Statement • Approach• Accomplishments/Successes • Status Summary

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Project Members

• AF POC: Dr. Ajit Roy• Project Lead: Dr. Dimitris C. Lagoudas• Research Collaborators:

– Dr. Gary D. Seidel (Postdoc)

• Students:– Kelli Boehringer (Undergraduate)

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� Electrical Conductivity governed by electron hopping

� Electrical Conductivity: 9 order increase at 1% wt (RoM: 12 Orders)

Motivation for Carbon Nanotube-Polymer Multifunctional Nanocomposites

► Large disparity between CNT, Polymer Properties:

► Measured nanocomposite properties less than some anticipated

� Young’s Modulus: CNT 2-3 Orders Larger than Epoxy

� Electrical Conductivity: CNT 14-18 Orders Larger than Epoxy

� Thermal Conductivity: CNT 4 Orders Larger than Epoxy

� Young’s Modulus: 20% increase at 1% wt (RoM: +550%)

� Thermal Conductivity: 30% increase to at 1% weight (RoM: +1200%)

► Nanoscale effects identified as having strong influence on nanocomposite properties:� Load transfer governed by van der Waals forces and

functionalization� Thermal Conductivity governed by interface thermal resistance

Objective:

Incorporate Nanoscale Effects in Continuum Micromechanics Models for CNT Nanocomposites

Challenge:

Can Micromechanics Provide Reasonable Estimates

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Nanocomposite Materials

impurity

Magnification: 200K

TEM Study of XD Grade Material

Single Wall

Double CNTs

Multiple CNTs

Twisted Bundle

• XD CNTs: mixture of single, double and multiwall CNTs optimized for enhanced electrical performance and cost savings at low loading levels (also contains amorphous carbon and impurities).

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Transmission Optical MicroscopyXD CNT-EPON 862 Nanocomposite

0.015 wt% XDCNT

Few percolating networks of smaller clusters were observed for 0.015wt% XDCNT specimens; big cluster sizes were observed for 0.03wt% XDCNT specimens which are well distributed forming percolated networks.Price: $50 per gramYield: 100 lbs/day Source: Carbon Nanotechnologies Inc. (CNI), Houston , Texas

250µm

0.03 wt% XDCNT

250µm

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Between 0.015wt% and 0.03wt% Conductivity Jumps 10 Orders of Magnitude and Becomes Frequency Independent Indicative of Percolation

Frequency Dependence Indicative of Insulating Material

Frequency Independent Indicative of Conducting Material

Measurement of Nanocomposite Electrical Conductivity

DC Equivalent

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Measurement of Nanocomposite Electrical Conductivity

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+14

1.E+16

0 0.001 0.002 0.003 0.004 0.005Cabon Nanotube Volume Fraction

Nor

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TAMU XD DATA TAMU SWCNT DATA

SWCNT Data

XD CNT Data

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Approach

� Generate micromechanics model for predicting the effective electrical conductivity of XD CNT nanocomposites

� Study the effects of metallic vs. non-metallic CNT fraction

� Study the effects of clustering of nanotube bundles

� Study the non-continuum effects of electron hopping

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� Dispersion difficulties lead to clustering of carbon nanotubes

� How to draw needed input from molecular dynamics simulations or nanoscale measurements

Nanocomposite Modeling Challenges

• Specimens Provided by Dr. E. Barrera, Rice UniversityTEM Imaging by Piyush Thakre, Texas A&M University

► Features which may have strong influence on model predictions:

� Interphase regions due to functionalization

� Orientation Effects due to Difficulty in alignment of carbon nanotubes

� Curvature/twisting effects of carbon nanotubes

� Nanoscale Load transfer

� Accounting for non-continuum effects

250 nm

100 nm100 nm

100 nm

20 nm

Objective:

Incorporate Nanoscale Effects in Continuum Micromechanics Models for CNT Nanocomposites

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Micromechanics Model for Nanocomposite Electrical Conductivity

1y

3y2y

Macroscale Boundary Value Problem

1x

3x2x

ˆi i i iJ n J n=

ˆφ φ=

Effective CNT + Interphase

2y% 3y%1y%

Microscale RVE

Nanoscale RVE (Composite Cylinder Assemblage)

Interphase

2y% 3y%

1y%

CNT

Effective Nanocomposite

Governing Differential Equations: Electrical ConductivityConservation of Charge Electric Field Electric Flux Constitutive Relation

0∇ ⋅ =J φ= −∇E eff=J σ E

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Micromechanics Model for Nanocomposite Electrical Conductivity: 2-Step Mori-Tanaka and CCM

Effective Nanocomposite Electrical Conductivity

Where the fraction of metallic CNTs is identified as:

Using Mori-Tanaka Method to get Concentration Factors

Effective Metallic and Semi-Conducting Conductivities Obtained from Composite Cylinder Model

Non-metallic CNTscloser to matrix in conductivity than metallic CNTs

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Electron Hop Layer

Matrix Material

2x 3x

1x

Model Parameters

CNT

Use micromechanics model to investigate both electron hopping and formation of conductive paths in a parametric study for XD CNT Nanocomposites

� Electron Hopping Parameters: range and frequency (thickness & conductivity)

� Metallic vs Non-Metallic CNT Fraction

� Distribution of CNTs: conductive path formation (effective aspect ratio)

� Fraction of SWCNT vs MWCNT in XD

� Geometry of CNTs: radius, length, number of walls

� Parameters or Interest:

Btwn Matrix and CNTBtwn Matrix and CNTHopping Conductivity

5nm – 30nm5nm – 30nmHopping Range

100 to Infinite500 to InfiniteAspect Ratio

1/3 to 11/3 to 1Metallic Fraction (λ)

MWCNTSWCNTVariable

� Estimated Ranges for Parameters or Interest:

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1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+14

1.E+16


Nor

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MWCNT AR = 100 Micromechanics Model SWCNT AR = 500 Micromechanics Model

MWCNT 100x AR Micromechanics Model SWCNT 100x AR Micromechanics Model

SWCNT Data

SWCNT Model

λ = 1/3

totalfc

XD CNT Data

MWCNT Model

SWCNT Model 100x AR

MWCNT Model 100x AR

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+14

1.E+16


Nor

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MWCNT AR = 100 Micromechanics Model SWCNT AR = 500 Micromechanics Model

SWCNT Data

SWCNT Model

λ = 1/3

totalfc

XD CNT Data

MWCNT Model

Effects of Aspect Ratio on Nanocomposite Conductivity

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+14

1.E+16


Nor

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TAMU XD DATA TAMU SWCNT DATAMWCNT AR = 100 Micromechanics Model SWCNT AR = 500 Micromechanics ModelMWCNT 100x AR Micromechanics Model SWCNT 100x AR Micromechanics ModelMWCNT Infinite AR Micromechanics Model SWCNT Infinite AR Micromechanics Model

SWCNT Data

SWCNT Model

λ = 1/3

totalfc

XD CNT Data

MWCNT Model

SWCNT Model 100x AR

MWCNT Model 100x AR

SWCNT Model Infinite AR

MWCNT Model Infinite AR

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Effects of Electron Hopping on Nanocomposite Conductivity

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+14

1.E+16


Nor

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ized

Ele

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SWCNT AR = 5000 Micromechanics Model SWCNT Infinite AR Micromechanics Model

SWCNT Model w/ 30nm Hop Cond 1e10xMatrix SWCNT Model w/ 131nm Hop Cond 1e10xMatrix

SWCNT Data

XD CNT Data

Electron HoppingRange: 30nmConductivity: 1E10 x Matrix(percolation at 0.011)

Electron HoppingRange: 130nmConductivity: 1E10 x Matrix


SWCNT Model

λ = 1/3

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1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+14

1.E+16


Nor

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ized

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SWCNT All Metallic

SWCNT Data

XD CNT Data


SWCNT Model 1/3 Metallic

SWCNT Model All Metallic

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+14

1.E+16


Nor

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SWCNT Model w/ 30nm Hop Cond 1e10xMatrix SWCNT Model w/ 131nm Hop Cond 1e10xMatrix

SWCNT Data

XD CNT Data

Electron HoppingRange: 30nm, 1/3 Metallic

Electron HoppingRange: 130nm,1/3 Metallic


SWCNT Model 1/3 Metallic1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+14

1.E+16


Nor

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ized

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TAMU XD DATA TAMU SWCNT DATASWCNT AR = 5000 Micromechanics Model SWCNT Infinite AR Micromechanics ModelSWCNT Model w/ 30nm Hop Cond 1e10xMatrix SWCNT Model w/ 131nm Hop Cond 1e10xMatrixSWCNT Model w/ 30nm Hop Cond 1e10xMatrix AM

SWCNT Data

XD CNT Data





Electron HoppingRange: 30nm, All Metallic

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

1.E+12

1.E+14

1.E+16


Nor

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TAMU XD DATA TAMU SWCNT DATASWCNT AR = 5000 Micromechanics Model SWCNT Infinite AR Micromechanics ModelSWCNT Model w/ 30nm Hop Cond 1e10xMatrix SWCNT Model w/ 131nm Hop Cond 1e10xMatrixSWCNT Model w/ 30nm Hop Cond 1e10xMatrix AM SWCNT Model w/ 131nm Hop Cond 1e10xMatrix AM

SWCNT Data

XD CNT Data







Effects of Metallic Fraction on Nanocomposite Conductivity

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Conclusions and Future Work

� Conclusions• Nanocomposite effective electrical conductivity is sensitive to changes in

aspect ratio (clustering).

� Future Work• Parametric study on SWCNT vs MWCNT fraction

• Computational micromechanics clustering model• Computational micromechanics model for combined effects clustering and

electron hopping.

• Electron hopping can result in a significant low volume fraction percolation event for SWCNTs if the hopping range is on order of 130nm.

• Increases in metallic fraction of CNTs can further decrease low volume fraction percolation limit associated with electron hopping.

Initial indication is that XDCNT-epoxy nanocomposites are good for electrostatic discharge applications, but several model parameters need to explicitly identified to improve model predictions.

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Acknowledgements:• The research acknowledges the support of U.S. Air Force AFRL Contract No. FA8650-

05-D-1912, Minority Leaders Program• Dr. Zoubeida Ounaies and Mr. Sumanth Banda at TAMU Electroactive Materials Lab• Dr. Yordanos Bistrat• Mr. Piyush Thakre for assistance with TEM imaging

Gary Don SeidelPostdoc

Texas A&M [email protected]

Dr. Dimitris LagoudasJohn and Bea Slattery Chair in Aerospace Engineering


Kelli BoehringerUndergraduate


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Status Summary

• Summary Gantt Chart would be most helpful.• Show a Gantt Chart or timeline for the overall proj ect by quarters• Show a Gantt Chart or timeline for each step of the project• Indicate major and minor milestones for the current contract period

and projected key event beyond the contract period (include current period and future milestones on Gantt Chart or Time line)

Project Schedule

Project Oct

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2.1.x.x RF Sensors Research

2.1.x.x a Title of 2.1.x.x a

2.1.x.x b Title of 2.1.x.x b

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Minority Leaders Sensors Program Review - Virginia Techgdseidel/SubPages/Access/ML_New_Orleans... · Minority Leaders Sensors Program Review Presented by ... conductive path formation