1. Northwestern University Rod Ruoff Nanotechnology Fracture Mechanics of One- Dimensional Nanostructures

2. Northwestern University Rod Ruoff Nanotechnology Carbon Nanotube Source SEM image of powdered cathode deposit core material with 30-40% MWCNT content from MER Corp. SEM image of separated MWCNTs on a silicon wafer, after fractionation. Arc-grown Multi-wall Carbon Nanotubes (MWCNTs) from MER Corp. AZ. were studied in this work. A simple fractionation process was used to remove some impurities and increase nanotube concentration.

3. Northwestern University Rod Ruoff Nanotechnology Testing Tool: Nanomanipulator A home-built nanomanipulator is used to perform mechanics study inside vacuum chamber of an scanning electron microscope (SEM). X-Y stage Piezo bimorph Z stage Cantilever Holder Specimen/ Cantilever Holder X-Y Stage Z-stage Piezoelectric Actuator Nanomanipulator inside vacuum chamber of FEI Nova 600 SEM (Ruoff group) Home-built nano-manipulator

4. Northwestern University Rod Ruoff Nanotechnology Nanoscale Tensile Test Experimental Setup X-Y Stage rigid cantilever soft cantilever Z Stage Tensile Test Schematic L L+  s Atomic force microscope (AFM) cantilevers are used as manipulation tools and force-sensing elements. MWCNT

5. Northwestern University Rod Ruoff Nanotechnology In situ Clamping - EBID Electron beam induced deposition (EBID) is the process of using a high- intensity electron beam to deposit structures on a scanned surface. EBID is commonly used to make clamps in situ inside SEM. A CNT in contact with an AFM tip, before and after EBID clamping EBID principle Hydrocarbon molecules EBID clamp Exposure area

6. Northwestern University Rod Ruoff Nanotechnology “Sword-in-sheath” Fracture Outer shell Inner shells Cross-sectional area: D   : inter-layer separation of graphite, 0.34 nm Multi-wall carbon nanotubes fracture in a “sword-in sheath” manner during tensile test.

7. Northwestern University Rod Ruoff Nanotechnology MWCNT Diameter Measurement (a) AFM chip holder model AFM cantilevers (c) Gatan TEM straining holder (model 654) (d) SEM and TEM images of a MWCNT fragment attached to an AFM tip. (b) An AFM chip in the AFM chip holder Cantilever holders were designed to hold a shortened AFM chip for nanotube diameter measurement in TEM.

8. Northwestern University Rod Ruoff Nanotechnology Stress & Strain Measurements The whole tensile testing process was recorded by taking SEM images at each loading step.

9. Northwestern University Rod Ruoff Nanotechnology MWCNT Tensile Testing Result Fracture Strength Elastic Modulus Average elastic modulus: ~ 910 GPa

10. Northwestern University Rod Ruoff Nanotechnology Multiple Loading (Tube #6) Test # Gauge Length (  m) Breaking Force (nN) Tensile Strength (GPa) Failure Strain (%) Elastic Modulus (GPa) 14.08220 21  1.41.8  0.31200  210 23.75240 23  1.41.9  0.31250  210 33.46420 41  2.63.0  0.21230  130 (1)(2)(3)

11. Northwestern University Rod Ruoff Nanotechnology Nanoparticle Chain Aggregates Breaking Force: 42  25 nN Tensile Strength: 40 -100 MPa Elastic Modulus : 200 - 600 MPa Particle Contact Force: 8  4 nN Tensile Testing Stretching a chain Contact Force Measurement Carbon nanoparticle chain aggregates Nanoparticle diameter: 25-35 nm Chain length: ~ 2  m

12. Northwestern University Rod Ruoff Nanotechnology Nonlinearity: Large Deflection + Misalignment where F x =F  sin  and F y =F  cos  (Transformation; Converting to elliptic integrals) F(k),F( ,k) complete and incomplete elliptic integral of first kind. k and  1 are obtained from angle  0 with following relationships: L F x y yy 00 xx  s FyFy FxFx (x,y)

13. Northwestern University Rod Ruoff Nanotechnology Experimental Data Analysis Slope  0 (degree) Loading Angle  (degree) Applied Load Vertical Deflection  y Linear (  N) Analytical (  N) Error (%) Measured (  m) Linear (  m) Analytical (  m) 11.036.825.329.714.842.942.242.3 17.45.523.524.95.668.770.870.3 9.2242.020.823.913.030.632.232.3 11.62.019.419.61.041.440.540.4 15.024.327.631.412.152.952.452.3 AFM cantilevers were used as force-sensing elements in our nanoscale tensile testing experiments on templated carbon nanotubes inside SEM. Large deflection of the cantilever beam was encountered in the tests along with non-ideal alignment of the specimens. The linear analysis underestimated the applied load up to 15 %.

14. Northwestern University Rod Ruoff Nanotechnology Error in Linear Estimation Normalization Linear analysis Analytical analysis