Exceptionally high Young's modulus observed for individual carbon nanotubes
TL;DR: In this article, the amplitude of the intrinsic thermal vibrations of isolated carbon nanotubes was measured in the transmission electron microscopy (TEM) and it was shown that they have exceptionally high Young's moduli, in the terapascal (TPa) range.
Abstract: CARBON nanotubes are predicted to have interesting mechanical properties—in particular, high stiffness and axial strength—as a result of their seamless cylindrical graphitic structure1–5. Their mechanical properties have so far eluded direct measurement, however, because of the very small dimensions of nanotubes. Here we estimate the Young's modulus of isolated nanotubes by measuring, in the transmission electron microscope, the amplitude of their intrinsic thermal vibrations. We find that carbon nanotubes have exceptionally high Young's moduli, in the terapascal (TPa) range. Their high stiffness, coupled with their low density, implies that nanotubes might be useful as nanoscale fibres in strong, lightweight composite materials.
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TL;DR: A review of recent advances in carbon nanotubes and their composites can be found in this article, where the authors examine the research work reported in the literature on the structure and processing of carbon Nanotubes.
4,709 citations
Cites background from "Exceptionally high Young's modulus ..."
...[34] Treacy MMJ, Ebbesen TW, Gibson TM....
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...Recent investigations have shown that carbon nanotubes possess remarkable mechanical properties, such as exceptionally high elastic modulus [34,35], large elastic strain and fracture strain sustaining capability [41,42]....
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...[34] first investigated the elastic modulus of isolated multi-walled nanotubes by measuring, in the Fig....
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TL;DR: In this paper, the Young's modulus, strength, and toughness of nanostructures are evaluated using an atomic force microscopy (AFM) approach. And the results showed that the strength of the SiC NRs were substantially greater than those found previously for larger SiC structures, and they approach theoretical values.
Abstract: The Young's modulus, strength, and toughness of nanostructures are important to proposed applications ranging from nanocomposites to probe microscopy, yet there is little direct knowledge of these key mechanical properties. Atomic force microscopy was used to determine the mechanical properties of individual, structurally isolated silicon carbide (SiC) nanorods (NRs) and multiwall carbon nanotubes (MWNTs) that were pinned at one end to molybdenum disulfide surfaces. The bending force was measured versus displacement along the unpinned lengths. The MWNTs were about two times as stiff as the SiC NRs. Continued bending of the SiC NRs ultimately led to fracture, whereas the MWNTs exhibited an interesting elastic buckling process. The strengths of the SiC NRs were substantially greater than those found previously for larger SiC structures, and they approach theoretical values. Because of buckling, the ultimate strengths of the stiffer MWNTs were less than those of the SiC NRs, although the MWNTs represent a uniquely tough, energy-absorbing material.
4,627 citations
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TL;DR: In this article, a review of the progress to date in the field of mechanical reinforcement of polymers using nanotubes is presented, and the most promising processing methods for mechanical reinforcement are discussed.
3,770 citations
Cites background from "Exceptionally high Young's modulus ..."
...[34] measured the amplitude of intrinsic thermal vibrations observed in the TEM....
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TL;DR: In this paper, in situ transmission electron microscopy studies provided information regarding composite deformation mechanisms and interfacial bonding between the multi-wall carbon nanotubes and polymer matrix, indicating significant load transfer across the nanotube-matrix interface.
Abstract: Multiwall carbon nanotubes have been dispersed homogeneously throughout polystyrene matrices by a simple solution-evaporation method without destroying the integrity of the nanotubes. Tensile tests on composite films show that 1 wt % nanotube additions result in 36%–42% and ∼25% increases in elastic modulus and break stress, respectively, indicating significant load transfer across the nanotube-matrix interface. In situ transmission electron microscopy studies provided information regarding composite deformation mechanisms and interfacial bonding between the multiwall nanotubes and polymer matrix.
2,431 citations
References
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01 Jan 1965
TL;DR: This book discusses ODEs, Partial Differential Equations, Fourier Series, Integrals, and Transforms, and Numerics for ODE's and PDE's, as well as numerical analysis and potential theory, and more.
Abstract: PART A: ORDINARY DIFFERENTIAL EQUATIONS (ODE'S). Chapter 1. First-Order ODE's. Chapter 2. Second Order Linear ODE's. Chapter 3. Higher Order Linear ODE's. Chapter 4. Systems of ODE's Phase Plane, Qualitative Methods. Chapter 5. Series Solutions of ODE's Special Functions. Chapter 6. Laplace Transforms. PART B: LINEAR ALGEBRA, VECTOR CALCULUS. Chapter 7. Linear Algebra: Matrices, Vectors, Determinants: Linear Systems. Chapter 8. Linear Algebra: Matrix Eigenvalue Problems. Chapter 9. Vector Differential Calculus: Grad, Div, Curl. Chapter 10. Vector Integral Calculus: Integral Theorems. PART C: FOURIER ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS. Chapter 11. Fourier Series, Integrals, and Transforms. Chapter 12. Partial Differential Equations (PDE's). Chapter 13. Complex Numbers and Functions. Chapter 14. Complex Integration. Chapter 15. Power Series, Taylor Series. Chapter 16. Laurent Series: Residue Integration. Chapter 17. Conformal Mapping. Chapter 18. Complex Analysis and Potential Theory. PART E: NUMERICAL ANALYSIS SOFTWARE. Chapter 19. Numerics in General. Chapter 20. Numerical Linear Algebra. Chapter 21. Numerics for ODE's and PDE's. PART F: OPTIMIZATION, GRAPHS. Chapter 22. Unconstrained Optimization: Linear Programming. Chapter 23. Graphs, Combinatorial Optimization. PART G: PROBABILITY STATISTICS. Chapter 24. Data Analysis: Probability Theory. Chapter 25. Mathematical Statistics. Appendix 1: References. Appendix 2: Answers to Odd-Numbered Problems. Appendix 3: Auxiliary Material. Appendix 4: Additional Proofs. Appendix 5: Tables. Index.
3,643 citations
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NEC1
TL;DR: In this article, the authors used a variant of the standard arc-discharge technique for fullerene synthesis under a helium atmosphere, where a carbonaceous deposit formed on one of the graphite rods, consisting of a macroscopic (diameter of about 5 mm) cylinder.
Abstract: INTEREST in carbon fibres1,2 has been stimulated greatly by the recent discovery of hollow graphitic tubules of nanometre dimensions3. There has been much speculation about the properties and potential application of these nanotubes4–8. Theoretical studies predict that their electronic properties will depend on their diameter and degree of helicity4,5. Experimental tests of these ideas has been hampered, however, by the lack of macroscopic quantities of the material. Here we report the synthesis of graphitic nanotubes in gram quantities. We use a variant of the standard arc-discharge technique for fullerene synthesis under a helium atmosphere. Under certain conditions, a carbonaceous deposit forms on one of the graphite rods, consisting of a macroscopic (diameter of about 5 mm) cylinder in which the core comprises pure nanotubes and nanoscale particles in high yield. The purity and yield depend sensitively on the gas pressure in the reaction vessel. Preliminary measurements of the conductivity of the bulk nanotube material indicate a conductivity of about 100 S cm–11.
2,908 citations
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TL;DR: It is found that the strain energy per carbon relative to an unstrained graphite sheet goes as the inverse square of the tubule radius, R, and is insensitive to other aspects of the lattice structure, indicating that relationships derivable from continuum elastic theory persist well into the small radius limit.
Abstract: Using both empirical potentials and first-principles total-energy methods, we have examined the energetics and elastic properties of all possible graphitic tubules with radii less than 9 \AA{}. We find that the strain energy per carbon atom relative to an unstrained graphite sheet varies as 1/${\mathit{R}}^{2}$ (where R is the tubule radius) and is insensitive to other aspects of the lattice structure, indicating that relationships derivable from continuum elastic theory persist well into the small-radius limit. We also predict that this strain energy is much smaller than that in highly symmetric fullerene clusters with similar radii, suggesting a possible thermodynamic preference for tubular structures rather than cage structures. The empirical potentials further predict that the elastic constants along the tubule axis generally soften with decreasing tubule radius, although with a distinct dependence on helical conformation.
840 citations
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TL;DR: Graphite whiskers have been grown in a dc arc under a pressure of 92 atmospheres of argon and at 3900°K as discussed by the authors, with recoverable lengths up to 3 cm. They are embedded in a solid matrix of graphite which builds up by diffusion of carbon vapor from the positive to the negative electrode.
Abstract: Graphite whiskers have been grown in a dc arc under a pressure of 92 atmospheres of argon and at 3900°K. They are embedded in a solid matrix of graphite which builds up by diffusion of carbon vapor from the positive to the negative electrode. Diameters range from a fraction of a micron to over five microns, with recoverable lengths up to 3 cm. They consist of one or more concentric tubes, each tube being in the form of a scroll, or rolled‐up sheet of graphite layers, extending continuously along the length of the whisker, with the c axis exactly perpendicular to the whisker axis. They exhibit a high degree of flexibility, tensile strengths up to 2000 kg‐mm−2, Young's modulus in excess of 7×1012 dyne‐cm−2, and values of room‐temperature resistivity of around 65 μohm‐cm, which approximates the single crystal value.
592 citations