^{1,2}, K. C. Kou

^{2}, Kostya (Ken) Ostrikov

^{1,3,a)}, J. Q. Zhang

^{2}and Z. C. Wang

^{2}

### Abstract

Here we report on an unconventional Ni–P alloy-catalyzed, high-throughput, highly reproducible chemical vapor deposition of ultralong carbon microcoils using acetylene precursor in the temperature range . Scanning electron microscopy analysis reveals that the carbon microcoils have a unique double-helix structure and a uniform circular cross-section. It is shown that double-helix carbon microcoils have outstanding superelastic properties. The microcoils can be extended up to 10–20 times of their original coil length, and quickly recover the original state after releasing the force. A mechanical model of the carboncoils with a large spring index is developed to describe their extension and contraction. Given the initial coil parameters, this mechanical model can successfully account for the geometric nonlinearity of the spring constants for carbon micro- and nanocoils, and is found in a good agreement with the experimental data in the whole stretching process.

This work is partially supported by the Australian Research Council, the China Scholarship Council, and CSIRO. The authors would like to thank A. Das Arulsamy for fruitful discussions. The authors also acknowledge the use of facilities and technical assistance at the Australian Microscopy and Microanalysis Research Facility, Electron Microscopy Unit of the University of Sydney, Australia.

I. INTRODUCTION

II. EXPERIMENTAL DETAILS

III. RESULTS AND DISCUSSION

A. Morphologies and microstructure of the CMCs

B. Stretching behavior of the CMCs

C. Mechanical model of CNCs and CMCs

1. CNCs

2. CMCs

IV. CONCLUSIONS

### Key Topics

- Coils
- 18.0
- Carbon
- 17.0
- Elasticity
- 14.0
- Mechanical properties
- 11.0
- Scanning electron microscopy
- 8.0

## Figures

SEM characterization of the as-grown CMCs.

SEM characterization of the as-grown CMCs.

Representative SEM image of the extended states of superelastic double-helix CMCs.

Representative SEM image of the extended states of superelastic double-helix CMCs.

A series of photos of continuous changes in the coil pitch angle and diameter.

A series of photos of continuous changes in the coil pitch angle and diameter.

Tensile model of a large-index spring with the ends fixed. Here, is the tensile load, is the torsional moment, is the wire diameter, is the spring radius, and is the pitch angle.

Tensile model of a large-index spring with the ends fixed. Here, is the tensile load, is the torsional moment, is the wire diameter, is the spring radius, and is the pitch angle.

(a) Developed elongation of the spring. (b) Calculation of the polar moment of inertia of the coil cross-section. (c) Spring cross-section with axial load. Here, is the spring length, is the spring elongation, is the initial pitch angle, is the final pitch angle, is the wire radius, is the wire area, and is the tensile load.

(a) Developed elongation of the spring. (b) Calculation of the polar moment of inertia of the coil cross-section. (c) Spring cross-section with axial load. Here, is the spring length, is the spring elongation, is the initial pitch angle, is the final pitch angle, is the wire radius, is the wire area, and is the tensile load.

The rate of contraction of the spring diameter vs the pitch angle for a single-helix spring with fixed ends. In the inset, curves 1, 2, 3, 4, and 5 correspond to the initial pitch angles of 0°, 5°, 10°, 15°, and 20°, respectively.

The rate of contraction of the spring diameter vs the pitch angle for a single-helix spring with fixed ends. In the inset, curves 1, 2, 3, 4, and 5 correspond to the initial pitch angles of 0°, 5°, 10°, 15°, and 20°, respectively.

The dependence of Poisson’s ratio on the deflection factor of a single-helix spring with fixed ends at . In the inset, curves 1, 2, and 3 correspond to , 0.30, and 0.35, respectively.

The dependence of Poisson’s ratio on the deflection factor of a single-helix spring with fixed ends at . In the inset, curves 1, 2, and 3 correspond to , 0.30, and 0.35, respectively.

Deflection factor vs the coil extension for a single-helix spring with fixed ends. Curves 1, 2, 3, 4, and 5 correspond to the initial pitch angles of 0°, 5°, 10°, 15°, and 20°, respectively.

Deflection factor vs the coil extension for a single-helix spring with fixed ends. Curves 1, 2, 3, 4, and 5 correspond to the initial pitch angles of 0°, 5°, 10°, 15°, and 20°, respectively.

Spring constant vs the coil elongation for a single-helix CNC. Here, the nanocoil radius , the nanowire diameter and the shear modulus . In (a), the inner diameter is zero, curves 1 and 2 correspond to the coil pitches of 120 and 2000 nm, respectively. In (b), the coil pitch is 2000 nm, curves 3, 4, 5, and 6 correspond to the ratios of 1/6, 1/4, 1/3, and 1/2, respectively.

Spring constant vs the coil elongation for a single-helix CNC. Here, the nanocoil radius , the nanowire diameter and the shear modulus . In (a), the inner diameter is zero, curves 1 and 2 correspond to the coil pitches of 120 and 2000 nm, respectively. In (b), the coil pitch is 2000 nm, curves 3, 4, 5, and 6 correspond to the ratios of 1/6, 1/4, 1/3, and 1/2, respectively.

Tensile load vs the coil elongation for a double-helix CNC. In the inset, the coil number , the initial length , , and , curves 1, 2, 3, and 4 correspond to the elastic moduli of 0.68, 0.70, 0.72, and 0.74 GPa.

Tensile load vs the coil elongation for a double-helix CNC. In the inset, the coil number , the initial length , , and , curves 1, 2, 3, and 4 correspond to the elastic moduli of 0.68, 0.70, 0.72, and 0.74 GPa.

Equivalent shear stress-extension diagrams for a single-helix microcoil with its ends fixed. Curves 1, 2, 3, and 4 correspond to the initial pitch angles of 0°, 5°, 10°, and 20°, respectively.

Equivalent shear stress-extension diagrams for a single-helix microcoil with its ends fixed. Curves 1, 2, 3, and 4 correspond to the initial pitch angles of 0°, 5°, 10°, and 20°, respectively.

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