Carbon Nanotubes with Temperature-Invariant Viscoelasticity from –196° to 1000°C

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Science  03 Dec 2010:
Vol. 330, Issue 6009, pp. 1364-1368
DOI: 10.1126/science.1194865

Shake It to Wake It

Viscoelastic materials combine the recoverable stretchiness found in elastic materials with the slow-flowing behavior of a thick fluid, like honey. When subjected to an oscillatory motion, the response will depend on the frequency. At low frequencies, the viscous behavior will dominate and lead to a dissipation of the applied energy as heat, while at fast frequencies the elastic behavior dominates. Xu et al. (p. 1364; see the Perspective by Gogotsi) developed a viscoelastic material with an exceptionally broad operating temperature range, based on a network of carbon nanotubes. The responsiveness of the material was probably caused by the “zipping” and “unzipping” of the nanotubes at points of contact.


Viscoelasticity describes the ability of a material to possess both elasticity and viscosity. Viscoelastic materials, such as rubbers, possess a limited operational temperature range (for example, for silicone rubber it is –55° to 300°C), above which the material breaks down and below which the material undergoes a glass transition and hardens. We created a viscoelastic material composed from a random network of long interconnected carbon nanotubes that exhibited an operational temperature range from –196° to 1000°C. The storage and loss moduli, frequency stability, reversible deformation level, and fatigue resistance were invariant from –140° to 600°C. We interpret that the thermal stability stems from energy dissipation through the zipping and unzipping of carbon nanotubes at contacts.

Viscoelasticity describes the ability of a material to both dissipate energy (viscous) and reversibly deform (elastic) and permeates all levels of our lives from human tissues, shoe soles, ear plugs, and mattresses to vibration isolators. Viscoelastic properties of existing materials, represented by rubbers, are inherently temperature dependent (1). This is because molecular motion that is the origin of viscoelasticity is a thermally activated process.

Carbon nanotubes (CNTs), with their exceptional mechanical properties and thermal stability (2), could be building blocks for various thermally stable elastic and viscoelastic materials. Aligned, sparse CNT arrays (3), films (4), and sponges packed with short, straight CNTs (5) have shown fatigue resistance, supercompressibility, and compressive elasticity, respectively. Reports of creep and buckling of aligned CNTs (6, 7) demonstrate that a specific assembly of CNTs can show viscoelasticity.

Our strategy to make a viscoelastic CNT material was to assemble traversing long CNTs with a very high density of intermittent physical interconnections, analogous to an aggregate of hair. We made a CNT network where each CNT made contacts with numerous other CNTs. A combination of reactive ion etching (RIE) to the catalyst film, water-assisted chemical vapor deposition (8), and compression was used for the synthesis. RIE exposure reduced the catalyst density needed to create randomly oriented and sparse CNTs. Water-assisted chemical vapor deposition synthesized very long and clean CNTs (~68% double-walled CNTs, ~22% single-walled CNTs, and ~10% tripled-walled CNTs; 0.009 g/cm3; height = 4.5 mm; carbon purity = 99.9%) that are essential to increase interconnection among CNTs and thereby increase cohesiveness and thermal stability. Compression increased the CNT material density fourfold (0.036 g/cm3) (Fig. 1A).

Fig. 1

Invariant energy dissipation of the CNT material, from –196° to ~1000°C. (A) Diagram showing the synthesis procedure. (B) Photograph of the flexible CNT material. (Inset) SEM image. (C) Stress-strain curves of CNT material and silicone rubber. (D) Temperature dependence of the storage modulus (black), loss modulus (blue), and damping ratio (red) of the CNT material (silicone rubber in gray for comparison). (E) Schematic of the impact test. (F) Split images of the ball tracks performed at –196°, 25°, and 1000°C (top, SEM; bottom, 3D mapping from laser microscopy). Bottom graph, all track profiles for all three cases.

Scanning electron microscope (SEM) observation of the CNT material revealed an intertube structure where individual CNTs traversed laterally, making interconnections with other CNTs. This feature allowed the CNT material to bear strain without fracture (Fig. 1B). The slow elastic recovery after release implied viscoelasticity. Stress-strain behavior from shear-mode dynamic mechanical analysis (DMA) showed up to 100% strain, high nonlinearity, and a closed hysteresis without abrupt changes, which were typical of viscoelastic, energy-dissipative, and highly deformable materials, for example, rubber. Silicone rubber was chosen as our strictest benchmark in terms of thermal stability because it is the most thermally resistant rubber. The observed dual slope of the stress-strain curve was associated with a change of the modulus as we approached the failure strain. The larger enclosed area of the hysteresis loop for the CNT material meant more energy dissipated in one cycle (Fig. 1C). Quantitatively, the viscoelastic properties (storage modulus, loss modulus, and damping ratio) by DMA showed that the CNT material possessed similar stiffness (storage modulus = 1 MPa) and higher dissipation ability (loss modulus = 0.3 MPa) and damping ratio (0.3) than silicone rubber at room temperature (fig. S6A). The viscoelastic properties of the CNT material strongly depend on the internal structure. For example, an increase in density results in a significant increase in both moduli. We compressed the as-prepared CNT material to increase the density four times, and this resulted in an increase of the storage (5 times) and loss (10 times) moduli and the damping ratio (2 times). In this way, our CNT material was specifically tuned to exhibit similar viscoelastic properties as silicone rubber at room temperature.

The viscoelastic properties (storage modulus, loss modulus, and damping ratio) measured by DMA in ambient N2 were nearly constant over an exceptionally wide temperature range (–140° to 600°C) in contrast to silicone rubber, which showed large variation because of hardening at –55°C and degradation at 300°C (Fig. 1D). Variation between CNT samples was within ~5%. As far as we know, commercial DMAs are limited to 600°C. As exemplified by the vibration isolator demonstration (fig. S2), the CNT material showed viscoelasticity beyond the limitation at –190°C (immersed in liquid nitrogen) and at >900°C (exposed to butane torch). To extend the temperature range studied, we implemented impact tests at –196°C, 25°C, and 1000°C by using a steel ball and analyzed the ball tracks. The ball tracks were identical for all cases as observed by SEM and three-dimensional (3D) mapping (Fig. 1, E and F), which suggested unvarying viscoelastic properties across this 1200°C temperature range. The absence of catalyst materials in our CNT material is crucial for our high thermal stability because oxidation would always limit the practical applications in air above ~400°C, particularly when catalyst material is present (9).

Further DMA characterization from –140° to 600°C demonstrated temperature-invariant frequency stability, the same level of reversible deformation, and fatigue resistance. Frequency-dependence test (Fig. 2, A to C) showed constant viscoelastic properties (storage modulus, loss modulus, and damping ratio) of the CNT material in the range of 0.1 to 100 Hz. Furthermore, the CNT material showed identical frequency-stability from –140° to 600°C.

Fig. 2

Viscoelastic properties of the CNT material over a wide temperature range. (A to C) Storage modulus, loss modulus, and damping ratio of the CNT materials as function of frequency (0.1 to ~100 Hz) at temperatures from –140° to 600°C. (D to F) Storage modulus, loss modulus, and damping ratio of the CNT materials as function of strain amplitude (1 to ~1000%) at temperatures from –140°C to 600°C.

Strain dependence tests (Fig. 2, D to F) showed that the critical strain, that is, the maximum strain allowing reversible deformation, was ~5%. Similarly, the CNT material retained the same level of reversible deformation from –140° to 600°C. The failure strain for the CNT material at room temperature was estimated as ~100% (fig. S6B). At the failure strain, the structure broke down, indicated by the degradation in the nonlinearity and hysteresis loops at 100% strain (fig. S9). The failure strain ranged from 50 to 100% between –140°C and 600°C, which we suspect results from the instability of gap between pressure heads at large strain because of thermal expansion and contraction.

Cyclic tests at 100 Hz showed identical viscoelastic moduli and stress-strain behavior even after 1,000,000 cycles at 1% strain (Fig. 3, B and E) that proved excellent fatigue resistance of the CNT material at room temperature. Identical fatigue resistance was observed at –140° and 600°C, as evidenced by similar viscoelastic moduli and cyclic behavior (Fig. 3, A, C, D, and F). This phenomenon means that not only are the viscoelastic properties temperature invariant but also unvarying over many cycles.

Fig. 3

Fatigue resistance of the CNT material across –140° to 600°C. Cyclic test (1% strain, 100 Hz, 106 cycles) at (A) –140°C, (B) 25°C, and (C) 600°C. Stress-strain curve of fatigue resistance test (102-th 104-th, 106-th cycle) at (D) –140°C, (E) 25°C, and (F) 600°C.

The porous nature of the CNT material allows for rapid and efficient heat dissipation, which prevents significant heat accumulation, the common cause for property degradation. We interpret that our CNT material exhibited this high level of reversible deformation from the entanglement of the long traversing CNTs throughout the material, like a network of springs creating elasticity.

To provide insight into the mechanism of viscoelasticity, we carried out SEM observations (Fig. 4A) and Herman’s orientation factor (HOF) calculations (Fig. 4B) under increasing shearing strains up to 1000%. HOF describes the degree of alignment (0 is random, and 1 is aligned) and was calculated from the fast Fourier transform (FFT) analysis of SEM images (10). Up to 100% strain, the traversing, randomly aligned CNTs structurally deformed into mutually aligned CNTs, and the HOF steadily increased from 0.07 to ~0.48. Beyond 100% strain, the HOF plateaued, showing no increase in alignment, and the intermittently contacting CNTs became increasingly bundled. This observation at 100% strain corresponded with the measured failure strain. From these results, we propose that the strain was absorbed at low level by reversible unfolding of the traversing CNTs and beyond 100% strain by an irreversible process of straightening, slipping, and bundling of CNTs (Fig. 4C).

Fig. 4

Energy dissipation model. (A) SEM images at varying shear strains. (B) Herman orientation factor (HOF) as a function of shear strain. (Inset) 2D FFT of the SEM images at 0% and 100% strain. (C) Schematic description of the change in intertube structure with strain. (Inset) TEM image of intertube structure at 1000% strain. (D) TEM image of the as-prepared intertube structure. (Inset) Selected section indicating nodes. (E) Schematic of the zipping and unzipping of nodes.

Transmission electron microscope (TEM) observation further revealed the intertube structure of the CNT material, which showed insight into the mechanism of energy dissipation (Fig. 4D). We found an intertube structure resembling a 3D highway network, where each CNT made contact with numerous other CNTs. This peculiar intertube structure was characterized by a high density of connections (nodes), that is, two to four CNTs intermittently contacting in parallel for only short spans (~150 nm). These nodes were separated mainly by isolated CNTs (struts). In addition, no CNT ends were observed, implying long, continuous CNTs, and the long CNTs were both randomly oriented and traversing. We interpret that this intertube structure of struts and nodes was the key for structural cohesiveness that allowed for large deformations. This structure differs from typically bundled CNT material (11) where CNTs are straight and contacts the same CNTs over long spans.

Although not directly observed, we believe that the CNTs in a node reversibly attached and detached through zipping and unzipping (Fig. 4E). This process would dissipate energy because of the energy consumed to overcome the large van der Waals (vdW) attraction (12) between CNTs when unzipped, yet no energy is required for zipping. We interpret that sliding among CNTs was not a significant contribution because the friction coefficient (0.003) is small (13). Because the CNT material possessed a very high density of these “detachable” nodes, we interpret that they were the source of the high energy dissipation ability. Within our model, under the critical strain, the nodes perpendicular to the strain direction could reversibly zip and unzip and thereby dissipate energy. Under increased strain, the number of detachable nodes gradually decreased through either unzipping or alignment (Fig. 4C), and eventually the ability to dissipate energy decreased. Beyond the critical strain, this zipping/unzipping process was no longer reversible, and upon cycling CNTs zipped at different places and/or became bundled and aligned, resulting in degradation. A similar irreversible process caused by the slipping among CNTs under large strain has been observed in CNT yarns (11).

We estimated the loss modulus to address the validity of the zipper model. The loss modulus (G″) of the nodes was approximated as a summation over all nodes multiplied by the energy per node to unzip and by a geometrical factor, <cosθ>, to account for the fraction aligned perpendicular to the strain directionEmbedded Image (1)with vdW adhesion energy per unit length to unzip two CNTs, EvdW; node density, N; node length, l = 150 nm (by TEM, fig. S7A); shear strain and rate, γ and Embedded Image, respectively; strain angular frequency, ω; and the angle between the node and the direction perpendicular to the strain, θ. The vdW adhesion energy, EvdW, was estimated as 0.36 nJ/m as calculated from the binding energy of two parallel cylinders following the Lennard-Jones potential (14). The CNT node density (4.5 × 1015 nodes per cm3) was estimated by multiplying the CNT tube density (4.24 × 1010 tubes per cm2), as estimated from the CNT bulk density (0.009 g/cm3) and individual tube density (1.5 × 10−13 g/cm), and the node density per tube (2.12 × 104 per tube), as estimated by the node frequency (1/300 nm) obtained by TEM images (fig. S7). With use of these values, the calculated G″ was 0.51 MPa and agreed well with experiment (0.3 MPa), which demonstrated that the energy dissipation stemmed from the unzipping vdW interaction at the nodes. In summary, the temperature invariance of the vdW interaction (15) and the thermal stability of CNT material provided this temperature invariant viscoelasticity.

Supporting Online Material

References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. We acknowledge partial funding by TASC. M.X. acknowledges technical consultations from Y. Hayamizu, A. Izadi-Najafabadi, and Y. Seki.
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