On the factors controlling the mechanical properties of nanotube films

CARBON

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available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/carbon

On the factors controlling the mechanical properties of nanotube films Fiona M Blighea, Philip E Lyonsa,b, Sukanta Dea,b, Werner J Blaua, Jonathan N Colemana,b,* a

School of Physics, Trinity College Dublin, University of Dublin, Dublin 2, Ireland Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN), Trinity College Dublin, University of Dublin, Dublin 2, Ireland

b

A R T I C L E I N F O

A B S T R A C T

Article history:

We have studied the mechanical and morphological properties of carbon nanotube films

Received 31 July 2007

prepared from tubes produced by a range of commercial suppliers. We find significant cor-

Accepted 24 October 2007

relations between mechanical parameters (modulus, strength, toughness and ductility)

Available online 4 November 2007

and morphological parameters (porosity and bundle diameter). Both strength and toughness scale linearly with the number of inter-bundle junctions per unit volume as calculated from the porosity and bundle size. Applying a simple model, we can use this data to find the average force and energy required to break a junction to be 113 pN and 0.7 eV, respectively. This latter value agrees well with the value of 0.9 eV estimated from the nanotube surface energy, indicating that adjacent bundles are bound predominately by van der Waals interactions.  2007 Elsevier Ltd. All rights reserved.

1.

Introduction

The outstanding thermal [1], electrical [1] and mechanical [2] properties of carbon nanotubes have made them the most studied of all nano-materials in recent years. Their low density, high aspect ratio and exceptional strength and stiffness suggest them as especially promising materials for mechanical applications. However is has been extremely difficult to turn this potential into a recipe for practical structural materials. The main reason for this is that, although strong, nanotubes are of course very small. Thus any real structural material will be fabricated from arrays or networks of nanotubes [3] or from composites of nanotubes embedded in a matrix [2]. In either case, the resulting mechanical properties will depend strongly on the stress transfer either between nanotubes or from matrix to nanotube. This has resulted in macroscopic nanotube based materials with mechanical properties much inferior to those of the nanotubes themselves. For example, fibers fabricated from nanotubes alone have demonstrated

strengths many times lower than the strengths of the individual nanotubes [4]. To make matters worse, single wall nanotubes tend to bundle together due to van der Waals interactions between them [5]. Although individual nanotubes are strong, bundles of tubes are weak and exhibit low shear modulus [6]. Thus, nanotube networks or fibers made from bundles would be expected to have different properties to those made from individual nanotubes. In composite materials, aggregation of nanotubes into bundles acts to decrease the nanotube surface area available to make contact with the chosen polymer, inhibiting their reinforcement capabilities [7]. Much work has been done to address this problem, most recently through investigation of carbon nanotube exfoliation in various solvents. Notably, Giordani et al. [5] have reported that SWCNTs can be dispersed in N-methyl-2-pyrrolidone (NMP), without significant aggregation, at concentrations below 0.02 mg/ml. A number of studies have looked at the mechanical properties of macroscopic materials fabricated solely from carbon nanotubes. These materials include sheets [3], films [8–11]

* Corresponding author: Address: School of Physics, Trinity College Dublin, University of Dublin, Dublin 2, Ireland. Fax: +353 1 6711759. E-mail address: [email protected] (J.N. Coleman). 0008-6223/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2007.10.028

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and fibers [4,12]. A very wide range of mechanical properties have been reported, with strengths for example ranging from 5 MPa for Buckypapers [11] to 1 GPa for fibers [4]. The common factor uniting these materials is that they are held together by van der Waals interactions between nanotubes or nanotube bundles. However, other than nanotube alignment it is not clear exactly what factors control the mechanical properties. In this work, we have fabricated and characterised carbon nanotube films (Buckypapers) prepared by the vacuum filtration of a range of pristine and functionalised carbon nanotube dispersions. Stress–strain measurements show the mechanical properties depend primarily on the morphology of the nanotube network, specifically the number density of interbundle junctions.

2.

Experimental

A range of commercially available nanotubes were used in this study. Purified HiPCO SWCNTs (www.cnanotech.com), as-prepared and annealed Elicarb SWCNTs (www.thomasswan.co.uk), Nanolab DWNTs (www.nano-lab.com) and Swent SWCNTs (swentnano.com) were purchased and used as supplied. As-prepared (AP) SWCNTs, along with several varieties of functionalized SWCNTs were purchased from Carbon Solutions Inc (www.carbonsolution.com) and also used as supplied. The SWNTs varied from 0.7 to 1.5 nm in diameter while the DWNT had diameters of 3 nm. In all cases the samples were free from amorphous carbon impurities except for the nanolab and carbon solutions as-produced samples where small amounts of non-nanotube carbon was observed by SEM. In all cases NMP [5] was used as a solvent unless otherwise specified. These functionalities were (acronyms in round brackets) [solvents used in square brackets] –COOH, both lightly and heavily functionalized (low-COOH, highCOOH), octadecylamine (ODA) [chloroform], poly-aminobenzene-sulfonic-acid (PABS) [water] and poly-ethylene-glycol (PEG) [water]. Dispersions were prepared by adding the SWCNTs to the appropriate solvent at a concentration of 0.33 mg/ml and sonicating for 3 min using a high-power ultrasonic tip (GEX600, 120 W, 60 kHz). To achieve a nanotube concentration of 0.08 mg/ml, i.e. one that minimises NT bundling [5] while still remaining practical, the initial dispersions were diluted twice, sonicating for 1 min between steps. These diluted dispersions underwent a further 4 h sonication in a low-power ultrasonic bath (Ney Ultrasonic) followed by 1 min under the sonic tip. They were then vacuum filtered trough a PVDF filter paper (Millipore, Durapore membrane filters, 0.45 lm pore size), washed with deionised water and acetone and dried at ambient temperature for 12 h in a vacuum oven. The films were free standing after being peeled from the filter paper and were cut into strips of width 2.2 mm and lengths of several centimeters. Film thicknesses ranged from 11 lm to 22 lm. The density of each film, qfilm, was calculated from measurements of the film weight and dimensions made using a microbalance and digital micrometer. Porosity, P, was calculated from P = 1qfilm/qNT, where the nanotube density was taken to be qNT = 1500 kg/m3 [10].

Scanning electron microscopy was preformed using a Hitachi S-4300 Field emission scanning electron microscope. Raman spectroscopy was carried out using a Horiba Jobin Yvon LabRam HR with the 633 nm excitation wavelength laser. Mechanical testing was performed with a Zwick tensile tester Z100 using a 100 N load cell with a cross-head speed of 0.5 mm/min on strips of dimensions 11 lm to 22 lm · 2.2 mm ·  2 cm. The direction of force was along the long axis of the strip.

3.

Results and discussion

One might expect that the mechanical properties of nanotubes films would depend on two main factors: the mechanical properties of the nanotubes themselves and the topological properties of the nanotube network. In order to explore the topological properties of the network we have used SEM as well as careful measurements of the film porosity. Direct measurement of the mechanical properties of the nanotubes themselves is less straightforward. However, we note that both nanotube strength and stiffness are sensitive to the population of defects present. Thus, we use the defect content as measured qualitatively by Raman spectroscopy as a proxy for nanotube mechanical properties. Scanning electron micrographs of SWCNTs films prepared from (top) Hipco SWCNT, (middle) Elicarb annealed SWCNT and (bottom) carbon solutions PEG functionalized SWCNT are shown in Fig. 1. These images are typical of films of Buckypaper. The film surfaces appear to consist of randomly orientated porous entanglements of nanotube bundles. The mean size of the nanotube bundles were measured from the SEM images and ranged from 9.8 nm for the SWCNT-high– COOH film to 21 nm for the SWCNT-low-COOH film. We recognise that these means are slightly overestimated as the SEM used here does not have the resolution to see bundles with diameters below 4 nm. In addition, it can be seen that all films appear porous. The porosity was calculated from the measured film densities and varied from 42% for the Swent sample to 72% for the SWCNT–PABS film. This range encompasses previous values observed for Buckypaper made from surfactant dispersions [11]. Raman spectra of each tube type are shown in Fig. 2 and typically exhibit two strong bands at approximately 1280 and 1580 cm1 that are known as the D-band and G-bands, respectively [13]. While the G-band is associated with tangential modes in pure sp2 hybridised graphitic carbon, the Dband corresponds to the presence of deviations from the hexagonal lattice such as sp3 type defects. Thus the ratio of intensities of the G and D bands, IG/ID, is a crude measure of the perfection of the nanotubes. These intensity ratios have been measured for all nanotube films studied and range from 12.3 for the Swent nanotubes to 3.2 for the SWCNT–PEG film. By and large, the IG/ID ratio was smaller for functionalized compared to the AP and Hipco tubes. Stress–strain curves were measured for each film type with representative curves plotted in Fig. 3 (all the stress– strain curves are plotted in figure S1). Four main mechanical parameters can be obtained from these curves: the Youngs’ modulus, Y, the strength (stress at break), rB, the toughness

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G D

Hipco Swent

Nanolab DWNT Elicarb Ann. Elicarb AP PABS PEG ODA -High-COOH -Low-COOH Carb Solns AP 0

500

1000

1500

2000

2500

3000

Raman Shift cm-1 Fig. 2 – Raman Spectra of NT films studied in this work.

7

3.0x10

7

Stress MPa

2.5x10

7

2.0x10

-high-COOH

Carbon Solutions AP LowCOOH HighCOOH ODA PEG HiPCO Elicarb Annealed

7

1.5x10

7

1.0x10

6

5.0x10

Fig. 1 – SEM images of surfaces of nanotube films prepared from (top) Hipco SWCNT, (middle) Elicarb annealed SWCNT and (bottom) carbon solutions PEG functionalized SWCNT.

(energy required to break per film volume), T, and ductility (strain at break), eB. For each film type, stress–strain curves were measured for five strips, the four mechanical parameters calculated and the mean and standard deviation computed. The ranges of values measured were: modulus (1– 3 GPa), strength (2–30 MPa), toughness (4 · 1032 · 105 J/m3), strain at break (1–2%). In general, these values are not so different to those observed for weak, brittle thermoplastic polymers such as polystyrene [14]. However, there is a significant deviation in each of the properties over the range of tube types studied. It is of interest to ascertain the reason for these deviations as this will lead to an understanding of the maximization of the mechanical properties of nanotube based solids. The topological properties of the network affect the properties of the film because the structure of the film determines the number and nature of bundle–bundle junctions. The importance of these junctions is that they are responsible for the transfer of stress between adjacent bundles. It is not

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Strain % Fig. 3 – Representative stress–strain curve for selected film types.

straightforward to measure directly the global topology of the film or even the exact nature and spatial distribution of the junctions. However, two film properties that are strongly coupled to the properties of the network but can easily be measured are the film porosity and mean bundle diameter. In addition, the mechanical properties of the nanotubes themselves might be expected to influence the mechanical properties of Buckypaper. Well-graphitized SWCNT have moduli and strengths of up to 1 TPa and 60 GPa, respectively [15]. However, the presence of defects can result in significant reduction in both strength and modulus [16]. Thus, one might expect the mechanical properties of nanotube films to depend on the density and nature of defects associated with the nanotubes themselves. While we cannot measure this directly, we can crudely quantify the presence of defects through the Raman G/D ratio (IG/ID) as described above.

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Thus, we expect the mechanical properties of the nanotube films to vary with film porosity, P, mean bundle diameter, D, and Raman Intensity ratio, IG/ID. Values for Y, rB, T and eB calculated from the stress–strain curves were each plotted individually as a function of P, D and IG/ID. For example, plots of the rB versus P, D and IG/ID are shown in Fig. 4. Unsurprisingly, as the bundle size and porosity values increase, rB falls off significantly. This makes sense as we would expect increasing bundle size and porosity to reduce the number of inter-bundle junctions within the film and so decrease the effective number of van der Waals interactions between adjacent NT bundles. Furthermore, rB displayed no clear trend with IG/ID. This suggests that the film strength is not affected by variations in the defect populations, and hence strength, of the tubes themselves. To fully understand this we need to consider the hierarchy of structures that make up a nanotube film. The film consists of a network of bundles connected at junctions. The bundles consist of a close packed array of nanotubes. The mechanical properties of the bundles are dominated by the low inter-tube shear modulus, not the mechanical properties of the individual nanotubes themselves [17]. However, while the bundles are weak, we would expect the junctions to be weaker still, due to the relatively

σB (MPa)

Elicarb-AP Elicarb-Annealed Nanolab DWNT Swent

Hipco AP Long chain COOH

10

2

4

6

8

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12

14

σB (MPa)

IG/ID

NJ ¼

10

8

10

12

14

16

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Bundle Size, D (nm)

σB (MPa)

small interaction area. Thus, we expect the mechanical properties of the film to be limited by the properties of the weakest links i.e. the junctions. It is worth noting that even if we could somehow strengthen the junctions significantly, we would then expect the properties of the film to be limited by the mechanical properties of the bundles which depend only weakly on the mechanical properties of the individual nanotubes. Thus, we expect the mechanical properties of the nanotubes themselves to have virtually no impact on the mechanical properties of nanotube solids. The dependence of Y, T and eB with P,D and IG/ID displayed similar trends (see supplementary figures S2, S3 and S4). All mechanical parameters decreased as both P and D increased. In addition, like the rB, both Tand eB proved invariant with IG/ID. The only exception to this trend was the Youngs modulus, which decreased consistently with increasing IG/ID from 2 GPa for the SWCNT–PEG to 0.6 GPa for the SWCNT–AP. Taken as a whole, these results mean that the mechanical properties of the nanotubes themselves have relatively little impact on the mechanical properties of the films. Much more important is the film morphology, with porous films made from high diameter bundles displaying much poorer properties. This strongly suggests that the number of inter-bundle junctions may be an important parameter. The scatter present in these plots can be accounted for by the fact that the mechanical properties of the films are most likely controlled by a combination of the bundle size and porosity. Thus, plotting the mechanical properties versus a combined parameter, which is a function of both P and D should reduce this scatter. As discussed above, we suspect that the number of interbundle junctions is the key factor in the mechanical properties of Buckypaper films. We can easily estimate the number of junctions per unit volume of film, NJ, by calculating the number of bundles per unit volume. This parameter is of course related to the film density and the bundle diameter. Multiplying by the half the mean number of junctions per bundle, a, gives:

10

35

40

45

50

55

60

65

70

75

Porosity, P % Fig. 4 – Strength at Break (rB) versus IG/ID, bundle Size (D) and porosity (P) of pristine and functionalized NT films. The dotted lines are not fits but guides to the eye. The maximum errors in IG/ID, D and P were less 10% (relative error), 1 nm and 3% (absolute error), respectively.

a qfilm =qNT 2ð1  PÞ ¼a 2 pD2 L=4 pD2 L

where L is the mean bundle length. We use a/2 to avoid double counting of junctions. We can estimate a by using the film density to calculate the average mass in a shell of thickness D surrounding a test bundle. We make the approximation that this mass is concentrated in bundles that are in contact with our test bundle. We should note that this approximation will result in an overestimation of a. Approximating the volume of one bundle intersecting the shell (at right angles) by a triangular prism gives the volume of intersection as 3D3/ 2. Averaging over all angles of intersection gives a mean volume of intersection of 3pD3/4. Then by dividing the average mass within the shell by the average intersecting volume per bundle, qNT3pD3/4, we can estimate the number of bundles within the shell and hence the number of junctions: a

qfilm 8L 8L ¼ ð1  PÞ 3D qNT 3D

Calculation of a, on a per unit length basis, gives values ranging from 73 to 160 junctions per micron for the low-COOH and

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HIPCO samples, respectively. Combining this with the previous equation, we get an expression for the number of junctions per unit volume: NJ 

16 ð1  PÞ2 3p D3

We can calculate the junction density to vary from 2.7 · 1022 m3 for the Nanolab DWNT tubes to 4.8 · 1023 m3 for the high-COOH sample. If the number of junctions per unit volume is a key factor, we would expect some or all of the mechanical parameters to scale with (1P)2/D3. Shown in Fig. 5A–D are plots of Y, rB, T

Hipco AP Carbon Soln Long Chain COOH

Y (GPa)

3

A

Elicarb AP Elicarb Annealed Nanolab DWNT Swent

PEG

2

1

0

σ B (MPa)

B 10

C 3

T (J/m )

105

104

3

Ductility, εB (%)

and eB as a function of junction number density, NJ  1.7(1P)2/D3. No overall relationship is apparent between the Young’s modulus and NJ. The dotted line shows a linear trend for comparison. While the functionalized nanotubes (open symbols) may display a weak dependence with NJ, overall the data is too scattered to confirm a definite relationship. This is almost certainly because the modulus, unlike the other parameters scaled with IG/ID as well as with the morphological parameters. However, in the case of rB, the dependence is close to linear as evidenced by the dashed linear fit line. It should be noted that three of the samples with low NJ lie slightly above the fit line (Nanolab DWNT, low-COOH and PEG). However interestingly, these samples lie perfectly on a linear fit with intercept (dotted line). For the toughness, the dependence is also linear, with the regression line well fitting all the data. Even the ductility tends to increase weakly with the junction number density. In the case of the tensile strength, we can easily take the analysis a step farther. We might speculate that fracture involves the breaking of junctions in a volume, VR  AL, where A is the film cross-section area and L is the mean bundle length. We further speculate that, on fracture, every bundle in this volume has half its junctions with other bundles severed. Taking the average force to break a junction as fJ, we can write the film strength as r

low-COOH

D

2 1 0 1023

1024

NJ=1.7(1-P)2/D3 (m-3) Fig. 5 – Youngs modulus (Y), strength at break (rB), toughness (T) and ductility (eB) versus the junction number density for functionalized and pristine NT films. In (A) the dotted line is not a fitline, it just illustrates linearity. In (B) and (C) the dashed lines are linear fits while in (B) the dotted line is a linear fit with intercept. The line in (D) is a fit to eB  N1=3 J Dmax . In all cases the relative error in NJ was less than 20%.

45

1 NJ AL fJ L 1:7ð1  PÞ2 fJ ¼  A 2 2 D3

we can fit this equation to the data in Fig. 5B to estimate fJ so long as we know L. Previous atomic force microscopy measurements of the length of bundles deposited from dispersions for Hipco, PABS, PEG, ODA and high-COOH tubes all give values close to 1 lm. Using this as an approximate length, applicable to all tube types, we can estimate fJ  113 pN. We recognise that bundle lengths in Buckypaper may be significantly longer than those in solution; thus we consider fJ  113 pN to be an overestimate. If we assume that the application of this force leads to an opening of the gap between bundles to 1 nm just before fracture, then we can calculate the fracture energy to be 0.7 eV per junction. This compares well with the value of 0.9 eV per junction calculated assuming a nanotube surface energy [18] of 70 mJ/m2 and a junction cross section of 1 nm2 (almost certainly an over-estimate). In fact, the agreement between the estimate of junction fracture energy from our mechanical measurements with that from surface energy considerations is remarkable given the approximate nature of our calculations. Attempting a similar calculation for the toughness of the film (fracture energy absorbed per film volume) in terms of the work done breaking junctions, wJ (estimated above at 0.7–0.9 eV above), gives the expression: T

wJ L  NJ 2l

where l is the gauge length of the film (0.02 m). Substituting in wJ  0.9 eV gives a value of dT/dNJ  3.6 · 1024 J, a value much smaller than the measured value (3.6 · 1019 J). While this discrepancy is larger than expected, it is consistent with the fact that most of the work of fracture is done deforming

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the entire network, not just locally breaking junctions in the region of fracture. We can also try to understand the weak dependence of breaking strain in NJ. The average inter-junction spacing is . If we assume that strain involves the motion of juncN 1=3 J 1=3 tions, then a given extension, ll0 N J lD where l is the gauge length and D is the average junction displacement when under strain. The strain at break is then eB  N1=3 J Dmax where Dmax is the average junction displacement at fracture. This expression has been fit to the data in Fig. 5D giving a reasonable fit. From the fit we get Dmax  0.34 nm. This means that film failure occurs when the average junction displacement is very close to the van der Waals distance. This suggests that the junctions fail by opening and subsequently debonding. This is rather surprising as one would expect the average junction to move along the bundle when under strain, rather than to open. Finally, it is important to consider the effect of the functional groups on the mechanical properties of our films. In general, the mechanical properties for all the films studied, including those fabricated from functionalized nanotubes, lie close to the (1P)2/D3 trend lines. The obvious exceptions are the SWCNT–PEG and SWCNT-low-COOH films. These materials display strengths slightly above where we might expect according to the analysis. However, the general scaling with (1P)2/D3 suggests that film morphology considerations are far more important than any interactions between functional groups of adjacent bundles. This is however not so surprising as the functional groups attached to these sort of nanotubes are expected to be predominately at the ends [19]. Furthermore, the agreement between the estimate of junction fracture energy from mechanical measurements with that from surface energy considerations suggests that inter-bundle interactions are similar to graphite–graphite van der Waals interactions rather than interactions between functional groups. In addition, the fact that the mechanical properties in general do not scale with the defect content confirms that the junctions are much weaker than the nanotubes themselves as one would expect. While the excess stiffness of the SWCNT–PEG samples may be due to some entanglement of PEG chains associated with neighbouring bundles, we feel that this is a small effect in these samples. However, if one wished to enhance this effect, it would be necessary to use nanotubes with a high degree of functionality along their bodies, leading to increased entanglement in the region of junctions. However, the large degrees of functionalisation required might very well reduce the mechanical properties of the nanotubes themselves to a level which could influence the film strength. The ideal situation would be to covalently attach cross-linking molecules that join adjacent nanotubes only at junctions. This would significantly increase junction strength while minimizing the degradation of nanotube strength. Overall, we feel that the role of the functionalities is to influence the dispersability of the nanotubes during the preparation stage, thus controlling the bundle size. The bundle size most likely then sets the porosity which, coupled with the bundle size, controls the junction number density.

4.

Conclusion

In conclusion we have measured both morphological and mechanical properties of a range of nanotube films made from different tube types. We find strong correlation between the mechanical properties of the nanotubes and film morphology but weak correlation with defect population as indicated by the Raman ratio, IG/ID. We show that the number density of inter-bundle junctions is related to both the film porosity and the mean bundle diameter. We find that both the film strength and toughness scale linearly with junction number density while the strain at break scales sub-linearly. Each of these trends can be explained by simple models. These results underline the importance of morphology to the mechanical properties of nanotube films. It is likely that these findings also apply to recently reported nanotube fibers [4,12] and sheets [3].

Acknowledgements The authors would like to acknowledge funding from Science Foundation Ireland and the Centre for Research on Adaptive Nanostructures and Nanodevices.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.carbon.2007. 10.028.

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