Orientation Distribution of Vertically Aligned Multiwalled Carbon

Article pubs.acs.org/JPCC

Orientation Distribution of Vertically Aligned Multiwalled Carbon Nanotubes Ulla Vainio,*,† Thea I. W. Schnoor,‡ Sarathlal Koyiloth Vayalil,§ Karl Schulte,‡,∥ Martin Müller,† and Erica T. Lilleodden† †

Institute of Materials Research, Helmholtz-Zentrum Geesthacht Centre for Materials and Coastal Research, Max-Planck-Str. 1, 21502 Geesthacht, Germany ‡ Institute of Polymers and Composites, Technische Universität Hamburg-Harburg, Denickestr. 15, 21073 Hamburg, Germany § Deutsches Elektronen-Synchrotron, Notkestr. 85, 22706 Hamburg, Germany ∥ Physics Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia ABSTRACT: Carbon nanotube “forests” show great promise in a variety of applications, from supercapacitors to fuel cells, but the realization of such materials for functional devices relies on a better control over processing routes such that targeted structures and associated properties can be reproducibly obtained. The orientation distribution of the nanotubes is a critical structural property affecting both electrical and mechanical response, yet it remains a challenging characteristic to quantify. Small-angle X-ray scattering (SAXS) is a technique well suited to investigate the vertical alignment of nanotubes. Here we show that the orientation distribution obtained from SAXS is not satisfactorily represented by the normal distribution or the Lorentzian, which have been used until now. Instead, an excellent agreement between model and data is found with the generalized normal distribution (GND). Such quantification of the carbon nanotube alignment can be used as direct input in simulations for optimizing structure−property relations.

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INTRODUCTION For the reproducible manufacturing of nanodevices and multiscale structures, it is necessary to obtain perfect control over the alignment of the nanosized building blocks. There are many ways to orientate nanosized objects, but every method will create a certain type of orientation spread, a distribution of orientations, which is fundamentally linked to the physical properties of the whole assembly, like demonstrated for example in experimental studies1,2 on single-walled carbon nanotubes. According to a recent theoretical study by Simoneau et al.,3 the orientation distribution selected for simulations has a drastic effect on the electrical properties of a carbon nanotube film. Therefore, it is of crucial importance that the correct statistical distribution is selected for such simulations and we find a way to control the experimental distribution in order to achieve optimum performance. Even though a lot of effort has been put in obtaining overall estimates of the orientation of carbon nanotubes in arrays, a detailed experimental quantification of the shape of the orientation distribution of carbon nanotubes is still lacking. A commonly used method to evaluate the orientation and size of multiwalled carbon nanotubes in aligned arrays is to count the nanotubes in highly magnified scanning electron microscopy (SEM) images4,5 or to use SEM power spectra.6−8 Despite the popularity of SEM, it is almost impossible to gain statistically meaningful, yet spatially resolved data from such © 2014 American Chemical Society

imaging techniques for large sample volumes. Small-angle X-ray scattering (SAXS), however, gives statistically averaged data and allows spatially resolved measurements over sample volumes of several cubic millimeters in just a few hours on a modern synchrotron X-ray source. In this method, just like a laser beam is scattered from a hair, X-rays are scattered from cylindrical objects only in the direction orthogonal to the cylinder axis. In principle, this makes SAXS the ideal tool for studying the orientation distribution of carbon nanotubes, although, as in the case of SEM power spectra analysis, we do not obtain the 3dimensional orientation distribution. Rather, the electron densities of the carbon nanotubes are projected onto the plane orthogonal to the film normal, as depicted in Figure 1a, and the observed distribution of orientations is the one of these projections. However, the projected distribution can be related to the 3-dimensional orientation distribution (Figure 1b) via mathematical relations. Several SAXS studies of carbon nanotube forests have focused on the Hermans orientation parameter as a quantification of the orientation distribution.9−11 The parameter is independent of distribution shape and thus easy to determine. In order to address the shape, the orientation Received: January 30, 2014 Revised: March 27, 2014 Published: April 16, 2014 9507

dx.doi.org/10.1021/jp501060s | J. Phys. Chem. C 2014, 118, 9507−9513

The Journal of Physical Chemistry C

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been paid to the macroscopic bulk properties of AA-CVD grown aligned MWCNT forests, and a detailed understanding of the growth process is lacking. Investigations into the orientation of the CNTs as a function of position within the MWCNT forest would provide critical information needed to understand and improve the AA-CVD process.

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EXPERIMENTAL SECTION Synthesis. Carbon nanotubes were produced using a conventional tube furnace AA-CVD technique reported elsewhere.20 The CVD system was heated up to 760 °C under argon flow. Multiwalled carbon nanotubes were grown on a silicon wafer with a native oxide layer by pyrolyzing an injected mixture of toluene and 5 wt % ferrocene under Ar/H2 (v/v % 10/1) at 760 °C. The reaction time was 5 h. The density of the MWCNT carpet, which was continuous over 7854 mm2, was estimated gravimetrically to be 0.02 g/cm3, and the MWCNT surface area was calculated according to Peigney et al.21 to be 35 m2/g and measured using a NOVA surface area analyzer to be 47 m2/g. The degree of graphitization, the Id/Ig ratio, obtained from Raman spectroscopy was measured to be 0.8, and the crystallinity index investigated using X-ray diffraction was calculated to be 42%. The oxidation resistance of the MWCNT was obtained from TGA. The oxidation starts at 480 °C, and 70% of the sample mass is lost at 500 °C. The residual mass of the inorganic iron oxides was 4.8%. Scanning Electron Microscopy. SEM images of the carbon nanotube film were taken using the InLens detector of a Leo Gemini 1530 equipped with a field emission gun at acceleration voltage of 15 kV and working distance of 5.8 mm. Semiquantitative analysis of SEM images gives an average diameter of 41 ± 17 nm and a length of 700 μm for the carbon nanotubes. The CNT waviness ratio in Figure 4 was defined as in ref 22 to be w = a/L, where a is the amplitude of the wave and L is the wavelength. At each film height the waviness was determined for at least 50 points by evaluating at least five different SEM pictures. Small-Angle X-ray Scattering. For SAXS experiments, a specimen was subsequently cut using a wafer cutter from the carbon nanotube film to obtain a narrow slice approximately 1 mm wide in X-ray beam direction and 1 cm long in horizontal direction. The MWCNT film was measured with SAXS in transmission geometry at beamline P03 at the synchrotron storage ring PETRA III of DESY in Hamburg, Germany. Details of the instrument can be found elsewhere.23 The X-ray beam (λ = 0.0957 nm) was focused to 24 μm (fwhm) horizontally and 17 μm (fwhm) vertically at the sample position. The scattered X-rays were detected using a 2dimensional Pilatus 300k detector (Dectris, Switzerland) at a distance of 3.95 m. Using exposure time of 0.5 s per image, the MWCNT film was scanned vertically in steps of 25 μm (24 steps) and horizontally in steps of 100 μm (11 steps). Transmission T was measured simultaneously to SAXS. To obtain the radial intensity as a function of the azimuth angle, φ, each scattering pattern was radially averaged over a q range 0.14−0.17 nm−1. Here, q = 4π sin(ϑ)/λ, where ϑ is half of the scattering angle. The nanotube radius was obtained by fitting a cylindrical core−shell model24 to the azimuthally averaged SAXS data, while using a log-normal radii distribution to add polydispersity. The number size distribution for the cylinder outer radii was a log-normal distribution defined as

Figure 1. (a) Orientation of a carbon nanotube. The SAXS signal comes from the electron density projected onto the zy plane, where the angle of a projected nanotube with respect to z axis is given by ω, and angle φ = π/2 − ω. (b) An example of a simulated 3-dimensional orientation distribution (3D-OD) and its projection (POD) onto the zy observation plane. Parameters α and β are the scale and shape parameters of the generalized normal distribution in eq 7. (c) SEM image showing the cross section through the MWCNT forest (scale bar 100 μm), along with higher magnification images (scale bar 10 μm) from different positions in the film.

distributions obtained by different methods have been fitted using the normal distribution function,12 Lorentzian distribution function,13 or a combination of both,14,15 despite apparent discrepancies between data and model. It remains an open question whether a more appropriate description of the orientation distribution shape can be obtained from SAXS data and what can be learned from such a description. To this end, we have investigated the orientation distribution of a multiwalled carbon nanotube (MWCNT) forest produced by the aerosol-assisted chemical vapor deposition (AA-CVD) process using an iron catalyst. AA-CVD has become one of the most efficient methods for large area, high yield production of aligned MWCNT forests, due to no need for catalyst pretreatment and simultaneous injection of the catalyst and carbon.16,17 The AA-CVD method works with a variety of low cost solvents (e.g., benzene, toluene, xylene) as carbon source, whereas in most cases ferrocene is used as the catalyst soluble in hydrocarbons.18 Adding nitrogen-containing hydrocarbons such as acetonitrile or ethylenediamine to the solvent19 opens up the possibility to produce nitrogen-doped aligned MWCNT forests with varying doping levels. So far, little attention has 9508


The Journal of Physical Chemistry C N (R ) =

⎡ (ln R − μ)2 ⎤ exp⎢ − ⎥ RS 2π ⎦ ⎣ 2S2

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iron catalyst, which according to SEM measurements is found homogeneously all over the film, (μ/ρ)Fe = 102.488 cm2/g.25 As volume fractions of carbon-based material and iron catalyst, we chose δg = 0.95 and δFe = 0.05, respectively. And finally, d = 0.1 cm is the thickness of the sample along the beam path. Uncertainties arise from the amount of iron within the film. The effective areal density of nanotubes ρA was calculated from ρ using the nanotube volume determined from SAXS

1

(1)

where μ = ln Rmed and Rmed is the median outer radius of the cylinder, S is the shape parameter of the distribution, and R is the outer radius of the cylinder. The standard deviation of the distribution, σ, is given by σ = (exp(S2 + 2 μ)[exp(S2) − 1])1/2. Using local monodisperse approximation, the intensity from noncorrelated polydisperse hollow cylinders and a power-law background can then be expressed I(q) = Aq

−4

+B+

∫0

ρA =

∞

N (R )P(q , R ) dR

(2)

(3)

Here, VS is the volume of the cylinder shell and VC is the volume of the empty cylinder core, while ρS is the scattering length density of the shell and RC is the radius of the core. The azimuthally averaged SAXS intensity was fitted over a narrow q range 0.12−0.27 nm−1, which covered just the first small hump coming from the first-order Bessel function J1(x). Larger fitting ranges allowed too many local minima for the minimization routine to work reliably for the whole data set. In total, six fitting parameters were used: A, B, C, S, R, and the ratio RC/R. To make the hump more pronounced in the fit, the data and the model were weighted with q3.5, and during the minimization each intensity point was assigned equal weight. To fit hundreds of curves with the same fitting range and conditions is a challenge, and thus in four cases Dmed or S reached the parameter limits set in the fitting procedure. The observed angular intensity distribution as a function of φ is a projection of the 3-dimensional orientation distribution given as a function of angle θ (see Figure 1a for the geometry). The projected orientation distribution (POD) can be calculated from a 3D orientation distribution (3D-OD) for example by Monte Carlo integration. For each γ ∈ [0, π/2] we calculate the corresponding projected angle on the plane orthogonal to the substrate ⎛ sin θ sin γ ⎞ ⎟ ω = arctan⎜ ⎝ cos θ ⎠

(6)

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RESULTS AND DISCUSSION SEM images of the cross section of the AA-CVD grown carbon nanotube film in Figure 1c show that the qualitative alignment of the nanotubes in the film varies along the film height. In order to quantify this variation in alignment, SAXS measure-

(4)

By further taking a histogram of the angles ω while weighing by sin θ to compensate for the different solid angles, we obtain the POD which is directly comparable to the measured orientation distribution from SAXS as a function of angle φ because the mean of the intensity distribution is shifted 90° with respect to the mean nanotube direction. The mass density ρ of the film at each height was calculated from the X-ray transmission through the sample with the Beer− Lambert law ⎧ ⎡ ⎫ ⎛ μ⎞ ⎤ ⎪ ⎪ ⎢ ⎛ μ⎞ I ⎥ ⎬ ⎨ T= = exp − δg ⎜ ⎟ + δ Fe⎜ ⎟ ρd I0 ⎝ ρ ⎠Fe ⎥⎦ ⎪ ⎪ ⎢⎣ ⎝ ρ ⎠g ⎭ ⎩

ρg π (⟨R med⟩ − ⟨R core⟩2 )⟨H /cos φ⟩

Here H is the height of the X-ray beam, the denominator gives the mass of an average MWCNT in the X-ray beam path, ⟨Rmed⟩ is the mean of the median outer radius of the nanotubes, ⟨Rcore⟩ is the mean of the median inner radius of the tubes, and ⟨H/cos φ⟩ is the mean length of the MWCNTs in the illuminated volume, obtained by weighing with the probability of the orientation distribution, and by using the angular distribution, i.e., the projected orientation distribution, we introduce a small error into the calculation. ⟨Rcore⟩ was approximated from outer diameter according to ⟨Rcore⟩ = 0.15⟨Rmed⟩, and for the mass density of graphite we use ρg = 2.1 g/cm3.

where A, B, and C are fitted constants and the form factor P(q,R) of a long hollow cylinder is approximated as24 2 J1(qR C) ⎞ J1(qR ) 1⎛ ⎟ P(q , R ) ∝ ⎜VSρS − VCρS q⎝ qR qR C ⎠

δgρH 2

Figure 2. (a) Close-up of a 2D-SAXS pattern on logarithmic scale from one spot within the vertically aligned MWCNT film, 500 μm below the top surface. The middle part is saturated for better visualization of the “eye pattern” typical for MWCNT films. The circles indicate the limits of radial averaging and the lines the limits of azimuthal averaging over φ in horizontal and vertical direction. (b) Azimuthally averaged intensities in vertical (Iv) and horizontal (Ih) direction, q2 normalized. The dashed lines mark the q range used for the radial averaging. The solid line shows a fit of the hollow cylinder model with a log-normal radii distribution N(R) having median outer radius Rmed = 22.6 nm, S = 0.33 nm, and Rcore/Rmed = 0.15.

(5)

where I is the X-ray photon flux after the sample and I0 is the photon flux before the sample. For the X-ray mass attenuation coefficient of graphite (μ/ρ)g at λ = 0.0957 nm, an interpolated value of 1.448 cm2/g was used, and further, to account for the 9509



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Figure 3. (a) Black dots show part of the radially averaged 2D-SAXS data from Figure 2a as a function of the azimuth angle φ. The same curve is drawn three times for clarity; the two upper curves have been shifted vertically. The lines represent the best fits to the data with Gaussian (ND), Lorentzian (LD), and the generalized normal distribution (GND). Below, the residuals (Idata − Imodel)/σdata of each fit. For the GND fit, β = 1.38 and α = 33°. (b) Examples of shapes of orientation distributions obtained from SAXS at different positions on the MWCNT film and the respective 3D orientation distributions which are drawn symmetrical also to the negative angles to aid the comparison of their shapes to the experimental ones.

ments were carried out with high spatial resolution. Simultaneously, the MWCNT diameter and the density of the MWCNT forest at each height are obtained. An example of a measured two-dimensional SAXS image is shown in Figure 2a. Azimuthally averaged data from this image can be used for the determination of the local nanotube diameter. The intensity in the horizontal direction should come from the fraction of the nanotubes that are vertically oriented. In Figure 2b, the scattering curve in the vertical direction has a different shape compared to the curve averaged in the horizontal direction, indicating that the intensity observed in the vertical direction results largely from defects in the nanotubes. The scattering from defects may be assumed to be similar in all directions, i.e., isotropic, and subtracting the two curves from each other gives a curve which arises mainly from oriented carbon nanotubes, which can be thought of as ideal hollow cylinders with a well-defined shell thickness. The subtracted curve was fitted with a hollow cylinder model described in ref 24 with the addition of a log-normal radii distribution. The exact shape of the projected MWCNT orientation distribution (POD) can be obtained from the 2-dimensional SAXS images after radial averaging of the data. We analyze only the nonisotropic part of the radially averaged SAXS intensity, ignoring the fairly constant background, which we assume to be mostly coming from impurities and defects. Because the distribution shape varies a lot along the film height, the question arises if one should use different models to describe the distribution at different heights or a combination of distributions. We chose to use only one model which gives us an overall picture of the changes in the distribution shape. The best fit to the radially averaged SAXS signal as a function of the azimuth angle φ was found with the generalized normal distribution, also called exponential power distribution in the literature26−28

Figure 4. From SAXS analysis, fitted α (scale) and β (shape) parameters of the generalized normal distribution, the Hermans orientation parameter f, the fitted median diameter Dmed and the standard deviation σ of the log-normal radii distribution for the MWCNTs, the mass density ρ, and the effective areal density ρA in the sample as a function of height (zero at top surface of the film). At each height, 11 measurements were taken at different horizontal positions. Waviness of nanotubes determined from SEM images is shown for comparison. A box in all the boxplots represents the band within which 50% of the data lie; the horizontal line represents the median of the distribution; and the whiskers show the lowest and highest data within 1.5 times the interquartile range from the respective quartile, thus covering nearly the entire distribution. The “+” symbols represent outlier data points.

GND(φ) =

⎡ ⎛ |φ − μ| ⎞ β ⎤ β ⎟ ⎥ exp⎢ −⎜ ⎢⎣ ⎝ α ⎠ ⎦⎥ 2α Γ(1/β)

(7)

where α is a scaling factor related to the width, β is the shape parameter determining the sharpness, and μ is the mean of the distribution. Γ denotes the gamma function. The GND reduces 9510



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Figure 5. Parameters related to alignment of the nanotubes ( f, α, β) as a function of the (a) nanotube median diameter Dmed, (b) the mass density ρ of the film, and (c) the effective nanotube areal density ρA at each height of the MWCNT film. All values are means from 11 horizontal measurement points. The error bars represent the standard deviations. Only a data point from the very top surface of the film has been omitted. The points close to the top surface have strongest color. Solid lines represent the best fit with orthogonal distance regression (ODR) for a line in case of (a) and (b) and for a logarithmic function of the form y = A ln(Bx) + C, where A, B, and C are fitting parameters, in the case of (c). The dashed lines show the corresponding 1σ errors for the linear fit.

to the normal distribution when β = 2 and to Laplace distribution when β = 1. An example fit of GND and other commonly used distribution functions to part of the radially averaged data is shown in Figure 3a together with the respective goodness-of-fit parameter χ2/N, which is close to 1 for the optimum fit. Visually inspecting, the GND fits the experimental data far better than the normal distribution or the Lorentzian, but in the GND we are also introducing one additional fitting parameter. According to a further test using Akaike information criterion (AIC),29 which takes into account not just the goodness of fit but also the number of fitting parameters, the GND was superior compared to the other two models for 99.4% of the data sets. Figure 3b collects together the typical projected distributions obtained for the sample with their corresponding 3D orientation distributions. Notably, for the Gaussian distribution and for the fully isotropic distribution, the shape of the POD is the same as that of the 3D-OD, while in case of the GND, the value of the shape parameter β increases for the POD, and the projection makes the distribution look less sharp, as demonstrated in Figure 1b. To compare different approaches for quantifying the orientation of the nanotubes, we also evaluated the Hermans orientation parameter,9,30 f. For perfect vertical orientation f = 1, for random orientation f = 0, and for horizontal orientation f = −0.5. All determined parameters at different heights of the MWCNT film are shown in Figure 4. Judging from the β parameter, the projected orientation distribution of carbon nanotubes is closer to the Laplace distribution than to the normal distribution, especially at the dense part of the film. This argument applies even more strongly to the 3-dimensional orientation distributions, which have even sharper shapes than the projected distributions. The width and the shape of the distribution are changing abruptly with height. To better understand the dependence between nanotube orientation and other properties of the film, possible correlations between the orientation parameters and film properties are examined. Figure 5 shows the most interesting cases. The commonly used Hermans orientation parameter, f, and the scale, α, and shape, β, identified from the projected

orientation distribution seem to be only weakly correlated with the nanotube diameter (Figure 5a). However, a linear correlation is found between the shape factor, β, and the mass density of the film within the studied density range, as shown in Figure 5b. Furthermore, when observing the orientation parameters as a function of the effective areal density of MWCNTs (Figure 5c), plateau regions are observed for all parameters at high effective nanotube areal densities. This shows that an increase in nanotube areal density does not necessarily lead to better alignment when this plateau region is reached. This may be due to the waviness of the nanotubes, which, as shown in Figure 4, stays finite even at the most aligned regions of the film. In the ideal case, it would be possible to control all the properties of the MWCNT film by changing the synthesis conditions. The growth mechanism of carbon nanotubes during catalytic chemical vapor deposition has been widely studied,31 but nearly no attention has been paid to the shape of the orientation distribution of the nanotubes; most studies have focused on obtaining a single figure of merit for the alignment. Recently, Bedewy and Hart32 have explained how mechanical coupling between MWCNTs during CVD growth enables the aligned growth of the MWCNTs but also leads to defects. Here we showed that instead of just pushing the distribution width, α, to smaller values, the self-confinement due to the coupling of the MWCNTs causes a sharper, nearly Laplace-like (β = 1), orientation distribution. It is important to note that the utility of the generalized normal distribution in materials science is not limited to carbon nanotubes. There are also other areas where self-confinement of anisotropic particles is creating aligned structures. For example, Förster et al.33,34 have fitted experimental orientation distributions of wormlike micelles using many distributions with special shapes. All of those distributions can be approximated to very high accuracy or even perfectly with the generalized normal distribution (plus a constant background in some cases). The shape parameter, β, of the GND is slightly over 1 for the distribution that Förster et al.33 found to fit their data best. Additionally, by fitting the generalized normal distribution to data that was published recently for aligned 9511



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piezoelectric nanofibers,35 we find the shape parameter of the projected orientation distribution of the aligned nanofibers to be between 1.3 and 1.5, depending on the fitted angle range. This suggests that the GND could be applied to the study of many aligned systems of aniostropic particles, e.g. nanowires and liquid crystals, or even biological systems. When preexisting theoretical models do not fit or do not exist, the generalized normal distribution can at least be used to quantify the distribution shape until a physically sound model is found.

Carbon Nanotube Arrays Produced by an Improved Floating Catalyst Chemical Vapor Deposition Method. Carbon 2010, 48, 2855−2861. (9) Wang, B. N.; Bennett, R. D.; Verploegen, E.; Hart, A.; Cohen, R. E. Quantitative Characterization of the Morphology of Multiwall Carbon Nanotube Films by Small-Angle X-ray Scattering. J. Phys. Chem. C 2007, 111, 5859−5865. (10) Bedewy, M.; Meshot, E. R.; Guo, H.; Verploegen, E. A.; Lu, W.; Hart, A. J. Collective Mechanism for the Evolution and SelfTermination of Vertically Aligned Carbon Nanotube Growth. J. Phys. Chem. C 2009, 113, 20576−20582. (11) Yang, X.; Yuan, L.; Peterson, V. K.; Minett, A. I.; Zhao, M.; Kirby, N.; Mudie, S.; Harris, A. T. Pretreatment Control of Carbon Nanotube Array Growth for Gas Separation: Alignment and Growth Studied Using Microscopy and Small-Angle X-ray Scattering. ACS Appl. Mater. Interfaces 2013, 5, 3063−3070. (12) Zhou, W.; Vavro, J.; Guthy, C.; Winey, K. I.; Fischer, J. E.; Ericson, L. M.; Ramesh, S.; Saini, R.; Davis, V. A.; Kittrell, C.; et al. Single Wall Carbon Nanotube Fibers Extruded from Super-Acid Suspensions: Preferred Orientation, Electrical, and Thermal Transport. J. Appl. Phys. 2004, 95, 649−655. (13) Hwang, J.; Gommans, H. H.; Ugawa, A.; Tashiro, H.; Haggenmueller, R.; Winey, K. I.; Fischer, J. E.; Tanner, D. B.; Rinzler, A. G. Polarized Spectroscopy of Aligned Single-Wall Carbon Nanotubes. Phys. Rev. B 2000, 62, R13310. (14) Wang, H.; Xu, Z.; Eres, G. Order in Vertically Aligned Carbon Nanotube Arrays. Appl. Phys. Lett. 2006, 88, 213111. (15) Das, N. Ch.; Yang, K.; Liu, Y.; Sokol, P. E.; Wang, Z.; Wang, H. Quantitative Characterization of Vertically Aligned Multi-Walled Carbon Nanotube Arrays Using Small-Angle X-ray Scattering. J. Nanosci. Nanotechnol. 2011, 11, 4995−5000. (16) Andrews, R.; Jacques, D.; Rao, A. M.; Derbyshire, F.; Qian, D.; Fan, X.; Dickey, E. C.; Chen, J. Continuous Production of Aligned Carbon Nanotubes: a Step Closer to Commercial Realization. Chem. Phys. Lett. 1999, 303, 467−474. (17) Mayne, M.; Grobert, N.; Terrones, M.; Kamalakaran, R.; Rühle, M.; Kroto, H. W.; Walton, D. R. M. Pyrolytic Production of Aligned Carbon Nanotubes from Homogeneously Dispersed Benzene-Based Aerosols. Chem. Phys. Lett. 2001, 338, 101−107. (18) Meysami, S. S.; Koós, A. A.; Dillon, F.; Grobert, N. AerosolAssisted Chemical Vapour Deposition Synthesis of Multi Walled Carbon Nanotubes: II. An Analytical Study. Carbon 2013, 58, 159− 169. (19) Koós, A. A.; Dowling, M.; Jurkschat, K.; Crossley, A.; Grobert, N. Effect of the Experimental Parameters on the Structure of Nitrogen Doped Nanotubes Produced by Aerosol Chemical Vapour Deposition. Carbon 2009, 47, 30−37. (20) Prehn, K.; Adelung, R.; Heinen, M.; Nunes, S. P.; Schulte, K. Catalytically Active CNT-Polymer-Membrane Assemblies: From Synthesis to Application. J. Membr. Sci. 2008, 321, 123−130. (21) Peigney, A.; Laurent, Ch.; Flahaut, E.; Bacsa, R. R.; Rousset, A. Specific Surface Area of Carbon Nanotubes and Bundles of Carbon Nanotubes. Carbon 2001, 39, 507−514. (22) Fischer, F. T.; Bradshaw, R. D.; Brinson, L. C. Fiber Waviness in Nanotube-Reinforced Polymer Composites - I: Modulus Predictions Using Effective Nanotube Properties. Compos. Sci. Technol. 2003, 63, 1689−1703. (23) Buffet, A.; Rothkirch, A.; Döhrmann, R.; Körstgens, V.; Abul Kashem, M. M.; Perlich, J.; Herzog, G.; Schwartzkopf, M.; Gehrke, R.; Müller-Buschbaum, P.; et al. P03, the Microfocus and Nanofocus X-ray Scattering (MINAXS) Beamline of the PETRA III Storage Ring: the Microfocus Endstation. J. Synchrotron Radiat. 2012, 19 (Pt 4), 647− 653. (24) Inada, T.; Masunaga, H.; Kawasaki, S.; Kobori, M. Y. K.; Sakurai, K. Small-Angle X-ray Scattering from Multi-Walled Carbon Nanotubes (CNTs) Dispersed in Polymeric Matrix. Chem. Lett. 2005, 34, 524− 525. (25) Hubbell, J. H.; Seltzer, S. M. Tables of X-ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients (Version 1.4), 2013.

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CONCLUSIONS The orientation distribution shape associated with MWCNT forests has been shown to vary strongly within the film. By using the generalized normal distribution, all shapes were easily described by a single function. We propose that the shape of the orientation distribution is directly linked to the MWCNT array density, and by applying these orientation distribution shapes in theoretical models, one may be able to model the properties of carbon nanotube materials more accurately.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (U.V.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Portions of this research were carried out at the light source PETRA III at DESY, a member of the Helmholtz Association (HGF). We thank Gonzalo Santoro, Shun Yu, Stephan Roth, and Torsten Boese for assistance in using beamline P03. We thank Julia Hütsch for assistance with the sample set up for the SAXS experiment. We gratefully acknowledge financial support from the German Research Foundation (DFG) via SFB 986 “M3”, projects B1, B4, and Z2, and the Graduiertenkolleg “Kunst und Technik”.

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REFERENCES

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Orientation Distribution of Vertically Aligned Multiwalled Carbon

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