Quantifying the Hierarchical Order in SelfAligned Carbon Nanotubes from Atomic to Micrometer Scale Eric R. Meshot,† Darwin W. Zwissler,†,∥ Ngoc Bui,† Tevye R. Kuykendall,‡ Cheng Wang,§ Alexander Hexemer,§ Kuang Jen J. Wu,† and Francesco Fornasiero*,† †
Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States ‡ Molecular Foundry and §Advanced Light Source, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, United States S Supporting Information *
ABSTRACT: Fundamental understanding of structure− property relationships in hierarchically organized nanostructures is crucial for the development of new functionality, yet quantifying structure across multiple length scales is challenging. In this work, we used nondestructive X-ray scattering to quantitatively map the multiscale structure of hierarchically self-organized carbon nanotube (CNT) “forests” across 4 orders of magnitude in length scale, from 2.0 Å to 1.5 μm. Fully resolved structural features include the graphitic honeycomb lattice and interlayer walls (atomic), CNT diameter (nano), as well as the greater CNT ensemble (meso) and large corrugations (micro). Correlating orientational order across hierarchical levels revealed a cascading decrease as we probed finer structural feature sizes with enhanced sensitivity to small-scale disorder. Furthermore, we established qualitative relationships for single-, few-, and multiwall CNT forest characteristics, showing that multiscale orientational order is directly correlated with number density spanning 109−1012 cm−2, yet order is inversely proportional to CNT diameter, number of walls, and atomic defects. Lastly, we captured and quantified ultralow-q meridional scattering features and built a phenomenological model of the large-scale CNT forest morphology, which predicted and confirmed that these features arise due to microscale corrugations along the vertical forest direction. Providing detailed structural information at multiple length scales is important for design and synthesis of CNT materials as well as other hierarchically organized nanostructures. KEYWORDS: carbon nanotube, order, hierarchical, multiscale, structure, X-ray
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As the structural order (e.g., arrangement of atoms, defects) within the individual nanocarbon building blocks determines their functional properties, in an analogous way, order and alignment of these building blocks within a larger ensemble strongly influence the material’s macroscale performance. For example, the anisotropic structure of vertically self-aligned carbon nanotube (CNT) “forests” is strongly tied to their potentially transformative properties for a range of applications such as supercapacitors,32−36 electronic interconnects,37,38 emitters,39,40 adhesives,41 mechanical materials,42 separation membranes,28,29,43−46 and advanced yarns and fabrics.31
ynthetic nanocarbon allotropes, such as fullerenes, nanotubes, and graphene, boast a range of exciting properties and promise to transform countless applications.1−6 Due to their exceptional thermal, mechanical, and electrical properties, there is significant interest to build macroscale assemblies from these nanoscale subunits to realize next-generation (multi)functional materials.7 Researchers continue to develop increasingly complex nanocarbon structures, comprising a single type of allotrope8−12 or hybrid mixtures of multiple allotropes,13−22 and often having hierarchical organization. Whether by bottom-up self-organization or top-down fabrication, various structural motifs in nanocarbon assemblies have been synthesized and shown to be potentially transformative for nanoelectronics,23,24 electrical storage devices,25−27 filtration membranes,28,29 mechanical cables and reinforcements,30 and transparent or flexible conductive films.31 © 2017 American Chemical Society
Received: November 30, 2016 Accepted: April 17, 2017 Published: April 17, 2017 5405
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popular route for semiquantitative evaluation of CNT alignment,50−52 and recent advances in 3D electron tomography techniques using TEM have proven promising for characterizing the alignment of CNTs within composites.53 Polarized Raman spectroscopy is nondestructive and has been used to provide information about both nanoscale alignment of CNTs as well as atomic scale defects,54,55 but it fails to provide structural information at larger length scales because the technique is inherently based on the vibration of chemical bonds at the atomic scale. Likewise, polarized near-edge X-ray absorption fine structure (NEXAFS) spectroscopy is limited to the atomic scale.56,57 Alternatively, X-ray scattering is a nondestructive technique that enables quantitative structural characterization of statistically significant populations of CNTs. It also has the added advantage of enabling spatial mapping58 and in situ experiments59,60 when leveraging the high photon fluxes of synchrotron sources. Previous studies have separately used wide-34,60,61 and small-angle58,59,62−66 X-ray scattering (WAXS, SAXS) to quantify order in CNT materials by virtue of the alignment at atomic and nanoscales, respectively. Small-angle neutron scattering (SANS) was also used to quantify nanoscale order in CNT forests.67 While ultrasmall-angle X-ray scattering (USAXS) was previously used by Verploegen et al. to investigate large-scale bundling in the meso/microscale regime,68 information regarding the orientational order was lacking because they were unable to record 2D scattering images. None of these studies captured and correlated order at multiple length scales or at extreme length scales (atomic and micrometer). Our work represents advancement over the state-of-art structural characterization of three-dimensional (3D) nanocarbon structures, exemplified here by a CNT forest, in three key ways. First, by leveraging a set of complementary X-ray scattering beamlines at the Advanced Light Source, we continuously and quantitatively mapped structural order across an expanded range of length scales, which spans 4 orders of magnitude from 2.0 Å to 1.5 μm. Therefore, we were able to fully describe multiscale structural features that dictate macroscale material properties, including the sp2-hybridized honeycomb lattice and graphitic walls (atomic), CNT diameter (nano), as well as the greater CNT ensemble (meso) and large corrugations (micro). Second, full 2D resolution in the scattering images enabled us to quantify alignment at all length scales. Combining these detailed measurements at each length scale, we revealed that the orientational order within a single CNT forest exhibited a cascading decrease as we probed finer structural feature sizes. In addition, we could investigate how structural order at one length scale affects order at subsequent length scales. To draw qualitative relationships, we synthesized single-, few-, and multiwall CNT forests having a range of structural characteristics. We show here that multiscale orientational order is strongly influenced by, and tracks with, CNT number density (CNT/cm2), while it is inversely related to CNT diameter, wall number, and atomic defects. Third, we resolved ultralow-q meridional scattering features that, to our knowledge, have not been previously captured or quantified by X-ray scattering. We built a phenomenological “coarse-grained” model of the large-scale CNT forest morphology, which predicted and confirmed that these scattering features arise due to microscale corrugations along the vertical forest growth direction. Experimental results
To clarify the relationship between the anisotropic structural hierarchy of CNT forests and their properties, let us consider a mechanics example. The equation for the effective Young’s modulus of an array of CNTs reads E = (ρN × L × τ ) × K ≈ ρN × τ × g (τ ) × J × G
(1)
where each parameter is defined by the following: • ρN is the packing number density (CNT/area) • L is the serpentine length of the CNT • τ is the tortuosity (defined by L divided by forest height) • K is the effective spring constant approximated here by the dominant torsional mode component47 • g(τ) is a complicated function of tortuosity (see Supporting Information, eq S2) • J is the torsional moment of inertia (∝ do4 − di4, where do is the mean CNT outer diameter and di the mean inner diameter) • G is the shear modulus of the CNT sidewall This expression of the effective modulus of a CNT forest in eq 1 elegantly illustrates how order at every length scale critically influences observable macroscopic properties. The value of G is dictated by the atomic-scale structural quality (i.e., defect density in the graphitic lattice) of an individual CNT, J depends on nanoscale features such as the CNT diameter, ρN is a meso/macroscale quantity inversely proportional to the CNT-CNT spacing, and the tortuosity term τ also embeds a characteristic length scale that is inversely correlated with the collective alignment of the nanoscale units (Figure S1). This is especially important in hierarchical materials whose structure is interdependent on adjacent hierarchical levels and length scales. Note also that the hierarchical organization of a CNT forest stems directly from the collective CNT growth process, and thus multiscale characterization of structure and order in a CNT forest is expected to contribute to understanding its selfassembly process. More specifically, during synthesis, hydrocarbon gas molecules dissociate at metal nanoparticle catalysts to form bonds (∼0.14 nm) within the growing graphitic lattice, which in turn drives the elongation of individual nanotubes (∼100−101 nm diameter). A multitude of physical interactions among adjacent CNTs and within CNT bundles (∼101−102 nm) influences the growth process and consequent structural order. These interactions play a role in creating both lattice defects at the atomic scale48 as well as tortuosity49 and corrugations at the nano/mesoscale (∼101−103 nm). These interactions are also thought to be responsible for the selfaligned, anisotropic morphology of CNT forests. While fundamental understanding of the self-assembly process and of structure−property relationships in such complex, hierarchical carbon nanomaterials is crucial for designing functionalities, quantifying their structure across order-of-magnitude differences in length scale is challenging. Electron microscopy is universally used to evaluate the structure of CNT materials. Scanning electron microscopy (SEM) captures the morphological structure from micrometer to nanometer scales, while transmission electron microscopy (TEM) is restricted to nanometer and atomic scales. Overall, both techniques are limited in the number of CNTs that can be sampled at once, with fewer CNTs at higher magnifications, which reduces the statistical relevance of the measurements. Additionally, sample preparation for SEM and especially TEM can be destructive and thus skew the measurements. Nevertheless, processing and filtering SEM images has become a 5406
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projection of the 3D structure. CNT forests are isotropic in the plane of the substrate, so the image is symmetric along the meridian, and thus, we show only one-half of the q space throughout this work. Figure 2 shows both inverse-space and real-space features of a typical multiwall CNT (MWNT) forest. The left column gives a schematic representation of the X-ray scattering image in the entire range of accessible q space. Experimental X-ray scattering and electron microscopy data in middle and right columns show the forest structure at various magnifications, from the atomic scale of the sp2 carbon lattice to the microscale of corrugations in the forest. Atomic Scale. Using a WAXS configuration, with high energy and a short SDD on the order of 0.3 m, we resolved atomic-scale features of the CNT walls, namely the intralayer carbon lattice structure (100) and interlayer graphitic spacing (002). The (100) intralayer spacing at around q = 30 nm−1 is the largest q-feature captured in this study. A sheet of graphene would in principle produce at this q value a diffraction pattern with six distinct intensity spots as vertices of a hexagon because of the inherent six-fold symmetry of the sp2 carbon lattice. However, the structure of a CNT forest deviates from the idealized case of a graphene sheet in two important ways. First, a forest is comprised of many CNTs each with its own chiral angle, which means the ensemble-averaged diffraction pattern is actually a continuous ring of intensity rather than the six distinct spots. While previous reports suggest there is a preferential distribution of chiral angles in randomly aligned SWNT powders (skewed toward armchair),69 we expect no dominant chirality in our CNT forests. Second, due to the 1D nature of a CNT, the graphene lattice is substantially larger in the direction of the CNT axis compared to the perpendicular direction, which produces more scattering in the direction along the CNT. Therefore, the anisotropy of this feature is tied in large extent to the alignment of the CNT axis. The next scattering feature in the WAXS regime observed at slightly smaller q (∼16.5−18.5 nm−1; Figure S7) is generated by diffraction from the interlayer spacing of multiple concentric sidewalls stacked together.70 These q-values correspond to an interlayer distance that decreases from 0.38 to 0.34 nm with increasing CNT diameter,71 thus approaching the (002) spacing of bulk graphite (∼0.34 nm) in our wider nanotubes. Scattering peak position and shape are functions of the interlayer spacing between walls of the CNTs as well as the number of walls, nw. Therefore, quantitative interpretation of this peak is ambiguous for CNT forests with large proportions of single-wall CNTs (SWNTs) because these CNTs do not scatter in this q range. Previous studies suggest that this peak may contain other contributions,72 such as diffraction from CNTs in contact with each other because inter-CNT separation distances should be similar to the (002) interlayer spacing. While we observe contributions in our data that are possibly consistent with this explanation, our results are not conclusive. Opposite of the (100) intralayer feature, (002) interlayer scattering results in maximum and minimum intensities in the horizontal and vertical directions, respectively. Nanoscale. In order to quantify CNT forest morphology at the nanoscale, we collected scattering over a range of moderate q values (∼10−1−100 nm−1) using a SAXS configuration, which employs high energy and a long SDD of about 1.8 m. To crossvalidate our experiments between the high- and low-energy beamlines, we also measured scattering in an overlapping q range using 1 keV and a relatively short SDD of 0.05 m. Data
suggest that coordinated vertical corrugations in the CNT morphology are more likely to arise in forests of lower density.
RESULTS AND DISCUSSION Multiscale CNT Forest Structure. In order to map structure across multiple length scales, we collected 2D X-ray scattering images in different q regimes, where q is the magnitude of the scattering vector as defined by q= =
4π ⎛⎜ 2θ ⎞⎟ sin λp ⎝ 2 ⎠ ⎡1 ⎛ pixel size × pixel # ⎞⎤ ⎟⎥ sin⎢ tan−1⎜ ⎝ ⎠⎦ ⎣2 hc SDD
4πEp
(2)
where λp and Ep are the wavelength and energy of the incident photons (X-rays), respectively, while h is Planck’s constant, c is the speed of light, and 2θ is the scattering angle. We accessed different q ranges piecewise by tuning the incident energy Ep and the sample-to-detector distance (SDD). Thereby, we achieved continuous q mapping with full 2D resolution (qy, qz) in the scattering images from q = 0.004 to 32 nm−1, which corresponds to an exceptionally wide real-space range, from >1.5 μm to 2.0 Å (using the conventional 2π/q relation). Figure 1 provides a schematic of the scattering geometry with an illustration of a full-range 2D image, which describes a 2D
Figure 1. Schematic of experimental setup for synchrotron X-ray scattering measurements. As the incident X-ray beam impinges upon the CNT forest, the intensity drops from I0 to I1 (as monitored by ionization chambers upstream and downstream of the forest). X-rays scattered at an angle defined as 2θ are collected downstream on a 2D detector at a tunable SDD. The detector displays an illustration of the full 2D inverse space explored in this study, showing scattering patterns across multiple length scales for the various CNT forest structural features (each labeled on the detector in white text). The inverse space is mapped using the inverse momentum transfer vector q, the magnitude of which is defined in eq 2. Here, φ represents the azimuthal angle about the X-ray beam axis. 5407
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Figure 2. Multiscale structure of a MWNT forest (sample “MW2”). Columns display from left to right: (1) Schematic of observed multiscale scattering pattern (with inset box indicating select q space probed experimentally); (2) real experimental X-ray scattering image (log intensity); and (3) independent electron microscopy images display prominent structural feature captured at the corresponding length scale. Rows display from top to bottom: (a) Atomic scale (100) intralayer spacing of sp2-hybridized carbon lattice (Ep= 10 keV, SDD = 0.3 m) with TEM image adapted from ref 92 with permission from The Royal Society of Chemistry; (b) atomic scale interlayer (002) spacing of CNT sidewall (Ep = 10 keV, SDD = 0.3 m); (c) nanoscale CNT cylindrical FF, where the real-space feature size dFF is essentially the mean CNT outer diameter do (Ep = 10 keV, SDD = 1.8 m); (d) mesoscale CNT spacing/bundling, where the real-space feature size dSF captures the polydisperse CNT-CNT spacing (Ep = 0.284 keV, SDD = 0.05 m); (e) microscale reflections (abbreviated “μm refl.”) describe CNT corrugations along growth direction, where dμm is equal to the characteristic microscale wavelength λC of the CNT corrugation (Ep = 0.284 keV, SDD = 0.15 m). 5408
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Figure 3. Multiscale anisotropy of a MWNT forest (sample “MW2”). (a) 1D sector averages I(qy) = ∫ +10 −100 I(q,φ)dφ of intensity versus q reduced from the experimental 2D images shown in Figure 2 (full images in Figure S4b). As indicated in the inset schematic X-ray pattern, the dark gray line represents the direction along which the sector average intensity profile was taken (qy), while the cyan line represents the sector average direction along the meridian (qz). The line profiles display four distinct structural features labeled (100), (002), FF, and structure factor (SF). (b) Normalized azimuthal intensity distributions extracted from 2D images by scanning the azimuthal angle interval π φ = ⎡⎣0, 2 ⎤⎦about the beam axis, at select q positions corresponding to these structural features. The azimuthal scan at (100) was performed ⎡ π , 0⎤ as shown in the inset schematic because the 1D nature of CNTs generates a maximum intensity at φ = π for this feature, yet it is still ⎣2 ⎦ 2 π⎤ ⎡ plotted ⎣0, 2 ⎦ for ease of comparison between all hierarchical levels. (c) Orientational order at each hierarchical level, where Hermans order parameter was calculated from the intensity distributions in b) (dashed gray line is a visual guide). (d) Schematic model shows structural hierarchy of an aligned CNT forest and how sensitivity to small-scale perturbations increases as q increases.
We observed scattering in the range of q = 10−2−10−1 nm−1, primarily oriented perpendicularly to the CNT axis, along the horizon. Previous studies showed that this broad shoulder/ feature can be attributed to a combination of the spacing between neighboring CNTs (pair−pair correlation function) as well as bundles of several CNTs, generally referred to as the structure factor scattering, SF.68 In this work, we differentiate between the mesoscale structure factor, SF, and the crystallographic structure factors indicated by the three Miller indices. The fact that CNTs are inherently tortuous means that the CNT spacing is highly polydisperse as the CNTs bend in and out of contact with each other. This also implies that there is an abundance of contact points between CNTs and polydisperse CNT bundle sizes. Both of these characteristics contribute to the broad shoulder and overall lack of a defined peak observed in this q range for our experiments. At still lower q (150 CNTs, consistently gave the same trend, with σλ/λC = 0.27, 0.36, 0.38 for (a−c), respectively. An interesting question emerging from these results is whether low orientational order (high tortuosity at low CNT forest density) can give rise to high order at a higher hierarchical level. To elucidate the origin of the meridional reflections along qz and their relationship to nanoscale tortuosity, we used simulation to map the microscale order across a structural parameter space larger than the one accessed experimentally. We built a phenomenological model consisting of a spatially distributed array of sinusoids to mathematically describe and systematically investigate forest morphology via tuning of the model’s inputs. We ran simulations across 700 unique parameter combinations, which included population distributions (mean and standard deviation) of CNT outer diameter do as well as the wavelength λC and amplitude AC of the CNT oscillations. Our custom MATLAB script generated a simulated 2D real-space image based on these input parameters that closely mimics the forest morphology observed in SEM. From this simulated real-space image, we computed the square of the 2D FFT to derive its corresponding frequency (q) space image and thereby simulate X-ray scattering (Figure S10).50,52,81 With this method, we first confirmed that the simulated peak position was indeed a function of λC, according to the relation q = 2π/λC (Figure S11). Second, informed by the experimental measurements of our CNT forest structure, we fixed the values of do (8 ± 2 nm) and λC (1000 nm), and we mapped out the degree of microscale order [i.e., order ∼ (fwhm/qC)−1] as a function of polydispersity in wavelength σλ (100−800 nm) and amplitude AC (5−250 nm) (Figure 8). In the limiting cases of our simulations, we found no observable peak when σλ was comparable to the mean wavelength (i.e., σλ/λC ≥ 0.4), while multiple reflections were possible for low polydispersity σλ/λC < 0.2 (e.g., Figure S10c). Order is a clear function of wavelength polydispersity, yet by converting the waviness of the CNT AC/ λC to the nanoscale tortuosity f FF (Figure S1), we show that microscale order does not depend on tortuosity of the CNTs (Figure 8d). Note that our simulation results are in good agreement with our SEM (σλ/λC) and soft X-ray (fwhm/qC) experimental measurements of the microscale order, as shown by the star data points in Figure 8. Figure 7a also confirms that the forest with the most prominent ripples and the sharpest soft X-ray scattering peaks also has the most monodispersed λC. Therefore, microscale order is tied to the tightness of the
Figure 7. Microscale structure and order in CNT forests analyzed by SEM (with inset FFT2) and soft X-ray scattering (Ep = 0.284 keV, SDD = 0.15 m). The SEM images shown were captured at 10,000× magnification, but the corresponding FFT was computed from an SEM image captured at 3000× magnification with a resolution of 3072 × 2304 pixels. The experimental 2D X-ray scattering images (log intensity) display up to 0.04 nm−1 in both qy, qz directions, and the linear-log plots of I(qz) profiles (scaled such that maximum intensity is 1) to the right of the images were extracted along the dashed gray line. (a) ρN = 4.5 × 1010 cm−2; (b) ρN = 7.8 × 1010 cm−2; (c) ρN = 2.1 × 1011 cm−2.
literature and its potential importance toward understanding forest growth, so far there has been a lack of robust, quantitative characterization of these ripples beyond the use of SEM or visible iridescence.88 Also, in the absence of external forces, it remains unclear whether the mismatch in local nanoscale growth rates and mechanical coupling generate such ordered microstructure,81 rather than simply a higher degree of uncorrelated tortuosity. In this section, we combined SEM imaging, soft X-ray scattering, and a phenomenological model to fully characterize these concerted vertical corrugations within a CNT forest and their dependence on other structural features. For our less dense forests, scattering experiments at ultralow qz (
