Highly Oriented Direct-Spun Carbon Nanotube Textiles Aligned by In Situ Radio-Frequency Fields

Carbon nanotubes (CNTs) individually exhibit exceptional physical properties, surpassing state-of-the-art bulk materials, but are used commercially primarily as additives rather than as a standalone macroscopic product. This limited use of bulk CNT materials results from the inability to harness the superb nanoscale properties of individual CNTs into macroscopic materials. CNT alignment within a textile has been proven as a critical contributor to narrow this gap. Here, we report the development of an altered direct CNT spinning method based on the floating catalyst chemical vapor deposition process, which directly interacts with the self-assembly of the CNT bundles in the gas phase. The setup is designed to apply an AC electric field to continuously align the CNTs in situ during the formation of CNT bundles and subsequent aerogel. A mesoscale CNT model developed to simulate the alignment process has shed light on the need to employ AC rather than DC fields based on a CNT stiffening effect (z-pinch) induced by a Lorentz force. The AC-aligned synthesis enables a means to control CNT bundle diameters, which broadened from 16 to 25 nm. The resulting bulk CNT textiles demonstrated an increase in the specific electrical and tensile properties (up to 90 and 460%, respectively) without modifying the quantity or quality of the CNTs, as verified by thermogravimetric analysis and Raman spectroscopy, respectively. The enhanced properties were correlated to the degree of CNT alignment within the textile as quantified by small-angle X-ray scattering and scanning electron microscopy image analysis. Clear alignment (orientational order parameter = 0.5) was achieved relative to the pristine material (orientational order parameter = 0.19) at applied field intensities in the range of 0.5–1 kV cm–1 at a frequency of 13.56 MHz.


Raman Analysis
. Raman spectra of various CNT samples produced by the internal RF electrode setup. There is no significant difference between the reference sample spectrum to the other spectra of materials produced under the influence of an electric field.

TGA Analysis
TGA analysis revealed that the CNT fraction within the textiles was consistent between all samples, ranging from 69.6 %wt. to 74.6 %wt. (Fig. S2). However, the contents of amorphous carbon (i.e., soot, defective carbon etc.) seemed to somewhat increase with the rise in HV (from ~4 to ~12% wt. in the reference and 300 W samples, respectively). As the G/D ratio of the samples remained similar (Fig.   S1), this increase should not be attributed to the change in the CNT quality but most probably to the incorporation of VGCF whisker pyrolysis products (Fig. S5). The greater the HV that was applied, the higher the temperature got in the extensional whiskers (Fig. S6), thus leading to a higher pyrolysis rate in the reducing atmosphere of the reactor. The TGA residue is mainly made from oxidized iron nanocatalysts. Lower residue concentrations in the higher field intensity samples may be a result of electrostatic deposition. This could be attributed to increased losses of floating catalysts due to electrostatic interactions with the reactor walls. These parts consist of the reactor's ceramic tube walls and other grounded metallic parts positioned next to the path of the continuously collected CNT aerogel and the aerosolized nanoparticles surrounding it. The higher the applied intensity used in the process, the more dominant these electrostatic interactions would become, presuming that particles are charged or have induced dipoles, contributing to higher electrostatic losses and lower residue concentrations. W (e-f) 250 W (g-h) 300 W. While all fracture surfaces contain CNT pullouts, the HV samples seem to have considerably more. The CNTs next to the fracture surface in HV samples show a considerable amount of alignment, whereas anisotropic nature is present in the reference. Figure S4. Bar plot summarizing the tensile properties of AC field-aligned CNT samples. The tenacity is shown in blue (referring to the left y-axis), and the specific elastic modulus is shown in red (referring to the right y-axis). Samples included materials produced under an AC field with an RF input power of 200, 250, and 300W and a reference sample collected without any applied field (0W). Error bars denote standard deviations using at least three different samples. Figure S5. VGCF formation in the FCCVD reactor. (a) VGCF whiskers radially grow from the RF electrode surface towards the reactor's walls. (b) SEM image of a whisker, revealing an isotropic network of VGCFs. Inset shows a single VGCF in higher magnification. (C) SEM image of a whisker produced under the influence of the HV, showing more alignment in the VGCF network. Inset shows that finer "dendrite"like whiskers are produced when the HV is applied during the whisker synthesis. Figure S6. VGCF "extensional" whisker growth in the FCCVD reactor. (a) VGCF whiskers axially grow from the RF electrode downstream, creating an extension to the RF electrode. (b) Some of the "extensional" whiskers grew to be 150 mm long. (c) SEM image of a VGCF "extensional" whisker made of long, aligned VGCFs. The inset shows a high magnification image revealing that the VGCFs are extremely thin (~100 nm in diameter) with a CNT core (arrow). Figure S7. SEM image of CNT material produced under a field intensity of 0.75 kV cm -1 . Arrows track the path of an ultra-long CNT bundle measuring more than 100 µm in length. Figure S8. Boxplots of curl ratios measured from SEM images at different field intensities. Whiskers are placed at 1.5 times the interquartile range. Orange lines indicate medians, and green triangles show means. Figure S9. SEM images of CNT materials produced at different field intensities. Colored lines show distinct traced CNT bundles for waviness calculations. Scale bar is shared between images.

RF current model
The RF model for SWCNTs, and thus the results of this section, are based on the transmission line description of a Luttinger liquid for electrons near the Fermi level by Burke. 1 In the Luttinger liquid, the four conducting states at the Fermi level split into four separate modes, only one of which carries a charge. The charge-carrying mode can be described by a transmission line model shown in Fig. S10 with distributed capacitance , inductance ℒ, and resistance ℛ per unit length. We also note that the model does not take current saturation explicitly into account. In practice, the current in the CNT cannot exceed the saturation current 0 . For simplicity, we will assume that the current simply does not increase further once it reaches 0 according to the model. A model where current saturation is fully taken into account via a modified resistance term should be considered in future work.
The equations governing the transmission line model are known as the telegrapher's equations, and with the extension of an AC voltage source are given by: The capacitance and inductance per unit length are parametrized based on the linear dispersion relation of electrons in a SWCNT near the Fermi level and follow from the finite energy spacing and electronic kinetic energy, respectively: where and ℎ denote the elementary charge and Planck's constant, ≈ 0.25 is the electronic interaction factor and F ≈ 8.0 × 10 5 m s −1 is the Fermi velocity for SWCNTs. 1 The two telegrapher's equations can now be combined into a single second-order PDE for the current: To find the steady-state solution, we calculate the Fourier transform of the PDE in time, and write in terms of the Fourier transforms of the current ( , ) and the electric field ℰ( ): Solving this ODE with respect to with boundary conditions ( , 0) = ( , ) = 0 yields: where ( ) denotes the propagation constant of the charge carrying mode: The AC electric field of angular frequency 0 and amplitude 0 is ( ) = 0 sin (   In this regime, i.e., for ω 0 " 2 π f 0 * , the current expression can be expanded to in 0 : Notice that there is no explicit time dependence of the current in that regime, and the current changes sign every half period of the AC field. Hence, we may assume the magnitude of the current is constant in time ( , ) = ( ). Furthermore, the current is a quadratic function with its extremum at the center of the CNT. In this approximation, the average magnitude of the current along the CNT and in time is: Using the same approximation, we can also calculate the length of the CNT for which the current exceeds the saturation current Δ L by solving ( ) = 0 for . Relative to the length of the CNT it is:

Statistical model
The CNT alignment with alternating electric fields can be described using the worm-like chain model with energy contributions from bending, electric polarization, and the additional electromagnetic interactions due to the z-pinch stiffening effect.
As justified in the main text, we will neglect any variation of the current magnitude in the CNT along its contour and in time. Without loss of generality, we fix the direction of the current to point along the tangent vector of the chain ( ) =( ). Here, we derive the free energy contribution of the z-pinch stiffening effect.

From current to pressure
Suppose a current ( ) =( ) is applied to the CNT. In this work, we will assume that a CNT can be modeled as a thin cylindrical shell with internal and external radii 1 , 2 . Assuming a uniform distribution of the current, the current density is given by: In the following, we will assume all electric and magnetic fields are quasi-static such that we can neglect all dynamical terms in the field equations. We introduce a set of cylindrical coordinates that follows the chain contour ( , , ) with corresponding coordinate unit vectors {̂( , ),̂( , ),( )}. In these coordinates, the resulting magnetic field can be computed using Ampère's law: In turn, the current experiences a Lorentz force due to the magnetic field, which is given by: Note that the force is pointing towards the center of the CNT and should result in compression in a mechanism analogous to the compression and confinement of a plasma using a z-pinch.
As the extension of -orbitals outside the surface can be considered small compared to the radius of the CNT, we can compute the mean pressure acting on the surface and take the limit of vanishing thickness: where is assumed to be the mean radius of the CNT and the pressure acting on the surface of the CNT is given by: Note that by taking this limit, the initial assumption of finite wall thickness disappears. Any finite current distribution in the CNT will lead to the same result for the pressure.

From pressure to force
As the WLC model describes an object that is inherently one-dimensional, we need to derive a contour force density from the pressure acting on the shell of the CNT. Let us first parametrize a point ( , ) on the surface of the CNT in cylindrical coordinates: ( , ) = ( ) +̂( , ).
Here, ( ) is the position vector of the CNT contour and ̂( , ) is the radial vector perpendicular to the tangent vector at ( ). Next, we define the Frenet-Serret basis {( ),̂( ),̂( )} of the chain: where ( ) is the local curvature of the chain. In this basis, the radial vector can be expanded as: With this parameterization, we can compute the differential surface element of the CNT: The line force density is then obtained by integrating out the angular dependence of the radial force: where = 2 is the cross-sectional area of the CNT. Hence, the pressure resulting from the current will always work against the curvature of the chain.

From force to energy
In the next step, we want to derive a free energy expression that will result in the correct force density that we have derived in the above section upon minimization. In order to fully specify one configuration of the chain, we will provide values for the tangent vectors at both ends of the chain ( 0),( ) as well the position of some point ( * ) along the chain. We will later show that the choice of * is unique rather than arbitrary. Further note that the variation of these quantities vanishes by definition. The virtual work done by the force density is given by: The resulting expression has the natural interpretation of a chain that is being stretched by two forces of magnitude pulling in the direction of both ends.
As the variation of the specified position ( * ) = 0, we may write for the virtual work: The variation of the potential of the force density is simply = − , such that we obtain the following expression for the potential: By imposing invariance under the given symmetry, we quickly find * = /2, such that we can write for the free energy of the internal pressure: Thus, we have arrived at the main modeling result of this work. Again, the above free energy expression has the natural interpretation of both halves of the chain being pulled in the direction of their respectively closest ends, with the mid-point of the chain being fixed in place.

Current, Cross-Sectional Area and Temperature
The current is taken to be an appropriate multiple of the saturation current 0 based on the number of CNT walls present in the structure.
The cross-sectional area is determined by the radius of the CNTs. In the case of SWCNT bundles, the sum of the cross-sectional areas of the SWCNTs is used. For MWCNTs, we choose the radius of the outermost CNT.
Temperature is taken into account by statistical averaging over the canonical ensemble of all WLC configurations. In all results presented in this work, the temperature was chosen as = 1200 K, but was generally found to only have a negligible effect on the resulting alignment compared to all other model parameters.

Stiffness Parametrization
In the above free energy expression, we still need to specify the stiffness of the CNT structure under investigation. For SWCNTs, we use the following empirical formula calculated for armchair CNTs using Molecular Dynamics simulations 2 : SWCNT = 63.80( /Å) 2.93 eV Å.
Bundles of SWCNTs have different scaling due to the interaction of the π-orbitals given by 3 : = SWCNT ( B ) 1.9 .
Finally, the scaling for MWCNTs follows by the addition of the bending moments, leading to the addition of the stiffnesses over the number of CNT walls W 4 : = ∑ SWCNT,i =1 .

T2 From 3D Model
The model described above is inherently three-dimensional. The order parameter T2 however describes alignment in two dimensions. For convenience, we repeat the definition of T2 from the manuscript: 2 = ⟨cos 2 θ 2D ⟩ − 1.
We, therefore, need to derive the above average in terms of the two-dimensional alignment angle from three dimensions. First, consider a general three-dimensional unit vector in spherical coordinates: ̂= ( cos ϕ sin θ 3D sin ϕ sin θ 3D cos θ 3D ) .
Assuming the 3D orientation distribution function of the system is a function 3D , we may calculate the mean value of the squared cosine of the two-dimensional alignment angle θ 2D as follows: ϕ sin θ 3D (θ 3D ) cos 2 θ 3D cos 2 θ 3D + sin 2 θ 3D sin 2 ϕ .
In the well-aligned regime, we have ⟨| cos 3D |⟩. ≈ ⟨ cos 3D ⟩, where we document how to calculate the latter average in the harmonic approximation in our previous work, to which the reader is referred to for details. 5