Electromagnetic and optical responses of a composite material comprising individual single-walled carbon-nanotubes with a polymer coating

The composites and thin films comprising individual single-walled carbon nanotubes with a polymer coating (p-CNTs) have been prepared and their electromagnetic responses have been studied in a wide range from low-frequency (25–107 Hz) up to the infrared region. In spite of the high volume fraction of the nanotubes (up to 3.3%), the polymer coating prevents direct p-CNT contacts and the formation of the percolation network in those composites, so that p-CNTs interact only via the electromagnetic coupling. Thereby it is an ideal model system to verify experimentally the fundamental issues related to carbon nanotube electromagnetics, such as the influence of inter-tube electron tunneling on the localized plasmon resonance in the terahertz range, or the infrared absorption enhancement of polymer molecules attached to the nanotube surface. Along with addressing the fundamentals, applied carbon nanotube electromagnetics got insights important for the applications of p-CNT based composites as dielectric media in the terahertz regime. In particular, we found that the real part of the permittivity of the p-CNT film in the terahertz range is rather competitive, i.e. 8–13, however the loss tangent is not so small (0.4–0.6) as has been predicted. The way to increase p-CNT terahertz performance is also discussed.


Results and discussions
Two types of p-CNT materials with 1.5 and 5 wt% single-walled CNTs were fabricated; then they were used to produce composites and films comprising p-CNTs (see Methods). A typical scanning electron microscopy (SEM) image of the p-CNT composite with 5 wt% CNTs is represented in Fig. 1 (the SEM images of 1.5 wt% CNT composite can be found as Supplementary Fig. S1). One can see that p-CNTs are in contact with each other and their lengths do not exceed 1 μm. The space between p-CNTs is occupied by air. Here we would like to stress that the tubes are mostly individual, as the bundles were removed by strong centrifugation at ca. 111000 g for 4 h (see Methods). This is confirmed by the atomic-force microscopy (AFM). Typical AFM images for bare CNTs and p-CNTs are shown in Fig. 2(a,b), respectively.
As obtained from AFM measurements, the diameter of bare CNTs is 1-1.4 nm, whereas the total diameter of p-CNTs is 4.5-5.5 nm 21,22 . This means that the thickness of the coating varies in the range 1.7-2.5 nm. The density of a polymer is about 1 g/cm −3 23 . After simple calculations made for CNT with a diameter of 1 nm and the thickness of the coating being 2 nm, we found that the ratio of the CNT mass to the mass of the polymer coating equals 0.11. Then, for the composite with 5 wt% CNTs, about 50% of the polymer is attached to the CNT surface, and about 50% of the polymer is free and does not cover the CNTs.
Let us also stress that fabricated p-CNT films comprise densely packed CNTs. The CNT volume fraction in 5 wt% p-CNT film has been estimated as F = 3.3%. The rest 96.7% of the volume is occupied by polymer. For the hypothetical ordered array of oriented CNTs, the value F = 3.3% corresponds to the average distance of 5.5 nm between axes of neighboring CNTs. Such a small distance may lead to a strong electromagnetic interaction between the neighboring tubes. Figures 3 and 4 show the permittivity and conductivity spectra for the polymer matrix, 1.5 wt% and 5 wt% p-CNT composites in the range 25 Hz-10 MHz. All the samples demonstrate strong frequency dependence of the permittivity. Since Re(ε) < Im(ε) below 10 5 Hz, all the samples are conductive in that range. In accordance with the Kramers-Kronig relation, the high imaginary part of the permittivity is accompanied by the high real part of the permittivity (see Fig. 3). Above 1 MHz, the samples can be considered as a dielectric with rather high losses, as Re(ε) >Im(ε) is true for them. Rather strong frequency dependence of the conductivity of p-CNT composites in Fig. 4 means the absence of the percolation effect. One may conclude that the polymer coating prevents the electron tunneling between the tubes. Further, we shall consider the high-frequency dielectric properties of 5 wt% p-CNT film having the highest (3.3%) volume fraction of CNTs (see details of the film fabrication and measurement techniques in Methods). Figure 5 demonstrates the frequency dependence of the permittivity and conductivity for 5 wt% p-CNT film. One can see, that the value of Im(ε) remains almost constant and equal to 5 in a wide range 0.2-1000 GHz, whereas the value of Re(ε) has approximately logarithmic frequency dependence; dotted line in Fig. 5(a) demonstrates fitting of the experimental data with a function Re(ε) = 108 − 3.63 ln(f), where f is in Hz. The conductivity of the composite is directly proportional to the frequency, see data fitted with a dashed line in Fig. 5(b). Dielectric loss tangent, tanδ = Im(ε)/Re(ε), is equal to 0.14 at 0.2 GHz and it increases monotonically with frequency and reaches the value of 0.63 at 1 THz. Let us notice that the permittivity of the polymer matrix in the range 0.2-1 THz is about 2.1 + 0.15i.
As predicted in 18 , the composite comprising individual short-length CNTs non-interacting with each other is expected to have a high real part of the permittivity and low loss tangent in the terahertz range. For example, it is expected that Re(ε) = 1000 and tanδ = 0.05 at frequency 0.5 THz for the composite with CNT volume fraction F = 20% and tube length L = 0.4 μm 18 . Moreover, the theory predicts an increase of the value of Im(ε) with frequency. However, for realistic composite, as shown in Fig. 5, it does not occur. For p-CNT film, we obtain Re(ε) ≈ 10 and tanδ = 0.47 at f = 0.5 THz, F = 3.3%, and L < 1 μm. The reason for the discrepancy between the theory and experiment could be that the electromagnetic interaction between neighboring CNTs has not been taken into account in the calculations, though it may lead to additional energy dissipation and to the modification www.nature.com/scientificreports www.nature.com/scientificreports/ of the local field acting on the CNTs. Let us notice that the value of Re(ε) can be increased by 2-3 times by orienting p-CNTs in the film. Figure 6 shows the frequency dependence of the real part of the permittivity and conductivity of the p-CNT film in the range 0.2-1 THz at different temperatures, 300 and 530 K. One can see that heating leads to a decrease of the value Re(ε). The sign of the value ∂Re(σ)/∂T changes at 0.5 THz. As discussed in 17 , the heating leads to an increase of the electron relaxation rate resulting in a broadening of the terahertz conductivity peak. The peak frequency increases as tube length decreases. Depending on the length of the nanotubes, the spectral position of the LPR peak with respect to the range 0.2-1 THz can be different. Therefore, it is expected that ∂Re(σ)/∂T > 0 for short-length tubes (<0.3 μm), and ∂Re(σ)/∂T < 0 for long-length tubes (>5 μm) in considered frequency range (see Fig. 1 in 17 ). p-CNTs have lengths of about 0.5 μm resulting in a sign variation of the value ∂Re(σ)/∂T, as shown in Fig. 6 In order to show the influence of the intertube electron tunneling on the conductivity spectra of a CNT composite material, we prepared two 1.5 wt% p-CNT films of the same thickness (see fabrication of the CNT-1 and CNT-2 films in Methods). In the first one (CNT-1), all the tubes are almost isolated from one another, and its dc-conductivity is 4 × 10 −5 S/cm. In the second film (CNT-2), the polymer coating of CNTs is partly damaged and CNTs have electrical contacts with each other so that the dc-conductivity of the film is 4 × 10 −3 S/cm; it is 200 times higher than that for CNT-1 film. Figure 7 shows the frequency dependence of the optical density and real part of the conductivity for the CNT-1 and CNT-2 films in the terahertz and far-IR ranges. All the spectra have a broad terahertz peak due to the LPR phenomena in CNTs. The conductivity on the low frequency side of the peak is higher for CNT-2 than for www.nature.com/scientificreports www.nature.com/scientificreports/ CNT-1. One may conclude that this part of the spectra is sensitive to the electron tunneling between the tubes. Moreover, one can see from Fig. 7 that an increase of a number of the electrical contacts between nanotubes leads to weaker frequency dependence of the conductivity on the low-frequency side of the LPR. In particular, in the range 0.2-2 THz, the dependence Re(σ(f)) follows power law with the exponents 1.0 and 0.65 for CNT-1 and CNT-2, respectively. Similar tendencies have been illustrated for hybrid films comprising single-walled CNTs and WS 2 nanotubes at different fractions of CNTs 17 . The terahertz conductivity peak is slightly modified at the central frequency and on the high-frequency side. This means that the intertube electron tunneling influences weakly the LPR in the tubes. Thus, we may conclude that the Waterman-Truell homogenization approach, that neglects intertube interaction, can be applied to describe the conductivity spectrum of CNT-based composite at and above the LPR frequency.     www.nature.com/scientificreports www.nature.com/scientificreports/ the field near the surface of CNTs. The standing surface waves are excited in CNTs exposed to the plane incident wave; this causes the near-field enhancement effect 4 .
The experimental observation of several times absorption enhancement for thymine-CNT complexes on a gold film has been reported in 19 . In order to check if this effect occurs in our samples, we have obtained the mid-IR absorbance spectra for the polymer and p-CNT films of the same thickness (see Fig. 8). As shown in Fig. 8(a), there are many absorption bands associated with different stretching vibrations. Simultaneously, there is also a background which is rather large for p-CNT film, it is associated with the absorption in CNTs. Figure 8(b) shows the absorption bands after background subtraction for both samples. One can see from Fig. 8(b) that there is no strong difference in the absorbance spectra of the polymer molecules with and without CNTs. Therefore, we cannot report on the absorption enhancement effect in the region above 18 THz (600 cm −1 ). As shown in 4 , the near-field enhancement effect is strong at and below the frequency of the LPR. However, it becomes weaker at higher frequencies (see Fig. 4 in 4 ). For our samples the LPR frequency is 3 THz (see Fig. 7). This explains why we could not observe the absorption enhancement effect in the range 18-52 THz.
In conclusion, dielectric and electromagnetic properties of the composite materials and films comprising a high volume fraction of individual single-walled CNTs with polymer coating have been measured and analyzed in a wide frequency range (from 25 Hz up to 100 THz). Polymer coating prevents aggregation of the tubes, and the percolation effect does not occur even at a high volume fraction of the inclusions (3.3%). p-CNT material demonstrates dielectric behavior in the microwave and terahertz ranges. The real part of the permittivity of the p-CNT film in the terahertz range is not so high and the loss tangent is not so small as predicted recently in 18 . The reason could be the electromagnetic interaction between the CNTs that has not been taken into account in the theoretical model.
Comparison between the p-CNT films with different numbers of intertube contacts demonstrates that the intertube tunneling strongly influences the low-frequency side of the terahertz conductivity peak and slightly modifies its central part and high-frequency side. This means that the interaction between the CNTs in the composite can be omitted and the simple Waterman-Truell approach can be applied for the calculation of the effective conductivity of the CNT-based composites at and above the LPR frequency.
The non-covalently functionalized CNTs (p-CNTs) were prepared as described elsewhere 21,22 . Briefly, HiPco single-walled CNTs (2 mg/mL) and the CTVB (5 mg/mL) were mixed in D 2 O and sonicated for 1 hour at 60 °C to exfoliate the SWNT bundles, which results in individually isolated CNTs with an adsorbed monolayer of CTVB. The counterions (VB − ) of CTVB were then polymerized using the free radical initiator (VA-044) at a polymerization temperature of 60 °C, permanently fixing the CTVB monolayer to the CNTs. To separate individually functionalized CNTs from the bundled ones, the suspension was ultracentrifuged at ca. 111000 g for 4 h.
The upper 70% of the suspension was then decanted and followed by freeze-drying at −55 °C for 3 days. The obtained p-CNT material has many pores of about 10-100 μm in size and has a density of about 0.2 g/cm 3 . Characterization of p-CNTs with UV-vis-NIR spectroscopy, atomic-force microscopy, and small-angle neutron scattering measurements is presented in previous reports 21,22 . Two p-CNT materials with 5 and 1.5 wt% CNTs have been produced. p-cnt composite fabrication. The plate was cut off from the p-CNT material and then it was compressed up to the thickness of 0.5-1 mm and density ≈0.9 g/cm 3 in order to remove all the pores. We shall refer to the compressed plate as a p-CNT composite.
p-cnt film fabrication. p-CNT material was dispersed by ultrasonic treatment (Ultrasonic device UZDN-2T, 44 kHz, maximum power) for 10 min in water. The suspension of p-CNTs was centrifuged at 8000 g for 20 min and then it was filtrated through a cellulose nitrate membrane filter (0.2 μm pore size, the thickness of 100 μm) causing a p-CNT film to form on the filter. The maximal film thickness that can be reached is 10 μm, as thick polymer film does not transmit water and it stops the filtration process. The film thickness was calculated knowing the mass and density of the material and the surface area of the film. Both dc and ac conductivity of the p-CNT film was found to be higher than that for a p-CNT composite. This is probably due to the preferred orientation of the tubes parallel to the film surface and higher densification of the material.
In order to bind the tubes withing the film and avoid dissolving of the film with acetone, water or alcohol, the filter with the p-CNT film was heated at 100 °C for 30 min. The filter was then dissolved with acetone and the p-CNT film was transferred on the metallic frame to obtain a free-standing film for infrared (IR) and terahertz measurements. Microwave measurements have been done for the p-CNT film on the filter, as the latter is transparent in the microwave range.
Fabrication of the CNT-1 and CNT-2 films. The polymer coating of p-CNTs was partly damaged by ultrasonic treatment of the p-CNT aqueous suspension at 90 °C for 5-10 min. We fabricated two 1.5 wt% p-CNT films, CNT-1 and CNT-2, comprising non-damaged and damaged p-CNTs, respectively. The intertube electrical contacts occur between damaged p-CNTs causing 200 times higher dc conductivity for CNT-2 than for CNT-1 film. SEM images of the CNT-1 and CNT-2 film cannot demonstrate their morphology, as CNTs are hidden by free polymer (see Supplementary Figs. S1-S2). Raman spectra of CNT-1 and CNT-2 films are found to be identical; they indicate high crystalline quality of CNTs in both films (see Supplementary Fig. S3).
The AFM measurements were carried out using a VEECO AFM instrument (Nanoman, SECPM). The sample for the AFM measurements was prepared by spin-coating of a p-CNT suspension at 4000 rpm for 1.5 min onto silicon wafers. The sample of bare CNTs was obtained by burning the p-CNTs on silicon wafers at 330 °C for 4 h to remove the CTVB coating from CNTs.

Measurement techniques.
The complex transmission of the films at normal incidence was measured in the frequency range f ∈ [0.2, 1] THz using time-domain terahertz spectrometer (THz-TDS, EKSPLA, Vilnius Lithuania). The permittivity ε and conductivity Re(σ) = 2πfε 0 Im(ε) of the films was then calculated using the Fresnel equations for a dielectric slab 24 ; ε 0 = 8.85 × 10 −12 Fm −1 . To investigate the temperature dependence of the terahertz conductivity of p-CNT film in the range 300-530 K in air, we employed the THz-TDS with a home-made furnace-style heating sample holder. Transmittance spectra of the films were obtained using a THz-TDS (0.2-2.0 THz, EKSPLA), and a Fourier-transform IR spectrometer Vertex 70 (2-100 THz, Bruker). The conductivity spectra of the films were calculated from the transmittance spectra using the Kramer-Kronig relation 25 . The microwave conductivity measurements were carried out in the ranges 0.1-18 GHz and 26-36 GHz by waveguide method 26 using a vector analyzer R4M-18 (MICRAN, Tomsk, Russia) and a scalar network analyzer R2-408R (ELMIKA, Vilnius, Lithuania), respectively. Dielectric properties of the composites in the range 25 Hz-10 MHz was measured with a broadband analyzer 7-28 (MNIPI, Belarus). The electrical dc conductivity of p-CNT films was measured using a four-point linear probe technique.