Carbon nanotubes (CNTs) have been widely investigated as additive materials for composites with potential applications in electronic devices due to their extremely large electrical conductivity and current density. Here, highly aligned CNT composite films were created using a sequential layering fabrication technique. The degree of CNT alignment leads to anisotropic resistance values which varies >400× in orthogonal directions. Similarly, the magnetoresistance (MR) of the CNT composite differs depending upon the relative direction of current and the applied magnetic field. A suppression of negative to positive MR crossover was also observed. More importantly, an overall positive magnetoresistance behavior with localized +/− oscillations was discovered at low fields which persists up to room temperature when the current (I) and in-plane magnetic field (B) were parallel to the axis of CNT (B∥I∥CNT), which is consistent with Aharonov-Bohm oscillations in our CNT/epoxy composites. When the current, applied magnetic field, and nanotube axis are aligned, the in-plane MR is positive instead of negative as observed for all other field, current, and tube orientations. Here, we provide in-depth analysis of the conduction mechanism and anisotropy in the magneto-transport properties of these aligned CNT-epoxy composites.

Individual, defect free carbon nanotubes (CNTs) have shown very high electrical conductivity and current density compared to conventional conductors due to their nanoscale diameter and near quantum conductance.1–4 These properties have been utilized to create field effect transistors (FETs) with current densities higher than Si and GaAs FETs.4 This discovery is potentially critical for fabrication of next generation devices that will be required as the semiconductor industry approaches theoretical quantum limits in silicon-based structures. These CNT FETs are also being considered for sensing applications and have been shown to detect ∼1 pico-molar DNA concentrations.5 However, the electrical properties of CNTs are affected by numerous factors and can exhibit significant variance. One such factor is the diameter of CNTs, which can vary from a few angstroms in single wall nanotubes to tens of nanometers in multiwall nanotubes,6,7 which means that conductivity can vary over several orders of magnitude. Furthermore, CNTs with different diameters usually exhibit different electron band structures, which are determined by the chiral angle and how the nanotube is folded. It is well known that CNTs can be metallic for armchair and zig-zag configurations whereas they can be semiconducting with a wide range of bandgaps depending on chirality.8 Similar to traditional metals and semiconductors, the resistivity of CNTs is a function of temperature.3,9–11 Carbon nanotubes also exhibit magnetoresistance (MR).12,13 Interestingly, the sign of the magnetic field, positive or negative, does not have a significant effect on the change of the resistance. For both field directions, magnetoresistance increases or decreases accordingly and is nearly symmetric about zero magnetic field. While the sign of the magnetic field does not have a significant effect on magnetoresistance, the directionality of the field relative to the current does play a major role. The perpendicular field magnetoresistance and in-plane magnetoresistance (MR) of CNT-based materials have been studied to achieve insight into the magneto-transport properties of CNT-based materials for potential applications in next generation sensing and switching devices.14 The magnetoresistance effect was initially investigated by Thomson and is common in magnetic materials as it relates to spin coupling between electrons and the applied magnetic field.15 When moving electrons in CNTs are exposed to a magnetic field applied normal to the plane of the sample, they are subjected to the Lorentz force. This causes the charge carriers to accumulate on one surface of the nanotube and is referred to as the Hall effect, and a quantized version of the Hall effect known as the quantum Hall effect (QHE) has also been reported in multiwall carbon nanotubes.16,17 One particular magnetic field orientation can have a significant impact on the electrical and magneto-transport properties of carbon nanotubes; when the magnetic field is applied parallel to the long axis of the carbon nanotube, there is a shift in the electron wave-function. This interaction is known as the Aharonov-Bohm effect (AB) and affects electrons travelling on the surface of a cylindrical conductor. An oscillating magnetoresistance with the increasing magnetic field is an indicator of Aharonov-Bohm interactions for surface conduction in the solid materials.18,19 However, theoretically, a single carbon nanotube exhibiting ballistic conduction will have a resistance value equivalent to the quantum resistance, Rq = h/2e2 = 12.9 kΩ.3 Since only the outer tube is carrying charge in MWCNTs, the resistivity must increase with an increase in diameter. Another source of variation in the electrical properties of CNTs arises when current flows from one tube to the next. In this scenario, the orientation of the carbon nanotubes becomes very important. Carbon nanotube assemblies with high degrees of alignment have highly anisotropic conductivity, which varies over several orders of magnitude in orthogonal directions.20 For carbon nanotubes adjacent to one another, evidence of hopping conduction has been reported in electrical measurements.11,21,22 Suppression of a positive to negative crossover in MR of CNTs at high fields has been observed via application of high pressure and chemical treatment that modifies the CNT band structure.23,24 Here, we report significant anisotropy in the magneto-transport characteristics and the observation of Aharonov-Bohm oscillations up to 300 K for a carbon nanotube structure, resulting from the highly aligned nature of the CNTs in the fabricated composites.

The vertically aligned carbon nanotube arrays (CNT length ∼1 mm and diameter of ∼30 nm) used in this experiment were synthesized using a floating catalyst chemical vapor deposition method described in previous work.25,26 Raman spectra were obtained on the CNTs prior to epoxy infusion using a 514 nm wavelength laser and were typical for MWCNTs. The spectra for the CNTs revealed graphite “G” and disordered “D” peaks with the G/D intensity ratio ∼3/1. After synthesis, the CNT arrays were spun into aligned CNT sheets, a structure critical for producing the anisotropic composites of interest for this study. The sheets also offer an interesting case for electronic transport because individually the CNTs have lengths of around 1 mm. The sheets are held together by numerous meandering CNT bundles. Even though the overall orientation of CNTs is very high, there is some degree of misalignment caused by inherent waviness of the CNTs. The CNT sheets were drawn onto the bottom of a 5 in. diameter glass mandrel wrapped in PTFE shown in Fig. 1(a). This orientation was used so that solution could be dropped onto the assembly, via the syringe pump shown in the upper left of Fig. 1(a) without the solution destroying the fragile CNT sheet. The solution was 1% Epotek 301-2 epoxy dissolved in 99% acetone and was applied at a constant rate.

FIG. 1.

(a) Modified X-winder used for CNT epoxy film fabrication. (b) Cured CNT film after removal from hot press. (c) SEM image of the aligned CNT structure.

FIG. 1.

(a) Modified X-winder used for CNT epoxy film fabrication. (b) Cured CNT film after removal from hot press. (c) SEM image of the aligned CNT structure.

Close modal

The drop rate and rotational velocity were chosen so that consecutive droplets would spread and form a continuous coating on the nanotubes while allowing the acetone to evaporate before the next layer of nanotubes was added. The mandrel was set to a rotational velocity of 0.7 RPM using a modified filament winding apparatus, X-Winder, and associated software. After 30 min, the nanotube epoxy film was removed from the mandrel and folded upon itself twice to increase the thickness. The sample was outgassed at room temperature in vacuum (∼10 Torr) for 30 min to ensure that the acetone had been removed from the sample; this procedure is similar to that described by others.27 Once removed from the vacuum oven, the sample was covered in a PTFE film and placed in a hot press under pressure <0.5 MPa and cured at 80 °C for three hours. Upon removal from the hot press, the sample thickness was approximately 50 μm and had a CNT mass fraction of ∼40%. Figure 1(b) shows the cured film with a width of 1 inch that matches the dimensions of the array and indicates that minimal spreading occurred during curing due to the pressure applied. The small segment of the film standing vertically on its side is intended to show the relatively small thickness of the sample in comparison to the width and length and is just a small section that was broken off the end of the sample shown. In Fig. 1(b), the CNT axes are aligned in-plane and perpendicular to the width measured by the ruler. The alignment of these drawn CNT films is highlighted in Fig. 1(c) with an SEM image showing portions of individual CNTs within the drawn sheet.

Once the CNT composite film had cured, resistance was measured as a function of temperature and magnetic field in a Quantum Design Physical Property Measurement System (PPMS). All electrical measurements were made using a four-point probe technique in the van der Pauw configuration with square probe geometry, and the measurements were carried out with the current flowing perpendicular (⊥CNT) and parallel (∥CNT) to the axis of the carbon nanotubes. A linear current-voltage relationship demonstrated good Ohmic contact to the samples over the current range measured (not shown). Subsequent to demonstration of good Ohmic contact, the sample was cooled to 5 K. Resistance measurements were taken in 5° increments from 5 to 300 K. Then, the magnetoresistance (MR) was investigated by applying magnetic fields to +/− 5 T (in 1 kOe increments) at 5, 25, and 300 K. For each current direction, (⊥CNT) and (∥CNT), the (MR) was measured with an applied out-of-plane magnetic field and in-plane MR measurements were performed along (⊥CNT) and (∥CNT) current directions with the applied field in the plane of the samples.

Figure 2 shows the resistance versus temperature behavior for current applied perpendicular (a) and parallel (b) to the nanotube axis, respectively. The temperature dependence in both directions reveals semiconductor-like behavior with resistance decreasing as temperature increases. One should note that the magnitude of the measured resistance in the perpendicular direction is ∼400× that in the parallel direction over the entire temperature range. The nature of the anisotropy is shown in the inset of Fig. 2 by the ratio of the resistance in the perpendicular R(⊥) and parallel R(∥) directions. This anisotropy in resistivity has been observed previously in thin films of aligned carbon nanotubes.10 Some SWCNTs exhibit metallic-like temperature dependence of resistivity at low temperatures and then switch to semiconducting like behavior at a variable transition temperature.9 

FIG. 2.

Temperature dependence of resistance with the current flowing (a) perpendicular and (b) parallel to the CNT axis. The inset shows the ratio of resistance perpendicular to that parallel to the CNT axis.

FIG. 2.

Temperature dependence of resistance with the current flowing (a) perpendicular and (b) parallel to the CNT axis. The inset shows the ratio of resistance perpendicular to that parallel to the CNT axis.

Close modal

Despite the large anisotropy in resistance values along the two current directions, charge transport in both current directions exhibits evidence of hopping conduction, as demonstrated by the plot of lnσT1/2 versus T1/4 in Fig. 3 that is a signature of hopping conduction. There is a strong linear correlation over the entire temperature range of 5–300 K with R2 values of 0.94 and 0.96. If we restrict our data to the same temperature range of anisotropy as reported in Ref. 11, then our R2 values increase to 0.99. Any contribution from the epoxy is assumed to be negligible since its resistivity is ∼1012 Ω cm.

FIG. 3.

Approximately linear relationship between the lnσT1/2 versus T1/4 indicating that charge carriers undergo hopping conduction from 5 to 300 K.

FIG. 3.

Approximately linear relationship between the lnσT1/2 versus T1/4 indicating that charge carriers undergo hopping conduction from 5 to 300 K.

Close modal

It is also interesting that the slope of the resistance ratio is negative from 5 to 100 K and then becomes positive at higher temperatures (see inset in Fig. 1). To explain the observed anisotropy in the resistance values along two different directions and their temperature dependence, we followed the methods described in Refs. 10 and 13.

The overall electrical transport behavior of the CNT-epoxy composites can be explained by considering the resistance as a combination of two components, the intrinsic resistance of the CNTs and the resistance associated with hopping conduction, R=Ri+Rh. The latter, Rh=NγΔKBT, depends on the number of intertube hopping events (N) which take place at temperature T(K) with an energy barrier (Δ), where γ has the dimension of resistance. The existence of hopping conduction in these CNT/epoxy composites has been confirmed by the lnσT1/2 versus T1/4 behavior as shown above in Fig. 3. The observed high R(⊥)/R(∥) ratio, 415 at 5 K, is attributed to the high aspect ratio of the CNTs in our CNT/epoxy composites.

The reported magnitude of the barrier height (Δ) for intertube hoping is 10 meV.13 At temperatures >100 K, (Δ)<KBT and the resistance curve is no longer thermally activated; consequently, the R(⊥)/R(∥) plot in Fig. 1 shows a negative slope. Down to 100 K where the barrier height (Δ)>KBT, intertube hoping events are suppressed that results in a positive slope of resistance vs. temperature plot from 100 to 5 K. The R(⊥)/R(∥) ratio increases ∼10% as temperature is lowered from 100 to 5 K as shown in the inset of Fig. 1. Additionally, as mentioned previously, the best fit of lnσT1/2 versus T1/4(R2 ∼0.99) is observed along the R(⊥) direction within the low temperature regime, 5–75 K, which again supports our hypothesis that hopping events are suppressed, and the resistance curve is thermally activated down to 100 K where the barrier height (Δ) > KBT.

To understand the distinct transport mechanism of the CNT systems, magneto-transport studies of the CNT systems have been performed and reported in the published literature.28,29 But a detailed systematic study of the CNT systems with both in-plane and out-of-plane applied magnetic fields is lacking. We have performed detailed out-of-plane and in-plane field magneto-resistance (MR) measurements on our CNT-epoxy composite samples in which aligned carbon nanotubes are embedded in the epoxy in an α geometry.

Figures 4(a) and 4(b) show out-of-plane field MR plots with current parallel to the axis of the CNTs (I∥CNT) and perpendicular to the axis of CNT(I⊥CNT), respectively (insets show the relative orientation of the current with the out-of-plane applied field). Here, the applied magnetic field is perpendicular to the plane of the CNT-epoxy composite and to the axis of the CNTs embedded in the composite.

FIG. 4.

(a) MR with current flowing along the CNT axis and the applied out-of-plane field is normal to the current and CNT axis. (b) MR with current flowing perpendicular the CNT axis and the applied out-of-plane field is normal to the current and CNT axis.

FIG. 4.

(a) MR with current flowing along the CNT axis and the applied out-of-plane field is normal to the current and CNT axis. (b) MR with current flowing perpendicular the CNT axis and the applied out-of-plane field is normal to the current and CNT axis.

Close modal

The observed MR is negative for both orientations of current with respect to the CNT axis, but the magnitude of the MR is higher for the current parallel to the axis of the CNT (I∥CNT) case. The intriguing feature of the MR plots is that there is no crossover from negative to positive MR to 5 T field over the 5–300 K temperature range investigated. A change in the sign of MR from negative to positive was reported at ∼4 T for CNT systems: with decreasing temperature, the magnitude of negative contribution increases at low fields.30,31 The crossover from negative to positive MR was reported to be suppressed by the application of high pressure and acid treatment to CNT composites and was attributed to significant changes in the band structure that enabled suppression of the crossover.23,24 In our samples, this crossover is completely suppressed and there is no change in the sign of the MR at 5 K up to fields of 5 T without any applied pressure and acid treatment. The suppression of crossover here suggests that our sample fabrication process, which results in high levels of alignment and significant bundling, may modify the band structure of the CNTs in the composite compared to that of single isolated tubes. This hypothesis is based on the earlier reports 23,24that band structure changes suppress the crossover.

The observed negative MR may originate from weak-localization of carriers. In the weak-localization effect, a quantum correction to Drude conductivity is observed due to destructive interference of the quantum wave function around a scattering center in a localized system where transport occurs via variable range hoping.31,32 The observation of negative MR at 300 K rules out the possibility of negative MR due to Landau level quantization in graphitic systems as the thermal energy is much greater than the energy between Landau levels near the Fermi energy.

In-plane MR measurements were also performed in four different current and field relative orientations, and the results are shown in Figs. 5(a)–5(d); the insets show the relative orientation of the current with the in-plane applied field.

FIG. 5.

(a) In-plane MR with current flowing perpendicular to the CNT axis and the applied in-plane field is normal to the current and parallel to the CNT axis, (b) In-plane MR with current flowing along the CNT axis and the applied in-plane field is normal to the current direction and the CNT axis. (c) MR with current flowing perpendicular to the CNT axis and the applied in-plane field is parallel to the current direction and normal to the CNT axis and (d) MR with current flowing along the CNT axis and the applied in-plane field is along the current direction and the CNT axis.

FIG. 5.

(a) In-plane MR with current flowing perpendicular to the CNT axis and the applied in-plane field is normal to the current and parallel to the CNT axis, (b) In-plane MR with current flowing along the CNT axis and the applied in-plane field is normal to the current direction and the CNT axis. (c) MR with current flowing perpendicular to the CNT axis and the applied in-plane field is parallel to the current direction and normal to the CNT axis and (d) MR with current flowing along the CNT axis and the applied in-plane field is along the current direction and the CNT axis.

Close modal

The observed in-plane MR is negative when the current and the in-plane field are normal to each other (I⊥CNT and B∥CNT) and the largest MR, ∼10.5% at 5 K, is observed when the current is along the axis of the CNT (I∥CNT) in the CNT-epoxy composite as shown in Fig. 5(b). The B⊥CNT and I⊥CNT configurations also revealed negative in-plane MR as shown in Fig. 5(c).

The most intriguing finding of this study was observed when the current and the applied in-plane field are parallel to the axis of CNTs in CNT-epoxy composites. An in-plane MR signal with an overall positive trend (0 to +/−5 T) and localized +/− oscillations (occurring over approximately 0.5–1 T ranges) is observed as shown in Fig. 5(d) when the current flow and in-plane field are both applied along the axis of the CNTs (B∥I∥CNT) . This observation of oscillatory low field positive MR in the carbon nanotube system persists up to room temperature. While a high field positive MR has been reported,23,31 a low field positive oscillatory MR signal has not been reported in the literature on CNT systems. We also point out that the oscillatory behavior observed in Fig. 5(d) was repeatable, and an instrumental artifact can be excluded since such oscillatory behavior was not observed in any of the other orientation combinations of field, current, and CNT axis.

There are three potentially relevant theories to explain the unique positive MR behavior of our CNT-epoxy composites in the B∥I∥CNT configuration: variable-range hopping (VRH), wave function shrinkage effect, and the Aharonov-Bohm (AB) effect can generate a positive MR in disordered materials such as CNT-epoxy composite.30 The wave function shrinkage theory can be excluded on the basis of existence of low field and high temperature positive MR. Additionally, the positive MR is only observed in the B∥I∥CNT configuration, whereas in all other orientations, the observed MR signal is negative. But, we cannot completely rule out the possibility of a VRH mechanism playing a role in the positive MR as it is supported by the variable temperature resistance measurements.

A plausible explanation for observation of an oscillatory positive MR is formation of an Aharonov-Bohm (AB) quantum phase in our CNT-epoxy composites when the current and field are parallel to the axis of CNT (B∥I∥CNT). In the Aharonov-Bohm effect, an Aharonov-Bohm phase is formed, and the bandgap is tuned and modulated periodically by the flux quanta, ϕ0 = e/h. The periodic modulation of the bandgap mediated by the location of the Fermi level produces an oscillatory behavior in magnetic and magneto-transport properties of CNT materials with formation of an AB phase.18,33 In order to estimate various parameters to confirm the presence of an Aharonov-Bohm phase in our samples, a detailed temperature and field dependent study of the positive MR is required.

Carbon nanotube/epoxy composite films have been fabricated with highly anisotropic electrical properties. Conductivity varies over 400× in directions parallel and perpendicular to the nanotube axis. The temperature dependence of resistance for both directions is negative across the temperature range investigated. However, the magnitude of this dependence is different in terms of absolute and percentage change. Both directions show evidence of hopping conduction with a linear lnσT1/2 versus T1/4 dependence. A high resistance ratio is attributed to the number of hopping events which is a function of temperature and the barrier height. The resistance curve is thermally activated down to 100 K and shows a positive slope. Negative out-of-plane field MR is observed for both orientations, and negative to positive crossover of the MR is suppressed due to the modified band structure of CNTs in our CNT-epoxy composites. The in-plane field MR shows negative trends in all orientations except when current, the in-plane field, and the axis of CNTs are parallel. An oscillatory positive MR behavior at low field and room temperature is observed when the current and field are parallel to the axis of CNT (B∥I∥CNT). All other five relative orientations of the current and field show the typical negative MR signals with the maximum MR% when the field is parallel to current (B∥I) and a unique behavior was observed in (B∥I∥CNT) orientation only.

This work was performed in part at the Analytical Instrumentation Facility (AIF) at North Carolina State University, which is supported by the State of North Carolina and the National Science Foundation (Award No. ECCS-1542015). The AIF is a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), a site in the National Nanotechnology Coordinated Infrastructure (NNCI). Funding: This work was supported by the Office of Naval Research Grant No. N00014-14-1-0652. K. Peters was also supported by the National Science Foundation, while working at the Foundation. Any opinion, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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