The generation mechanism of negative permittivity in multi-walled carbon nanotubes/polyaniline composites

Abstract

Conductive polymers filled with carbon nanotubes have been proved to have negative permittivity but the mechanism of its strange properties has not been intensively studied. Thus we need to study the mechanism of negative permittivity of conductive polymer metamaterials and reveal the relationship between the permittivity and fillers. Polyaniline (PANI) filled with multi-walled carbon nanotubes (MWCNTs) is chosen as the target to explore the generation mechanism of the negative dielectric properties. PANI with low resistivity (CPA0) and MWCNTs/CPA0 composites synthesized are found to possess negative permittivity. A structure model of “double nano wires” is initially constructed after some structure and properties analysis, and the amplification mechanism of MWCNTs on negative permittivity of CPA0 and the transition phenomenon of permittivity from negative to positive value are correlated with this model. In order to verify the model, PANI with high resistivity (CHK0) and MWCNTs/CHK0 composites are prepared. The surface of MWCNTs is then coated with polyvinylpyrrolidone (PVP). These results further demonstrate the validity of the structure model of “double nano wires” to account for the negative permittivity of MWCNTs/PANI composites. This study provides an experimental basis on further exploration of metamaterials of carbon nanotube/conductive polymer composites.

---

1 Introduction

Metamaterials are artificial composite structures or composite materials which possess physical properties without existence in natural materials proposed by Veselago in the 1960's.¹ From 1996 to 1999, Pendry found that an array with parallel metal wires exhibited effective negative permittivity properties in some certain frequency bands, and analytical formulas of the relationship between the structural parameters of the array and the equivalent permittivity were derived from plasma theory.^2,3 In 2000 Smith used this structure combined with split-ring resonators to realize left-handed metamaterial.⁴ In fact, the concept of plasma frequency was first proposed by L. Tonks et al. and the plasma resonance was first found in the laboratory in 1929.⁵ As early as 1962, Rotman pointed out that an array with parallel metal wires could be used to simulate electric plasma.⁶ J. D. Jackson associated the permittivity with the Drude model and found that the equivalent permittivity was negative when the frequency was below the plasma frequency.⁷

The special properties of structural metameterial are derived from the arrangement of ordered structures. However, doped conductive polymers without obvious periodic array were found possessing such negative permittivity in recent years. Negative permittivity of doped conductive polymers obviously depended on compositions, types and distributions of constitutive materials. These metamaterials are so-called intrinsic metamaterials. These results have greatly expanded the scope of metamaterials. Epstein reported that polyaniline doped with camphor benzene sulfonic acid showed negative permittivity in the microwave frequency range in 2001.⁸ Gu et al. also found negative permittivity in graphene/polyaniline composites or multi-walled carbon nanotube (MWCNTs)/polyaniline composites after 2011.^9–12 MWCNTs/polypropylene composites prepared by Qian and MWCNTs/phenolic resin composites prepared by Zhang also showed negative permittivity.^13,14 Quasi 3D variable range hopping behavior of electrons in composite was used to explain the mechanism in above papers. The addition of carbon materials enhanced the transfer capability of electrons and weakened immobilization of charged particles so that the permittivity of the composites was reduced.

At present, the generation of negative permittivity in structural metamaterials and intrinsic metamaterials is explained by different mechanisms. Whether the internal mechanism of property of these two types of metamaterials is similar deserves to intensively study. In fact, Zhong et al. considered CNFs in CNFs/PI composites similar with the fine wires in the study of Pendry, which was essential for the realization of negative permittivity of nanocomposites, but there is no sufficient evidence to support more.¹⁵ In our study, MWCNTs/PANI composites was prepared to study the mechanism of the generation and improvement of their negative permittivity and the structure model of “double nano wires” of PANI and MWCNTs was firstly constructed. Through comparing the permittivity of MWCNTs/CPA0 (PANI with low resistivity) composites, MWCNTs/CHK0 (PANI with high resistivity) composites and PVP coated MWCNTs/CHK0 composites, the validity of the structure model of “double nano wires” is demonstrated.

2 Experimental

2.1 Chemicals

Aniline, ammonium persulfate (APS), hydrochloric, potassium dichromate, p-toluene sulfonic acid (PTSA), and polyvinylpyrrolidone (PVP) k-30 were purchased from Sinopharm Chemical Reagent Co. Ltd. China. Multi-walled carbon nanotube were purchased from Cheaptubes. All the chemicals were used as-received without any further treatment.

2.2 Fabrication of low resistivity PANI and MWCNTs/PANI composites

Firstly, PTSA (proton acid, 5.167 g), APS (oxidant, 4.108 g) and different contents of MWCNTs (0–10 wt%) were dispersed in 300 ml distilled water with ultrasonic for 40 min (power 320 W). The resultant dispersion was placed into a crystallizing dish containing a mixture of ice and water. Next, aniline (An, 3.35 g) in 60 ml water was added dropwise into the dispersion solution under a magnetic stirring with 1000 rpm speed for 10 min when temperature of the dispersion solution was lower than 10 °C. This dispersion with An was treated with ultrasonic for 60 min (320 W) and reacted for 6 h in the ice/water mixture. Finally, the product solution was filtrated in a sand core funnel and washed with deionized water and ethanol until the supernatant was transparent. MWCNTs/PANI composites were obtained after 6 hours of drying in an air blast oven at 80 °C. These are designated as CPA n (n = 0, 1, 3, 5, 10) (the C in CPA represented filled nanoparticles as MWCNTs, P represented proton acid PTSA, A represented oxidant APS and n represents the mass fraction of the filler).

2.3 Fabrication of high resistivity PANI/MWCNTs nanocomposites

Hydrochloric acid (3.55 g), potassium dichromate (7.05 g) and different contents of MWCNTs (0–15%) were dispersed in 300 ml distilled water with ultrasonic for 40 min (power 320 W). The resultant dispersion solution was placed into a crystallizing dish containing a mixture of ice and water. Next, aniline (An, 3.35 g) in 60 ml water was added dropwise into the dispersion solution under a magnetic stirring with a 1000 rpm speed for 10 min when temperature of the dispersion solution was lower than 10 °C. And then the dispersion with An was treated with ultrasonic for 60 min (320 W) and reacted for 6 h in the ice/water mixture. Finally, the product solution was filtrated in a sand core funnel and washed with deionized water and ethanol until the supernatant was transparent. MWCNTs/PANI composites were obtained after 6 hours of drying in an air blast oven at 80 °C. In order to simplify we used CHK n (n = 0, 1, 3, 5, 10, 15) to represent the materials prepared by this method.

2.4 Fabrication of high resistivity PANI/MWCNTs–PVP composites

MWCNTs (1.5 g), PVP (4.5 g) were added to 100 ml deionized water in a round bottom flask of 250 ml and heated in an oil bath pot at 90 °C with magnetic stirrer (1000 rpm) for 6 h. The resultant solid matter was removed, filtrated, repeated washed with deionized water, dried for 12 h in a vacuum oven at 80 °C and then ground into powder.

Hydrochloric acid (3.55 g), potassium dichromate (7.05 g) and different contents of MWCNTs–PVP (10 wt%, 15 wt%, according to mass of MWCNTs) were dispersed in 300 ml distilled water with ultrasonic for 40 min (power 320 W). The resultant dispersion was placed into a crystallizing dish containing a mixture of ice and water. Next, aniline (An, 3.35 g) in 60 ml water was added dropwise into the dispersion under a magnetic stirring with 1000 rpm speed for 10 min when the temperature of the dispersion solution was kept lower than 10 °C. The dispersion with An was treated with ultrasonic for 60 min (320 W) and reacted for 6 h in the ice/water mixture. Finally, the product solution was filtered in a sand core funnel and washed with deionized water and ethanol until the supernatant was transparent. MWCNTs/PANI composites were obtained after drying for 6 hours in an air blast oven at 80 °C. These samples are designated as CPHK n (n = 10, 15).

2.5 Characterization

Fourier transform infrared spectra (FT-IR) of the samples were recorded with a EQUINOXSS/HYPER FT-IR infrared spectrometer in the range of 4000–400 cm⁻¹. X-ray diffraction (XRD) analysis of the samples was by D/MAX 2550VB3+/PC under the test condition of diffraction angle 10–75°, continuous scanning 5° min⁻¹, tube voltage 40 kV and current 35 mA. Scanning electron microscope (SEM) images were taken on a Quanta FEG 250 field emission scanning electron microscopy. Dielectrical properties were investigated by an LCR meter (Agilent, E4980A) equipped with a dielectric detector (Agilent, 16451B) at the frequency of 20 Hz to 2 × 10⁶ Hz at room temperature. The sample was a wafer with the diameter of 10 mm and thickness of 1–3 mm prepared by moulding composite powder in 8 MPa pressure. The wafer was coated with conductive silver paste on top and bottom surface and dried in vacuum at 80 °C for 4 h in order to form two electrodes before test. Resistivity was tested by electrochemical work station CHI660E in the frequency range of 1 to 1 × 10⁵ Hz.

3 Results and discussion

3.1 Negative dielectric properties and generation mechanism of MWCNTs/PANI with low resistivity composite

The permittivity of CPA0 (PANI with low resistivity) filled with different content of MWCNTs is shown in Fig. 1(a). The permittivity of CPA0 possesses a large negative value (−2.3 × 10⁴) in the frequency range of 20 to 2.3 × 10⁴ Hz at room temperature. To our knowledge PANI with such a large negative permittivity has not been reported. PANI had a small negative permittivity (close to −1.2 × 10³), or positive permittivity in other studies.^9,12 The negative permittivity of the MWCNTs/CPA0 composites with different contents of MWCNTs is decreased compared to that of CPA0. CPA1 in the frequency of 20 Hz possesses the smallest negative permittivity value of −2.4 × 10⁵. CPA3 possesses the smallest negative permittivity value of −2.5 × 10⁵ in the frequency of 23.3 Hz. Fig. 1(b) shows local amplification curves of Fig. 1(a), from which the positive and negative transition of the permittivity can be clearly seen. The permittivity of PANI in the range of 20 to 2.3 × 10⁴ Hz is increases from −2.3 × 10⁴ to 0 and the permittivity becomes positive when the frequency is above 2.3 × 10⁴ Hz, while the permittivity of MWCNTs/PANI composites added with 1 wt%, 3 wt%, 5 wt% and 10 wt% MWCNTs becomes positive at 0.27 × 10⁴ Hz, 0.86 × 10⁴ Hz, 3.99 × 10⁴ Hz and 13.6 × 10⁴ Hz, respectively.

Fig. 1 Permittivity of CPA0 (PANI) filled with different content of MWCNTs and transition curves of negative permittivity to positive permittivity of PANI and MWCNTs/PANI composites.

What are the reasons for the magnification of negative permittivity of MWCNTs/CPA0 composites? In order to answer this question, the structure of MWCNTs/CPA0 composites required Fig. 2(b) gives the XRD curves of MWCNTs, CPA0 and MWCNTs/CPA0 composites. PANI has two weak and broad crystallization peaks in 20.38° and 25.08°, one represents periodic vertical to main chains, and the other is periodic parallel to main chains.^17,18 which indicate PANI possesses the crystalline region. The results are consistent with the other studies in literature.^16,19,20 Two peaks of 25.82, 42.88 can be clearly seen in the curve for the MWCNTs, indicating (002) and (100) crystal plane characteristic peaks respectively, while there is no characteristic peak of MWCNTs in the MWCNTs/CPA0 composites perhaps due to their small content. Crystallization peaks in the MWCNTs/CPA0 composite indicate existence of some crystalline regions in the PANI matrix. The full width at half maxima (FWHM) of the composites added with MWCNTs is found to increase compared with CPA0, which indicates the grain size of the MWCNTs/PANI composite decreases with the addition of MWCNTs.

Fig. 2 Structural analysis of MWCNTs/CPA0 composites (a) ATR curves of CPA0, CPA3, CPA10 and MWCNTs, (b) XRD patterns of CPA0, CPA1, CPA3, CPA5, CPA10 and MWCNTs, (c) SEM image of CPA1, (d) SEM image of CPA3, (e) SEM image of CPA5, (f) SEM image of CPA10.

SEM images of CPA1, CPA3, CPA5 and CPA10 are shown in Fig. 2(c–f). The distribution of MWCNTs is uniform in all of the MWCNTs/CPA0 composites. MWCNTs in the images look denser with the increase of MWCNTs content. The materials with a certain length–diameter ratio can be clearly seen in the images, while the white core structures should be MWCNTs and the transparent outer layer is PANI. Such images indicate that MWCNTs covered with PANI is uniformly distributed in the PANI matrix, which corresponds with the results of XRD and ATR. Some long and interconnected MWCNTs can be found in Fig. 2(e and f) because of the high content of MWCNTs, which can help electron delocalization in a broad range.

The resistivity of CPA0, CPA1, CPA3, CPA5, CPA10 is shown in Fig. 3. It can be seen that the difference of resistivity is not large, respectively 1.54 ohm cm, 1.35 ohm cm, 1.24 ohm cm, 0.89 ohm cm, 0.76 ohm cm at 20 Hz. All the resistivity is in the edge of the semiconductor resistivity (close to the conductor) and decreases with the increase of MWCNTs content. This is because the resistivity of MWCNTs is lower than that of PANI and the content of MWCNTs gradually reaches the percolation threshold of MWCNTs when it increases. The “skin effect” will occur on the sample surface with frequency increasing, so the resistivity of the samples increases.

Fig. 3 Resistivity of CPA0 and MWCNTs/PANI composites with different content of MWCNTs.

Pendry found that the structure of an array with parallel metal wires in certain frequency band could show characteristics of negative permittivity in 1996.^2,3 Then Maslovski et al. used a thin metal rod with the unit length as an inductor for studying the negative permittivity through equivalent circuit methods.²¹ The equivalent circuit method can also be used to analysis MWCNTs/PANI composites. Long chains in PANI have two states of existence. One state is an ordered arrangement of neat chains in tiny crystalline regions, and another state is disordered arrangement of long chains existing between crystalline regions as shown in Fig. 4(a). These long chains of PANI are similar to metal thin wires because of their electrical conductivity, and here should be “nano wires” because of their dimension. Such MWCNTs are also nano wires with good electrical conductivity and regular shape, as shown in Fig. 4(b). Therefore, there are two kinds of nano wires in MWCNTs/PANI composites (MWCNTs and PANI), so we establish a structure model of “double nano wires” to investigate the generation mechanism of the negative permittivity of MWCNTs/PANI composites.

Fig. 4 Structure models of CPA0 (PANI) and MWCNTs/PANI composites (a) “nano wires” model, (b) “double nano wires” model.

The real situation in the materials is very complex so it is very difficult to present an accurate description only through Maxwell's equation groups. We can simplify the internal condition of the composite for analysis although we cannot provide a full accurate description of the internal condition of the composite. So how can “nano wires” generate negative permittivity? First, PANI long chains and MWCNTs with high length–diameter ratio can be equivalent to inductors with certain resistance. Under an alternative electric field, the phase of the electric field is ahead of the phase of current for π/2, as shown in Fig. 5(a). Alternating current is equivalent to an oscillating electric dipole, the phase of current is ahead of the phase of oscillating electric dipole for π/2, as shown in Fig. 5(b). Therefore, the phase of the electric field is ahead of the phase of oscillating electric dipole for π. That means the direction of the electric field strength E_f (free of charge) is always opposite to that of the induced electric field strength E_i (induced charge). These alternating dipoles have about 1–2 cycle of oscillation and overlap with new E_i to form ∑E_i by multiple effects. When the sum of the induced electric field ∑E_i and polarization electric field E_p (polarization charge) is more than the original electric field E_f, the negative permittivity of the composite will appear, as shown in Fig. 5(c).

Fig. 5 Diagrams of generating mechanism of negative permittivity in the CPA0 (PANI) (a) generation of π/2 phase difference between alternating current and alternating electric field. (b) Generation of π/2 phase difference between alternating current and alternating current dipole. (c) Generation of negative permittivity under the alternating electric field.

So how do “double nano wires” in MWCNTs/PANI composites exert their effect? MWCNTs/PANI composites have two kinds of inductors, PANI and MWCNTs. Similar to the generating mechanism of the negative permittivity in the PANI above, the two inductors in MWCNTs/PANI composites are equivalent to double nano wires and result in alternating currents under an external alternating electric field. These alternating currents also generate alternating current dipoles, leading to the sum of E_i and E_p being more than E_f. However, there is a difference in the permittivity of MWCNTs/CPA0 composites and that of CPA0, for example, the permittivity of CPA1 at 20 Hz (−2.42 × 10⁵) and the permittivity of CPA3 at 20 Hz (−2.39 × 10⁵) are 10 times less than the permittivity of CPA0 (−2.3 × 10⁴). This is because the two kinds of nano wires in the composites produce a synergistic effect. Nano wires of such MWCNTs seem better than those of the CPA0 due to their more regular shape and lower resistance (shown in Fig. 3), so MWCNTs themselves can produce a larger alternating electric field E_i under an alternating electric field with the help of CPA0, and at same time, they can also help CPA0 produce a larger alternating electric field E_i through improving polarization of alternating current dipoles in CPA0. Therefore, E_i (MWCNTs) + E_i (PANI) + E_p > E_i (PANI) +E_p > E_f, MWCNTs/PANI composites accordingly possess a much larger negative permittivity. This is the structure model of “double nano wires” as shown in the Fig. 4(b). It is worth mentioning that only the MWCNTs parallel to or less than 45° the direction of the electric field can be equivalent to inductors to generate alternating currents and alternating current dipoles.

It can be seen from Fig. 1(a) that CPA3 possesses the largest negative permittivity (−2.52 × 10⁵) for all the MWCNTs/CPA0 composites, exceeding the maximum value of CPA1 because the content of MWCNTs in CPA3 is more. It also can be seen that negative permittivity of CPA5 increases while negative permittivity of CPA10 decreases. There are some MWCNTs coated with long chains of PANI in CPA5, which intertwine and form structures similar to a parallel ones so as to reduce the resistance of the long chains, result in the decrease of the inductor effect (as shown in Fig. 2(e)). The decrease in negative permittivity of CPA10 is because the better arranged MWCNTs in the MWCNTs/CPA0 composite can compensate for above problem (as shown in Fig. 2(f)), but the negative permittivity of CPA10 is greatly increased compared to that of CPA1 and CPA3. It can be observed in Fig. 1(a) that negative permittivity always appears at low frequency, and even an initial frequency of 20 Hz. This is because MWCNTs/CPA0 composites are still semiconductors and their resistance value is relatively high. Also the composite material inside belongs to a micro-nano structure so the resistance to an external electric field change is weaker compared to a large metal inductor. When the frequency is above 20 Hz, inductive reactance has become an obstacle to current.

The resistivity of PANI and its composites increase with the increasing frequency leading to the weakness of the ability of electrons to follow the external electric field. Electrons are difficult to hop between chains so that E_i is decreased, as shown in Fig. 5(c). Therefore, the sum of E_i and E_p will gradually reduce and the permittivity will gradually increase. The permittivity will translate from negative to positive value when the sum of E_i and E_p is less than E_f, and so negative permittivity phenomenon disappears.

Fig. 1(b) shows the transition curves of negative permittivity to positive permittivity of PANI and MWCNTs/PANI composites. When the content of MWCNTs in the MWCNTs/PANI composites is small, PANI may play a main role to the negative dielectric phenomena. The decrease of the grain size of PANI perhaps is due to that the addition MWCNTs destroys the grain structure of PANI, so the local resistivity of the MWCNTs/PANI composites will increase, the effect of the inductor is lost in advance and the transition frequency of the permittivity from negative to positive value will accordingly decrease. Although MWCNTs may compensate for the decrease of the resistivity in theory, it is not enough because of small content. With the increase of the content of MWCNTs in the composites, a large number of long MWCNTs can be seen (as shown in Fig. 2(e) and (f)). Because the resistivity of MWCNTs is lower than that of CPA0, MWCNTs can adapt more easily on influence of the external electric field so that the transition frequency of the permittivity from negative to positive value increases. It can also be seen from Fig. 1(b) that the transition frequency of the permittivity from negative to positive value decreases and then increases with the increase of the content of MWCNTs (0–10 wt%). In the study of WO₃/PANI composite,⁹ the transition points can also be observed.

Curves of tan δ versus frequency of PANI with different contents of MWCNTs are shown in Fig. 6(a). It can be seen that tan δ of all samples increases first and then decreases with frequency increasing. Though with lower negative permittivity at lower frequency, tan δ of CPA0 and CPA5 is far higher than that of the other three samples (as shown in Fig. 6(b)). Combined with the variation tendency of the negative permittivity of MWCNTs/PANI composites in Fig. 1(a), it can be indicated from another point of view that the magnification of negative permittivity of MWCNTs/PANI composites is not caused by high dielectric loss. In the study of J. Zhu,⁹ the dielectric loss of pure PANI at low frequency is also higher than that of its composites.

Fig. 6 Curves of tan δ versus frequency of PANI with different contents of MWCNTs.

It can be known that the values of tan δ are 6587.96, 808.341, 392.714, 3542.43 and 1504.83 with the increase of the content of MWCNTs at 20 Hz. So the addition of MWCNTs can basically reduce the dielectric loss. The peaks of tan δ appear at 2.16 × 10⁴ Hz, 3.1 × 10³ Hz, 1 × 10⁴ Hz, 3.9 × 10⁴ Hz and 1.36 × 10⁵ Hz, with values of 9.3 × 10⁴, 4.4 × 10⁴, 6.6 × 10³, 2.6 × 10⁴ and 4.9 × 10⁴, respectively. It is not difficult to find that the maximum peak of tan δ appears near the transition frequency of permittivity from negative to positive value shown in Fig. 1(b). This is because the current may fully flow into the capacitor without flowing through the inductor near the loss peak. At such frequency, the current will jump from one turn to another, which requires a large amount of energy, resulting in a large amount of dielectric loss. After crossing the peaks, tan δ decreases with the increase of frequency and is always lower than that at low frequencies. For example, the values of tan δ at 2 × 10⁶ Hz are 113.857, 33.3805, 38.0846, 37.9785, 98.8486. Compared to the low frequency range, tan δ of the MWCNTs/PANI composite at higher frequency shows a large reduction because the long range migration of some weakly bound conductive particles decreases, so the low frequency leakage and dielectric loss decrease with increase of frequency. At the same time, “the skin effect” will occur on the sample surface with frequency increasing, and so resistivity of the samples increases as shown in Fig. 3. In addition to loss peak range, the loss values of samples with MWCNTs are much lower than that of PANI in the range of 20 to 2 × 10⁶ Hz, as shown in Fig. 6(a). The tan δ of MWCNTs/CPA0 composites is higher than that of composites in the study of Gu.¹²

3.2 Further verification of the structure model of “double nano wires” that MWNTs/PANI composites generate negative dielectric effect

3.2.1 Effects on the dielectric properties of MWCNTs/PANI composites by increasing the resistivity of polyaniline. In order to verify the structure model of “double nano wires”, hydrochloric acid was used as proton acid and K₂Cr₂O₇ as oxidant to synthesize the pure PANI with much higher resistivity (CHK0) compared to CPA0. With the very high resistivity CHK0 as the matrix in MWCNTs/CHK0 composites, one of the nano wire-PANI was deliberately weakened or eliminated in the structure model of the composites, and the effect of other nano wire-MWCNTs on the negative permittivity of the MWCNTs/CHK0 composites was investigated.

Fig. 7(a) provides curves of permittivity versus frequency of the CHK0 and the CHK0 composites with 1 wt%, 3 wt%, 5 wt%, 10 wt% content of MWCNTs (samples of CHK1, CHK3, CHK5, CHK10). It can be shown that the permittivity of CHK0, CHK1, CHK3 and CHK5 changes in the range of positive value in the frequency range of 20 to 2 × 10⁶ Hz at room temperature. In study of Gu, PANI synthesis by potassium dichromate as oxidizing agent also has positive permittivity.¹² The permittivities of CHK10 and CHK15 have high values at low frequency. The permittivity of CHK10 reaches 1.56 × 10⁵ at 20 Hz, and then it decreases to the negative dielectric region at 2 × 10³ Hz, and it can reach the extreme negative value of −189.78 at 1.2 × 10⁴ Hz. Similarly, the permittivity of CHK15 reaches 1.53 × 10⁵ at 21.6 Hz and decreases to the negative dielectric region at 2.8 × 10³ Hz, and it can reach the extreme negative value of −183.021 at 3.8 × 10³ Hz. The permittivities of CHK10 and CHK15 go up gradually in the negative region from the frequency of the extreme negative permittivity to 2 × 10⁶ Hz.

Fig. 7 Properties and SEM patterns of high resistivity PANI (CHK0) and its composites (a) real permittivity of PANI (CHK0) and PANI/MWCNTs composites with a MWCNTs loading of 1 wt%, 3 wt%, 5 wt%, 10 wt%, 15 wt% synthesized by hydrochloric acid as protonic acid and K₂Cr₂O₇ as oxidant as CHK1, CHK3, CHK5, CHK10, CHK15; (b) curves of resistivity versus frequency of CHK0, CHK1, CHK3, CHK5, CHK10, CHK15; (c) SEM image of CHK10.

Such a permittivity trend in MWCNTs/CHK0 composites is due to the change of oxidizing agent and protonic acid, resulting in a substantial increase in the resistivity of the PANI matrix, as shown in Fig. 7(b). The resistivity of CHK0 is close to the insulator while the resistivity of CPA0 is close to the conductor. The resistivity of CPA0, CPA1, CPA3, CPA5, CPA10 is respectively 3.8 × 10⁷ ohm cm, 2.02 × 10⁷ ohm cm, 2.19 × 10⁷ ohm cm, 1.06 × 10⁷ ohm cm, 15 ohm cm, 0.12 ohm cm at 20 Hz. Such a high resistivity is caused by fewer free electrons on the long chains of CHK0. The CHK0 synthesized with this approach is close to the fully oxidized state and the delocalization of electrons on the chains to be difficult due to a large proportional difference of phenylenediamine and quinonediimine in the doped polyaniline, so the function of “nano wire” of PANI is weakened or eliminated in the MWCNTs/CHK0 composites. While CHK10 and CHK15 with low resistivity is due to the increased content of MWCNTs is more than the percolation threshold of MWCNTs. The MWCNTs inside the composites is overlapped with each other. High resistivity CHK0 possesses low positive permittivity, similar with other ordinary polymer dielectrics. As one of the “double nano wires” mentioned above, MWCNTs has not lost their ability to conduct electrons. When the content of MWCNTs is low in the MWCNTs/CHK0 composites, MWCNTs are coated with high resistivity of polymer chains (as shown in Fig. 7(c)) and no conductive network is formed. The resistivity of CHK0 is high and so the alternating current dipoles cannot be conducted, although the MWCNTs still play the role of “nano wires”. When MWCNTs reach certain content, where the percolation threshold is exceeded, the resistivity of the MWCNTs/CHK0 composites rapidly decreases to a very low value, as shown in Fig. 7(b). Some of the MWCNTs have been able to transfer charges to form a conductive network when the content is up to 10 wt% in the MWCNTs/CHK0 composites. The alternating currents generated by the nano wires-MWCNTs can be passed in the conductive network, and so generate the negative permittivity. The negative permittivity of CHK10 is achieved at frequencies of more than 2.0 × 10³ Hz and the negative permittivity of CHK15 is achieved at the frequencies of more than 2.8 × 10³ Hz. In conclusion, this result shows that the conductive network generated by nano wires is the primary condition for negative permittivity generation.

3.2.2 Effects of coated MWCNTs on the dielectric properties of MWCNTs/PANI composites. In order to verify that the conductive network generated by nano wires is the primary condition for the negative permittivity of MWCNTs/PANI composites, on the basis of the synthesis of pure CHK0 in which hydrochloric acid as proton and K₂Cr₂O₇ as oxidizing agent, a further experiment was carried out. The MWCNTs coated with PVP (MWCNTs–PVP) were filled in the CHK0 to prepare the samples of CPHK10 and CPHK15. It can be seen in Fig. 8(a) that CPHK10 and CPHK15 with MWCNTs–PVP synthesized by PVP coated carbon nanotube have positive permittivity in the frequency range of 20 to 2 × 10⁶ Hz. PVP, a polymer with insulating property, blocks the transmission of alternating current and alternating dipoles in MWCNTs, and so makes MWCNTs lose the role of “nano wires”, so that the resistivities of CPHK10 and CPHK15 are accordingly higher than that of CHK10 and CHK15 shown in Fig. 8(b). The resistivity of CHK10, CHK15, CPHK10, CPHK15 is shown in Fig. 8(b). It can be seen from the figure that CPHK10 and CPHK15 have large resistivity, respectively 3950 ohm cm and 2649.26 ohm cm at 20 Hz, much larger than that of CHK10 and CHK15 at 20 Hz. Thus both of the two kinds of nano wires all lose their functions under this situation. The phenomenon of negative permittivity of the MWCNTs/PANI composites cannot appear even if the content of MWCNTs exceeds to the percolation threshold. This study fully confirms further that the conductive network generated by nano wires is the primary condition of the negative permittivity of the MWCNTs/PANI composites.

Fig. 8 Properties and structures of MWCNTs–PVP/CHK0 composites (a) real permittivity of MWCNTs/CHK0 composites and MWCNTs–PVP/CHK0 loading of 10 wt%, 15 wt% simply called as CHK10, CHK15, CPHK10, CPHK15; (b) curves of resistivity versus frequency of CHK10, CHK15, CPHK10, CPHK15.

4 Conclusion

The structure model of “double nano wires” in MWCNTs/PANI composites is constructed to provide a generation mechanism of their negative permittivity. “Nano wires” of low resistivity PANI can generate alternating currents and alternating electric dipoles under the action of external alternating electric fields, which lead to the emergence of negative permittivity of the MWCNTs/PANI composites. The synergistic effect of the two kinds of “nano wires” of MWCNTs and PANI makes the MWCNTs/PANI composites possess magnified negative permittivity. To verify that “double nano wires” generate the negative permittivity of the MWCNTs/PANI composites, PANI with high resistivity (CHK0) and its MWCNTs composites were prepared. The function of the nano wire of PANI is weakened or eliminated and the phenomenon of negative permittivity cannot be observed only after the percolation threshold of MWCNTs in the MWCNTs/CHK0 composites. MWCNTs–PVP/CHK0 composites were further synthesized through coating with polyvinylpyrrolidone (PVP) on the surface of MWCNTs for weakening or eliminating another kind of “nano wire” MWCNTs. It is found that no matter what the content of MWCNTs–PVP is, MWCNTs–PVP/PANI composites no longer possessed the negative permittivity. These two experimental studies fully prove the validity of the “double nano wires” model.

Acknowledgements

We also thank Dr Jiwei Zhai in School of Materials Science & Engineering, Tongji University for the help of microwave dielectric measurements.

References

1. V. G. Veselago, Phys.–Usp., 1968, 10, 509–514.
2. J. B. Pendry, A. J. Holden, W. J. Stewart and I. Youngs, Phys. Rev. Lett., 1996, 76, 4773–4776.
3. J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, J. Phys.: Condens. Matter, 1998, 10, 4785–4809.
4. D. R. Smith and N. Kroll, Phys. Rev. Lett., 2000, 85, 2933.
5. L. Tonks and I. Langmuir, Phys. Rev., 1929, 33, 195.
6. W. Rotman, IRE Trans. Antennas Propag., 1962, 10, 82–95.
7. J. D. Jackson, Classical Electrodynamics, Wiley, New York, 1975.
8. V. N. Prigodin and A. J. Epstein, Synth. Met., 2001, 125, 43–53.
9. J. Zhu, S. Wei, L. Zhang, Y. Mao, J. Ryu, A. B. Karki, D. P. Young and Z. Guo, J. Mater. Chem., 2010, 21, 342–348.
10. J. Zhu, H. Gu, Z. Luo, N. Haldolaarachige, D. P. Young, S. Wei and Z. Guo, Langmuir, 2012, 28, 10246–10255.
11. X. Zhang, S. Wei, N. Haldolaarachchige, H. A. Colorado, Z. Luo, D. P. Young and Z. Guo, J. Phys. Chem. C, 2012, 116, 15731–15740.
12. H. Gu, J. Guo, Q. He, Y. Jiang, Y. Huang, N. Haldolaarachige, Z. Luo, D. P. Young, S. Wei and Z. Guo, Nanoscale, 2014, 6, 181–189.
13. L. Qian, L. Lu and R. Fan, RSC Adv., 2015, 5, 16618–16621.
14. X. Zhang, X. Yan, Q. He, H. Wei, J. Long, J. Guo, H. Gu, J. Yu, J. Liu, D. Ding, L. Sun, S. Wei and Z. Guo, ACS Appl. Mater. Interfaces, 2015, 7, 6125–6138.
15. B. Li, G. Sui and W. H. Zhong, Adv. Mater., 2009, 21, 4176–4180.
16. H. Gu, Y. Huang, X. Zhang, Q. Wang, J. Zhu, L. Shao, N. Haldolaarachchige, D. P. Young, S. Wei and Z. Guo, Polymer, 2012, 53, 801–809.
17. J. P. Pouget, M. E. Jozefowicz, A. J. Epstein, X. Tang and A. G. MacDiarmid, Macromolecules, 1991, 24, 779–789.
18. Q. Yao, L. Chen, W. Zhang, S. Liufu and X. Chen, ACS Nano, 2010, 4, 2445–2451.
19. H. Kavas, M. Günay, A. Baykal, M. S. Toprak, H. Sozeri and B. Aktaş, J. Inorg. Organomet. Polym. Mater., 2013, 23, 306–314.
20. J. Zhu, M. Chen, H. Qu, X. Zhang, H. Wei, Z. Luo, H. A. Colorado, S. Wei and Z. Guo, Polymer, 2012, 53, 5953–5964.
21. S. I. Maslovski, S. A. Tretyakov and P. A. Belov, Microw. Opt. Tech. Lett., 2002, 35, 47–51.

---