Dielectric behaviors of carbon nanotube/silicone elastomer composites

1 Introduction

As an important member of the high-performance rubbers, silicone elastomer (SE) is irreplaceable in modern high-technology and aerospace and other fields. SE is a polymer with a backbone of Si-O units and side chains of organic groups, which shows apparent differences in structure and performance with polymers that have a backbone of C-C units. Because SE is a typical semi-inorganic and semi-organic polymer, it possesses both the heat resistance of inorganic matter and the flexibility of organic polymer. SE has good cold resistance, electrical insulating and weather resistance properties.

Since their discovery in 1991 [1], carbon nanotubes (CNTs) have attracted enormous attention because of their fundamental behavior and their use in a wide variety of applications. Owing to their structural characteristics and their electrical and mechanical properties, one of the most important opportunities in the future is the emergence of a new generation of composite materials, as relatively low CNT loading within polymeric matrices is required for various applications [2–4]. CNTs have been widely used with different types of polymers [5–7].

Fundamental and practical CNT/SE studies have shown possible applications in many fields, especially in the structures and properties of room-temperature vulcanized SE-based composites. Jiang et al. [8–12] had a systematic study on the effect of modification and aspect ratio of CNTs to CNT/SE composites. The results showed that modified nanotubes could be dispersed homogeneously and had a tight bonding behavior with the rubber matrix. The composites with low-concentration nanotubes at low aspect ratio values show great resistance-pressure sensitivity. At the same concentration of CNTs, the composites with high aspect ratio tubes display large resistance-pressure sensitivity. Liu and Fan [13] investigated the electrical conducting properties of CNT networks in the flexible SE as a function of applied voltages. The results indicated that the I–V curves showed nonlinear relationships that can be fitted to quadratic functions. The electrical resistance of the samples varies with the voltages more sharply in the lower range. Effects of surface modification of CNTs on the electrical properties of CNT/SE composites were studied in Jiang et al.’s papers [14, 15]. Significant enhanced electrical conductivity was discovered in the modified CNT/SE composites, which is seven orders of magnitude larger than that of the rubber host. Compared to the unmodified CNT/SE composite, modified CNT/SE composite has better interface compatibility.

There has been little research on CNT/SE composites focusing on the dielectric loss, permittivity and theoretical analysis of their mechanism. In this study, the dielectric properties of the CNTs/SE composites with different frequencies of outer electric field were investigated. The effect of the aspect ratio of CNTs was also studied.

2 Materials and methods

3 Results and discussion

The morphology of CNTs was observed by using TEM. An ethanol suspension of previously sonicated multiwall CNTs was placed onto copper grids for observation. Figure 1 shows TEM images of CNTs. Two types of CNTs are chosen to be embedded into the SE matrix. Figure 1A and B reveals CNTs of about 40 nm in diameter and about 2 μm long with a lower aspect ratio (S-CNTs). Figure 1C and D shows CNTs (L-CNTs) with higher aspect ratio (diameter about 40 nm and length about 5 μm). In this article, the KH550-modified S-CNTs are the S-CNT-KH550, and the KH550-modified L-CNTs are the L-CNT-KH550.

Figure 1

TEM images of CNTs with different aspect ratios.

The FTIR spectra of CNTs are shown in Figure 2. Compared to curve A, curve B (CNT-KH550) displays the characteristic absorption bands of -OH at 3730 cm^-1, which is on the surface of CNTs, 2349 cm^-1 of Si-O-C and 657 cm^-1 of Si-C. The results reveal that the KH550 was grafted on the surface of raw CNTs to form CNT-KH550. The mechanism of CNT surface modification is shown in Figure 3.

Figure 2

FTIR spectra of CNT. (A) Raw CNTs, (B) CNT-KH550.

Figure 3

Mechanism of CNT surface modification.

The morphology of fracture surfaces of the CNT-KH550/SE composites with 5 phr (parts per hundred parts of rubber) CNT-KH550 is shown in Figure 4. It can be observed that the dispersion of the S-CNT-KH550 and L-CNT-KH550 is good in the SE matrix. This is probably due to the modification of KH550, through which the interaction between CNTs and SE could be improved.

Figure 4

SEM images of tensile-fractured surfaces of the CNT-KH550/SE composites with 5 phr CNT-KH550: (A) S-CNT-KH550/SE, (B) L-CNT-KH550/SE.

Relative dielectric permittivity is an important parameter for the description of polarization behavior. It is affected by the polarization of the composites.

There are two important mechanisms that give rise to the molecular polarization ability. The first is that the application of an electric field to a molecule can cause the electric charge distribution within it to change and so induce an electric dipole, leading to a contribution called the deformation polarization. The second, called the orientation polarization, is that the molecules of some materials have permanent electric dipoles even in the absence of any electric field.

There is also another important polarization mechanism, called interface polarization, on the interface between the two types of materials in the composites. It is caused by inductive electric charges through the interface.

Significantly, the response times of these three types of polarization are different. It can be ordered as deformation polarization<orientation polarization<interface polarization according to their origin.

Figure 5 shows the relative dielectric permittivity of S-CNT-KH550/SE composites with different frequencies of outer electric field. With increasing frequency of electric field, the relative dielectric permittivity of S-CNT-KH550/SE composites decreases.

Figure 5

Relative dielectric permittivity of S-CNT-KH550/SE composites with different frequencies of outer electric field.

The main reasons causing this phenomenon are the following. First, as a polar substance, CNT has a strong π electron delocalization, which has more deformation polarization and orientation polarization. If an electric field is applied to such a material, the molecules tend to rotate so that the dipoles become aligned with the field direction, which gives rise to an orientation polarization. Thermal agitation will, however, prevent the molecules from aligning fully with the field, so the resulting polarization will depend both on the field strength and on the temperature of the material. This contribution is considered first. For the sudden application of an electric field that then remains constant, the deformation polarization can be considered to take place “instantaneously”, or more precisely in a time of the order of 10^-14 s.

Because all the three polarization mechanisms are present in the S-CNT-KH550/SE composites and with different response times, the phenomenon can be explained. When the frequency of outer electric field is about 10 kHz or lower, all the three polarization mechanisms can follow the change of the outer field so the relative dielectric permittivity reaches a highest level. With the increasing of the frequency from 10 to 60 kHz, the interface polarization that has the longest response time cannot catch up with the change of the outer field. The relative electric permittivity decreases. When the frequency becomes higher, from 60 to about 160 kHz, there is a “flat roof” on the permittivity curves. Between this frequency interzone, the interface polarization disappears. The main causes that maintain the relative dielectric permittivity of the composites are orientation and deformation polarization. They all can follow the alternation of the outer field. The outer field cannot affect the two polarizations much. As it becomes higher from 160 kHz, the alternation of the frequency of the outer field is too swift to catch up with one of the remaining polarizations, the orientation polarization. Thus, with the increase in frequency from 160 to 200 kHz, the orientation polarization becomes more and more weak, causing a decline of the relative dielectric permittivity.

Theoretically, CNT has a strong π-electron delocalization, which has more deformation polarization and orientation polarization. Embedded into the SE matrix, CNT has an ability to enhance the relative dielectric permittivity of the composites, but with 1–2 phr S-CNT-KH550, as shown in Figure 5, the relative dielectric permittivity is a little lower than that of the blank sample, and then, with the subsequent increase of the S-CNT-KH550 content, the permittivity of the composites is enhanced and is higher than that of the pure SE. Perhaps. when the S-CNT-KH550 content is lower (1–2 phr), modifications of the CNTs will confirm the interaction and weaken the displacement between fillers and matrix. This mechanism may weaken the interface polarization and cause a lower relative permittivity. In these S-CNT-KH550 contents, the contribution of permittivity increasing caused by embedded CNTs is weaker than that of permittivity decreasing caused by weakening of the interface polarization. Thus, the total permittivity of the composites containing 1–2 phr S-CNT-KH550 is a little lower than that in the blank sample. When the CNTs content increases from 2 phr, the total impact factors will become a “positive state”. The relative dielectric permittivity increases with the increasing of the CNTs content.

Figure 6 shows the relative dielectric permittivity of L-CNT-KH550/SE composites with different frequency of outer electric field. It can be seen clearly that, different from the phenomenon of S-CNT-KH550/SE samples, with the increasing of the L-CNT-KH550 content, the permittivity of composites increases. Even at a lower content (1–2 phr), there is no “negative state”. The reason is that the L-CNT-KH550 has a larger aspect ratio. This may cause much more π electron delocalization. The increasing of the deformation and orientation polarization is much larger than the decreasing of the interface polarization. The total effect is “positive” all the time. At the same time, as shown in Figure 5, the permittivity of L-CNT-KH550/SE samples are much higher than that of S-CNT-KH550/SE samples at the same CNT content and outer field frequency because of the abundant π electron delocalization.

Figure 6

Relative dielectric permittivity of L-CNT-KH550/SE composites with different frequencies of outer electric field.

Another important parameter describing the dielectric properties is dielectric loss. A polymer medium will be polarized along the outer alternate electric field. At the same time, a loss will be caused. The electric energy will be changed into thermal energy. This is called dielectric loss.

The dielectric loss of the polymer and its composites may include four parts. They are (1) electric conductance loss caused by oozy electric current of carrying particles, (2) polarization loss caused by relaxation of the dipoles, (3) ionization loss caused by the process of ionization, and (4) configuration loss caused by asymmetry of structures.

Figure 7 shows the dielectric loss of S-CNT-KH550/SE composites with different frequencies of outer electric field. It can be seen that the dielectric loss increases with the increasing of outer field frequency from 10 to 160 kHz and decreases with the increase of outer field frequency from 160 to 200 kHz. There is a maximum dielectric loss at the frequency of 160 kHz.

Figure 7

Dielectric loss of S-CNT-KH550/SE composites with different frequencies of outer electric field.

The main reasons causing this phenomenon can be explained as follows. In an alternate electric field, the dielectric permittivity and polarization of a medium should obey the Debye dispersion theory and Debye equation [Eq. (1)]:

where N is the number of molecules in a unit volume, ε₀ is the dielectric permittivity of vacuum, a_∞ is the polarization ratio in a much higher outer field frequency, a_p is the polarization ratio of the dipoles, and τ* is the time of polarization.

At the right side of Eq. (1), the first term represents deformation polarization, and the second term is orientation polarization.

When the outer field frequency is very low, ω approaches zero, and Eq. (1) will be changed into Eq. (2).

where ε_s is the dielectric permittivity in a direct current field.

When the outer field frequency is very high, ω approaches infinity, and Eq. (1) will be changed into Eq. (3).

With the simultaneous Eqs. (1), (2) and (3), and the definition of dielectric loss, a new and important equation is obtained [Eq. (4)].

When the outer field frequency ω approaches zero, the limit of tan δ (represents dielectric loss) as ω approaches zero equals zero.

limω→0tanδ=0.

When the outer field frequency ω approaches infinity, the limit of tan δ as ω approaches infinity is equal to zero.

limω→∞tanδ=0.

Make the first derivative of Eq. (4) with respect to ω and command dtan/dω=0. A result can be obtained. When ω equals a special value, tan δ will reach a maximum value.

ω=εsε∞, tanδmax=εs-ε∞21εsε∞.

On the basis of the above analysis, the explanations can be summarized as follows. When the frequency of the outer electric field is lower (about 10 kHz or lower), the orientation of the dipoles can catch up with the field alternate. There is almost no loss in the composites. With the increase in the field frequency (from 10 to 160 kHz), orientation polarization cannot follow the frequency of the outer field. A resistance will appear between orientation and field, which could consume some parts of the electric energy. The loss will become larger and larger till a maximum value in the frequency of 160 kHz. With the continual increasing frequency (from kHz to 200 kHz), the orientation of the dipoles cannot follow with the field completely and orientation polarization will disappear little by little.

Consider a parallel RLC circuit shown in Figure 8. The output complex impedance of A-B can be expressed by the following equation [Eq. (5)]:

where Z is the complex impedance, R_L is the inductance of the element L, R is the resistance of the element R, R_C is the capacitance of element C, L is the inductance coefficient, and C is the capacitance coefficient.

Figure 8

Sketch map of RLC parallel circuit.

The output complex impedance will be changed when the outer field frequency changes.

When the outer field frequency is very low, the limit of Z as ω approaches infinity equals R, which is a constant.

limω→0Z=R.

When the outer field frequency ω approaches infinity, the limit of Z as ω approaches infinity equals zero.

limω→∞Z=0.

Make the first derivative of Eq. (5) with respect to ω, and command dZ/dω=0. A result can be obtained, as in Eq. (4). When ω equals a special value, tan δ can reach a maximum value.

ωmax=L-RCLC,Zmax.

When the outer field frequency ω approaches zero, it will be equivalent with the direct field. The element C is an open circuit, and the element L is a short circuit. When the field frequency ω approaches infinity, the element C will be a short circuit and L will have an infinite inductance.

Compared with Figure 7, a similar trend can be seen. Perhaps there is some linking between CNT/SE composites and the parallel RCL circuit.

Figure 9 shows the dielectric loss of L-CNT-KH550/SE composites with different frequencies of outer electric field. With the changes in the outer field, the dielectric loss of L-CNT-KH550/SE composites exhibits a similar trend as S-CNT-KH550/SE samples. They all obey the above analysis. Comparing Figures 7 and 9 carefully, a phenomenon can also be seen. With the increase in CNT-KH550 contents, all the dielectric loss is enhanced, but the increasing ranges of S-CNT-KH550/SE samples are smaller than that of L-CNT samples. It means that L-CNT-KH550/SE samples can reach a higher dielectric loss at a lower CNT content. L-CNTs have a larger aspect ratio. Compared with S-CNT samples, the aspect ratio of the L-CNT is too large to polarize at the frequency of ω_max of S-CNT-KH550/SE samples.

Figure 9

Dielectric loss of L-CNT-KH550/SE composites with different frequencies of outer electric field.

4 Conclusion

KH550-modified CNTs were dispersed as dielectric properties affecting fillers in an SE matrix, and the resulting dielectric properties with different CNT content, different CNT aspect ratios, and different electric field frequencies were analyzed. The results showed that with the increasing of field frequency, a polarization mechanism or two would not catch up with it because of the three extant polarization mechanisms and their different response times into the CNT/SE composites. The dielectric loss and permittivity would obviously be affected by them. The CNTs with larger aspect ratios have a more effective dielectric loss and permittivity-enhancing effect. According to the Debye equation, CNT/SE composites had a similar function with a parallel RLC circuit somehow. Our future research will focus on these internal relationships to try to find out the exact mathematical model of dielectric properties of CNT/SE composites. In addition, the dielectric properties of CNT-silica/SE hybrid composites will be investigated.