Chapter 11: Electromagnetic properties of polymer–carbon nanotube composites – Polymer-Carbon Nanotube Composites


Electromagnetic properties of polymer–carbon nanotube composites

F. Nanni and M. Valentini,     INSTM–University of Rome ‘Tor Vergata’, Italy


The use of plastic materials as shielding enclosures, electromagnetic (EM) absorbing materials, and radio frequency (RF) components has greatly increased in the past few years. Shielding deals with the protection of workspaces from external radiation, usually achieved by conductive materials by means of wave reflection. In absorbing media, the incident wave energy is dissipated within lossy medium. Such EM properties can be modulated by adding conductive fillers (such as carbon nanotubes, CNTs) to an insulating matrix. In this chapter, the shielding and absorbing performance of CNT-loaded polymers is described and their intrinsic electromagnetic properties (complex permittivity and conductivity) are correlated to material composition and microstructure.

Key words

electromagnetic properties

electromagnetic wave absorbing materials

shielding materials

11.1 Introduction

Full comprehension of, as well as possible modeling and simulation of the electromagnetic behavior of materials in waves is extremely interesting in view of the many possible engineering applications such as antennas, circuits, RFID devices, absorbing or shielding media, etc. Historically, the electromagnetic behavior of materials in waves was widely studied during the Second World War for military purposes with the introduction of radar and stealth technologies, nevertheless very little data was divulged in the scientific literature due to strategic needs. More recently, the advent of computers and the spread of electronic devices have brought to light new concerns regarding electromagnetic interference (EMI) phenomena that are at least harmful, if not seriously dangerous, when occurring in particular instances such as airplane electronic systems and radar air traffic control communications. Moreover, unlike the past century, today tremendous progress in material science has been made (up to the advent of nanomaterials and nanotechnology), so that new phenomena must be considered and, possibly, explained when dealing with materials in waves.

Generally the topic of EM waves’ interaction with materials can be dealt with by starting either from a macroscopic approach (Maxwell’s equations and constitutive relations1), or a microscopic point of view, that considers the interaction between waves and material microstructure. The former is the prerogative of electromagnetic engineering, while the latter is more pertinent to material science engineers.

It is well known that an incident electromagnetic wave (EI) passing through a material undergoes three main processes: reflection (ER), transmission (ET) and absorption (EA = EI – ER – ET) (Fig. 11.1). All these phenomena are strictly related to the medium’s intrinsic properties, namely, electric conductivity (σ), complex permittivity (ε* = ε′ – jε″), and complex permeability (μ* = μ′ – jμ″), as well as to its geometrical characteristics, in particular, thickness.2 From time to time, depending on the application, any one of the aforesaid mechanisms can be promoted by performing an appropriate component design, that involves both the right choice of material, in relation to its intrinsic properties (i.e. σ, ε* and μ*), as well as geometrical considerations.3 When shielding is required, in fact, the material has to be mostly conductive to reflect the incident wave and preserve the environment behind the shield (zone B in Fig. 11.1).4 In the case of absorbing, instead, both reflection of the incident wave and transmission through the medium are unwanted (both zones A and B in Fig. 11.1 have to be preserved) and therefore the energy associated with the material has to be somehow dissipated.5 It can be noted that an absorbing structure implies the function of shielding, while the contrary is not true.

11.1 Reflection (ER), transmission (ET) and absorption (EA) of an EM wave through a medium.

As previously mentioned, the prospect of designing and realizing materials with specific EM properties is of great interest, nevertheless this need translates into the feasibility to tailor material composition and microstructure to achieve the required electromagnetic specifications. This is why the research in this field usually involves composite materials (more often polymer matrix composites, PMCs), due to their natural versatility and potential to mix and incorporate fillers, with different intrinsic electromagnetic properties, to gain specific EM characteristics. Moreover, PMCs are low density materials, a property which makes them attractive in many applications where weight is a big concern. Generally, in both shielding and absorbing applications, lossy materials with a different degree of conductivity are involved. This is because in the case of shielding reflectivity has to be assured, while in the case of absorbing, one of the main mechanisms of energy dissipation (the predominant one when dealing with conductive elements in an insulating medium as in the case of carbon nanotube (CNT) in polymer matrix) is its conversion into heat, by means of the joule effect.

Understanding material behavior in waves when involving composite materials is, however, particularly challenging, since the effect of mixing two or more distinct materials is not always easily predictable, due to the rise of interaction effects. Many attempts at numerical modeling are reported in the literature,6, 7 even if a complete dissertation that includes all the different aspects and that is valid under all conditions is still lacking, due to the complexity of the involved phenomena. Usually the proposed models either make too stringent a hypothesis, or are confined to the case of well-dispersed non-interacting geometrical perfect particles, or follow an experimental approach, whose validity is confirmed only under specific conditions.8, 9 Therefore, the current state of the art concerning EM properties of PMC reports mainly experimental results. In this situation, modeling the electromagnetic behavior of composites containing nanofillers is even more challenging, due to the lack of knowledge in understanding phenomena at the nanoscale level, that can be very different from their corresponding micrometric analogs.

Many studies have been carried out in past years regarding the electromagnetic properties of PMC,10, 11 many of which involve the use of carbon as a conductive filler in the form of either long and/or short fibers, or particles.12,13 In this regard, though, the advent of nano-sized carbon fillers (as carbon nanofibers and nanotubes) was a remarkable innovation. In fact, recently many papers have been published on EM properties and performance achievable when involving nanofillers and, in particular, CNTs, and trying to explain why such fillers seem to be tremendously more efficient than the more traditional carbon black or graphite. Distinctive features of CNTs are the high aspect ratio and electrical conductivity, that achieve composites with electric properties comparable and even superior to those shown by today’s more used carbon black (CB) loaded polymers, with much lower nanofiller content, allowing avoidance of, or at least minimizing, the degradation of other composite performance such as mechanical properties, aesthetic aspect, processability, etc. Moreover, the cost of nanofillers and CNTs, that nowadays is a still a big concern, is thought to become absolutely comparable to those of today’s more common fillers in view of the introduction of mass production.

The following paragraphs are devoted to the description of the main mechanisms that achieve an absorbing and shielding performance in CNT-loaded polymers, considering the latest available scientific researches. Particular attention has been paid to link materials’ microstructure and CNT intrinsic properties to the final macroscopic EM performance.

11.2 Electromagnetic wave absorbing CNT composites

The main aim of an electromagnetic wave absorbing material is to dissipate the energy associated with the incident wave, by transforming it in to other forms to avoid any reflection and/or transmission. Reflection can be controlled by achieving good impedance matching between free space and the material surface,14 while transmission is hindered by means of energy dissipation, enhancing magnetic and/or dielectric loss.

For an EM wave incident normal to a slab, the coefficients of reflection (ρ)and transmission (τ) are respectively:5



where Z1 and Z2 are the impedance of the media, one of which can be equal to Z0 (impedance of free space, 377 Ω) in the case of propagation in air. Impedance matching to avoid reflection can be achieved by tailoring material electromagnetic characteristics (complex permeability and permittivity, respectively μ* and ε* in Equation 11.2) so that its characteristic impedance (Zm in Equation 11.2) becomes as close as possible to that of free space:


Often, to increase the bandwidth of the operation, multilayer absorbing structures are designed15, 16 where, for example, a thin slab is sandwiched between two media. In this case, the analysis is made tractable by drawing upon an analog in the transmission line theory, that gives, for the case depicted in Fig. 11.2, the following equation:5

11.2 EM wave propagation through a thin slab between two semiinfinite media: (a) schematic sketch; (b) transmission line equivalent.


where Zin is the input impedance at the surface of the absorber, γ is the propagation constant and d the thickness of the absorber. The reported equations (that present different forms depending on the propagation condition, presence of metal backing, oblique incidence, etc.) highlight how and by how much electromagnetic and material designs overlap.

As previously reported, the ability shown by some materials to absorb the electromagnetic energy associated with incident waves passing through them, is due to the presence of loss mechanisms that allow energy dissipation. Such dissipation, at the material microscopic level, occurs by means of different mechanisms such as power loss during domain rotation in magnetic materials, transformation of power into heat (with mechanisms analogous to the way energy is consumed by a resistor) in not-perfect conductors, and power loss due to dipole rotation in pure dielectric materials.

Generally speaking, CNTs can be considered to be non-magnetic fillers, being the only possible magnetism associated with the residual presence of catalysts (usually consisting of magnetic metals as Co or Ni),17 therefore, all contributions to energy dissipation deriving from magnetic loss can usually be ignored. It is advisable, though, to check CNT purity or to perform preliminary EM measurements to ascertain the assumption of absence of any magnetism.

Mechanisms of energy dissipation in CNT-loaded polymers have therefore to be searched in dielectric loss, since the system is a lossy material made of conductive elements within a dielectric medium. It is customary (engineers are usually interested in the cumulative effect) to group the effects of dielectric loss under one term, named permittivity, that is a material intrinsic property. The effective permittivity for linear, isotropic materials, that includes DC conductivity, is defined as18


where ε0 is the permittivity of vacuum, ε′ is real part of permittivity, ε″ is the imaginary part of permittivity (i.e. the polarization loss, an entropic term owed to all intrinsic losses arising from the delay of the material in changing polarization in frequency) and σ is the electric conductivity. Thus ε′ is an enthalpic term, which accounts for the energy stored in the material. The term in brackets in Equation 11.4 embodies all dielectric losses for the system under consideration, that are due to electric conductivity and polarization effects.

It is well known that materials can show many possible polarization mechanisms such as ionic polarization, dipole rotation polarization, electronic displacement polarization, interface polarization, etc., any of which can be ignored or become the main absorbing mechanism, depending on operation frequency and material intrinsic properties. Electronic and ionic polarizations, for instance, produce loss at very high frequency (time to rotate the dipoles 1014–1015 s), while dipole polarization occurs at lower frequencies (time to rotate the dipoles 108–102 s).19, 20 Interface polarization at the CNT–polymer interface is very important in CNT-loaded polymers, due to the large surface area of CNT.21

As reported, in order to achieve good absorbing performance, good impedance, matching and high losses (usually encountered by means of a high tangent loss tgδ = ε″/ε′) are required. The latter involves material design and composition. But, how can this target be reached in CNT composite materials? This question can be answered when understanding the origin of dielectric losses in such systems. In CNT composites many factors strictly related to filler type, amount and characteristics (such as intrinsic permittivity, permeability and conductivity, size, morphology, etc.) as well as its distribution within the matrix, affect the resulting electromagnetic behavior. Generally, a system of CNTs dispersed in an insulating resin can be regarded as a system of resistors in a theoretical resistance-capacitance (RC) network22, 23 (Fig. 11.3).

11.3 System of CNT forming a resistance-capacitance network: (a) well-dispersed few CNTs; (b) well-dispersed numerous CNTs; (c) numerous aggregated CNTs.

In such a system, the losses are introduced by means of electrically conductive fillers, the amount of which is the first parameter affecting ε″ (Fig. 11.4b). In particular, it was proved23, 24 that an increase of CNT results in an increase of ε″, due in part to the mere increase of conducting elements (σ in Equation 11.3) and in part to the formation of more numerous and more closely spaced microcapacitors, thus promoting either the formation of conductive paths and/or electrons flow by means of tunneling effects (Figs 11.3 (a and b)). Often the increase in imaginary permittivity becomes steeper above a certain CNT concentration. Such an event has been attributed to the onset of percolation,25 when the system shifts from insulator to conductive. It is important not to make the mistake of thinking that the larger the complex permittivity, the better is EM absorption. This is because materials that exhibit too large permittivities tend to reflect a large part of the incident wave,26 and therefore this parameter has to be properly chosen each time according to practical need. Increasing CNT content leads to an increase of ε′ too (Fig. 11.4a), and this, recalling the RC model, is due to the enlarged contribution of the increased number of microcapacitors to the capacitive term.

11.4 Real and imaginary permittivity vs frequency of MWCNT loaded epoxy samples (%) at different CNT loading (wt%) measured in the x-band frequency range by means of wave guide technique.1 Note: 1EM measurements carried out at CEmIn s.r.l., Via della Farnesina 363, 00135 Rome, Italy.

Once the RC network scheme has been accepted, then it follows that CNT distribution in the matrix is another important parameter affecting dielectric losses. On equal CNT content, in fact, well-disentangled and well-dispersed nanotubes increase the number of microcapacitors and decrease the distance between them.27 When, instead, highly entangled CNTs are dispersed within the matrix, then the RC scheme is still valid if considering the microcapacitors formed by CNT agglomerates27 (Figs 11.3 (b and c)). In this case, though, the efficiency of the CNT loading is somehow limited and the advantage deriving from their use that is linked to their high aspect ratio is not fully exploited. CNT distribution in the matrix is in turn affected by their amount: if CNT concentration is small, then intramolecular van der Waals interactions between tubes are weaker, so that it is easier to disentangle them, so that CNTs result randomly oriented and well dispersed in the matrix.22

Since CNT dispersion in resin is a crucial parameter, it follows that the composite manufacturing process plays a role. In ref. 28, wave attenuations of SWCNT–PC composites manufactured by either lamination, coagulation or melt-extrusion were compared, indicating that the higher attenuation performance, shown by samples prepared by coagulation, has to be referred to the resulting different microstructure made of more finely spread SWCNT. In ref. 29, the co-precipitation method and melt-blending were compared when preparing MWCNTs in poly ε-caprolactone (PCL) composites. It was found that in composites prepared by melt blending, MWCNTs show an extended breakdown, thus hindering percolation and reducing electromagnetic absorbing. Such an effect was proved to be more evident in thick (average outer diameter ≈ 25 nm) than in thin (average outer diameter ≈ 10 nm) MWCNTs, that are more fragile, due to the presence of more numerous structural defects.

As previously seen, conductivity is an important parameter in CNT-loaded polymers, since it affects energy dissipation. Therefore, CNTs’ intrinsic conductivity and purity are very important features. SWCNTs are small-diameter structures (diameter < 5 nm) with a wide range of electrical conductivity changing from metallic behavior (even showing ballistic transport at low temperature30) to semiconductors depending on their structure and chirality.31 On the other hand, MWCNTs, made of concentric SWCNTs of larger diameter (> 5 nm), present a weak semi-metallic behavior. The accurate choice of CNT is therefore an important start to build a material that can fulfill the required final properties.

Purity of CNT is another important aspect affecting conductivity. As a matter of fact, it was proved32 that the same MWCNTs exhibit different electric conductivity in the as-fabricated or graphitized state. In fact, thermal treatment eliminates microstructural defects and promotes the graphitic structure, both features that result in an increase of conductivity. Contemporarily, for the same reason, the permittivity spectra up to 2 GHz is reduced in magnitude. For modeling purposes, moreover, it has to be remembered that the conductivity of graphite is highly anisotropic, with the c-axes conductivity over 103 less than the in-plane value.33

11.3 Electromagnetic shielding CNT composites

There is an increasing demand for electromagnetic interference (EMI) shielding materials, mainly due to the increase in radio-frequency radiation sources. Electromagnetic shielding (SE) is needed to protect the environment and workspaces from radiation coming from computers and telecommunication equipment, as well as to protect sensitive circuits. Historically metals were used as EMI shields due to their high conductivity, consequently reflection was the main active mechanism. Nevertheless, metals present some shortcomings due to their heavy weight (particularly relevant in aeronautic and aerospace applications), physical rigidity and corrosion. Therefore metal-coated polymers first,34, 35 and conductive composites later,36 were proposed as an alternative. Conductive composites, made of electrically conductive fillers (as metal fibers37 or carbon fibers or particles38) in an insulating matrix, offer very interesting shielding performance (commercial applications require SE above 20 db, i.e. less than 1% transmission of the EM wave), nevertheless usually a high amount of common filler (such as carbon black) is required to achieve an adequate level of conductivity. Even more recently, carbon nanofibers and nanotubes polymer composites have been shown to be very effective, reaching a higher shielding performance than that of micro-sized carbon filler composites, at a lower filler content.39 This is because CNTs are very proficient, high aspect ratio conductive nanofillers.

Shielding in CNT-loaded polymers cannot be ascribed to pure reflection (as in homogeneous conductive media) but to the concurrent presence of three mechanisms (Fig. 11.5): reflection (R), absorption (A) and multiple reflections (MR) occurring within the shield.40

11.5 Absorption (A), reflection (R) and multiple reflections (MR) within a thin slab.


Multiple reflections decrease the shielding performance if the shield is thinner than the skin depth,41 which is defined as the depth at which the electric field drops to (1/e)42 and is given by:


with δ skin depth, f frequency, μ magnetic permeability and σ electrical conductivity. According to ref. 43, multiple reflections can be ignored if the distance between reflecting surfaces (i.e. shield thickness) is larger than the skin depth. If the thickness is equal to skin depth, instead, shielding has to be considered primary due to reflection.40 It follows that the mechanism of multiple reflections has to be taken into account when dealing with films and coatings. As a rule of thumb, MR have practically no influence when SE is over 15 dB.44, 45

The power absorbed (Pab) in EMI shields is an inverse function of conductivity46 (symbols as above).


It results from Equation 11.5 that, on equal frequency and if multiple reflection can be ignored, the larger the conductivity the lower is the power absorbed, and reflection becomes the predominant occurring phenomenon.

Actually the influence of the three cited mechanisms (i.e. A, R and MR) on the overall shielding performance of respectively MWCNT/polypropylene (PP) and SWCNT/polyurethane (PU) composites is very well described and discussed.44, 45 In particular, it can be deduced45 that the predominant effect in SE depends on material tangent loss (i.e. tanδ = ε″/ε′), that indicates the ability of a material to convert stored energy into heat (therefore dissipating energy), as well as pointing out how well a material can be penetrated by an electrical field. If tanδ >>,1 the material is a good conductor and SE is mainly decided by σ, not ε, while if tanδ < < 1, then the material is a weak conductor and dissipation has to be mainly referred to ε. In relative conductive CNT-loaded polymers, however, although reflection remains an important mechanism, absorption is likewise important, being the low amount of power blocked by absorption due to the lower power transmitted into the sample.40 If, finally, tanδ ≈ 1 then both σ and ε combine to bring out shielding. In such cases the increase of CNT content as well as, on equal filler content, the increase of frequency, shifts the predominant shielding mechanism from reflection to absorption.45 An explanation of this trend has been attempted considering that absorption is linked to tanδ, that increases fast with frequency. As reported, tanô is the ratio between imaginary and real permittivity, therefore it is clear that when dealing with SE or absorbing systems (particularly in the case of CNT-loaded polymers), the knowledge of both entities is just as important as well as the knowledge of conductivity.

Generally speaking, conductivity in CNT-loaded polymer is a function of nanotubes content. In particular, it is well known that, above a definite CNT content, the nanotubes become sufficiently contiguous to form a conductive network, so that electrical conductivity, and hence SE, increase sharply. Many papers, in fact, report a clear correlation between the increase of CNT content and SE enhancement, both when using SWCNTs46 and MWCNTs.47 Moreover, although this behavior has always been verified, it is important to note that EMI shielding was found to increase much faster at low CNT loading than it does at high CNT content.46

Practically, conductivity of the medium, frequency of operation and thickness of the shield are concurrent factors determining the overall SE performance and predominant mechanism. This is why, depending on the specific system, SE and the investigated frequency spectrum, SE can be found to remain constant,39,47 increase48 or decrease31 with increasing frequency.

In SE performance, CNT morphology plays a role as well.31 On equal filler content, high aspect ratio CNTs show higher SE than low aspect ratio nanotubes. This is most probably due to the fact that ‘long’ (i.e. high aspect ratio) SWCNTs reach percolation at a lower filler content than ‘short’ SWCNTs, since they more easily form a conductive network. In ref. 49, it was shown that the SE of CNF-loaded polyvinylidene fluoride (PVDF) coatings containing short CNF, obtained with 1 hour of ball-milling, was half that obtained with longer not-milled nanofibres.

Even ‘annealing’, i.e. thermal treatment of SWCNT, has an effect on SE. In fact, it is hypothesized that the removal of wall defects and functional groups by means of thermal treatment results, ceteris paribus, in an increase in SE,31 since it improves conductivity. In the same work, though, it is shown that aspect ratio is an effective parameter influencing SE more than annealing does.

The importance of CNT dispersion in the resin has already been highlighted when discussing the absorbing properties, nevertheless it affects SE too. In particular, SE can be reached at lower filler content if a sufficiently good and homogeneous distribution of CNT in the matrix is insured. This is because, with equal filler content, a more efficient system of conductive pathways is formed, that behaves like a conductive mesh, intercepting the electromagnetic wave. The importance of the formation of an efficient conductive net in view of EMI shielding applications is pointed out,50 where it is reported that a slight addition of 1 wt% nanotubes to a larger amount of carbon nanofibers (CNF, 5 or 10 wt%, respectively around or above percolation) in polystyrene (PS) results in a dramatic improvement of SE, even if, in samples with CNF content above percolation, the same improvement was not registered for electrical conductivity.

Some researchers51 investigated the SE performance of metal-coated (nickel or silver) CNT in siloxane/poly(urea urethane) (PDMS-based PUU) between 400 and 1300 MHz, suggesting this methodology to increase SE at low filler content. The results, though, showed that there is not a clear improvement of SE when involving metal coating, nevertheless it was undoubtedly proved that, when using this method, coating thickness is the key parameter that influences the final SE performance. In particular, too thick coatings lead to aggregation of CNT, reducing the network structure and, hence SE. Moreover, the use of Ni-coated CNT showed better SE than that obtained when employing Ag-coated ones. The authors attribute this result to the magnetic properties of Ni, so that some degree of magnetic loss arises. This hypothesis is supported by the fact that it was seen52 that poly(methylmethacrylate) (PMMA) loaded with raw MWCNTs, synthesized by chemical vapor deposition using Fe as the main catalyst, possesses higher SE than purified CNT-loaded PMMA, again referring this result to the magnetic nature of iron.

Coming back to the concept of multiple reflections, previously introduced when dealing with EM wave propagation within a slab, it is important to point out that such phenomena can occur even between CNT walls (Fig. 11.6). The skin depth of a single carbon nanotube, with negligible permeability and a conductivity of 1 × 105 S/m, has been calculated, in the x-band, in the range of 14–18 μm,40 which is far higher than the CNT diameter, implying that in such a system multiple reflections cannot be ignored. Moreover, the MR occurring between the CNT internal surfaces are expected, per se, to produce a negative effect on EMI SE. Instead, if a system of CNTs dispersed in the resin is considered (as previously depicted in Fig. 11.3 (a)) and if the model proposed in53 is assumed valid, then a possible positive contribution to SE can be taken into account. Such a positive increase in SE derives from the presence of additional surfaces that combine to bring out wave reflection, and is expected to arise when the surface area/diameter ratio and spacing among CNT are optimized.

11.6 Multiple reflection occurring between a CNT wall.

11.4 Other CNT composites’ electromagnetic applications

The advent of CNT with their terrific properties and potential has aroused great attention for many electronic and electromagnetic applications as plastic transceiver modules,54 RFID55 and antennas (it is reported that an array of aligned carbon nanotubes can behave like an electromagnetic antenna).56 Antennas can receive different wavelengths depending on their dimensions57 and therefore, due to their nanoscale dimensions, CNT can be naturally employed to develop nanoantennas for terahertz, IR and optical ranges.58 As happens when dealing with other properties or applications, nanoantennas require that both theoretical and experimental investigations will be done in a qualitatively new context, since, for instance, the capabilities of the frequency, spatial and polarization filtration and noise characteristic of nanoscale objects are basically different from those of the corresponding macroscopic analogs.59 The working principle of CNT-based antennas is to some extent analogous to that of macroscopic vibrator antennas, the main difference being the slowing modes of the vibrator that are strongly slowed down surface plasmons in contrast to weakly slowed down quasi-TEM modes in single wire line.59 In metallic achiral CNT antennas, the radiation field is formed by the successive reflections of CNT edges that are fundamental to form the antenna pattern.

At the Department of Physics at the University of Berkeley (research team K. Jensen and others60) the first ‘nanoradio’ (i.e. a functioning, fully integrated radio receiver) from a single carbon nanotube has been constructed. The single nanotube serves, at once, as all the major components of a radio: antenna, tuner, amplifier, and demodulator. Moreover, the antenna and tuner are implemented in a radically different manner than traditional radios, receiving signals via high frequency mechanical vibrations of the nanotube rather than through traditional electrical means.

Up to now, one of the big concerns in nanotechnology has been to connect nanoelectronic devices with the macroscopic world, i.e. to microscopic electronic devices. Therefore, topics like electric field analysis, and other important parameters like field distribution, gain, radiation patterns and radiation efficiency of CNT antennas, are of great interest.59 As is widely known, a CNT is a sheet of graphite rolled up into a tube, and, from an electromagnetic point of view, it can be seen as an electric dipole with a cylindrical shape. Array patterns, instead, can be considered as an assortment of single dipoles made up of identical elements, that, in the case under examination, can be an assortment of CNTs. Numerical simulations59 of both single dipole and array patterns showed that, while a single dipole exhibits low gain and efficiency, these parameters can be changed by introducing an appropriate pattern. Particularly, in the cited work, it was demonstrated that the antenna’s gain can be significantly enhanced by working on CNT length, quantity (i.e. number of dipoles) and intertube distance, which means strict control on material processing and, particularly, CNT manipulation. Intertube distance, for instance, relates again to the degree of CNT disentanglement, that is confirmed as a very important parameter when dealing with EM properties. CNT antenna design and simulations are based on the hypothesis of well-separated individual nanotubes with specific lengths, while, in practice, although CNTs are easy to find commercially, they are usually available in entangled bundles. This explains why, in recent years, many attempts have been made, for what concerns this field of research, to improve and focus CNT synthesis methodologies on these parameters. Control of CNT length is particularly crucial with regard to enlarging the potential applications of nanomaterials to lower frequency applications, such as microwaves. Nanoelectronic devices made up of nanotubes, nanoparticles and nanowires, in fact, offer negligible coupling to microwaves, due to the fact that microwave wavelength (centimeters) is much larger than device scale. Fortunately, many successful improvements have been made6163 to control and optimize CNT synthesis so that CNTs with a length in the range of millimeters to centimeters, to suit microwave and RF applications, have been fabricated. In ref. 64, for example, it is reported that SWCNTs were grown under controlled conditions so that the fabrication of a dipole antenna was attempted. In particular, an electrode pattern for an antenna probing made up of 5 micron square islands separated by 100 pm was realized. On these islands, made of catalyst deposited by standard lithography, single long (5 mm) metallic CNTs were grown and their orientation controlled by gas flow.

11.5 Conclusion

In this chapter, the most recent literature in the field of electromagnetic materials based on CNT-loaded polymers was reported. It was highlighted that the overall electromagnetic performance (either when shielding or absorbing is required) is strongly linked to material composition and microstructure; both features that can modify electromagnetic intrinsic parameters such as conductivity and complex permittivity. In particular, the following can be noted:

• Conductivity increases with increasing CNT content, and this is why SE usually follows the same trend.

• Real and imaginary permittivity increase with increasing CNT content: the former because a large number of microcapacitors are formed, the latter because conductivity (and hence losses) are enhanced.

• Real and imaginary permittivity increase with increasing efficiency of CNT dispersion.

• It is not possible to give the ‘perfect recipe’ to obtain efficient absorbing or shielding materials, because material composition and microstructure have to be tailored from time to time to suit the electromagnetic design that actually takes into account many other features such as frequency of operation, thickness, geometrical shape, etc.

It is important to note that, when dealing with this type of application, strict control on CNT manipulation is fundamental to reach the desired material properties and microstructure (either when making shielding, absorbing materials or nanoscale antennas), nevertheless, even more important is to insure a confident degree of repeatability, that is essential in view of wide industrial productions. It is, in fact, without a doubt that these innovative materials will occupy an outstanding position in the field of electromagnetic materials, due to their very interesting EM performance, as soon as the costs of CNT become comparable to those of today’s more common fillers.

11.6 References

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