Keywords

1 Introduction

Microwave dielectric materials play a key role in global society, with a wide range of applications from terrestrial and satellite communication to environmental monitoring via satellites. Recently, an increasing interest has been shown in the development of mechanically flexible electronic devices in various fields such as wireless communication, automotive, biomedical, and aerospace. For many applications, particularly in the biomedical field and body-worn antenna, electronic circuits are to be conformally wrapped around curved surfaces. In such systems, the circuits must be not only flexible but also stretchable. Flexible electronics is an emerging field in electronic industry which enable a wide range of applications such as capacitors for energy storage, wireless communication, electronic packaging, and electromagnetic interference (EMI) shielding. The development of EMI shielding materials is increasing in recent years in order to prevent the electromagnetic radiations emitting from modern electronic devices [1, 2]. Modern electronic industry requires systems that can be fitted into non-planar forms which can be folded and unfolded for packaging or storage [3, 4]. The flexible substrates have many potential applications from neural prosthetics in the medical field to microwave devices in electronics, which provides the advantage of three-dimensional designs of conformal structures [5, 6]. The requirements of a material to be used for flexible substrate applications are low relative permittivity, low loss tangent, low CTE, high TC, good mechanical flexibility, low moisture absorption, etc. Ceramics with optimum relative permittivity and low dielectric loss are available. But their brittle nature precludes them from practical applications in flexible electronics. Low-loss polymers with good flexibility are also available. However, their high CTE and low TC restrict their practical use. Hence, the use of polymers or ceramics alone is limited. The polymer–ceramic composites can deliver better performance than their constituent phases. There are several polymer–ceramic composites such as polytetrafluoroethylene (PTFE), polystyrene, polyether ether ketone (PEEK), and polyethylene with fillers such as silica, alumina, titania, and glasses, and some of these are commercially available. The reader is referred to the recent review by Sebastian and Jantunen [7] on polymer–ceramic composites for details. Conventional polymers filled with ceramic are rigid and cannot be bend or stretched. Stretchability means that the circuits should have the capacity to absorb large levels of strain without degradation in their electronic properties. In this context, the elastomer–ceramic composites can be used for stretchable and bendable electronic applications. However, not much attention was paid on bendable and stretchable materials such as elastomer–ceramic composites. In this chapter, we discuss the recent advances in low-loss butyl rubber–ceramic composites for microwave applications.

1.1 Butyl Rubber

Butyl rubber is a copolymer of 98 % polyisobutylene with 2 % isoprene distributed randomly in the polymer chain as shown in Fig. 1.

Fig. 1
figure 1

Butyl rubber

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Polymerization of isoprene results in the incorporation of a double bond or unsaturation into the polymer chain. These double bonds serve as cross-linking sites. Vulcanization of the butyl rubber with sulfur results in the formation of a network structure in the form of a cross-linked rubber. As such butyl rubber is a thermoset polymer and once vulcanized, it cannot be reformed into a new shape [8, 9]. Butyl rubber is amorphous and viscoelastic with low Young’s modulus and high yield strain as compared to other polymer materials due to its weak intermolecular attractive forces. Butyl rubber exists above the glass transition temperature, and hence, considerable segmental motion is possible. The glass transition temperature of butyl rubber is around −63 °C. At ambient temperatures, rubbers are relatively soft and deformable. The chain segments of elastomers can undergo high local mobility, but the gross mobility of chains is restricted by the introduction of a few cross-links into the structure. The long polymer chains cross-link during curing, and the process is known as vulcanization. The covalent cross-linkages ensure that the elastomer will return to its original configuration when the stress is removed. In the absence of applied stress, [10] molecules of elastomers usually assume coiled shapes. Consequently, elastomers exhibit large elongation (up to about 1000 %) from which they recover rapidly on removal of the applied stress.

Among elastomers, vulcanized butyl rubber has excellent dielectric properties, excellent heat/ozone resistance, high damping properties at ambient temperatures, mechanically flexible, air tight and gas impermeable, low glass transition temperature, good resistance to oxidizing chemicals, good weathering, and heat and chemical resistance. The main use of butyl rubber is in tyre-curing bladders and inner tubes and also used for seals, adhesives, and molded flexible parts [11–13]. These excellent properties of butyl rubber are the result of low levels of unsaturation between the long rubber chain segments. The molecular structure of butyl rubber can be oriented to resist stress, and thus, the mechanical properties are retained over a relatively wide stiffness range since reinforcement is not required for good tensile and tear strength [14].

Materials with varying relative permittivity are required for practical applications in electronic industry. Although butyl rubber is mechanically flexible and has excellent dielectric properties, it cannot be used for flexible electronic applications due to its low ε r and poor thermal properties. The relative permittivity of butyl rubber can be tailored over a wide range by reinforcing with low-loss ceramics having different range of relative permittivity. For electronic packaging and substrate applications, materials must have a low relative permittivity to minimize capacitive coupling and signal delay along with low loss tangent to reduce signal attenuation. High-permittivity ceramic materials can be used to make butyl rubber composites for flexible dielectric waveguide and capacitor applications. In addition, thermal properties of butyl rubber composites can be improved by the addition of ceramics, since ceramics have high TC and low CTE. Elastomer–ceramic composites can combine the advantageous properties of both elastomer and ceramics which can satisfy diverse requirements of present-day electronic industry. Today elastomer–ceramic composites found applications ranging from ultrathin health monitoring to advanced imaging devices. Although extensive researches were done on the microwave dielectric properties of rigid polymer–ceramic composites [7], very little attention was paid on elastomer–ceramic composites. Recently, we have reported the microwave dielectric properties of butyl rubber composites with SrTiO3, Sr2Ce2Ti5O16, SiO2, Ba(Zn1/3Ta2/3)O3, Ba0.7Sr0.3TiO3, Al2O3, BaTiO3, and TiO2 composites [15–22]. The microwave dielectric properties of the ceramics used and butyl rubber are given in Table 1.

Table 1 Microwave dielectric properties of ceramics and butyl rubber [23]
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High-purity alumina has a very low loss tangent of about 10−5. The very high TC (30 W m−1 K−1) and low CTE (6–7 ppm/°C) of alumina make it a suitable electronic packaging material [23]. Elastomer–alumina composites are well studied for its mechanical and curing characteristics [24, 25]. Silica is a low-permittivity ceramic with excellent dielectric properties (ε r = 3.8, tan δ ≈ 10−4) [26] and good thermal properties such as TC = 1.4 W m−1 K−1 and CTE = 0.5 ppm/°C. Silica is important reinforcing filler in elastomers for industrial applications. The effect of silica on dielectric properties of styrene-butadiene rubber was investigated by Hanna et al. [27] in the frequency range of 60–108 Hz at room temperature. Ba(Zn1/3Ta2/3)O3 is a complex perovskite ceramic with ε r = 28, tan δ ≈ 10−4, and a nearly zero temperature coefficient of resonant frequency (τ f  = 1 ppm/°C). BaTiO3 is a ferroelectric material having relatively high permittivity greater than 1500 and does not resonate in the microwave frequency due to the high dielectric loss factor and has thermal properties such as TC = 2.6 W m−1 K−1 and CTE = 6 ppm/°C. Butyl rubber is a synthetic elastomer with excellent dielectric properties in the microwave frequencies (ε r = 2.4, tan δ ≈ 10−3), good mechanical flexibility, aging resistance, and weathering resistance [28].

2 Preparation of Butyl Rubber (BR)–Ceramic Composites

The raw materials of alumina, silica, and rutile were procured from Sigma-Aldrich. The SrCO3, BaCO3, and ZnO from Aldrich, Ta2O5 from Treibacher Industries, and CeO2 from Indian Rare Earths Ltd. were used for preparing Ba(Zn1/3Ta2/3)O3 (BZT), Sr2Ce2Ti5O15 (SCT), SrTiO3, BaTiO3, and Ba0.7Sr0.3TiO3 by conventional solid-state ceramic route. The stoichiometric amount of chemicals were mixed by ball milling and dried. The mixtures were then calcined followed by sintering at appropriate temperatures and ground well. The powders were sieved through a 25-μm sieve and then used for preparing butyl rubber–ceramic composites [15–22]. The nanoalumina (<50 nm particle size), nanorutile (100 nm), and nano-BaTiO3 (100 nm) powders were purchased from Sigma-Aldrich, USA, and were used for preparing butyl rubber–nano composites in the present work. The nanopowders were dried at 100 °C for 24 h before use.

The butyl rubber used for present investigation was IIR grade. The process involving incorporation of ingredients such as activators, accelerators, vulcanizing agent, and fillers into the virgin rubber is known as compounding of rubber [15–22]. The compounding of butyl rubber mix was done by sigma blend method using a kneading machine. The butyl rubber was first masticated through the two counter rotating sigma blades in order to make it soft and more processable. Then, the additives are incorporated one by one as per the order given in Table 2. The additives such as zinc oxide and stearic acid act as activators for vulcanization, tetramethylthiuram disulfide acts as accelerator, and sulfur acts as vulcanizing agent. Finally, appropriate amount of ceramic filler was added. The mixing was done for about 30 min to get uniform composites. Thus, obtained composites were hot pressed at 200 °C for 90 min in suitable dies or molds under a pressure of 2 MPa. After hot pressing, the composites with desired shapes were used for characterization. The physical properties of butyl rubber are given in Table 3. In this review, we describe two representative materials, i.e., butyl rubber composites with alumina and barium titanate. Al2O3 is a very low-loss dielectric ceramic, whereas BaTiO3 is ferroelectric ceramic with high relative permittivity and loss factor. Figure 2 shows the photograph of a typical butyl rubber–ceramic composite.

Table 2 Formulation of rubber mix [29]
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Table 3 Physical and electrical properties of butyl rubber [22]
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Fig. 2
figure 2

Photograph of butyl rubber–strontium cerium titanate ceramic composite

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Since alumina is a widely used ceramic packaging material, the effect of filler particle size on dielectric, thermal, and mechanical properties of butyl rubber–ceramic composites was studied in butyl rubber–alumina composites. The alumina (micron and nano) powders were dried at 100 °C for 24 h before using for composite preparation. The butyl rubber–micron alumina (BR/AL) and butyl rubber–nanoalumina (BR/nAL) composites were prepared as described earlier. The BR/AL composites were prepared with micron alumina loading up to a volume fraction (v f ) 0.42. The nanoalumina has high surface area and large ceramic volume. Hence, the possibility of agglomeration of nanoparticles increases with filler loading. This makes the processing of BR/nAL composites difficult at higher filler loading [30]. Hence, a maximum loading of 0.1 volume fraction of nanoalumina was possible in the case of BR/nAL composites. It was found that the use of coupling agent such as silane treatment although slightly improve the relative permittivity and mechanical properties degrades the microwave dielectric loss factor [22].

3 Dielectric Properties

The dielectric properties of the composites were measured in the radio frequency range by the parallel plate capacitor method employing a LCR meter and using thin pellets of about 1 mm thickness and diameter 11 mm. The dielectric properties at microwave frequency range were measured by the split-post dielectric resonator (SPDR) method. The SPDR is an accurate method for measuring the dielectric properties of substrates and thin films at a single frequency in the frequency range of 1–20 GHz [31–33]. In this method, the sample should be in the form of a flat rectangular piece or a sheet. The SPDR uses a particular resonant mode which has a specific resonant frequency depending on the resonator dimensions and the relative permittivity. The resonator mainly consists of two dielectric disks in a metal enclosure. The sample under test is placed in the gap between the two parts of the resonator. Figure 3 schematically shows SPDR fixture for the measurement of the relative permittivity of dielectric and loss tangent of sheet samples. SPDR usually operates with the TE01δ mode. The relative permittivity of the sample is an iterative solution to the following equation [31]

$$ \varepsilon_{\text{r}} = 1 + \frac{{f_{\text{o}} - f_{\text{s}} }}{{hf_{\text{o}} K_{\varepsilon } (\varepsilon_{\text{r}} ,h)}} $$
(1)

where h is the thickness of the sample under test, f o is the resonant frequency of empty resonant fixture, f s is the resonant frequency of the resonant fixture with dielectric sample, and K ε is a function of ε r and h and has been evaluated using Rayleigh–Ritz technique [32]. The loss tangent of the sample can be determined by

$$ \tan \delta = \left( {Q_{\text{u}}^{ - 1} - Q_{\text{DR}}^{ - 1} - Q_{\text{C}}^{ - 1} } \right) /\rho_{\text{es}} $$
(2)

In Eqs. 1 and 2

$$ p_{\text{es}} = h\varepsilon_{\text{r}} K_{1} (\varepsilon_{\text{r}} ,h) $$
(3)
$$ Q_{\text{c}} = Q_{{{\text{c}}0}} K_{2} (\varepsilon_{\text{r}} ,h) $$
(4)
$$ Q_{\text{DR}} = Q_{\text{DR0}} \frac{{f_{\text{o}} }}{{f_{\text{s}} }} \cdot \frac{{p_{\text{eDR0}} }}{{p_{\text{eDR}} }} $$
(5)

where p es and p eDR are the electric energy filling factors for the sample and for the split resonator, respectively; p eDR0 is the electric energy filling factor of the dielectric split resonator for empty resonant fixture; Q c0 is the quality factor depending on metal enclosure losses for empty resonant fixture; Q DR0 is the quality factor depending on dielectric losses in dielectric resonators for empty resonant fixture; and Q u is the unloaded quality factor of the resonant fixture containing the dielectric sample. The values of p eDR, p es, and Q c for a given resonant structure can be calculated using numerical techniques.

Fig. 3
figure 3

Schematic representation of SPDR for microwave measurement [23]

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The sample should be flat and must be positioned such that it extends beyond the diameter of two cavity sections. The position of the sample in z-direction is not sensitive to the measurement results. This provides the accuracy of a resonator technique without machining the sample. The uncertainty of the permittivity measurements of a sample of thickness h is Δε/ε = ±(0.0015 + Δh/h), and uncertainty in loss tangent measurement is Δ(tan δ) = 2 × 10−5. The sample dimensions required for SPDR operating at 5.155 GHz are 50 × 50 × 1.8 mm3.

Table 4 gives the dielectric properties measured at 1 MHz and moisture absorption of BR/AL and BR/nAL composites. The relative permittivity of both composites increases with filler loading. This is due to the high relative permittivity of alumina compared to butyl rubber matrix. From Table 4, it is clear that the composite with nanoalumina has higher relative permittivity than that with micron alumina. The composites filled with nanoparticles have large interfacial area for the same filler loading which promotes interfacial polarization mechanism leading to higher relative permittivity of BR–nanoalumina composites. The loss tangent is the main factor affecting the frequency selectivity of a material and is influenced by many factors such as porosity, microstructure, and defects [23]. The loss tangent of both composites shows same trend as that of relative permittivity.

Table 4 Dielectric properties at 1 MHz and water absorption of BR/AL and BR/nAL composites [22]
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Figure 4a, b [22] shows the variation of relative permittivity and loss tangent of BR–nanoalumina and BR–micron alumina composites at 5 GHz. As the relative permittivity of alumina is higher than that of butyl rubber, the ε r of BR/AL composite and BR/nAL composite show an increasing trend with filler content. The nanoalumina-filled butyl rubber composites have higher relative permittivity than micron composites. Similar behavior was observed in PTFE–silica, PTFE–rutile, and PEEK–SrTiO3 composites [34–36]. It was reported that the nanofiller has more polarization at interface region due to its high surface area and also due to its large interface region between the filler and matrix. The nanocomposites also have higher moisture content due to its large surface area. These factors will contribute to the higher relative permittivity of nanocomposites. The relative permittivity of BR/AL composite increases from 2.40 to 4.68 as the micron alumina content increases from 0 to 0.42 v f and that of BR/nAL composite from 2.40 to 3.15 when the nanoalumina loading increases from 0 to 0.1 v f. It is also noted that the loss tangent increases with the increase in filler content of both micron and nanosized alumina and a higher loss tangent is exhibited by the nanoalumina-filled composites. The main reason for the higher loss tangent of nanocomposite is due to its high moisture content. A similar observation was reported in PTFE/rutile, epoxy/SiO2, and PTFE/alumina composites [35, 37, 40]. The loss tangent of BR–micron alumina composite increases from 0.0017 to 0.0027 as the ceramic loading increases from 0 to 0.42 v f and that of BR–nanoalumina composite increases from 0.0017 to 0.0140 as the nanoalumina content increases from 0 to 0.1 v f at 5 GHz.

Fig. 4
figure 4

Variation of a relative permittivity and b loss tangent of BR/AL and BR/nAL composites at 5 GHz [22]

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The dielectric properties at 1 MHz and water absorption values of both butyl rubber–micron BaTiO3 and butyl rubber–nano BaTiO3 composites are given in Table 5. The relative permittivity and loss tangent of both BR/BT and BR/nBT composites show an increasing trend with ceramic content since the relative permittivity and loss tangent of BaTiO3 are higher than those of butyl rubber matrix. The relative permittivity and loss tangent of nano-based composites are higher than those of the micron-based composites for the same volume fraction of the filler.

Table 5 Dielectric properties at 1 MHz and water absorption of BR/BT and BR/nBT composites [20]
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Figure 5a shows the variation of relative permittivity of BR/BT and BR/nBT composites with ceramic content at 5 GHz. The ε r of both composites shows the same trend as at 1 MHz. The nano-BaTiO3-filled butyl rubber composite shows higher relative permittivity than micron-based composites due to the presence of higher moisture content in the nanocomposite since the relative permittivity of water is high (ε r ~ 80). The interface region between the filler and matrix is large in the case of nanocomposites which can also contribute to higher relative permittivity [34]. The relative permittivity of BR/BT composite is 7.03 for ceramic loading of 0.24 v f and that of BR/nBT composite is 8.79 for the same loading of nano-BaTiO3. Although ε r of BaTiO3 is much higher than that of matrix, the composite cannot attain higher relative permittivity. The relative permittivity of polymer–ferroelectric ceramic composite cannot increase to a very high value even at maximum filler loading [38] since the 0–3 type composite follows an exponential relationship between relative permittivity of composite and the volume fraction of the filler. Logarithm of the relative permittivity of such composites (ε′composite) is linearly proportional to the volume fraction of the filler (ϕ filler) with the slope dependent on the dielectric properties of both components:

$$ \log \varepsilon^{\prime }_{\text{composite}} = \, \phi_{\text{filler}} \, { \log }\left( {\varepsilon^{\prime }_{\text{filler}} /\varepsilon^{\prime }_{\text{polymer}} } \right) + \log\, \varepsilon^{\prime }_{\text{polymer}} $$
(6)
Fig. 5
figure 5

Variation of a relative permittivity and b loss tangent of BR/BT and BR/nBT composites at 5 GHz [20]

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In general, it is difficult to prepare polymer composite with ceramic loading higher than 0.40 v f. In order to get a polymer composite with relative permittivity higher than 100 based on typical polymers with relative permittivity of the order of 5, the relative permittivity of the filler must be higher than 9000 [38]. Xie et al. [39] prepared core–shell-structured polymethylmethacrylate–BaTiO3 nanocomposites by in situ atom transfer radical polymerization of methyl methacrylate from the surface of BaTiO3 nanoparticles. For 76.88 wt% of BaTiO3 content, the composite achieved ε r of 14.6 and tan δ of 0.00372 at 1 kHz [39]. The addition of ceramic fillers gradually increased the relative permittivity. The increase in the relative permittivity depends on the amount of ceramic filler, its relative permittivity, and the frequency of measurement.

The variation of loss tangent of both BR/BT and BR/nBT composites with filler loading is also shown in Fig. 5b. The loss tangent of both composites increases with filler volume fraction since the loss tangent of BaTiO3 is higher than that of butyl rubber. The tan δ of butyl rubber–nanobarium titanate composite is higher than that of butyl rubber–micron barium titanate composites. This is due to the presence of higher moisture content in the nanocomposites, larger surface area, and reactivity of nanoparticles. The presence of large amount of grain boundaries and structural defects like lattice strain can also increase the loss tangent of nanocomposites [40]. The tan δ of micron composite is 0.0140 for a filler loading of 0.24 v f and that of nanocomposite is 0.0190 for the same filler loading.

3.1 Theoretical Modeling of Relative Permittivity

The prediction of effective relative permittivity of polymer–ceramic composites is very important for engineering applications. In order to understand the physical mechanisms controlling the relative permittivity of a heterogeneous system, the experimental values of ε r were compared with values predicted using different theoretical models. Several numerical relations have been proposed to predict the relative permittivity of polymer–ceramic composites [41–47]. These models can also be used to determine the extent of filler dispersion and filler/matrix compatibility by comparing the predicted values with the experimental data. The relative permittivity of the composites is influenced not only by the relative permittivity of the individual components but also by other factors such as morphology, porosity, the presence of moisture, impurities, agglomerates, mechanical and chemical coupling between rubber and filler, and dispersion and interaction between the two phases [21, 37, 39, 47–51], and hence, the prediction of relative permittivity of composites is very difficult. The following equations are used to predict the relative permittivity of the rubber–ceramic composites theoretically:

  1. (a)

    Lichtenecker’s equation:

The most widely used relation for the prediction of ε r is Lichtenecker’s logarithmic law of mixing. It considers the composite system as randomly oriented spheroids that are uniformly distributed in a continuous matrix [44].

$$ \ln \varepsilon_{\text{eff}} = \left( {1 - v_{\text{f}} } \right)\ln \varepsilon_{\text{m}} + v_{\text{f}} \ln \varepsilon_{\text{f}} $$
(7)

where ε eff, ε f, and ε m are the relative permittivity of the composites, filler, and matrix, respectively, and v f is the volume fraction of the filler.

  1. (b)

    Maxwell-Garnett equation:

The Maxwell-Garnett mixing rule was initially used to calculate the effective permittivity of a system where metal particles are encapsulated in an insulating matrix. This mixing rule was modified for polymer–ceramic composites incorporating homogeneous distribution of spherical ceramic particles, and the excitation of dipolar character is considered [45].

$$ \frac{{\varepsilon_{\text{eff}} - \varepsilon_{\text{m}} }}{{\varepsilon_{\text{eff}} + 2\varepsilon_{\text{m}} }} = v_{\text{f}} \frac{{\varepsilon_{\text{f}} - \varepsilon_{\text{m}} }}{{\varepsilon_{\text{f}} + 2\varepsilon_{\text{m}}}} $$
(8)
  1. (c)

    Jayasundere Smith equation:

    $$ \varepsilon_{\text{eff}} = \frac{{\varepsilon_{\text{m}} \left( {1 - v_{\text{f}}} \right) + \varepsilon_{\text{f}}v_{\text{f}}\left[ {\frac{{3\varepsilon_{\text{m}} }}{{\varepsilon_{\text{f}} + 2\varepsilon_{\text{m}}}}} \right]\left[ {1 + \left( {\frac{{3v_{\text{f}} \left( {\varepsilon_{\text{f}} - \varepsilon_{\text{m}}} \right)}}{{\varepsilon_{\text{f}} + 2\varepsilon_{\text{m}}}}} \right)} \right]}}{{1 - v_{\text{f}} + v_{\text{f}} \left[ {\frac{{3\varepsilon_{\text{m}}}}{{\varepsilon_{\text{f}} + 2\varepsilon_{\text{m}}}}} \right]\left[ {1 + \left( {\frac{{3v_{\text{f}}\left( {\varepsilon_{\text{f}} - \varepsilon_{\text{m}}} \right)}}{{\varepsilon_{\text{f}} + 2\varepsilon_{\text{m}}}}} \right)} \right]}} $$
    (9)

Jayasundere–Smith equation is a modification of well-known Kerner equation by incorporating the interactions between neighboring spheres. This equation considers composite as a biphase system of dielectric spheres (ε f) dispersed in a continuous medium (ε m) and is valid only when ε f ≫ ε m [46].

  1. (d)

    Effective Medium Theory (EMT):

In EMT model, composites are treated as an effective medium whose relative permittivity is obtained by averaging over the relative permittivity of the constituents. The basic concept of EMT model is that when a random unit cell (RUC) is embedded in an effective medium, it cannot be detected in the electromagnetic experiment. A RUC is defined as a core of ceramic surrounded by a concentric shell of the polymer [47]. A correction factor ‘n’ is used to compensate for the shape of the fillers and is called morphology factor which is related to ceramic particle and can be obtained empirically.

$$ \varepsilon_{\text{eff}} = \varepsilon_{\text{m}} \left[ {1 + \frac{{v_{\text{f}} \left( {\varepsilon_{\text{f}} - \varepsilon_{\text{m}}} \right)}}{{\varepsilon_{\text{m}} + n\left( {1 - v_{\text{f}}} \right)\left( {\varepsilon_{\text{f}} - \varepsilon_{\text{m}}} \right)}}} \right] $$
(10)

where n is the shape factor in EMT model.

The modeling techniques give relative permittivity of a composite system in terms of the relative permittivity of all the constituent components and their volume fractions. Figure 6 compares the experimental and theoretical relative permittivities of BR/AL and BR/nAL composites at 5 GHz. All the models are matching with the experimental values of ε r of both BR/AL and BR/nAL composites up to 0.1 v f. In Maxwell-Garnett model, only the excitation of dipolar character is considered to be important and the correlations between these excitations are not taken into account. The multipolar contributions to the local field are also neglected. It may be noted that these assumptions are valid only in dilute systems [46]. Hence, the Maxwell-Garnett model shows deviation at higher filler content. The most widely used relation for the prediction of ε r is Lichtenecker’s logarithmic law of mixing [44]. The deviation of experimental values of ε r of both composites from Lichtenecker’s equation at higher filler loadings may be due to the lack of consideration of interfacial interaction between the polymer and the filler particles. The EMT model is also in agreement with experimental values of ε r of both composites at lower filler loadings and shows deviation at higher filler content. The experimental values of ε r of both composites are matching with those values calculated from Jayasundere–Smith equation and show deviation at higher filler loadings. It is found that EMT and Maxwell-Garnett models are matching more with experimental results. The deviation of all theoretical models at higher filler loading is due to the imperfect dispersion of filler particles in the butyl rubber matrix. The effective permittivity of a composite depends on the various factors such as relative permittivity of individual components in the system, their volume fractions, shape, size, porosity, interphase polarizability, and interphase volume fractions. All these parameters cannot be accounted in a single equation. Hence, the experimental results show deviation from the theoretical values at higher filler content.

Fig. 6
figure 6

Comparison of theoretical and experimental relative permittivity of BR/AL and BR/nAL composites at 5 GHz [19]

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Figure 7 compares the experimental and theoretical relative permittivities at 5 GHz for both butyl rubber–micron BaTiO3 and butyl rubber–nano-BaTiO3 composites. The experimental values of ε r of both BR/BT and BR/nBT composites are in agreement with Lichtenecker’s equation and EMT model at low filler loadings. The ε r of BR/BT composites shows deviation from both models above a filler loading of 0.24 v f of BaTiO3 content. The relative permittivity of BR/nBT composites is matching more with Lichtenecker’s equation and EMT models. The deviation at higher filler loading may be due to the inhomogenous dispersion of nanofiller particles in the rubber matrix.

Fig. 7
figure 7

Comparison between experimental and theoretical relative permittivity of BR/BT and BR/nBT composites at 5 GHz [20]

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3.2 Temperature Coefficient of Relative Permittivity (τ εr)

The relative permittivity of a material should be stable within the operational temperature range of electronic devices for practical applications. The temperature coefficient of relative permittivity of the present composites was measured by parallel plate capacitor method. The sample is kept in a chamber, and ε r is measured from 25 to 75 °C.

Figure 8a, b shows the temperature dependence of relative permittivity of BR/nAL and BR/AL composites, respectively. From the figure, it is clear that all the composites are almost thermally stable within the measured temperature range. Figure 9a, b shows the temperature variation of relative permittivity of both BR/nBT and BR/BT composites at 1 MHz, respectively. The relative permittivity of all the composites of butyl rubber–micron BaTiO3 and butyl rubber–nano-BaTiO3 is also nearly stable in the measured temperature range. From the Figs. 8 and 9, it is clear the relative permittivity of composites shows a slight decrease with increase in temperature. The small decrease in relative permittivity with temperature may be due to the large difference in thermal expansion coefficient of butyl rubber and the ceramics [52, 53]. The thermal stability of relative permittivity is one of the important properties of the substrate materials that control the overall performance of the device.

Fig. 8
figure 8

Variation of relative permittivity of a BR/nAL and b BR/AL composites with temperature [22]

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Fig. 9
figure 9

Variation of relative permittivity of a BR/nBT and b BR/BT composites with temperature at 1 MHz [20]

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3.3 Bending

The bending effect on dielectric properties is important as far as flexible electronic applications are concerned. Bending measurements of the composites were carried out by bending the samples manually in such a way that every part of the sample had undergone 180o bending. The bending cycle was repeated for 125 times, and the microwave dielectric properties were measured by SPDR method after every 25 cycles. Figures 10 and 11 show the variation of dielectric properties of BR/AL and BR/nAL composites with bending. It is clear from Fig. 10a, b that the relative permittivity of all the composites is nearly independent of bending. It is evident from Fig. 10a, b that the loss tangent of the nanocomposites is almost independent of bending and that of micron composite shows slight variation with bending. Figures 12 and 13 show the effect of bending on dielectric properties of BR/BT and BR/nBT composites at 5 GHz. The relative permittivity of both composites is almost independent of bending as is evident from Fig. 13a, b. The loss tangent of both BR/BT and BR/nBT composites shows a slight variation in mechanical bending, but the variations are marginal. Vrejoiu et al. [54] observed a similar behavior in PFCB (perfluorocyclobutene (poly 1,1,1-triphenyl ethane per-fluorocyclobutyl ether)−BaTiO3 composites. They observed that repeated mechanical bending up to 50 cycles does not change ε r and tan δ of the composites. The bending of the composites does not considerably affect the microwave dielectric properties, and hence, they are suitable for flexible electronic applications.

Fig. 10
figure 10

Variation of relative permittivity of a BR/nAL and b BR/AL composites with bending [22]

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Fig. 11
figure 11

Variation of loss tangent of a BR/nAL and b BR/AL composites with bending [22]

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Fig. 12
figure 12

Variation of relative permittivity of a BR/nBT and b BR/BT composites with bending [20]

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Fig. 13
figure 13

Variation of loss tangent of a BR/nBT and b BR/BT composites with bending [20]

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4 Thermal Conductivity

Heat dissipation from integrated circuits is a crucial problem for electronic industry that affects potential miniaturization, speed, and reliability. The thermal conductivity (TC) of polymers is very low, ranging from 0.14 to 0.60 W m−1 K−1 [55], and can be improved by the addition of ceramic fillers as the TC of ceramic is higher than that of polymers. The TC of the composites depends on the intrinsic thermal conductivities of filler and matrix, shape and size of the filler, and the loading level of filler [56]. The variation of TC of both BR/AL and BR/nAL composites with filler content is shown in Fig. 14. The TC of both composites shows increasing trend with ceramic loading. This is quite expected since the TC of alumina (30 W m−1 K−1) is higher than that of butyl rubber matrix (0.13 W m−1 K−1). From the inset plot in Fig. 14 [22], it is clear that the TC of nanoalumina-loaded composites is slightly higher than that of micron composite.

Fig. 14
figure 14

Variation of thermal conductivity of BR/AL and BR/nAL composites with filler content [22]

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Figure 15 shows the variation of TC of BR/BT and BR/nBT composites with ceramic loading. As the ceramic loading increases, the TC of both composite increases since the TC of BaTiO3 (2.6 W m−1 K−1) is higher than the butyl rubber (0.13 W m−1 K−1). As the filler loading increases, distance between the filler particles decreases and thus filler becomes the main channels for thermal conduction. Hence, TC of both composites can also increase with filler content [56]. From Figs. 14 and 15, it is clear that the nanocomposites have higher TC than that of micron-based composites. The matrix/filler interface plays a critical role in nanocomposites due to its large surface area. The number of particles increases with decreasing particle size for the same filler content [57, 58]. This will leads to the formation of large number of heat-conductive channels in nanofiller-added composites. Hence, the TC of nano-based composite is higher than micron-based composites. The butyl rubber–micron barium titanate composite with ceramic loading of 0.24 v f has a TC of 0.31 W m−1 K−1 and that of butyl rubber–nanobarium titanate composite is 0.36 W m−1 K−1.

Fig. 15
figure 15

Variation of thermal conductivity of BR/BT and BR/nBT composites with filler content [20]

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4.1 Theoretical Modeling of Thermal Conductivity

The effective TC of a heterogeneous system is strongly affected by its TC of individual components, composition, crystal structure, distribution within the medium, and contact between the particles. Numerous theoretical models were proposed for predicting the TC of composites [59, 60]. The following models are used to predict the TC of the composites:

  1. (a)

    Series mixing rule:

    $$ \frac{1}{{k_{\text{c}}}} = \frac{{v_{\text{f}}}}{{k_{\text{f}}}} + \frac{{v_{\text{m}}}}{k_{\text{m}}} $$
    (11)

    where kc is the effective TC of the composite, km and kf are the TC of matrix and filler, respectively, and v m and v f are the volume fractions of matrix and filler, respectively.

  2. (b)

    Parallel mixing rule:

    $$ {\text{k}}_{\text{c}} { = }{\text{v}}_{\text{f}} {\text{k}}_{\text{f}} {\text{ + v}}_{\text{m}} {\text{k}}_{\text{m}} $$
    (12)

    The physical structures assumed in the series and parallel models are of layers of phases aligned either perpendicular or parallel to the heat flow [59]. The series and parallel model of TC gives only lower and upper limits of TC values of composites, respectively.

  3. (c)

    Geometric mean model [60]:

    $$ k_{\text{c}} = k_{\text{f}}^{{v_{\text{f}}}} k_{\text{m}}^{{1 - v_{\text{f}}}} $$
    (13)
  4. (d)

    Maxwell-Eucken Model:

    $$ k_{\text{c}} = k_{\text{m}} \left[ {\frac{{k_{\text{f}} + 2k_{\text{m}} + 2V_{\text{f}} (k_{\text{f}} - k_{\text{m}})}}{{k_{\text{f}} + 2k_{\text{m}} - V_{\text{f}} (k_{\text{f}} - k_{\text{m}})}}} \right] $$
    (14)

    The Maxwell model assumes a dispersion of small spheres within a continuous matrix of a different phase, where spheres being far enough apart such that the local distortions to the temperature distributions around each of the spheres do not interfere with their neighbors’ temperature distributions [60].

  5. (e)

    Cheng–Vachon Model:

    Cheng and Vachon assumed a parabolic distribution of the discontinuous phase in the continuous phase based on Tsao’s model [61]. The constants of this parabolic distribution were determined by analysis and presented as a function of the discontinuous phase volume fraction. Thus, the equivalent TC of the two-phase solid mixture was derived in terms of the distribution function and the TC of the constituents.

    $$ \frac{1}{{k_{\text{c}}}} = \frac{1}{{\sqrt {C(k_{\text{f}} - k_{\text{m}})[k_{\text{m}} + B(k_{\text{f}} - k_{\text{m}})]} }}\ln \frac{{\sqrt {[k_{\text{m}} + B(k_{\text{f}} - k_{\text{m}})]} + \frac{B}{2}\sqrt {C(k_{\text{f}} - k_{\text{m}})} }}{{\sqrt {[k_{\text{m}} + B(k_{\text{f}} - k_{\text{m}})]} - \frac{B}{2}\sqrt {C(k_{\text{f}} - k_{\text{m}})} }} + \frac{1 - B}{{k_{\text{m}}}} $$
    (15)

    where

    $$ B = \sqrt {{\raise0.7ex\hbox{${3V_{\text{f}}}$} \!\mathord{\left/ {\vphantom {{3V_{\text{f}}} 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}} \quad C = - 4\sqrt {{\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 {3V_{\text{f}}}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${3V_{\text{f}}}$}}} $$
    (16)

Figure 14 also compares the experimental TC of both BR/AL and BR/nAL composites with theoretical models. The series and parallel model of TC gives only lower and upper limits of TC values of composites, respectively [59]. The experimental TC values of both composites are within the range of series and parallel model. The geometric mean model is in good agreement with experimental TC of both composites up to a volume fraction of 0.1 and has a lower value than predicted TC at higher micron alumina loading. This may be due to the agglomeration of filler particles at higher filler loadings. The models Cheng–Vachon and Maxwell-Eucken are matching with experimental TC of both composites. Figure 15 also shows the comparison between experimental and theoretical TC of BaTiO3-based composites. The series and parallel mixing rule of both composites shows the same trend as that of alumina-based composites and does not match with experimental profiles. All the other theoretical models are matching with TC of BR/nBT composites at low filler loading and show deviation at higher nano-BaTiO3 content. The TC of butyl rubber–micron BaTiO3 composites is in agreement with Cheng–Vachon and geometric mean models. Maxwell-Eucken equation holds good at low filler loading and deviates at higher micron BaTiO3 content [62].

5 Mechanical Properties

The mechanical flexibility is the prime requirement for flexible electronic applications. Tensile test is useful to evaluate mechanical properties of materials in which the sample is pulled to failure in a relatively short period of time. The sample is elongated at a constant rate, and the load required to produce a given elongation is measured as a dependent variable. A stress–strain curve may be plotted from the results of a tension test, and from the plot, the toughness of the material can be assessed [63, 64]. The stress–strain properties of the composites were measured using a universal testing machine (Hounsfield, H5K-S UTM, Redhill, U.K.) with a rate of grip separation of 500 mm/min. Tensile tests were conducted using dumbbell-shaped samples of width 4 mm and thickness in the range 1.5–2 mm.

Figure 16 shows the stress–strain curve of BR/AL and BR/nAL composites. The mechanical properties of a particulate composite depend on the strength of the adhesive bond between the different phases, the type of dispersion, and the amount of particle agglomeration. From the figure, it is clear that the stress needed for ceramic-filled butyl rubber composite is greater than that of unfilled sample. Among BR-0, BR/AL-5, and BR/nAL-5, the stress required for BR/nAL-5 composite is high. This may be due to more homogeneous dispersion of nanoparticles in the rubber matrix. Chee et al. [65] reported that at lower filler loading, the nanoalumina particle orients along the direction of stress and this would reinforce and increase the stiffness of the nanocomposite. Figure 17 shows the stress–strain curves of BR/BT-7 and BR/nBT-5. As the filler loading increases, the stress needed for elongation and also stiffness of the composite increases [66]. This figure shows that the nanocomposite is slightly stiffer than micron composite. Both the composites were not broken up to an elongation of 1000 %, which indicates the excellent mechanical flexibility of the composites.

Fig. 16
figure 16

Stress–strain curves of BR/AL and BR/nAL composites [19]

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Fig. 17
figure 17

Stress–strain curves of BR/BT and BR/nBT composites [20]

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6 Moisture Absorption of Composites

The moisture content is an important parameter for materials used for practical applications. Absorption of moisture from the working atmosphere will degrade the dielectric properties since water is a polar molecule. The moisture absorption characteristics of the composites were measured using the samples with dimensions 50 mm × 50 mm × 2 mm. The samples were weighed accurately and immersed in distilled water for 24 h. The samples were then taken out and again weighed after removing the excess water from the surface. The volume % of water absorption was then calculated using the relation,

$$ {\text{Volume}}\;\% \;{\text{water}}\;{\text{absorption}} = \frac{{(W_{\text{f}} - W_{\text{i}})/\rho_{\text{w}}}}{{(W_{\text{f}} - W_{\text{i}})/\rho_{\text{w}} + W_{\text{i}}/\rho_{\text{c}}}} \times 100 $$
(17)

where W i and W f are the initial and final weights of the sample, and ρ w and ρ c are the densities of distilled water and composite, respectively.

It is evident from Tables 4 and 5 that as the filler content increases, the volume % (vol.%) of water content increases for both composites since the ceramic is hydrophilic in nature. Compared to micron composite, nanocomposites have a high tendency to absorb moisture due to the large surface area of the nanoalumina or barium titanate, and also, higher nanofiller loading leads to the formation of pores in the composites due to the agglomeration of the particles. The loss tangent and moisture absorption of butyl rubber–nanoceramic composites are much higher as compared to the micron composites. The dielectric properties of the composites are affected by the presence of moisture content. The absorbed moisture interacts with polymer matrix and also with the filler–matrix interface [67] and thus affects the dielectric properties of composites.

7 Coefficient of Thermal Expansion

Figures 18 and 19 show the variation of coefficient of thermal expansion (CTE) of butyl rubber–alumina and barium titanate composites with filler content. The CTE of both the composites decreases with ceramic loading since the CTE value of the ceramics is smaller than that of rubber matrix, and also, the mobility of loose molecular bonds in the polymer chains is restrained by the ceramic loading [68, 69]. The BR–nanocomposites show much lower CTE value compared to that of micron composites. The physical cross-linking points are more in the case of nanoparticles because of its high specific surface area, and this will increase the mechanical interaction between the filler and rubber matrix [70]. Hence, the nanocomposites have lower CTE than that of micron composites.

Fig. 18
figure 18

Variation of CTE of BR/AL and BR/nAL composites with filler content [19]

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Fig. 19
figure 19

Variation of CTE of BR/BT and BR/nBT composites [20]

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8 Conclusions

The butyl rubber–ceramic composites can be prepared by sigma mixing followed by hot pressing. The composites were found to be flexible, bendable, and stretchable. The microwave dielectric and thermal properties are improved with ceramic loading. The composite preparation is difficult for ceramic loading higher than 40 vol.%. The nanopowder can be loaded to a much lower level. The relative permittivity essentially depends on the rubber matrix, and one can get a relative permittivity of about 15 even with maximum loading with high-permittivity ceramics. The TC of the composites increased and CTE decreased with ceramic content. The water absorption increases with increase in ceramic loading and is higher for nanoceramic loading. The composite with nanoceramic filler has inferior microwave dielectric properties. Table 6 gives the microwave dielectric properties of several butyl rubber–ceramic composites. The BR/AL and BR/BT composites are found to be suitable candidates for microwave substrate and electronic packaging applications. More recently, butyl rubber–single-walled carbon nanotube (BR-SWCNT) composites were prepared by a solution mixing process and reported to be useful EMI shielding applications. The BR-SWCNT composite shows enhanced relative permittivity of 14 with a loss tangent of 0.07 at 15 GHz for 8 phr SWCNT [71]. The EMI shielding effect increased with SWCNT content.

Table 6 Microwave dielectric, thermal, and physical properties of several butyl rubber-–ceramic composites [22]
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