X-band EMI shielding mechanisms and shielding effectiveness of high structure carbon black/polypropylene composites

The materials used in this study were kindly provided by the manufacturers. The conductive filler was Black Pearls 2000 HS-CB from Cabot (surface area 1487 m² g⁻¹, particle size 12 nm [35]). The polymer was Huntsman HO-500 PP having a MFI and density of 5 g/10 min and 0.9 g ml⁻¹, respectively. HS-CB/PP composites with 1, 3, 5, 7.5 and 10 vol% HS-CB were compounded in a Haake Rheomix batch mixer. The volume per cent of HS-CB in PP composites was calculated using 1.8 g ml⁻¹ as the density of HS-CB. Prior to compounding, the PP pellets were dried under vacuum for 16 h at 80 °C. The PP pellets were fed to the mixer, previously heated to 200 °C, and mixed for 3 min at 50 rpm. Then the required amount of HS-CB was added and mixed for an additional 5 min at 50 rpm. For EMI SE and electrical conductivity characterization, rectangular plates 42 × 25 mm² of three different thicknesses 0.34, 1.0 and 2.8 mm were moulded in a Carver compression moulder at 200 °C for 4 min under 14 MPa pressure. The reported results represent an average of at least two different specimens for each formulation.

The dc electrical conductivity measurements were conducted using a Loresta GP resistivity meter connected to an ESP four-pin probe. The four-pin probe was used to eliminate the effect of contact resistance. For composites with electrical conductivity higher than 10⁻⁴ S m⁻¹, a Keithley 6517A electrometer connected to 8009 test fixture was used. The dc electrical conductivity (σ_dc) is expected to be different from the ac electrical conductivity (σ_ac) at the microwave frequency. Park and co-workers [36] found that for CNT/ethylene terpolymer nanocomposites containing less than 4 vol% CNT, σ_ac is higher than σ_dc. However, at CNT loadings above 4 vol%, σ_dc was found to approach σ_ac. EMI SE in the X-band frequency range was measured using the set-up described in detail elsewhere [14] and schematically sketched in figure 4. The set-up consists of an HP 8757D scalar network analyser, an HP 83752A sweep oscillator, three HP 11664A detectors, four coaxial to waveguide adapters and two HP X752C waveguide directional couplers connected back to back, i.e. a reflectometer. The set-up dynamic range, i.e. the difference between the minimum and maximum signals measured by the set-up, is 50 dB. The input power used for all tests were 0 dB m, corresponding to 1 mW. Equation (1) shows that the EMI SE is the logarithm of the ratio of the transmitted power when there is no shield (P_I) to the transmitted power when there is a shield (P_T) [37]:

$$\begin{equation} {\rm SE}=10\log ({P_{\rm I}}/{P_{\rm T}}). \end{equation} \tag{ 1 }$$

Figure 1 shows the dc electrical conductivity of the HS-CB/PP composite as a function of HS-CB content. The electrical conductivity (σ_dc) of the composite increased with the increase in HS-CB concentration. It is apparent that the electrical percolation threshold is between 1 and 3 vol% HS-CB. The increase in electrical conductivity when increasing filler concentration from 1 to 3 vol% is almost 14 orders of magnitude. This considerable increase is due to the formation of conductive filler networks within the polymer matrix [38]. However, increasing the filler concentration from 3 to 7.5 vol% led to only one order of magnitude increase in the electrical conductivity. This indicates that the formation of additional conductive CB networks has little influence on the composite's electrical conductivity. However, for CNT/PP composites [14], three orders of magnitude increase in electrical conductivity was reported when the CNT concentration was increased from 2.5 to 7.5 vol%. This remarkable difference in the percolation behaviour, i.e. the response of composite conductivity to the change in filler concentration, can be ascribed to the geometrical differences between HS-CB and CNT.

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Figure 2 depicts the influence of filler concentration and shielding plate thickness on the EMI SE of HS-CB/PP composites in the X-band frequency range. The reported EMI SE values in the figure are the average values in the 8.0–12.4 GHz frequency range. The results were reported without the standard deviation because it was less than 0.8 for all the composites. As expected, the results show that there is an increase in the EMI SE with the increase in filler concentration and/or shielding plate thickness. For a shielding material of a specific thickness, the increase in EMI SE with the increase in filler concentration can be ascribed to the increase in shielding by reflection and absorption. However, the increase in EMI with the increase in shield thickness is mainly related to the increase in shielding by absorption, since reflection is independent of the shield thickness. The rate of the increase in EMI SE with the increase in filler concentration increases with increase in shielding plate thickness (i.e. the slope of the EMI SE curves increases with the plate thickness). Comparing the EMI SE of the HS-CB/PP composite with those we obtained for CNT/PP composites [14] showed that, at the same filler loading, CNT composites have higher EMI SE capabilities. For example, at 7.5 vol% filler loading, the EMI SE for a 1 mm plate made of CNT/PP composite was 35.4 dB, compared with 17.3 dB for the HS-CB/PP composite.

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Conductive materials are known to attenuate EMI by three mechanisms, namely: reflection, absorption and multiple reflections [3, 37, 39]. The latter mechanism, i.e. multiple reflections, represents the internal reflections between the internal surfaces of the shielding material. For a single-phase material, this mechanism is typically ignored if the shielding plate is thicker than the skin depth. For cases where the shielding plate is thinner than the skin depth, multiple reflections reduce the overall shielding because the re-reflected waves increase the transmitted energy. The skin depth is the distance at which the strength of electric field drops to (1/e) of the incident strength. Mathematically, this can be calculated using equation (2) [3, 37]:

$$\begin{equation} \delta =(\sqrt {\pi f\mu \sigma} )^{-1}, \end{equation} \tag{ 2 }$$

where δ is the skin depth, f is the frequency, μ is the shield's magnetic permeability (μ = μ_oμ_r), μ_o is equal to 4π × 10⁻⁷ H m⁻¹, μ_r is the shield's relative magnetic permeability and σ is the shield's electrical conductivity. Assuming that we can deal with the composite material as a single-phase material (bearing in mind that this assumption might be invalid), figure 3 illustrates the influence of the composite's conductivity on the skin depth. In the calculations, the frequency was set at 8 GHz and the shield's relative magnetic permeability was assumed to be 1. The results show a significant decrease in skin depth with increase in conductivity. Based on the figure, all composites studied in this work are expected to suffer from the negative influence of multiple reflections except the 2.8 mm plates made of the 5, 7.5 and 10 vol% composites, and the 1 mm plates made of the 10 vol% composite.

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Multi-reflected waves will be transmitted and/or absorbed within the shielding. Thus, the attenuation of EM radiation will be mainly by reflection and absorption. In this work, the contribution of absorption loss and reflection loss to the overall SE was evaluated by analysing power data collected from the EMI SE characterization set-up schematically shown in figure 4. The EMI SE characterization set-up directly measures the transmitted power (T) using detector B, reflected power (R) using detector A and the incident power (I) using detector R. Thus, the absorbed power (A) can be calculated as follows [15, 40]:

$$\begin{equation} A=I-(T+R), \end{equation} \tag{ 3 }$$

For all measurements the incident power was 1 mW.

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Figures 5–7 show the power curves of the plates with thicknesses of 0.34 mm, 1.0 mm and 2.8 mm, respectively, as a function of CB/PP composite's conductivity. The power values are the average values in the X-band frequency range. From the figures, it is apparent that the transmitted power decreases with increase in the composite's conductivity. The reflected power is seen to increase with the increase in composite's conductivity, whereas for the power attenuated by absorption, two behaviours can be observed based on the plate thickness. For the 0.34 mm plates, with increasing composite's conductivity, the power initially increased, then reached a plateau, and then decreased again. For the 1.0 and 2.8 mm plates, the power absorbed was almost constant in the conductivity range 1.2–6.5 S m⁻¹, and then decreased. From all figures, it can be clearly seen that there is a certain conductivity at which the power blocked by reflection and the power blocked by absorption are the same. Above this conductivity, the power blocked by reflection becomes higher than that blocked by absorption. The decrease in the absorbed power is due to the lower power transmitted into the sample as a result of better reflection. The contribution of absorption to the overall shielding should be based on the ability of the material to attenuate the power that has not been reflected [41, 42].

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EMI SE is the logarithm of the ratio of transmitted power when there is no shield to the transmitted power when there is a shield (T). The transmitted power when there is no shielding material is typically equal to the incident power (I). Using the power balance data, the overall shielding is a sum of net shielding by reflection (SE_R) and net shielding by absorption (SE_A). The term net was used to account for the effect of multiple reflections. Equations (4)–(6) are the mathematical interpretation of these definitions [14].

$$\begin{eqnarray} &&\fl\mbox{Overall SE}={\rm SE}_{\rm R} +{\rm SE}_{\rm A}\nonumber\\ &&=10\log \frac{I}{I-R}+10\log \frac{I-R}{T}=10\log \frac{I}{T} \end{eqnarray} \tag{ 4 }$$

$$\begin{equation} {\rm SE}_{\rm R} =10\log \frac{I}{I-R} \end{equation} \tag{ 5 }$$

$$\begin{equation} {\rm SE}_{\rm A} =10\log \frac{I-R}{T}. \end{equation} \tag{ 6 }$$

Table 1 lists the overall shielding, reflection loss and absorption loss of the HS-CB/PP composites as a function of the filler content, composite conductivity and shielding plate thickness. The shielding values reported in the table are the average values in the X-band frequency range. The following can be observed from the table.

• Reflection loss and absorption loss are clearly seen to increase with the increase in composite's conductivity.
• Regardless of the filler loading and shielding plate thickness, shielding by absorption is higher than that by reflection. Shielding by absorption is 69–87% of the overall shielding.
• The results also show a small increase in the shielding by reflection with the increase in shield thickness, especially when the shield thickness increases from 0.34 to 1.0 mm. This increase can be ascribed to the difficulty in controlling the surface properties of hot moulded plates and/or the influence of skin depth on the shielding by reflection.
• There is an increase in the shielding by absorption with the increase in the shield thickness. However, this increase is much lower than the theoretical predictions. For a conductive material, absorption loss is [3, 37]
  $$\begin{equation} {\rm SE}_{\rm A} =\frac{8.7d}{\delta}, \end{equation} \tag{ 7 }$$
  where d is the shield's thickness. The skin depth (δ) is constant for a certain material and electromagnetic radiation of specific frequency. Thus, under such conditions, shielding by absorption is expected to increase linearly with increase in shield thickness (d). For HS-CB/PP composites, this is not the case. Let us consider the case of the 10 vol% composite. The absorption loss of the 2.8 mm thickness plates is 1.9 times that of the 1.0 mm plates; however, it is theoretically supposed to be 2.8 times that of the 1.0 mm plates.
• Shielding by absorption is also seen to be a function of the composite's conductivity and/or spacing between filler particles. For example, the 2.8 mm thick plate made of the 5 vol% composite contains more CB particles than the 1.0 mm thick plate made of the 10 vol% composite. However, shielding by absorption of the latter sample (filler is more packed and the composite is more conductive) is higher than the former sample (filler is less packed and the composite is less conductive). Theoretically, the negative influence of multiple reflections between external surfaces on the overall SE decreases with increase in spacing between reflecting surfaces [37]. Thus, it might be concluded that shielding by absorption depends only on the composite conductivity.
• For a composite of certain thickness, the increase in absorption loss was not linear with the increase in filler content. For example, for the 2.8 mm thickness plates, increasing the filler content from 5 vol% to 10 vol% increased the absorption loss from 13.6 dB to 36.4 dB, respectively, i.e. absorption loss increased by 2.7 times. However, based on the amount of CB added, this was supposed to increase by 2 times. This observation reveals that the absorption loss for composite materials depends on the composite's conductivity rather than the filler amount.
• Increasing filler loading on the per cent of EMI SE by absorption is a function of the shielding plate thickness. Per cent of EMI SE by absorption decreased with increasing filler concentration for the 0.34 and 1.0 mm plates, while it was increased with increasing filler loading for the 2.8 mm plates.

Theoretically, the EMI SE of conductive materials can be estimated using the following derived model [3, 37]:

$$\begin{equation} {\rm EMI\ SE}={\rm SE}_{\rm R} +{\rm SE}_{\rm A} +{\rm SE}_{{\rm MR}} \end{equation} \tag{ 8 }$$

$$\begin{equation} {\rm SE}_{\rm R} =39.5+10\log \frac{\sigma}{2\pi f\mu} \end{equation} \tag{ 9 }$$

$$\begin{equation} {\rm SE}_{\rm A} =8.7\frac{d}{\delta}=8.7d\sqrt {\pi f\mu \sigma} \end{equation} \tag{ 10 }$$

$$\begin{equation} {\rm SE}_{{\rm MR}} =20\log \vert 1-{\rm e}^{-2d/\delta}\vert, \end{equation} \tag{ 11 }$$

where SE_MR is the shielding due to the multiple reflections. The estimation of the EMI SE from the above model is based on the knowledge of the material's plate thickness, electrical conductivity and magnetic permeability and the EM radiation frequency. For systems with absorption loss greater than 10 dB, i.e. when the shield is thicker than the skin depth, SE_MR can be ignored [3, 37]. It is worth noting that the above model was derived for single-phase conductive plates and its applicability for heterogeneous systems, such as polymer composites, requires more investigation and modification. However, the model was used to estimate the EMI SE of the 1.0 and 2.8 mm plates made of the 10 vol% HS-CB/PP composite. Both 1 and 2.8 mm plates exhibit an absorption loss higher than 10 dB. The model results along with the experimental data are listed in tables 2 and 3 for the 1 mm and 2.8 mm samples, respectively.

Comparing the theoretical shielding estimation with the experimental values indicates that the ability of the theoretical model to estimate the absorption loss depends on the sample thickness and frequency. Good estimation was achieved for the 2.8 mm plates, especially at higher frequencies (>11 GHz), where the difference between the estimated and experimental values was less than 2.4 dB. Close estimation was also found for the 2.8 mm plates made of the 5 and 7.5 vol% composites (composites with absorption loss higher than 10 dB). For the 1 mm thick plates, theoretical estimation was lower than experimental values by 30–50%. Table 2 reports this for the 10 vol% HS-CB/PP composites. The model also underestimates the EMI SE of the 1 mm plates made of the 5 and 7.5 vol% composites. For the reflection loss, the accuracy of estimation was a function of the composite's conductivity. In general, the model overestimates the reflection loss of the 10 vol% CB. However, for the composites with CB loading of 7.5 vol% or less (the results are not shown in the tables), corresponding to samples with conductivities lower than 20 S m⁻¹, the model underestimated the reflection loss. Nevertheless, in terms of decibels, the difference between the experimental and theoretical values, for the samples that are >20 S m⁻¹ in conductivity and 1.0 mm in thickness, was insignificant (less than 2 dB).