AC impedance analysis and EMI shielding effectiveness of conductive SBR composites.

INTRODUCTION

AC impedance has proven to be a powerful tool in characterizing electrochemical reaction mechanisms of conducting polymers and their composites [1]. Recently, the method has been extended into the characterization of pure conducting polymers and conducting polymer composites [2-5]. Conducting polymers and conducting polymer composites can be described with a parallel resistor-capacitor circuit. The capacitor can be imagined to be formed from induced double layers on the surfaces of conducting particles, which are separated by non-conducting polymer layers. Sometimes, an unexpected inductive effect has also been found in such systems [6]. The parameters describing the equivalent circuit of these composites can be obtained from Nyquist plots [7]. Many works have been found on the studies of the complex AC impedance and the effect of frequency, composition on it [8-11]. The conducting polymer composites have been found to possess interesting properties, which are exploited in a variety of applications such as touch control switch, electromagnetic interference (EMI) shielding, electrostatic dissipation (ESD) of charges, electrically conductive adhesives, and circuit components in microelectronics [12-17]. In this paper the effect of frequency, composition, and thickness on the complex AC impedance are presented. The equivalent circuits describing the conduction behavior of the composites are presented along with electromagnetic shielding effectiveness of the composites at microwave frequencies.

EXPERIMENTAL

The polymer, styrene-butadiene rubber (SBR-1502, styrene content 23.5%, ML1 4 100[degrees]C, 51), was supplied by Synthetic and Chemicals Ltd. (Barielley, India). The filler, conductive carbon black (CCB; Vulcan XC-72), was procured from Cabot India Ltd. Other ingredients used in the preparation of the composites were procured from standard suppliers, and a standard formulation given in Table 1 has been used to prepare the composites. The rubber, carbon black (in different concentrations expressed in phr, i.e., parts in weight/100 parts of rubber), and the various ingredients were mixed in a two roll mill to get the final composite product. The mixed composites were then molded into rectangular waveguide flanges with varying thicknesses of 0.65, 1.3, and 7 cm. The complex impedance spectra of the composites at the microwave frequency of 7.8-12.4 GHz was measured using a standard rectangular waveguide transmission line set up connected with a VSWR meter. Smith Chart was used to determine the complex impedance of the composites from the experimental data. EMI shielding effectiveness of the composites was also measured with the aforementioned setup but connected with a HP Power meter. The block diagram of the experimental set-up used for EMI SE measurement is shown in Fig. 1, and the cross section and dimensions of the sample window is depicted in Fig. 2. Physical characteristics of conductive black Vulcan XC-72 is given in Table 2.

RESULTS AND DISCUSSIONS

Studies on Complex AC Impedance

Effect of Frequency. The effect of AC frequency in the microwave range of 7.8-12.4 GHz on the SBR-CCB composites was investigated. The DC conductivity of these composites was reported in our earlier work and was found that around 20 phr of carbon black loading the composites become some what conductive and reaches the percolation at around 30 phr [18]. Hence, the composites containing carbon black loading from 20 to 60 phr are discussed. The effect of frequency on the complex impedance of the composites containing 30 and 60 phr of carbon black is shown in Figs. 3 and 4. The complex impedance Z* for any system is represented as

[FIGURE 1 OMITTED]

Z* = Z' [+ or -] jZ" (1)

where Z' and Z" are the real and imaginary parts of the complex impedance Z*. Z' consists of the resistive part of the system and Z" consists of the reactance arising due to the capacitive/inductive nature of the system. Z" carries a negative sign when the system is capacitive and a positive sign if the system is inductive. From the careful observation of Figs. 3 and 4 it can be seen that Z" of the composites behave in a similar manner with respect to frequency. It reaches the maximum and then decreases with further increase in the frequency. This behavior can be attributed to some dielectric relaxation process of the composites, as Z" is related to the loss factor of the system. It is known that the conduction of current in conductive composites is mainly through the continuous conductive network, which is formed at percolation through aggregation of conductive particles in the insulating matrix. Apart from this, the electron hopping is also an important mode of conduction, which becomes more significant at microwave frequencies, thereby adding to the conductivity already existing, and this is reflected in the continuous decrease of Z' with increase in frequency, which represents the resistive part of the composites [19].

Effect of Filler Loading. The effect of filler loading on the complex impedance of the composites was investigated and the variation in complex impedance at the frequency 10 GHz and sample thickness of 1.3 cm for the different filler loadings are shown in Fig. 5. From the plot it is observed that both Z' and Z" continuously decrease with the increase in filler loading and this is quite obvious because, with the increase in filler loading, the number of conductive paths formed inside the composites increases giving rise to decrease in resistance. The increase of capacitance is due to the increase of conductive filler concentration in insulating matrix [18].

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Effect of Thickness. The effect of sample thickness on the complex impedance of the composites was investigated and is shown in Fig. 6. It can be clearly seen that Z' of all the composites increase with increase in thickness. Though the pure resistive component of any material is independent of thickness and dimensions, the impedance component of conductive/lossy system is found to be dependent on dimension of the material. As reported, Z can be represented as Z(l, t) where l is the thickness of the material [19]. With the increase in conductive/lossy system's sample thickness, the flow of microwaves through it gets more interrupted. In fact, extrinsically, conductive system (where conductivity is due to addition of conductive filler) may be considered as heterogeneous in nature. The insulating polymer is transparent to microwave but conductive component either reflect or interact or absorb the microwave. So as the thickness increases, the chance of microwaves to interact with conductive component increases and thereby reduces the impedance. This can be attributed to the increase in real part of the impedance with increase in filler loading. It is also found that the imaginary part of Z of all the composites increase with increase in thickness and this can also be explained by the same logic as earlier.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Mathematically, Z' and Z" can be represented as follows:

Z' = tan[delta]/2[pi]f[C.sub.s] = R and Z" = 1/2[pi]f[C.sub.s] (2)

where [C.sub.s] is the capacitance of the sample; f is the frequency of measurement; R is the resistance of the sample; and tan 8 is the loss factor of the sample. Equation 2 explains the increase of Z" with the increase in thickness, because increase in thickness leads to increase in the overall capacitance [20].

Nyquist Plots

The electrical characteristic of conductive polymer composites in general may be explained in terms of the equivalent circuit shown in Fig. 7. Nyquist plots are nothing but the complex plane diagram of the complex impedance Z* = Z' [+ or -] jZ" where j = [square root of -1] is the imaginary unit. The real part of the aforementioned equation Z' is varied on the x-axis and the imaginary part Z" on the y-axis. In fact, the Nyquist plot has great similarity with the well known Cole-Cole plot used to define dielectric characteristics of materials. The real part of the impedance Z' is related to capacitance (storage of charge) and imaginary part Z' is related to loss factor (loss of accumulated charges, the conductive component). In the circuit, [C.sub.d1] is a double layer capacitance caused by a discontinuous distribution of conducting material in a less conducting medium, here, the insulating rubber matrix. [R.sub.d1] is the resistance between conducting layers. [R.sub.b] is the bulk resistivity of the conducting particles. We can roughly estimate the values for [C.sub.d1], and [R.sub.b] by using the relationships [C.sub.d1] = l/([[omega].sub.max][R.sub.d1] and [R.sub.b] = [R.sub.DC] - [R.sub.d1], where [[omega].sub.max] is the measurement frequency at the top of the semi-circle formed in the Nyquist plot (i.e., the frequency at which Z" is the maximum against Z'), [R.sub.d1] is the diameter of the semi-circle, and [R.sub.DC] is the measured four-probe resistance. Also it must be noted that these parameters are related to the equivalent circuit in Fig. 7 and are not necessarily true material parameters [7].

[FIGURE 8 OMITTED]

Nyquis Plot for SBR-20CCB System. The Nyquist plots for SBR-20CCB composite with varying thickness of 0.65, 1.3, and 7 cm were plotted from the complex impedance spectra obtained in the measured frequency range. The Nyquist plot for SBR-20CCB sample with a thickness of 7 cm is shown in Fig. 8. It can be observed from the plot that instead of a perfect semicircle, a skewed semicircle (i.e., an arc followed by a linear portion) has appeared. The perfect semicircle is the characteristic of a single time constant (i.e. single relaxation time). However, the real electrochemical impedance plots for different materials in general often contain several time constants. Depending on the spread of frequency scan we can often find portions of a single or double semicircle. This may be due to the fact that the system under consideration may have more than one relaxation process operative within the measured frequency domain. In present case, the plots can be either considered as two parts of two semicircles or a skewed semi-circle and a linear extension. In general, polymer composites are always considered capacitive in nature, as described earlier. When a semi-conductive material is placed in the path of an electromagnetic wave, especially at microwave frequencies, the processes of reflection, absorption, and transmittance of the waves takes place at different interfaces of the wave and the material. A net combination of all these processes depending on the microstructure of the material brings out either the capacitive or inductive nature of the material. Exceptionally, the SBR-20CCB composite at 0.65 cm thickness alone shows some inductive effect at some frequencies. The inductive behavior may be resulting from non-homogeneous current distribution in the system and the waveguide inductance [21]. For determining the equivalent circuit and its parameters, a representative equation of circle was evaluated from the available Nyquist plot by the combination of curve fitting and mathematical solution through logical means. The equation and parameters are listed in Table 3. It is found that the double layer resistance [R.sub.d1], the resistance between one conducting element and the other, increases with the increase in thickness. This may be due to the arrangement of additional [R.sub.d1] in the series, arising out of increased thickness. The [C.sub.d1] values are found to be almost unaffected with the increase in thickness.

[FIGURE 9 OMITTED]

Nyquis Plot for SBR-30CCB System. The Nyquist plot for SBR-30CCB sample with a thickness of 7 cm is shown in Fig. 9. From the plot it can be observed that the system is totally capacitive in nature. This is because with the increase in filler loading, the number of conducting elements (formed due to particle aggregation) and the corresponding amount of discontinuous region between successive conducting elements increases, thereby leading to a large number of individual capacitive layers, which in turn results in the total capacitive nature of the composites. The parameters of the equivalent circuit for the SBR-30CCB composite are listed in Table 4. It is found that [R.sub.d1], which is the resistance between two conducting elements, increases with thickness and can be explained in the same way as before. The [C.sub.d1] values are found to be decreasing with increase in thickness because of the decrease in the overall double layer capacitance.

[FIGURE 10 OMITTED]

Nyquis Plot for SBR-60CCB System. The Nyquist plot for SBR-60CCB sample with a thickness of 7 cm is shown in Fig. 10. From the plot it can be observed that the system is totally capacitive in nature like the SBR-30CCB system and similarly its electrical characteristics may be explained. The parameters of the equivalent circuit for the SBR-60CCB composite are listed in Table 5. It is found that [R.sub.d1], [R.sub.b], [C.sub.d1] all behave in a similar manner as that of 30 phr system and same explanation holds good for this system also.

Complex Electric Modulus. The real and imaginary parts of complex electric modulus of the composites may be calculated using complex impedance data Z' and Z" into the following equations [20]:

M' = Z'/(Z')[.sup.2] + (Z")[.sup.2] and M" = Z"/(Z')[.sup.2] + (Z")[.sup.2]. (3)

The complex plane diagram of the electric modulus M' vs M" are shown in Figs. 11 and 12. The figures can be considered as a part of a circle or as a combination of the circular arc preceded by a linear portion. It can be seen from these plots that the radius of the M' vs M" plots for composites with lower filler loading is higher compared to that of higher loading ones. This may be due to the increase in conductivity of the composites with increase in filler loading [20].

Electromagnetic Shielding Effectiveness

Electromagnetic interference (EMI) is the disturbance created in the performance of an electronic device because of the electric field set up by another device placed nearby. The electromagnetic interference shielding effectiveness (EMI SE) is defined and calculated based on the following expression:

EMI SE = 10 [log.sub.10]incident power density/transmitted power density [19]. (4)

The EMI SE of all the composites have been determined by using the aforementioned expression through the measurement of the incident power density at a point before the composite shield is installed and by the measurement of the transmitted power density at the same point when the composite shield is installed.

Effect of Frequency. The effect of AC frequency on EMI SE of the SBR-CCB composites was measured for different thicknesses of the composites. The EMI SE of the composites at a thickness of 7 cm is shown in Fig. 13. The maximum EMI SE of around 67 dB is obtained for the SBR-60CCB composite at a frequency of 9 GHz. It can be seen from the plot that for all composites under investigation, the EMI SE initially increases with the increase in frequency, reaches the maximum value, and then decreases with further increase in frequency. Similar observations were reported earlier, including systems with conductive coating based on acrylonitrile [22]. Though the reason for this behavior is, however, yet to be established definitely, we can argue in the following manner. As mentioned earlier, whenever a composite shield is placed in the passage of an electromagnetic field, three processes namely reflection, absorption, and transmittance thus become operative. EMI SE may be also categorized due to reflectance, absorption, and transmittance. The overall EMI SE is the net result of the processes. However, the major contribution may come from one of the three processes depending on the nature of the system.

[FIGURE 11 OMITTED]

It is well-known that the EMI SE is proportional to the conductivity as well as permittivity of the material. Both these properties may work simultaneously and affect the EMI SE values. However, the quantification of this relationship through some function that is universally applicable to all materials at all frequencies is yet to be reached. The EMI SE not only depends on the conductivity but also on the reflection and absorption coefficient of the conductive filler, its shape, size, and distribution in the matrix. The distribution of the filler in the rubber matrix determines the void space between the filler aggregates. To achieve high shielding, the conductive particles should form a closed packed array throughout the matrix, more like a conducting mesh that could be used as EMI shielding [23-25]. The voids in the conductive composite affect absorption and return loss due to their effect on internal reflection. The dependency of EMI SE of the composites is mainly due to the distribution of filler in the matrix. With the increase in frequency, the wavelength of the microwaves become shorter and thereby they pass through the conducting mesh formed by the filler aggregates easily and hence decreasing the EMI SE at higher frequencies. However, from the experimental observations, an optimum frequency at which the EMI SE is maximum can be determined.

[FIGURE 12 OMITTED]

[FIGURE 13 OMITTED]

Effect of Filler Loading. The effect of filler loading on the EMI SE of the SBR-CCB composites was studied, and the results for a sample thickness of 1.3 cm at 9 GHz are represented in Fig. 14. It can be observed that with increase in filler loading the EMI SE of the composites increase continuously. EMI SE and the conductivity are related by the equation

EMI SE = 20 log(1 + [sigma]d[Z.sub.0]/2) (5)

where [sigma] is the conductivity (ohm cm)[.sup.-1], d is the thickness of the sample, and [Z.sub.0] is the free-space wave impedance (377 ohm) [26]. From this equation, we can see that EMI SE is directly proportional to the conductivity of the shielding material. Increase in filler loading increases the conductivity of the SBR-CCB composite system and obviously EMI SE also goes up with filler loading, which can be understood directly from Eq. 5. Basically, the combination of conducting mesh formed by the conductive filler in the insulating matrix absorbs the electromagnetic waves. With increase in filler loading, the quantity of the mesh and the possibility of its interaction with the waves increases, which increase absorption and hence the increase in EMI SE [23].

[FIGURE 14 OMITTED]

[FIGURE 15 OMITTED]

Effect of Thickness. The effect of sample thickness on the EMI SE for the SBR-CCB composites was studied and the results at a frequency of 10 GHz are represented in Fig. 15. It can be observed that with increase in thickness, the EMI SE of the composites increase continuously. This phenomenon of increase of EMI SE with increase in thickness can be explained by Eq. 5. The increase in thickness of the sample places more amount of conducting mesh and interception of individual conducting layers, which affects both absorption and internal reflection, thus contributing to the increase in EMI SE with thickness [23].

SUMMARY AND CONCLUSIONS

The real part of the complex impedance of the SBR-CCB composites was found to decrease with increase in frequency, whereas the imaginary part passes through a maximum with frequency. The complex impedance of the composites was found to decrease with increase in filler loading and was found to increase with increase in thickness. All the composites exhibited capacitive nature except the exception of SBR-20CCB at thickness of 0.65 cm. The EMI SE of the composites passed through a maximum with the frequency. With thickness and filler loading the EMI SE was found to increase continuously. All the SBR-CCB composites can find application as EMI shielding materials, especially the SBR-60CCB composite with an EMI SE of 67 dB can be used as a good EMI shielding material.

REFERENCES

1. G. Sandi and P. Vanjsek, Synth. Mater., 64, 1 (1994).

2. D.C. Trivedi and S.K. Dhawan, Polym. Adv. Technol., 4, 335 (1993).

3. M. Tomkiewicz, Electrochim. Acta, 38, 1923 (1993).

4. Y. Cao, A. Andreatta, A.J. Heeger, and P. Smith, Polymer, 30, 2305 (1989).

5. M. Angelopoulos, A. Ray, and A.G. MacDiarmird, Synth. Mater., 21, 21 (1987).

6. Y. Li and R. Quian, Synth. Mater., 55-57, 3637 (1993).

7. P. Passiniemi and K. Vakiparta, Synth. Mater., 69, 237 (1995).

8. C.A. Edmondson, P.E. Stallworth, M.E. Chapman. J.J. Fontanella, M.C. Wintersgill, S.H. Chung, and S.G. Greenbaum, Solid State Ionics, 135, 419 (2000).

9. C.A. Edmondson, P.E. Stallworth, M.C. Wintersgill, J.J Fontanella, Y. Dai, and S.G. Greenbaum, Electrochim. Acta, 43, 1295 (1998).

10. M.C. Wintersgill and J.J. Fontanella, Electrochim. Acta, 43, 1533 (1998).

11. J.J. Fontanella, M.C. Wintersgill, R.S. Chen, Y. Wu, and S.G. Greenbaum, Electrochim. Acta, 40, 2321 (1995).

12. G.C. Psarras, E. Manolakaki, and G.M. Tsangaris, Compos. Part A: Appl. Sci. Manuf., 34, 1187 (2003).

13. J.H. Sung, S.J. Kim, and K.H. Lee, J. Power Sourc., 124, 343 (2003).

14. V. Singh, A.N. Tiwari, and A.R. Kulkarni, Mater. Sci. Eng. B, 41, 310 (2001).

15. M. Narkis and A. Vaxman, J. Appl. Polym. Sci., 29, 1639 (1984).

16. J. Regan, in Polymer-Plastics Technology and Engineering, L. Naturman, editor, Marcel Dekker, New York, 47 (1974).

17. K. Kakizawa, Int. Polym. Sci. Technol., 13, 40 (1986).

18. G.T. Mohanraj, T.K. Chaki, A. Chakraborty, and D. Khastgir, J. Appl. Polym. Sci., 92, 2179 (2004).

19. Matthew N.O. Sadiku, Elements of Electromagnetics, 3rd ed., Oxford University Press, New York (2002).

20. E.S. Matveeva, Synth. Mater., 79, 127 (1996).

21. J.R. Macdonald, Impedance Spectroscopy: Emphasizing Solid Materials and Systems, Wiley Interscience, New York (1987).

22. C.Y. Huang and W.M. Wei Mo, Surf. Coat. Technol., 55, 154 (2002).

23. P.K. Pramanik, T.N. Saha, and D. Khastgir, J. Elastom. Plast., 23, 345 (1991).

24. D.M. Bigg, in Proceedings of the 15th Akron Polymer Conference on Advances in Polymer Processing, University of Akron, May 24, 25 (1984).

25. M.S. Ahmad, M.K. Abdelazeez, and A.M. Zihlif, J. Mater. Sci., 24, 1795 (1989).

26. N.F. Colaneri and L.W. Shacklette, IEEE Trans. Instrum. Meas., 41, 291 (1992).

G.T. Mohanraj, T.K. Chaki, Rubber Technology Centre, Indian Institute of Technology, Kharagpur 721302, India

A. Chakraborty

Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur 721302, India

D. Khastgir

Rubber Technology Centre, Indian Institute of Technology, Kharagpur 721302, India

Correspondence to: Prof. D. Khastgir; e-mail: [e-mail]

Contract grant sponsor: Indian Space Research Organization (ISRO).

TABLE 1. The formulation used for the preparation of the composites.

Ingredients     Loading (phr)

SBR 1502        100.0
Zinc oxide        5.0
Stearic acid      1.5
Antioxidant TQ    1.0
Vulcan XC-72     10-60
Process oil       1-7
MBTS              1.0
TMT               0.2
Sulfur            2.0

TABLE 2. Physical characteristics of Vulcan XC-72 carbon black.

Properties                               Values

Nitrogen surface area (m/g)              180
DBP absorption number (ml/100 g)         178
Average Particle diameter (nm)            29
Electron microscopic surface area (m/g)   86
CTAB surface area (m/g)                   86

DBP, dibutyl phthalate; CTAB, cetyl trimethyl ammonium bromide.

TABLE 3. Parameters of the equivalent circuit obtained from Nyquis plots
for SBR-20CCB system.

Approximated representative equation  Thickness (cm)  [R.sub.b] (ohms)

(Z' - 28.11)[.sup.2] +                0.65            1056.82
  (Z" - 4.4)[.sup.2] = 289
(Z' - 34.21)[.sup.2] +                1.3             1055.54
  (Z" - 4.36)[.sup.2] = 311.17
(Z' - 49.12)[.sup.2] +                7               1054.62
  (Z" - 26.06)[.sup.2] = 327.61

Approximated representative equation  [R.sub.d1] (ohms)  [C.sub.d1] (nF)

(Z' - 28.11)[.sup.2] +                34                 0.0031
  (Z" - 4.4)[.sup.2] = 289
(Z' - 34.21)[.sup.2] +                35.28              0.0031
  (Z" - 4.36)[.sup.2] = 311.17
(Z' - 49.12)[.sup.2] +                36.2               0.0032
  (Z" - 26.06)[.sup.2] = 327.61

TABLE 4. Parameters of the equivalent circuit obtained from Nyquis plots
for SBR-30CCB system.

Approximated representative equation  Thickness (cm)  [R.sub.b] (ohms)

(Z' - 18.12)[.sup.2] +                0.65            13.47
  (Z" - 1.08)[.sup.2] = 25
(Z' - 22.22)[.sup.2] +                1.3             13.09
  (Z" - 4.15)[.sup.2] = 26.94
(Z' - 25.01)[.sup.2] +                7               10.87
  (Z" - 4.14)[.sup.2] = 39.69

Approximated representative equation  [R.sub.d1] (ohms)  [C.sub.d1] (nF)

(Z' - 18.12)[.sup.2] +                10                 0.0091
  (Z" - 1.08)[.sup.2] = 25
(Z' - 22.22)[.sup.2] +                10.38              0.0088
  (Z" - 4.15)[.sup.2] = 26.94
(Z' - 25.01)[.sup.2] +                12.6               0.0076
  (Z" - 4.14)[.sup.2] = 39.69

TABLE 5. Parameters of the equivalent circuit obtained from Nyquis plots
for SBR-60CCB system.

Approximated representative equation  Thickness (cm)  [R.sub.b] (ohms)

(Z' - 2.02)[.sup.2] +                 0.65            5.14
  (Z" - 1.58)[.sup.2] = 1.09
(Z' - 3.75)[.sup.2] +                 1.3             5.03
  (Z" - 1.55)[.sup.2] = 1.21
(Z' - 4.52)[.sup.2] +                 7               5.05
  (Z" - 1.88)[.sup.2] = 1.19

Approximated representative equation  [R.sub.d1] (ohms)  [C.sub.d1] (nF)

(Z' - 2.02)[.sup.2] +                 2.09               0.046
  (Z" - 1.58)[.sup.2] = 1.09
(Z' - 3.75)[.sup.2] +                 2.2                0.042
  (Z" - 1.55)[.sup.2] = 1.21
(Z' - 4.52)[.sup.2] +                 2.18               0.043
  (Z" - 1.88)[.sup.2] = 1.19