March 15, 2014 / Vol. 39, No. 6 / OPTICS LETTERS
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EMI shielding and conductivity of carbon nanotubepolymer composites at terahertz frequency Debanjan Polley,1,2 Anjan Barman,2 and Rajib Kumar Mitra1,* 1
Department of Chemical, Biological and Macromolecular Sciences, Unit for Nano Science and Technology, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India 2 Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India *Corresponding author:
[email protected] Received December 27, 2013; revised February 7, 2014; accepted February 7, 2014; posted February 10, 2014 (Doc. ID 203838); published March 12, 2014 We investigate the shielding effectiveness and complex conductivity of single-walled carbon nanotubes (SWNT) distributed in a polyvinyl alcohol (PVA) matrix in the THz frequency range. SWNTs are dispersed in PVA matrices with varying SWNT content (keeping the thickness of SWNT/PVA film constant) using a slow-drying method, and terahertz time-domain spectroscopy (THz-TDS) is performed at room temperature in transmission geometry in the frequency range of 0.3–2.1 THz. The transmittance spectra show a possible application of SWNT/PVA composites as low-bandpass filters in the THz frequency region. Shielding effectiveness of all the samples is measured, and, at a particular probing frequency, they tend to follow a linear relationship with SWNT weight fraction in the polymer matrices. THz conductivity of the composite system is described in the light of a.c. hopping conduction. © 2014 Optical Society of America OCIS codes: (160.4236) Nanomaterials; (300.6495) Spectroscopy, terahertz. http://dx.doi.org/10.1364/OL.39.001541
With the development of high-frequency electronic devices comes the essential need of electromagnetic interference (EMI) shielding in the corresponding frequency range. EMI is defined as the adverse effect caused by the electromagnetic (EM) waves emanating from some sources on the performance of other devices operating nearby at similar frequency range [1]. Therefore development of EMI shielding materials is gaining much needed attention in the scientific community in the present era. While most of the works regarding shielding properties of different materials are concentrated in MHz to GHz frequency range [2], with the increasing popularity and significance of THz spectroscopy, scientists are now paying attention on the shielding properties in the elusive THz frequency range [3–7]. Shielding effectiveness (SE) of a system is governed by three processes, namely, reflection, absorption, and multiple internal reflection and depends upon various parameters such as conductivity, permittivity, permeability, and thickness, with most of these factors being crosslinked to each other. Nowadays composite materials (conductive filler in dielectric host) are particularly obtaining much interest as potential shield material due to their unique properties such as tunable conductivity, resistance to corrosion, flexibility, and low cost [2]. Single-walled carbon nanotubes (SWNTs) have extensively been used in a broad spectrum of science, including EM shielding in a large frequency range considering their fascinating electronic, optical, and mechanical properties. SWNTs dispersed in polymer matrices have attracted a great deal of attention for their unique combination of conductivity, mechanical flexibility, resistance to corrosion and processing advantages [2]. SWNT-polymer composites have been studied extensively for their excellent lightweight shielding properties at frequencies ranging from 10 MHz to several GHz using network analyzer systems [2,8]. With the ever-increasing speed of electronic devices, it is imperative to look into 0146-9592/14/061541-04$15.00/0
the EMI shielding (EMIS) properties of SWNT–polymer composites in the THz frequency range, as this frequency domain still remains largely unexplored. There have only been a handful of studies in this frequency range [3–7]. Seo et al. [5] have shown that acid-treated SWNT films are more capable for shielding compared to pristine SWNT films and found a highest SE of 8 dB for acidtreated SWNT films. In the present study, we have fabricated SWNTs dispersed in polyvinyl alcohol (PVA) films with varying SWNT weight fraction [1 mg (S1), 4 mg (S2), 8 mg (S3), 10 mg (S4), 16 mg (S5), and 20 mg (S6) SWNT in 1 g PVA or 0.1%, 0.4%, 0.8%, 1.0%, 1.6%, and 2.0% weight percentage] in the polymer matrix and performed THz timedomain spectroscopic (THz-TDS) measurements in transmission geometry at room temperature in the frequency range of 0.3–2.1 THz. THz conductivity of the composite material instead of the SWNT alone are extracted since (1) SE of the composite strongly depends on the composite conductivity and not solely on the SWNT conductivity, which has been found to be following a complicated Drude–Lorentz behavior in this frequency range [9]; (2) finding the exact volume fraction of SWNT inside the polymer matrix [10] and then applying the appropriate effective medium theory to extract SWNT conductivity still remains a debatable issue [9,10]. Conductivity of the composite system has been analyzed using a universal a.c. hopping conductivity model. The essence of this study lies in the investigation of SE of SWNT/PVA composites in the THz frequency range and modeling their conductivity. SWNT (>90% carbon content, >77% SWNT, diameter ∼0.9–1.2 nm) and PVA (>99% hydrolyzed) were purchased from Sigma-Aldrich and used without further purification. 1 g granular PVA was dissolved in 10 ml de-ionized (DI) water with continuous magnetic stirring for 45 min at 80°C to produce a clear solution. The required amount of SWNT powder was mixed with © 2014 Optical Society of America
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5 ml DI water and ultrasonicated for 30 min for uniform dispersion. A uniformly dispersed SWNT solution was then added to the clear PVA solution and magnetically stirred for another 45 min before pouring into a glass petridish, which was kept at an ambient condition for slow drying for 10 days to prepare the samples for spectroscopic measurements. A pure PVA film was also prepared for the reference measurements. Thicknesses of all the films were found to be within the range of 300 μm 30 μm. The details of the THz measurements could be found elsewhere [11,12]. The advantage of PVA as a choice for the polymer matrix is two-fold [11]: it has an uncharacteristic optical response in the measured frequency range (n ∼ 1.8 and α 40 cm−1 at 1 THz), and it provides robustness and flexibility to the shield material. Figure 1 shows the THz time-domain amplitude through bare PVA sample and SWNT/PVA composites while the corresponding fast Fourier transform (FFT) spectra are shown in the inset. The peak-to-peak THz amplitude decreases with increasing SWNT content in the polymer due to highly percolated behavior of the SWNTs with increasing weight fraction. The FFT spectrum of the sample S6 is limited by S/N ratio of up to 1.4 THz, whereas for the remaining samples FFT spectra can be analyzed from the 0.3 to 2.1 THz frequency range with good S/N ratio. We do not consider sample S6 for further analysis. Transmittance (T) profile of all the samples in the aforementioned frequency range is depicted in Fig. 2(a). Transmittance is defined as T jE s ω∕E a ωj2 , where E s ω and E a ω are the complex THz electric fields passing through the sample and incident on the sample, respectively, in the frequency domain. As evident from the figure, T for all the samples decreases steadily with increasing frequency due to high absorption of SWNT at high frequencies. This also indicates that the present composites are capable of acting as good low-bandpass filters that effectively screen the THz wave beyond 1.25 THz, especially for samples with higher SWNT content (S3, S4, and S5). SE of the samples are calculated using the following formulae: SEtot −10 log T [1]. It can be noted that total SE is a combination of absorptive (SEa ), reflective (SEr ), and internal (SEi ) shieldings; however, our experimental configuration (transmission geometry) allows us to
Fig. 2. (a) Transmission spectra of the samples. (b) SE at 0.5, 1.0, and at 2.0 THz as a function of SWNT content in the PVA matrices fitted with straight lines. The variation of the slope of the fitted straight line as a function of frequency is shown in the inset.
measure SEtotal only. For most of the shielding materials, where the thickness of the material is much larger than the skin depth of the sample, as also in the present system, SEi is negligible [2]. Thus it is safe to assume that the main contributions to SEtotal come from SEr and SEa . SEtotal increases with increasing probing frequency and also with increasing SWNT content due to high absorption of THz waves by SWNT at high frequencies and the well-percolated region with increasing SWNT content, respectively. SE as a function of SWNT content in the composite is plotted in Fig. 2(b) at three different probing frequencies—0.5, 1.0, and 2.0 THz—and all three systems show good linear fits. The slope of the fitted straight line in a frequency range of 0.3–2.0 THz is plotted in the inset of Fig. 2(b). It can be observed that, at lower frequencies, the slope of that fitted straight line increases steeply. However, at higher frequencies the slope changes very slowly, and within the frequency range of 1.2–2.0 THz, it can be estimated as 0.73 0.075 [red demarcated region in Fig. 2(b)]. Thus SE of these composites can be predicted in the prescribed frequency range without performing direct measurements if one knows the SWNT weight fraction in the composite. Such a frequency-dependent response of SE has also been observed previously using graphite–polymer composite in a frequency range of 0.2–0.9 THz [10]. The SE of 1.6% SWNT sample (S5) has been found to be larger than 20 dB beyond 1.25 THz and steadily increases up to 29 dB at 2.1 THz. This composition provides a promising EMI shielding behavior at high frequencies for potential industrial applications since an SE greater than 20 dB (implying 1% power transmission through the shield) covers most of the real applications [2]. As SE of a composite material is closely related to its conductivity, we will now discuss the conductivity in the THz frequency domain. The complex conductivity of the samples are derived using the following equations: ε~ ε∞ σ r ωε0 εim
Fig. 1. THz electric field amplitude in time domain with increasing SWNT content in PVA matrices. Inset shows the FFT amplitude of corresponding samples in the frequency domain.
iσ~ ; ωε0
and σ im ωε0 ε∞ − εr ;
(1) (2)
where ε~ εr iεim is the complex dielectric function, ε∞ is the dielectric constant at high frequency, ε0 is the dielectric constant of air, and σ~ σ r iσ im is the complex frequency-dependent conductivity of the composite. The frequency-dependent extinction
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coefficient κω, index of refraction nω, and the complex dielectric constant ε~ εr iεim (~ε nω i κω2 ) were deduced by numerically solving Fresnel’s transmission coefficient for each film using THz transmission data [11]. In general, ε∞ is obtained as a fitting parameter during the fitting of the SWNT dielectric function [9]. The possible value of ε∞ varies with the physical parameters of SWNTs; thus it is difficult to estimate its value correctly, which makes the calculation of σ im uncertain. We therefore have led our attention on the real a.c. conductivity of the composite systems, which has been modeled using the following relation [13]: σ real σ0 Aωs ;
(3)
where σ0 is the static conductivity of the composite and A is a fitting parameter, which depends on temperature and the frequency exponent s0 < s < 1 is a function of both frequency and temperature depending on the nature of the composite system. The frequency exponent s is defined as s dlnσ∕dlnω [13]. This model has successfully been applied for a large class of composite materials in the frequency range starting from near d.c. value to THz frequency range [13–18]. In general, the conductivity remains almost constant ∼σ0 up to a characteristic onset frequency ω0 , defined as σω0 1.1σ0 [14], and then it increases following a power law Aωs . For SWNT-PVA composites with varying SWNT content ω0 lies in the kHz to MHz frequency range [15–17], which is several orders of magnitude smaller compared with the present frequency range of interest. We therefore do not observe the d.c. conductivity plateau in the present investigation. We plot lnσ real as a function of lnω for all the samples with different SWNT inclusions [Fig. 3(a)]. All the data show good linear fit, and s is obtained from the slope of the fitted lines [Fig. 3(b)]. This observed linear behavior suggests that the exponent s is independent of the frequency in the studied domain. Variation of the frequency exponent s as a function of SWNT content in the polymer matrices in this probed frequency region is shown in the inset of Fig. 3(b). Conductivity is found to increase with frequency and with the SWNT weight fraction [Fig. 3(a)]. However, at high frequency, it is almost independent of SWNT content as observed from Fig. 3(a). This behavior can be explained in the following way: a correlation length λ exists for SWNT/polymer composites, which can be defined as the distance between the junctions and the nodes. Whenever an alternating wave is applied to this
Fig. 3. (a) Real part of conductivity of different SWNT-PVA composites. The straight lines show linear fits. (b) s values as a function of SWNT content in the PVA matrices.
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composite, the charge carriers travel a distance, which is proportional to the period of the exciting wave. At lower frequencies, carriers travel long distances and probe a longer distance (lω ) and vice versa [15]. When lω > λ (i.e., at low frequencies), probed length contains multiple junctions; hence conductivity is lower due to the increased junction resistance. With increasing frequency, lω becomes comparable to λ, and conductivity increases due to the reduced junction resistance. However, at much higher frequency, it increases almost insignificantly with higher SWNT weight fraction, as lω gets limited within the intra-tube lengths [17]. Conductivity rises with increasing SWNT content in the polymer matrices due to the increase in SWNT loading (conductive element) well above the percolation threshold as well as due to local aggregation [17]. The frequency-dependent conductivity of SWNT/polymer composites at and below room temperature has previously been explained using a correlated barrier hopping model [15–17]. According to this model, s does not depend on frequency and decreases with increasing temperature. However, the dependence of s on the concentration of conductive elements inside the matrices has not yet been studied conclusively, though it was shown that s indeed decreases with increasing conductive elements, which is confirmed by the present measurements [17–19]. For very small SWNT (conductive) inclusion in the dielectric matrices, the value of s is found to be slightly larger than 1, which is probably due to a stronger response of the insulating component [18]. For higher SWNT inclusions, the value of s is found to be smaller than 1 and decreases steadily with increasing conductive element in the polymer matrix. Such behavior is well in accordance with random resistor–capacitor (RC) model [20,21], in which dielectric matrices and conductive elements are modeled as resistors and capacitors, respectively. It has been shown explicitly that in such a model the frequency exponent s decreases systematically with increasing resistive element fraction into the system [21,22]. In summary, we have prepared SWNT–polymer composite samples via slow-drying method with varying SWNT content in PVA matrices. Transmittance is found to be significant at lower frequencies (between 0.3 and 0.8 THz) but is close to zero at higher frequencies (beyond 1.25 THz) showing a possible application of these composites especially with a higher amount of SWNT contents for low-bandpass THz filters. Shielding properties of the samples were studied in the frequency range of 0.3–2.1 THz. SE shows a linear relationship with SWNT weight fraction at a particular probing frequency, and, in a broad frequency range from 1.2 to 2.0 THz, SE can be expressed as SE ∝ 0.73 0.075w where w is the SWNT weight fraction. SE of the 1.6% SWNT composite was found to be greater than 20 dB at 1.25 THz and rises steadily up to 29 dB at 2.1 THz. Room temperature THz conductivity of the system was found to vary according to a power law, σ ∝ ωs with frequency exponent s decreasing slowly from approximately 1–0.6 with increasing SWNT content inside the polymer matrices, which has been supported by random RC model. However, for very small SWNT content, s is found to be slightly greater than 1, which is attributed to strong response of insulating component.
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