Electromagnetic Shielding Effectiveness of Carbon Nanotubes Hydrogel Nanocomposites in the Frequency Range from 1.7 to 6.0 GHz

Abstract

Carbon nanotube-based nanocomposites are being increasingly utilized in materials for electromagnetic shielding purposes due to their exceptional electrical and mechanical properties. The current study optimizes a simple procedure to prepare multi-wall carbon nanotubes (MWCNTs)-based hydrogel nanocomposites out of water, gelatin, and glycerol. The content ratio of each component in the hydrogel composite is carefully selected to optimize the dielectric properties over the electromagnetic (EM) wave frequency of 0.5 to 20 GHz. The hydrogel nanocomposites were prepared with MWCNT concentrations ranging from 0.1 to 0.9 wt%. The dispersion of MWCNTs in the nanocomposites was investigated and confirmed using a scanning electron microscope (SEM). The dielectric parameters, including the real dielectric constant ${\epsilon }^{\prime }$, imaginary dielectric constant ${\epsilon }^{″}$, and tangent loss tan $\delta$ along with the DC and AC electrical conductivity (${\sigma }_{DC}$,${\sigma }_{AC}$) were investigated. The study shows a significant enhancement in the dielectric parameters of the prepared nanocomposites as the MWCNT concentration is increased. The shielding effectiveness (SE) of the hydrogel nanocomposites against electromagnetic waves in the frequency range from 1.7 to 6.0 GHz is investigated and found to be enhanced as the concentration of MWCNTs and frequency have increased. The shielding effectiveness of the prepared hydrogel nanocomposites ranges from 10 dB to 26 dB, equivalent to shielding of 90% and more than 99% of incident radiation, respectively.

1. Introduction

Since their discovery, electromagnetic waves have been extensively implemented in transmission and reception circuits in many everyday technological applications. However, associated with such use, electromagnetic pollution or electromagnetic interference (EMI) has become an issue that must be prevented or mitigated to eliminate negative impacts on electronic devices and human well-being [1,2]. A common approach to prevent EMI usually involves using shielding materials that reflect or/and absorb unwanted electromagnetic waves [3]. The selection of shielding materials can be based on their electric, dielectric, magnetic, and mechanical properties [4]. Among such materials are carbon nanotube-based composites that are extensively utilized in many applications due to their extraordinary ability to provide protection against EM radiation [5,6,7].

Carbon nanotubes (CNTs), since they were discovered by Iijima in 1991, have been extensively investigated by researchers targeting new technological applications [8]. CNTs are commonly used as nano-fillers in many nanocomposites due to their exceptional electrical properties (e.g., their electrical conductivity ranges from ${10}^3$ to 10⁶ S/m for long MWCNTs [9]), high aspect ratio (e.g., its value for long MWCNTs is around 100 [10]), outstanding mechanical strength (e.g., the average tensile strength and Young’s modulus of millimeter-long MWCNTs can be around 0.85 GPa and 34.65 GPa, respectively) [11], availability, and low cost when compared to other kinds of nanoparticles [12]. The incorporation of CNTs into a polymer matrix results in the formation of nanocomposites that exhibit superior electric [13], thermal [14], and mechanical properties [15,16]. These improved characteristics make nanocomposites attractive for various technological applications, including electronics [17], biomedical [18], solar photovoltaic [19], packaging [20], and the aerospace industry [21]. As the electric and dielectric properties of nanocomposites are enhanced, one of the most direct consequences of such enhancement is an improvement in the shielding properties of the resulting composites against EM waves. The shielding properties of a CNT-based nanocomposite depend on many factors, including the concentration, conductivity, geometry, or aspect ratio, CNT type, e.g., single-wall (SWCNTs) or multi-wall (MWCNTs), and the electric and dielectric properties of the hosting polymer. Polymers, whether synthetic or natural (e.g., gelatin in the current study), are the prime components of any nanocomposite. They are chosen based on their physical and chemical characteristics to meet the requirements of a desired application [22,23,24,25].

Gelatin, when combined with water, forms a hydrogel that can serve as an excellent hosting material for preparing nanocomposites, especially those related to research and applications in the medical field [23,24,25,26,27]. This can be achieved due to the hydrogel’s properties, such as the ease of casting, biocompatibility (e.g., cell viability > 98% in cytotoxicity tests [28]), biodegradability (e.g., gelatin hydrogels degrade down to 62 wt.% dry weight of the original mass in five weeks [29]), availability, and the low cost of gelatin. Even though many studies have investigated the electric and dielectric properties of CNT–hydrogel nanocomposites, their shielding characteristics against EMI have gained less attention. Numerous studies have focused on using synthetic polymers (e.g., polyester, polydimethylsiloxane (PDMS)) as shielding materials due to their resilience to mechanical and thermal stresses and harsh weather conditions [22,30]. For example, in a study by Seng et al., the achieved total shielding effectiveness (SE) for MWCNTs/polyester nanocomposite was around 35 dB (more than 99% shielding of incident radiation) for 20 wt% concentration of MWCNTs in the frequency range from 8.2 to 18 GHz [22]. In another study by Shetty et al., the PDMS composite filled with MWCNTs, carbon-coated iron nanoparticles, and graphite has achieved a total SE of 20 dB in the GHz frequency range [30]. In another approach, hydrogels were prepared out of borax and polyvinyl alcohol (PVA) doped with graphene oxide nanostructures along with other nano-scale additives, in which the absorption of the microwave radiation has improved so that the total SE value was increased from 10 to 20 dB in the frequency range from 1.2 to 18 GHz [31]. While many attempts have been made to investigate the addition of MWCNTs to hydrogel to improve the electric and dielectric properties of the resultant nanocomposites, few studies have been conducted to investigate the integration of MWCNTs into the hydrogel matrix to improve the electromagnetic shielding effectiveness.

The initial objective of the present study is to prepare hydrogel composites using different ratios of gelatin, water, and glycerol. Out of the resultant composites, a selected composite will be used as a hosting material for the CNTs in the second stage of the study. We believe that achieving this objective will provide researchers with valuable information about the dielectric properties of prepared composites or hydrogels, which can be beneficial in medical field applications. Our second objective is to determine the enhancement level in the electric and dielectric properties as MWCNTs are dispersed in the composite with concentrations up to 0.9 wt% in the frequency range from 0.5 to 20 GHz. The final objective of our study is to investigate the level of electromagnetic shielding effectiveness as the concentration of MWCNTs is gradually increased from 0 wt% to 0.9 wt% and to determine the contribution percentage of each mechanism responsible for electromagnetic shielding in these nanocomposites. The current work will shed more light on the contribution of the absorption and reflection mechanisms to the total electromagnetic shielding effectiveness.

2. Materials and Methods

2.1. Materials

The gelatin used in the current study is a B-type powder obtained from bovine skin supplied by Sigma-Aldrich (St. Louis, MO, USA). The demineralized water used in preparing the hydrogel was supplied by Tedia Company, Inc. (Fairfield, OH, USA), and deionized locally. The used CNTs were MWCNTs purchased from Cheap Tubes Co. (Grafton, VT, USA), with a purity greater than 95 wt.%, length ranges from 10 to 20 μm, and outer diameter starting from 30 to 50 nm. The used glycerol in the study has a purity of 99.5%, purchased from AZ Chem for Chemicals Company, Inc. (Selangor, Malaysia). The 40% formaldehyde solution was supplied by Sigma-Aldrich (St. Louis, MO, USA).

2.2. Composites Preparation

The sample preparation was carried out in two stages. In the first stage, several hydrogel composites were prepared using different concentrations of water, gelatin, and glycerol. Each component in the composite plays a crucial role in determining final mechanical and electrical properties. For instance, water acts as a solvent for the gelatin powder, at the same time, its distinguished dielectric parameter values help produce a wide range of hydrogel composite samples with diverse dielectric properties, depending on the water amount in the mixture. Gelatin has low dielectric constants; however, it forms an excellent matrix that can freeze CNTs in random orientation and serves with water as the dielectric material between the conductive CNTs. Glycerol serves as a plasticizer that provides elasticity to the hydrogel after curing and enhances the longevity of the samples [24].

In the second stage of the sample preparation process, MWCNTs are dispersed in a hydrogel composite selected from those prepared in the first stage. The key factors for choosing the host hydrogel composite include ease of handling and casting, dielectric, and electric properties, and most importantly, its ability to have high dispersion levels when MWCNTs are added. Another important factor to consider is the limitation in the measurement range of the dielectric parameters. For the current setup, it is recommended to have the measured dielectric constants (${\epsilon }^{\prime }$, ${\epsilon }^{″}$) be in the range from 5 to 100 [32]. The following subsections cover the details of the two stages.

2.2.1. Preparation of the Hydrogel Composite

In the first stage, hydrogel composites are prepared by mixing water and gelatin in different concentrations with a fixed amount of glycerol.

Table 1. Components weight percentages in the prepared hydrogel composites.

Sample #	Glycerol wt%	Water wt%	Gelatin wt%
S0	10	90	0
S1	10	85	5
S2	10	80	10
S3	10	75	15
S4	10	70	20

summarizes the weight percentages of each component in the prepared hydrogel composites.

The hydrogel composites were prepared by mixing the desired percentages of water and glycerol using a magnetic stirrer with a hot plate at a temperature of 50 °C at 650 rpm for 10 min. After that, the desired quantity of gelatin powder is added gradually while mixing (650 rpm) until the mixture becomes clear and all of the gelatin is dissolved completely. Next, the mixture is placed in a 50 °C water bath with sonication (provided by Elma Schmidbauer GmbH, Singen, Germany) for 10 min to remove suspended air bubbles. After cooling the mixture to around 40 °C at room temperature, 0.120 mL of 40% formaldehyde solution is added to the mixtures to enhance the cross-linking of gelatin molecules network and to preserve the samples against microorganism growth. Finally, the mixture is poured into a 50 mL beaker wrapped with plastic sheets to prevent water evaporation from the samples and left to cure at room temperature for 24 h, after which they will be ready for the dielectric measurement. This procedure was repeated three times for each sample, preparing three samples of $S_0$ to $S_4$.

As will be discussed in the next sections of this work, the selected hydrogel composite to host MWCNTs is sample $S3$, which is composed of 15 wt% gelatin, 75 wt% deionized water, and 10 wt% glycerol.

2.2.2. Preparation of the Hydrogel Nanocomposite

The hydrogel nanocomposite samples with MWCNT concentrations of 0.1, 0.3, 0.5, 0.7, and 0.9 wt% were prepared using hydrogel composite sample $S3$ according to the following procedure described in Figure 1.

(i) First, an aqueous solution of gelatin in deionized water is prepared by adding 4.0 g of gelatin powder to 50.0 g of water, and the solution is prepared in a 100 mL flask (labeled by A). Another aqueous solution of gelatin and deionized water is prepared by mixing 14.0 g of gelatin with 40.0 g of deionized water and 12.0 g of glycerol, and the solution is prepared in a 100 mL flask labeled by B. (ii) In the second step, both flasks A and B are placed in shaking water bath (model 1083, made by GFL, Bugwedel, Germany) at 50 °C with medium shaking speed for 60 min until all gelatin granules in both flasks dissolved completely and the solutions become clear. (iii) At this stage, the desired mass of MWCNTs is added to flask A, an ultrasonic homogenizer (model UP100H, made by Hielscher, Teltow, Germany) operated at a frequency of 30 kHz and a maximum amplitude of 0.8 for 10 min is used to disperse the MWCNTs in the flask (labeled by A′). (iv) The resultant solution with MWCNTs in the flask (A′) is then mixed with the content of flask B in a 200 mL beaker using a magnetic stirrer at 50 °C and 650 rpm for 10 min. (v) The resulting mixture from the previous step is then sonicated in a water bath of 50 °C for 10 min after which 0.6 mL of formaldehyde is added. (vi) Then, the mixture is poured into the waveguide shims and covered with a thin sheet of transparency film to ensure a smooth flat surface after curing. The remaining mixture was poured into a 25 mL beaker for the electric and dielectric measurements. At this stage, the 0 wt% composite was remade according to the same procedure excluding the steps that involve adding and dispersing MWCNTs. It is worth mentioning that, in the current work, to increase the dispersion of CNT fillers, MWCNTs were added to mixture A, which has less viscosity when compared to mixture B. This approach is believed to reduce the MWCNTs agglomeration level to a great extent [33].

2.3. Measurements and Characterization

2.3.1. Surface Morphology Characterization

The surface morphology of hydrogel composite and nanocomposite samples was investigated using a scanning electron microscope SEM model FEI Quanta FEG 450 (FEI Co., Hillsboro, OR, USA). The nanocomposite samples were mounted on aluminum stubs by double-sided sticky disks of conductive carbon. The samples were coated with around 5.0 nm gold using a Quorum Sputter coating unit (model Q150R) supplied by Quorum Technologies Ltd. (Laughton, UK), with a current of 15.0 mA for 5.0 min.

2.3.2. Dielectric Properties Characterization

The dielectric properties of a material or a composite can be described in terms of the real dielectric constant ${\epsilon }^{\prime }$ and the imaginary dielectric constant ${\epsilon }^{″}$. These values depend on the applied electric field (EM waves in general) frequency where many models can be used to describe ${\epsilon }^{\prime }$ and ${\epsilon }^{″}$ as a function of frequency. The most common model that successfully describes the dielectric properties of nanocomposites is the Havriliak–Negami Model which provides the complex dielectric constant of a material as [34]:

$$ϵ\left(\omega \right)={ϵ}_{\infty }+{\displaystyle \frac{{ϵ}_s-{ϵ}_{\infty }}{{[1+{\left(i\omega \tau \right)}^{1-\alpha }]}^{\beta }}}$$

(1)

where $ϵ\left(\omega \right)$ is the complex dielectric constant as a function of angular frequency $\omega$ which can be written in terms of frequency f in units of Hz as $\omega$ = 2$\pi$f, ${ϵ}_s$ is the dielectric constant at low frequency or constant electric field, ${ϵ}_{\infty }$ is the dielectric constant at the high-frequency range, $\tau$ is the relaxation time which is the time needed for the electric polarization to drop to $e^{-1}$ of its maximum value, $\alpha$ and $\beta$ are mathematical parameters count for the distribution and asymmetry of relaxation time, respectively, and $i=\sqrt{-1}$. In the Havriliak–Negami Model, the values of $\alpha$ and $\beta$ are in the ranges of 0$\le \alpha <$ 1 and 0 $<\beta \le$ 1, respectively. However, when the relaxation time provides a symmetrical plot as the imaginary dielectric constant ${\epsilon }^{″}$ plotted as a function of the real dielectric constant ${\epsilon }^{\prime }$ the value of $\beta$ is set to 1, the model is reduced to the Cole–Cole model as follows [34]:

$$ϵ\left(\omega \right)={ϵ}_{\infty }+{\displaystyle \frac{{ϵ}_s-{ϵ}_{\infty }}{1+{\left(i\omega \tau \right)}^{1-\alpha }}}$$

(2)

To explore how nano-fillers contribute to a host matrix’s complex effective dielectric constant ${\epsilon }_{eff}$, effective medium theory can be applied. One model that can be used within this framework is the Maxwell Garnett model, which is expressed as follows [35]:

$${\epsilon }_{eff}={\epsilon }_h+3f{\epsilon }_h{\displaystyle \frac{{\epsilon }_i-{\epsilon }_h}{{\epsilon }_i+2{\epsilon }_h-f({\epsilon }_i-{\epsilon }_h)}}$$

(3)

where ${\epsilon }_h$ is the permittivity of the host material, ${\epsilon }_i$ is the permittivity of the inclusion material (MWCNTs in the current study), and f is the volume ratio of the inclusion material. It is worth mentioning that the Maxwell Garnett model can explain the effective dielectric constant at very low inclusion volume ratios f so that f ≪ 1 and for far enough non-interacting inclusion particles [36]. However, for higher-volume-ratio inclusions and interacting inclusion particles, the Maxwell Garnett model cannot explain the effective dielectric constant of the composite. Using the Bruggeman model can be more suitable to account for higher f values and to account for interaction between the inclusion particles according to the following formula [36,37]:

$$f{\displaystyle \frac{{\epsilon }_i-{\epsilon }_{eff}}{{\epsilon }_i+2{\epsilon }_{eff}}}+(1-f){\displaystyle \frac{{\epsilon }_h-{\epsilon }_{eff}}{{\epsilon }_h+2{\epsilon }_{eff}}}=0$$

(4)

The above formula will be used in the current work to investigate the effective dielectric constant of the nanocomposite as MWCNTs are introduced with different concentrations.

The dielectric properties of the prepared nanocomposite were measured using a network analyzer (model number: E5071C, Keysight Technologies, Penang, Malaysia) connected to an open-ended coaxial dielectric probe (model number 85070E, Keysight Technologies, Penang, Malaysia), as described in our previous works [23,38].

2.3.3. Electromagnetic Interference Shielding Characterization

As electromagnetic radiation incident at the surface of some material, it experiences a reflection, absorption, and transmission through the material. These effects can be investigated by studying the so-called S-parameters, which describe how electromagnetic radiation scatters between two measurement ports. This scattering process can be represented by a 2 × 2 matrix as follows:

$$\mathbf{S}=\left(\begin{array}{cc}{S}_{11}& S_{12}\\ S_{21}& S_{22}\end{array}\right)$$

where the $\mathbf{S}$ matrix is related to the amplitude of the incident EM radiation $a_1$, reflected EM radiation $b_1$, transmitted radiation $b_2$ and incident EM radiation $a_2$ (if the second port used as a source) according to the following matrix representation:

$$\left(\begin{array}{c}{b}_1\\ b_2\end{array}\right)=\left(\begin{array}{cc}{S}_{11}& S_{12}\\ S_{21}& S_{22}\end{array}\right)\left(\begin{array}{c}{a}_1\\ a_2\end{array}\right)$$

The S-parameters, $S_{11}$ and $S_{21}$, are detected by ports 1 and 2 of the testing device, respectively, as described in Figure 2.

Starting from the measured S-parameters, one can calculate the transmissivity (T), which is defined as the ratio of the transmitted power to the incident power as in Equation (5); reflectivity, which is defined as the ratio of reflected power to the incident power as in Equation (6); and absorptivity (A), which is defined as the ratio of absorbed power to the incident power as in Equation (7) [3,39]:

$$T={\displaystyle \frac{P_t}{P_i}}={\left|S_{21}\right|}^2$$

(5)

$$R={\displaystyle \frac{P_r}{P_i}}={\left|S_{11}\right|}^2$$

(6)

$$A=1-R-T$$

(7)

The total shielding effectiveness $S{E}_{total}$ for any material under study is the ratio of EM radiation incident power to EM radiation transmitted power (in dB units). The $S{E}_{total}$, as presented in Equation (8), is the sum of the shielding effectiveness due to the reflection capability of the material ($S{E}_R$), as in Equation (9), the shielding effectiveness due to the absorption capability of the material ($S{E}_A$) as in Equation (10), and the shielding effectiveness due to the multiple-reflection capability of the material ($S{E}_M$) [39]. The $S{E}_M$ is due to the multiple internal reflections on the material boundaries and considered as an adjustment term written in terms of absorption term $S{E}_A$ as in Equation (11). The contribution of the $S{E}_M$ can be neglected in the cases in which the $S{E}_A$ value is greater than 10 dB [40].

$$S{E}_{total}=S{E}_R+S{E}_A+S{E}_M$$

(8)

$$S{E}_R=-10{log}_{10}[1-R]$$

(9)

$$S{E}_A=-10{log}_{10}\left[{\displaystyle \frac{T}{1-R}}\right]$$

(10)

$$S{E}_M=20{log}_{10}(1-{10}^{-(S{E}_A/10)})$$

(11)

Inserting Equations (9) and (10) into Equation (8), and neglecting the $S{E}_M$ term, the total shielding effectiveness $S{E}_{total}$ can be simplified, as shown in Equation (12):

$$S{E}_{total}=-10{log}_{10}T$$

(12)

The EMI shielding effectiveness capabilities of the prepared hydrogel nanocomposites were studied at room temperature using a waveguide transmission line presented in Figure 3.

The waveguide transmission line is implemented with the same network analyzer used for the dielectric measurements. The SE properties were investigated over the frequency range from 1.7 to around 6.0 GHz using three different waveguide transmission line setups. The first setup is used to study the shielding properties in the range from 1.7 to 2.6 GHz, which consists of two right angle adapters (part number: WR-430, supplied by A-info Inc., Beijing, China) and a shim with a thickness of 10.0 mm, in which the nanocomposite is cast. The second setup operates in the range from 2.6 to 4.0 GHz and consists of two right-angle adapters (part number: WR-284, supplied by A-info Inc., Beijing, China) and a shim with a thickness of 8.0 mm in which the nanocomposite is cast. The third setup operates in the range from 4.0 to 6.0 GHz and consists of two right angle adapters (part number: WR-187, supplied by A-info Inc., Beijing, China) and a shim with a thickness of 7.0 mm in which the nanocomposite is cast.

2.3.4. Electrical Conductivity Characterization

The electric conductivity of a material is defined as the ability of a material to allow the electric current to pass, and it is equal to the reciprocal of resistivity. The direct current (DC) electrical conductivity can be represented in terms of the geometry of the sample (length denoted as l and cross-sectional area denoted as A), as well as current I and applied voltage $\Delta V$ as follows:

$${\sigma }_{dc}={\displaystyle \frac{Il}{A\Delta V}}$$

(13)

It is worth mentioning that the DC conductivity of a nanocomposite depends on the concentration of the conductive nano-fillers added to the composite. As the nano-filler concentration increases, the nanocomposite conductivity remains almost constant until reaching a specific concentration, after which conductivity rises dramatically in a step transition. Such a concentration is called the percolation threshold, after which the nano-fillers touch each other and form conductive paths for the current to flow [41]. Increasing the concentration of the nano-fillers beyond the percolation threshold makes a small change in the electrical conductivity as the conducting paths are already established, and adding more nano-fillers will not result in more sudden changes [42].

The DC conductivity is measured using a two-port resistance scheme using a regular lab voltmeter, an ammeter, a power supply, and two locally made flat electrodes to sandwich the samples.

3. Results

3.1. SEM Analysis of Nanocomposite

The surface morphology of the prepared hydrogel composite and nanocomposites was investigated and displayed before and after the addition of MWCNTs as in Figure 4.

The SEM images in Figure 4a,b illustrate the surface morphology of the composite before the addition of MWCNTs, while the images in Figure 4c–f show the surface morphology after the addition of the MWCNTs. Comparing the images in Figure 4a,c, it is evident that MWCNTs are dispersed in the nanocomposite with some regions of agglomerated carbon nanotubes (labeled by the green dashed arrows in the figure). Zooming in on the area labeled by the yellow arrows presented in Figure 4c–f, it becomes apparent that MWCNTs are not damaged or degraded during nanocomposite preparation. Moreover, the images in the same figure reveal that MWCNTs are dispersed well in the composite, with some in contact with each other. This explains the slight increase in the conductivity of the hydrogel nanocomposites for high-MWCNT concentration fillers. The image in Figure 4b reveals a repetitive pattern in the surface morphology of the (empty) hydrogel composite attributed to hydrogel polymer formation. At the same magnification for the image in Figure 4d, the effect of the addition of MWCNTs on the surface roughness is also observed. The image in Figure 4f provides a detailed view of the MWCNTs embedded in the gelatin polymer matrix. This image also shows MWCNTs separated by small distances, leading to the formation of the micro-capacitor responsible for increasing the real dielectric constant as will be presented in the next section.

3.2. Dielectric Properties

The dielectric parameters of various hydrogel composites with different concentrations of water and gelatin are investigated initially before adding the MWCNTs. The purpose of this maneuver is to find a composite with suitable dielectric constants so that their values are within the measurement setup detectable range (5 to 100${\epsilon }_0$) after introducing MWCNTs, in addition to the other factors presented in Section 2.2. Figure 5 shows the measured dielectric constants of the prepared hydrogel composites as the concentration of water and gelatin are varied according to the percentages in Table 1.

In Figure 5a, one can track the drop in the real dielectric constant ${\epsilon }^{\prime }$ values over the entire frequency range starting from the pure water, e.g., from 79${\epsilon }_0$ down to 70${\epsilon }_0$ at 0.5 GHz as glycerol is initially introduced with a concentration of 10 wt% in S₀. After adding gelatin in a step of 5 wt% until reaching 20 wt% of the hydrogel composite, the drop in the ${\epsilon }^{\prime }$ values continues until reaching 35${\epsilon }_0$ at 0.5 GHz for composite $S_4$. In Figure 5b, one can observe the drop in the imaginary dielectric constant ${\epsilon }^{″}$ as glycerol is initially added, especially for frequencies higher than 4 GHz. For the rest of the samples, the ${\epsilon }^{″}$ values continue to drop as the gelatin portion is increased over the entire frequency range except for the frequencies less than 2 GHz which can be attributed to the increase in residual salts in the composite as the concentration of gelatin is increased [23]. The drop in the dielectric constants of ${\epsilon }^{\prime }$ and ${\epsilon }^{″}$ is associated with the increase in gelatin and glycerol concentrations in the composite, which both have much lower dielectric constants than water [24]. It is worth noting that the uncertainty in the measured dielectric constants is minimal due to the excellent homogeneity of the samples.

When plotting ${\epsilon }^{″}$ as a function of ${\epsilon }^{\prime }$ in the so-called Cole–Cole plot (see Figure 5c), the contribution of each constituent in the hydrogel composite can be recognized. For the water trace, one dominant relaxation process is associated with the dielectric dipole in the water molecules [43]. For the mixture of water (90 wt%) and glycerol (10 wt%), four relaxation processes are related to the relaxation of free water molecules, pure glycerol molecules, confined water molecules to the glycerol molecules network, and bound water molecules surrounding glycerol molecules [43].

Considering the Cole–Cole plot for the $S_1$ sample one can observe three distinguishable regions, among which the far right linear region is due to the contribution of DC conductivity due to the existence of residual salts remained in the gelatin after fabrication, as provided by the supplier [44]; this part becomes more prominent as the salts concentration increased with increasing gelatin starting from sample $S_1$ to $S_4$. In the same figure (Figure 5c), it can be seen that the $S_1$ trace has two minor arcs due to the interaction of water and glycerol through hydrogen bonds with gelatin, as reported previously [24]. As the concentration of gelatin is increased, the far right arc starts to disappear due to the domination of the DC conductivity in the mixture due to the higher concentration of residual salts in the gelatin. The arc-shaped curve to the left is due to the average relaxation process contributed by gelatin, glycerol, and water. Figure 5d shows the imaginary dielectric constant of the prepared hydrogel composites in the range from 1.7 to 6.0 GHz for the samples from $S_1$ to $S_4$, which is the range of interest for the shielding effectiveness study. Figure 5d shows that as the concentration of gelatin is increased, the composite becomes less lossy, e.g., the value of the ${\epsilon }^{″}$ drops from 13 down to 6${\epsilon }_0$ at the middle of the frequency range at 4.0 GHz.

After obtaining the dielectric constants for the hydrogel composites, the hydrogel composite in sample $S_3$ is selected to host the MWCNTs for the following reasons: (i) the dielectric constants of $S_3$ are close to the lower end of the measured dielectric constants limited by the measurement setup [32]. This enables us to monitor the changes in the dielectric parameters over a wider range as MWCNTs are added in the next stage, namely (ii) the change in the ${\epsilon }^{″}$ over the desired frequency of study is small (from 8 to 10.5${\epsilon }_0$), which helps to produce composites with linear EMI shielding to start with (iii) the amount of gelatin in the hydrogel composite in $S_3$ (during preparation), which produces a mixture with suitable viscosity in which CNTs disperse easily without settling down. (iv) The amount of gelatin and glycerol in $S_3$ enables casting the hydrogel composite more easily in the waveguide shims.

After selecting the hydrogel composite $S_3$ to host MWCNTs based on the reasons mentioned above, MWCNTs were added in five different concentrations (0.1, 0.3, 0.5, 0.7, and 0.9 wt%) and their dielectric properties were investigated. Figure 6a shows the effect of the addition of MWCNTs on the ${\epsilon }^{\prime }$ value as a function of frequency. It is clear that, as the concentration of MWCNT increased, the ${\epsilon }^{\prime }$ value is increased from around 45${\epsilon }_0$ for the pristine hydrogel composite to 90${\epsilon }_0$ at 0.7 wt% MWCNT concentration. Such an increase in the ${\epsilon }^{\prime }$ value is due to polarization at the interface between the conductive MWCNTs and the hydrogel composite matrix, which leads to the formation of micro-capacitors [24,38,45]. However, as the concentration of MWCNTs increased to 0.9 wt%, the ${\epsilon }^{\prime }$ value started to drop due to the agglomeration formation. Agglomeration began to form at such concentration, reducing MWCNT–hydrogel interface per unit volume when more carbon nanotubes started to bundle with each other [46].

In Figure 6b, the value of ${\epsilon }^{″}$ is dramatically increased, especially for the low-frequency range around 0.5 GHz ( i.e., from 15 up to 130${\epsilon }_0$). The increase in ${\epsilon }^{″}$ is attributed to the composite being more electrically dissipating when its conductivity is increased due to the formation of conductive networks when more MWCNTs are added. Moreover, the ${\epsilon }^{″}$ is increased due to the interfacial polarization that takes place at the interfaces between MWCNTs and the hydrogel matrix leading to higher dielectric loss [24]. The inset in Figure 6b shows a magnified plot of the ${\epsilon }^{″}$ in the range from 1.7 to around 6 GHz in which ${\epsilon }^{″}$ values increased by 65${\epsilon }_0$ at 1.7 GHz and by 30${\epsilon }_0$ at 6.0 GHz as the concentration of MWCNTs increased from 0 to 0.9 wt%. The dielectric constants of ${\epsilon }^{\prime }$ and ${\epsilon }^{″}$ in Figure 6a,b show a good agreement with the Bruggeman model introduced earlier in Equation (4), as can be seen in the curve fitting in the dashed lines in the figures. Using a Python code, the dielectric constant of the MWCNTs (${\epsilon }_i$) is found to be proportional to the concentration of MWCNTs, while setting the dielectric constant of the ${\epsilon }_h$ to equal the dielectric constants of the hosting hydrogel sample $S_3$. The Maxwell Garnett model could not fit the introduced experimental data due to the strong interaction of MWCNTs since the model is built for non-interacting fillers or diluted medium in the first place. The Cole–Cole plot in Figure 6c and its inset show the evolution of dielectric constants of ${\epsilon }^{\prime }$ and ${\epsilon }^{″}$ as the concentration of the MWCNTs has increased where the far right region in the curves has grown larger as the contribution of the DC conductivity has increased. Also, one can see that the part of the arc length has become smaller, indicating that the average relaxation time $\tau =1/\omega$ is occurring at a higher frequency, meaning a shorter average relaxation time [23].

The tangent loss measures the medium’s ability to dissipate EM energy when an oscillating electric field is applied [47]. To compare the level of EM energy dissipation in the prepared hydrogel nanocomposites, the tangent loss, which is defined as tan $\delta$ = ${\epsilon }^{″}$/${\epsilon }^{\prime }$, is calculated and plotted in Figure 7a.

The figure shows that, as the concentration of MWCNTs is increased in the nanocomposite, the tan $\delta$ values are increased. It can be observed that the tan $\delta$ values are greater than 0.1 over the inter-frequency range of the study (i.e., 0.2 < tan $\delta$ < 1.0), this indicates that all of the prepared nanocomposites, even the one with 0 wt% MWCNTs, are categorized as lossy mediums [47]. For all the nanocomposites, especially for the high-concentration fillers (0.5, 0.7, and 0.9 wt%), the tan $\delta$ have a minimum value between 8 and 9 GHz. Also, the slope of the loss tangent curves becomes sharper for frequencies less than 9 GHz as the concentration of MWCNTs is increased, while all the curves are parallel and only shifted to a higher tan $\delta$ value for frequencies larger than 9 GHz (see Figure 7a). It is worth mentioning that, the loss tangent originates when the orientation polarization of the electric dipoles lags behind the oscillating applied electric field [48].

The hydrogel nanocomposites’ AC and DC conductivity are physical quantities expected to be enhanced as MWCNTs are introduced to the composite. Both quantities are investigated for the prepared nanocomposites and presented in Figure 7b,c. The AC conductivity is obtained using the relation ${\sigma }_{AC}$ = 2$\pi$f${\epsilon }_0$${\epsilon }^{″}$, where f is the frequency of the applied EM waves in units of Hz and ${\epsilon }_0$ is the permittivity of free space. As the concentration of MWCNTs is increased up to 0.9 wt%, ${\sigma }_{AC}$ is enhanced, e.g., at 4.0 GHz, ${\sigma }_{AC}$ is enhanced by 5-fold. The increase in the conductivity is due to the formation of conductive network paths in the nanocomposites along with interfacial polarization effects [39].

The DC conductivity is also measured using the setup described earlier in Section 2.3. As shown in Figure 7c, the DC conductivity of the composite started to increase just after adding CNT by 0.1 wt%, whilst adding more MWCNTs to the nanocomposite resulted in a slight change in the DC conductivity. When MWCNTs were added up to 0.5 wt% the DC conductivity started to increase slightly to reach $0.8\times {10}^{-3}$ S/cm at an MWCNT concentration of 0.9 wt%. It is known that the increase in conductivity is due to the formation of conductive paths when the MWCNTs touch each other as can be seen in the SEM pictures in Figure 4 [39]. However, due to the low concentration of MWCNTs added to the composite, the conductive paths created by MWCNTs are short. Such short conductive paths cannot allow currents to flow with less resistance since the percolation concentration was not reached due to agglomeration of MWCNTs [24].

3.3. EMI Shielding Effectiveness

Using the experimental setup introduced earlier in Figure 3, the prepared nanocomposite’s ability to shield EM radiation is investigated as MWCNTs’ concentration increases for the three indicated frequency ranges. The EM shielding-related physical quantities that have been studied are the transmissivity (T), reflectivity (R), absorptivity (A), and total shielding effectiveness (SE_totel). The quantities of T, R, and A are obtained using Equation (5), Equation (6), and Equation (7), respectively. The insets labeled with a-i, b-i, and c-i in Figure 8 show the hydrogel nanocomposites’ reflectivity over the study’s frequency ranges. In the first two frequency ranges of 1.7 to 2.6 GHz and 2.6 to 4.0 GHz, it is clear that, as the concentration of MWCNTs increases, the surface’s reflectivity increases from 30% to around 56% at 1.9 GHz (in Figure 8(a-i)) and from 40% to 56% at 3.0 GHz (in Figure 8(a-ii)). For the frequency range from 4.0 to 6.0 GHz (in Figure 8(a-iii)), the reflectivity is the highest for the samples with the highest concentrations of MWCNTs; for example, at a frequency of 5 GHz, the 0.9 wt% sample achieved the highest reflectivity.

In Figure 8, for the insets labeled with a-ii, b-ii, and c-ii, the absorptivity of the prepared hydrogel nanocomposites was investigated over the same frequency ranges as above. In the first frequency range from 1.7 to 2.6 GHz, the maximum absorptivity is found for the hydrogel composite with 0 wt% concentrations of MWCNTs and the minimum for the 0.9 wt% nanocomposite. Such behavior is attributed to the fact that, as the conductivity of the composite is increased, the skin depth (the depth at which the wave intensity drops to e⁻¹) becomes smaller, which reduces the ability of the medium to absorb EM waves [49]. The same can be said for the second frequency range from 2.6 to 4.0 GHz, in which the absorptivity of the samples is at its maximum for the composite with 0 wt% MWCNT concentration and lower for the higher concentrations of MWCNTs. Such a drop in absorptivity is attributed to the drop in the skin depth (inversely proportional to ${\sigma }_{AC}$), which can be confirmed from the same figure (Figure 8(b-ii)), in which, at higher frequencies, the absorptivity for the different MWCNT concentrations composites is converging to the same value around 50%. In the third frequency range from 4.0 to 6.0 GHz, the absorptivity of the prepared composites is found to have a small change as the concentration of MWCNTs is increased, keeping in mind that the skin depth is smaller compared to the other lower frequency ranges. Another factor to consider is the thickness of the sample (7.0 mm) which has a different impedance matching compared to the other samples with different thicknesses [49]. It is important to remind the reader that the samples’ AC conductivity depends on the imaginary dielectric constant, meaning EMI-related shielding quantities strongly correlate with ${\epsilon }^{″}$.

The third quantity to observe for the prepared nanocomposites is transmissivity, defined as the ratio of the transmitted EM wave power to the incident EM wave power. Over the studied frequency range, the transmissivity of the samples decreases as the concentration of MWCNTs is increased, as can be seen in the insets of Figure 8(a-iii,b-iii,c-iii). The same set of insets confirms that the transmissivity of the nanocomposites decreases as the frequency increases, which is attributed to the drop in the skin depth as the frequency and AC conductivity are increased. The different samples’ thicknesses used for the different frequency setups in the study are responsible for the mismatching of quantity values from the end of a frequency range to the start of the next frequency range. Based on the data presented in Figure 8, one can confirm that both mechanisms of reflection and absorption are responsible for the shielding in the nanocomposites, in contrast with other composites in which reflection is the dominant mechanism [39].

The total shielding effectiveness ${SE}_{total}$ is another quantity to consider when studying the capability of a medium to block EM waves due to the different sources of reflection and absorption in the units of dB. Using Equation (12), the ${SE}_{total}$ values are obtained for the prepared nanocomposites with different MWCNT concentrations for the frequency ranges of the study and the results are plotted in Figure 9.

The insets a, b, and c in Figure 9 show an increase in ${SE}_{total}$ as the MWCNT concentration has increased and as the frequency of EM waves increased from one setup to another.

The reason behind the increase in the ${SE}_{total}$ as the MWCNT concentration is increased is related to the fact that the nanocomposite medium becomes lossy due to the increase in the imaginary dielectric constant ${\epsilon }^{″}$, which increases the ability to absorb EM power and changes it into heat. Another important reason for the increase in the ${SE}_{total}$ is the increase in the ability to reflect electromagnetic (EM) waves as a result of the increase in conductivity as the concentration of MWCNTs is increased. It is worth mentioning that a total SE of 20 dB corresponds to 99% shielding of incident radiation. When searching for a shielding material, it is essential to look for a material with ${SE}_{total}$ to be larger than 10 dB over a wide frequency range, equivalent to 90% shielding of incident radiation.

4. Conclusions

In this study, hydrogel nanocomposites are prepared using a simple casting method out of water, gelatin, and glycerol, along with different concentrations of MWCNTs. The initial outcome of the work is the production of hydrogel composites with diverse dielectric parameters capable of hosting a wide variety of nanomaterials. Incorporating MWCNTs at different concentrations is found to dramatically enhance the dielectric parameters of the hydrogel nanocomposites, paving the way for numerous technological applications, such as energy storage, medical devices, and EMI shielding. The SEM images of the hydrogel nanocomposites confirm a good level of dispersion of the MWCNTs and support the origin of dielectric parameter enhancements. The achieved enhancement level of the dielectric constants of ${\epsilon }^{\prime }$ and ${\epsilon }^{″}$ for the prepared nanocomposites was around 2-fold and 7-fold at a frequency of 0.5 GHz, respectively, as the MWCNT concentration increased up to 0.9%. Regarding the conductivity of the hydrogel nanocomposites, while there is no sudden change in the DC conductivity as the MWCNT concentration has risen to 0.9 wt.% (percolation concentration was not reached), the AC conductivity is enhanced, showing direct proportionality to the increased ${\epsilon }^{″}$ values. The study shows that nanocomposites with MWCNT concentrations greater than 0.7 wt.% show agglomeration, as the ${\epsilon }^{\prime }$ starts to drop due to limitations in the dispersion level of MWCNTs.

Investigating the shielding effectiveness of the hydrogel nanocomposites reveals that, as the concentration of MWCNTs increased from 0 to 0.9 w.%, the total shielding effectiveness increased from 10 dB to 26 dB, which implies shielding more than 90% to 99% of incident EM radiation, respectively. Another important finding of the current study is that the prepared hydrogel nanocomposites show reflectivity and absorptivity ranging from 35% to 60% depending on the frequency, concentration of MWCNTs, and samples’ thickness. This indicates that the shielding effectiveness results from both reflection and absorption mechanisms, each contributing different percentages based on the aforementioned factors.