Electrical characteristics of different concentration of silica nanoparticles embedded in epoxy resin

Different characteristics analyses were conducted to confirm the successful preparation of the epoxy nanocomposite using SEM-EDS (MIRA-TESCAN, Czech Republic). SEM-EDS technique was utilized to observe the element distribution of the unfilled and nanocomposite samples. Figure 2 shows the elemental distribution of the unfilled epoxy, showcasing the individual representation silicon (Si). In the unfilled epoxy. Si concentration was found 1.68% of the epoxy components and it exhibited a near-uniform distribution across the entire sample surface. Figure 3 shows the distribution of silicon in the nanocomposite samples. It was also observed that there are large aggregations of silicon in the epoxy composites. These aggregations contribute to the formation of immobilized nanolayers between the silica and epoxy [7]. Table 1 shows weight percentages of silica in the unfilled and nanocomposite epoxy.

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Transmittance spectra of the samples were acquired by vacuum Fourier transform infrared (FTIR) Vertex 70v (Bruker, USA). The silica nanoparticles impact on functional groups of the epoxy resin was investigated using an FTIR spectroscopy. Figure 4 shows the FTIR spectra of pure epoxy and epoxy/SNPs spectra, the assignments for their primary transmittance bands are listed in table 2, which display bands at 3065 cm⁻¹ that are attributed to the C–H stretching mode of the epoxide group [19]. While those at 2957 and 2875 cm⁻¹ are associated with the -CH₂ and -CH₃ stretching vibration modes of aromatic and aliphatic chains, respectively [5, 6, 9]. Some weakly intense bands at 1670 cm⁻¹ show the presence of amine N-H functional groups of amines. The peaks at 1035 and 1570 cm⁻¹ show the imide C–N bonds. Both N-H and C–N bonds are likely from the epoxy resin hardener [8, 20]. The medium to strong transmittance bands located at 1612 and 1507 cm⁻¹ are related to the C=C and C-C stretching vibrations of the phenyl ring [8]. The characteristic transmittance band at 972 cm⁻¹ allows for the identification of the epoxide groups contained in the resin [6, 9]. The sharp band at 830 cm⁻¹ is attributed to the out-of-plane bending of the H-C= vibration occurring in maleimide rings [9]. The bands located at 570 cm⁻¹ and 465 cm⁻¹ were attributed to C–H out-of-plane transmittance of aromatic rings and Cl-C [5, 9], respectively. Finally, the weak peak of Si–OH and O–H bending peak at 3400 cm⁻¹ [5, 6, 21]. As can be observed, the intensity nearly remained unchanged as the concentration of SNPs increased. This indicates that no new bonds were formed between the SNPs and epoxy resin. It is evident from the FTIR data that no bond appeared between silica and epoxy.

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The Raman microscope (Witec Alpha 300R- Oxford WiTec, Germany) was used to monitor the crosslinking response of epoxy resin and SNPs. To prevent any interference from any external light source, all spectrum was obtained without any ambient lighting. At room temperature, the Raman spectra of unfilled epoxy and six samples of epoxy/ SNPs with various concentrations of SNPs were recorded as shown in figure 5. It is evident from the Raman spectroscopy data that no bond appeared between silica and epoxy. Following that, it was determined which chemical groups were involved in the curing reaction.

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Figure 5 illustrates that the epoxide ring vibration band is located at 1452 cm⁻¹ [6, 22] , while the epoxide's vibrations are represented by Raman bands ranging from 1230 cm⁻¹ to 1280 cm⁻¹, these bands overlap other bands, -C-O-C- ether stretch at 1232 cm⁻¹ and the aromatic C-H stretch at 3065 cm⁻¹ [23, 24]. In addition to these bands, the symmetric CH₂ stretching band at 2875 cm⁻¹, associated with the formed link between the amine and epoxy, increases in intensity as the reaction proceeds [24], while the symmetric terminal epoxide =CH₂ stretch at 3010 cm⁻¹ disappears as the cure reaction proceeds [24, 25]. Raman peaks at wavelengths of 1112 cm⁻¹ and 1608 cm⁻¹ can be used to identify the resin backbone (phenyl band) vibrations [22]. Moreover, the C-H out-of-plane bending of the para-disubstituted phenyl group at 638 and 830 cm⁻¹ [24, 25]. Raman shift values for epoxy composite samples are presented in table 3.

Table 3. Raman band assignment of epoxy resin.

Raman shift (cm−1)	Assignment
638 , 830,	C-H out-of-plane bending of the phenyl group
1112 and 1608	Phenyl group
Between 1230 and 1280	Epoxide's vibration
1232	Epoxide vibration overlaps other bands, -C-O-C- ether stretch.
1452	Epoxide ring
2875	Symmetric CH2 stretching
3010	Symmetric terminal epoxide =CH2 stretch
3065	Epoxide vibration overlaps aromatic C–H stretch

Dielectric measurements were carried out on the Novocontrol Alpha-A analyser equipped with Quatro cryosystem by Novocontrol Technologies GmbH & Co. KG, Germany. The measurements were conducted across a wide frequency range spanning from 10⁻² Hz–10⁷ Hz. The duration of a single sweep did not exceed 15 ms and the measurement across the full frequency range with 63 measuring points takes about 35 min. The samples were investigated at room temperature. All samples and the electrode had a diameter of 20 mm and a thickness of 800 μm. A voltage of 1 V_RMS was applied during the measurements.

The number of extant dipoles and their capacity to orient with an applied field at the measurement frequency determine the contribution of oriented dipoles to the measured dielectric permittivity. All dipoles orient in the low-frequency limit, and a high permittivity is seen. There is a decrease in permittivity at high frequencies where the dipoles are unable to obey the applied electric field. The dipolar relaxations are described by the Havriliak–Negami (HN) function, which is composed of the Cole-Cole and Cole-Davidson functions [20, 26], and it can be described as:

$$\begin{eqnarray}&&\hat{\varepsilon }(\omega )={\varepsilon }_{{\rm{\infty }}}+\frac{\unicode{x02206}\varepsilon }{{\left[1+{\left(j\omega \tau \right)}^{\alpha }\right]}^{\beta }}\end{eqnarray} \tag{ 1 }$$

Where $\hat{\varepsilon }$ the complex permittivity, $\unicode{x02206}\varepsilon ={\varepsilon }_{s}-{\varepsilon }_{\infty }.$ ${\varepsilon }_{\infty }$ is the permittivity at infinite frequency also called optical permittivity, ${\varepsilon }_{s}$ is the static permittivity at zero frequency, α describes the flatness/width of the maximum, β expresses the skewness (asymmetry) of the complex dielectric permittivity, where α $\lt 1$ and 0 < β ≤ 1, these parameters show the changes in the relaxation time distribution. ω is the angular frequency and τ is the relaxation time. The complex permittivity can be decomposed into the real ε'(ω) and imaginary ε''(ω) parts as follows [26–28]:

$$\begin{eqnarray}&&{\rm{\varepsilon }}^{\prime} (\omega )={\varepsilon }_{\infty }+\frac{\unicode{x02206}\varepsilon \cos (\beta \unicode{x000D8})}{{\left[1+{2\left(\omega \tau \right)}^{\alpha }\cos \left(\frac{\pi \alpha }{2}\right)+{\left(\omega \tau \right)}^{2\alpha }\right]}^{\beta /2}}\,\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\rm{\varepsilon }}^{\prime\prime} (\omega )={\varepsilon }_{\infty }+\frac{\unicode{x02206}\varepsilon \sin (\beta \unicode{x000D8})}{{\left[1+{2\left(\omega \tau \right)}^{\alpha }\cos \left(\frac{\pi \alpha }{2}\right)+{\left(\omega \tau \right)}^{2\alpha }\right]}^{\beta /2}}\end{eqnarray} \tag{ 3 }$$

The energy dissipation of dielectric material during the application of an electric field is measured by the dielectric loss factor. Both the ${\rm{\varepsilon }}^{\prime\prime} (\omega )$ and the tan(δ) are zero in the ideal condition [20]. In the case of the capacitor made by two plates separated by an epoxy nanocomposite, the dielectric loss factor is given by the ratio of the imaginary part and the real part of permittivity, and it can be written as [28] :

$$\begin{eqnarray}&&\tan {\rm{\delta }}=\frac{\varepsilon ^{\prime\prime} (\omega )}{\varepsilon ^{\prime} (\omega )}=\frac{{\left(\omega \tau \right)}^{\alpha }\sin (\beta \unicode{x000D8})}{1+{\left(\omega \tau \right)}^{\alpha }\cos \left(\frac{\pi \alpha }{2}\right)}\end{eqnarray} \tag{ 4 }$$

According to figure 6(a), the addition of 1 wt% and 3 wt% SNPs to epoxy led to the formation of easily polarizable bonds when subjected to an electric field. This contributes to increasing the relative permittivity of the epoxy/1 wt% and 3 wt% SNPs samples more than the relative permittivity of unfilled epoxy. However, the relative permittivity value started dropping when the SNPs concentration in the epoxy was raised to 5 wt% [5, 10]. This behaviour can be attributed to the interaction between the SNPs and polar groups within the epoxy, resulting in the formation of an immobilized nanolayer. However, at 5 wt% SNPs, the mobility of the polymer close to the immobilized nanolayers is not significantly affected due to the large average distance between the particles, but the relative permittivity value continues to decrease. In the case of 10 wt% and 15 wt% concentrations of SNPs, a noticeable reduction in the average interparticle distance. This decrease in interparticle distance hindered the mobility of epoxy chains between the silica nanoparticles (SNPs), consequently promoting the formation of an immobilized nanolayer. As a result, a significant decrease in relative permittivity was observed. In addition, the space charge polarization contributes to the reduction of the permittivity, where it arises due to the polarization between the base resin and the nanoparticles resulting from the accumulation of space charges within the resin system [5, 27, 29]. But since interfacial polarization occurs in the lower frequency bands up to 10³ Hz, it can be ignored.

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A distinct rise in dielectric permittivity was observed at an SNPs concentration of 20 wt%. This sudden increase in active permittivity can be explained by the logarithmic Lichtenecker-Rothe mixing rule': where the permittivity of the resulting nanocomposites is more significantly influenced by the permittivity of the filler as the loading concentration increases. The logarithmic Lichtenecker-Rothe mixing rule can be written as [5, 27]

$$\begin{eqnarray}&&\mathrm{log}\,{\varepsilon }_{c}=a\,\mathrm{log}\,{\varepsilon }_{e}+b\,\mathrm{log}\,{\varepsilon }_{s}\end{eqnarray} \tag{ 5 }$$

where, ${\varepsilon }_{c}$ is the relative permittivity of the epoxy nanocomposite, ${\varepsilon }_{e}$ is the permittivity of epoxy, ${\varepsilon }_{s}$ is the permittivity of silica, while a and b are the concentrations of epoxy and silica, respectively. Since the permittivity of silica is higher than that of the epoxy resin [10], this may be one of the factors that led to high permittivity at higher concentration loading. Furthermore, percolation theory, which is considered a typical theory in polymer nanocomposites, can be employed to explain this phenomenon [16, 30, 31]. The dielectric permittivity of epoxy nanocomposites near the percolation threshold can be described by equation (6) as follows [16, 32]:

$$\begin{eqnarray*}&&{\varepsilon }_{{eff}}\propto {\varepsilon }_{{epoxy}}{\left({f}_{c}-f\right)}^{-S}\,{for}\,f\lt {f}_{c},\end{eqnarray*}$$

where ${\varepsilon }_{{eff}}$ is the effective permittivity, ${\varepsilon }_{{epoxy}}$ dielectric permittivity of the matrix, f is the volume fraction of the filler, ${f}_{c}$ is the percolation threshold and s is the critical exponent. As expected, the dielectric properties of the epoxy nanocomposite show a typical percolation transition behaviour as the mass fraction of SNPs in the epoxy matrix increases. The approximate percolation threshold for the epoxy/SNPs nanocomposites is near 20 wt%.

Figure 6(b) depicts the imaginary part of the relative permittivity as it appears in composite samples. At frequencies lower than 10 Hz, the increase in the imaginary part of the relative permittivity is due to interfacial polarization. It turned out that the addition of SNPs up to 5 wt% increased the number of electric dipoles, leading to an increase in interfacial polarization. Consequently, this led to an increase in the imaginary part of the relative permittivity. The formation of immobilized nanolayers was observed to reduce the value of the imaginary relative permittivity, for samples epoxy/10 wt% of SNPs and epoxy/15 wt% of SNPs, due to the obstruction of the immobilized nanolayers to the movement of space charges. However, increasing the concentration of SNPs to 20 wt% led to a rise in the ${\rm{\varepsilon }}^{\prime\prime} (\omega )$ value which can be explained by the mixing rule. At high frequencies, the peaks observed at 10⁶ Hz in figure 6(b) are associated with the β-relaxation, which is indicative of the motion of dipolar species generated during the curing process. It was observed that the position of relaxation peaks did not change with the increase of the filler concentration.

Additionally, figure 6(c) shows the variation in loss factor (tan δ) value for both epoxy nanocomposites and unfilled epoxy. The tan δ value of epoxy/SNPs and unfilled epoxy sample dropped at higher frequency ranges. The unfilled epoxy and epoxy/SNPs exhibited a minimum value of tan δ at approximately 100 Hz. After this point, the tan δ values began to rise until they reached their maximum values around 10⁶ Hz. The tan δ value of unfilled epoxy is lower than that of epoxy/SNPs samples in the lower frequency range (less than 100 Hz) except for epoxy/15 wt%. At 20 wt% of SNPs concentration, owing to the formation of electrical paths in the epoxy matrix, the dielectric loss also increases near the percolation threshold, whereas the β-relaxation property of net epoxy resin predominates in the fluctuation in the range of 10⁶ Hz [16].

Figure 6(d) shows the relationship between ε'(ω) and ε''(ω) using Cole—Cole diagram for all epoxy nanocomposites samples. The results indicate depressed semicircles with dispersed relaxation times and non-Debye behaviour. The complex permittivity plot ε'(ω) versus ε''(ω) is known to be significantly distorted at its low-frequency region for materials with high DC conductivity [33].

The semicircle is attributed to the bulk relaxation process, and it indicates the presence of a capacitive component. The semicircle is followed by a linear increase for all epoxy nanocomposite samples. Moreover, the line is ascribed to electrode polarization on the interface between the sample and the electrodes where the conductivity increases for the material [34]. Table 4 shows the frequency value at which epoxy nanocomposites are converted into a conductor.

Due to constraints on the generation of mobile charge and the movement of charge carriers in polymer dielectrics, which are caused by the presence of SNPs inside epoxy, the electric conductivity will decrease, especially at lower frequencies where the conductivity will be more crucial. Thus, the electrical conductivity of SNPs is a crucial factor in changing the value of $\tan \delta$ in the low-frequency range. The real part of the conductivity $\sigma ^{\prime} (\omega )$ can be expressed as [35, 36]:

$$\begin{eqnarray}&&{\rm{\sigma }}^{\prime} \left(\omega \right)=\omega {\varepsilon }_{0}\varepsilon ^{\prime\prime} \left(\omega \right)\end{eqnarray} \tag{ 6 }$$

The epoxy/1 wt% SNPs sample in figure 7 shows the highest conductivity values, due to the increased space charges within the sample. The value of conductivity begins to decrease gradually, starting from a concentration of 3 wt% due to the restriction of the mobility of space charges. At a concentration of 5 wt% SNPs, immobilizer nanolayers begin to form, consensually, decreasing epoxy nanocomposite conductivity. Also, at a concentration of 15 wt% SNPs, the conductivity of the epoxy nanocomposite is less than the conductivity of the unfilled epoxy due to the significant increase in the formation of immobilized nanolayers.

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The conductivity of the epoxy/20 wt% SNPs sample suddenly increased to a value higher than that of the unfilled epoxy, due to the formation of the conductive pathway. At the 20 wt%, which represents the concentration threshold, the fillers were unable to effectively establish full contact with each other, resulting in a limited increase in conductivity compared to the unfilled epoxy. Due to their insulating nature, the conductivity curves show a strong dependence on the frequency.

It is expected if the filler concentration rises to 30 wt% or more, the conductivity further increases, and an insulator–semiconductor transition will be observed. This is caused by the formation of effective physical electrical pathways in the composites. At this filler loading content, the composites exhibit a conducting feature that is nearly frequency independent. This conclusion is supported by the literature [15, 16].

Based on figure 7, all epoxy nanocomposite results exhibit two threshold frequencies, f₁ and f₂, which divide the entire variance into three regions. The frequency response of conductivity can be interpreted in terms of the jump relaxation model [37–40]. This model explains the mechanism of ion transport in a dielectric material, where the frequency dependence is related to relaxation processes of the jumping ions environment [37, 38]. At low-frequency region, when f < f₁, the conductivity is almost frequency-independent (${{\boldsymbol{\sigma }}}_{{\boldsymbol{DC}}})$ [39]. And the ${{\boldsymbol{\sigma }}}_{{\boldsymbol{DC}}}$ is a few orders of magnitude less than the AC conductivity (${{\boldsymbol{\sigma }}}_{{\boldsymbol{AC}}}).$ This is because the ${{\boldsymbol{\sigma }}}_{{\boldsymbol{DC}}}$ is determined by the most complex transition in complete percolation channels between the electrodes. Whereas ${{\boldsymbol{\sigma }}}_{{\boldsymbol{AC}}}$ is governed by the easiest local movement of the charges [40].

At moderate frequencies region, where ${{\boldsymbol{f}}}_{{\bf{1}}}\lt {\boldsymbol{f}}\lt {{\boldsymbol{f}}}_{{\bf{2}}}$ the conductivity rises linearly with the frequency. This shows that the translational hopping motion corresponds to the conduction mechanism in this area [39, 40]. At high frequencies region, where ${\boldsymbol{f}}\gt {{\boldsymbol{f}}}_{{\bf{2}}},$ the conductivity increases linearly with the frequency. This demonstrates that the well-localized hopping and/or reorientation motion corresponds to the conduction mechanism in this range of frequencies [39, 40].

Impedance is the resistance to alternating current (AC) flow in a complex system. A passive complex electrical system includes two elements, the energy dissipator (resistor) and energy storage (capacitor). In this work resistor and capacitance were connected in series. Impedance is a complex quantity because the current has a different phase than the applied voltage and it can be represented by the following formula [35]:

$$\begin{eqnarray}&&Z=Z^{\prime} +{iZ}^{\prime\prime} \end{eqnarray} \tag{ 7 }$$

where $Z^{\prime}$ is the real part impedance and $Z^{\prime\prime}$ is the imaginary part impedance and both can be written as [41]:

$$\begin{eqnarray}&&Z^{\prime} =\frac{R}{1+({\omega \tau )}^{2}}\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&Z^{\prime\prime} =\frac{\omega \tau R}{1+({\omega \tau )}^{2}}\end{eqnarray} \tag{ 9 }$$

where τ is the relaxation time (τ = RC), and ω is the angular frequency. Figure 8 exhibits frequency-dependent plots of log |Z''| as a function of frequency. From figure 8(a), it can be depicted that the value of Z' declines with the increase in frequency. The impact of free charges on impedance becomes noticeable below 0.1 Hz, as it appeared in figure 8(a). It can be depicted that the value of Z' declines continuously with the decrease in frequency. Moreover, the impedance value decreased to its lowest level when the filler concentration was 1 wt% SNPs even lower than the impedance value of the unfilled epoxy. At 3 wt% and 5 wt% of SNPs concentration, the impedance gradually starts to rise, but it continues to be lower than that of the unfilled epoxy. So, it can be concluded that when the concentration of silica filler is less than 5 wt%, there is an increase in space charges as explained earlier, which decreases the impedance value, signifying an increase in conductivity [42]. Whereas, when increasing the filler concentration between 10 wt% and 15 wt%, an increase in the resistivity value due to the formation of immobilized nanolayers that limit charge polarization, as detailed previously. The effects of the mixing rule and percolation threshold become evident in the case of a 20 wt% concentration, manifesting as an increase in impedance value. Nevertheless, a concurrent rise in conductivity is observed. These findings in the present section are consistent with the results presented in section 3.1 pertaining to permittivity and conductivity.

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Figure 8(b) shows the frequency dependence of Z' and reveals a transition between capacitive and ohmic behaviour. A linear increase at high frequency is followed by a small quasi-constant plateau at low frequency. Additionally, as filler concentration rises, the plateau's shift towards the high-frequency band suggests modifications to the electrical characteristics and ionic behaviour [42]. Generally, this result is matched with the results for the imaginary part of permittivity obtained in section 3.1.

When examining the capacitance response to frequency variations it was as depicted in figure 9. Based on the figure, capacitance depends on variations in the epoxy nanocomposite's permittivity value. Due to the enhanced permittivity (see figure 6(a)), the capacitance values at 1 wt% and 3 wt% of SNPs increased and are greater than those of the unfilled epoxy. However, at concentrations of 3 wt%, 5 wt% and 10 wt% of SNPs the capacitance value continued to fall, and at 15 wt% of SNPs, it nearly reached the capacitance value of unfilled epoxy. The high value of capacity at low frequencies may be attributed to space charge polarization.

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It is important to note that the capacity dramatically increased when the filler concentration reached 20%, which is a result of the rise in permittivity at this concentration, despite the increased conductivity. That was covered in section 3.1.

The dielectric constant of a substance or material signifies its ability to store electrical energy. It quantifies how much electric flux a substance can store or concentrate. Mathematically, the dielectric constant is defined as the ratio of a material's capacitance ${(C}_{M})$ to the capacitance of free space ${(C}_{0}),$ as in equation (10). Additionally, it serves as the electrical equivalent of relative magnetic permeability [43].

$$\begin{eqnarray}&&\varepsilon ^{\prime} =\frac{{C}_{M}}{{C}_{0}}=\frac{{C}_{M}d}{A{\varepsilon }_{0}},\end{eqnarray} \tag{ 10 }$$

where ${\varepsilon }_{0}$ the permittivity of the free space, d is the distance between the electrode, and A is the area of the electrode. The dielectric constant values are calculated by putting the values ${\varepsilon }_{0}$ = 8.854 × 10⁻¹² CV⁻¹ m⁻¹, A = 12.56 cm² and d = 800 μm. Using equation (10), the values of the dielectric constant are determined. Table 5 shows the capacitance and dielectric constant values for all samples at room temperatures at frequency of 10⁻² Hz.

Table 5. Shows the capacitance and dielectric constant values for all samples at room temperatures, at a frequency of 10⁻² Hz.

Sample	Unfilled	Epoxy/ 1 wt% SNPs	Epoxy/ 3 wt% SNPs	Epoxy/ 5 wt% SNPs	Epoxy/ 10 wt% SNPs	Epoxy/ 15 wt% SNPs	Epoxy / 20 wt% SNPs
${{\bf{C}}}_{{\bf{M}}}({\bf{pF}})$	0.13	0.19	0.22	0.2	0.15	0.12	0.27
${\boldsymbol{\varepsilon }}^{\prime}$	4.5	6.7	7.9	7.3	5.9	4.4	9.7

In the frequency domain, the complex electrical modulus and complex electrical permittivity are related by the following [1]:

$$\begin{eqnarray}&&\hat{M}\left(\omega \right)=\frac{1}{\hat{\varepsilon }(\omega )}=M^{\prime} \left(\omega \right)+{iM}^{\prime\prime} \left(\omega \right)\end{eqnarray} \tag{ 11 }$$

The real ${M}^{{\prime} }\left(\omega \right)$ and imaginary ${M}^{{\prime\prime} }\left(\omega \right)$ part of the complex electrical modulus is calculated using the following relation [41, 43]:

$$\begin{eqnarray}&&M^{\prime} \left(\omega \right)=\frac{{\rm{\unicode{x003AD}}}(\omega )}{{\left({\rm{\unicode{x003AD}}}\left(\omega \right)\right)}^{2}+{\left({\varepsilon }^{\prime\prime} \left(\omega \right)\right)}^{2}}\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&M^{\prime\prime} \left(\omega \right)=\frac{{\rm{\unicode{x003AD}}}^{\prime} \,\left(\omega \right)}{{\left({\rm{\unicode{x003AD}}}\left(\omega \right)\right)}^{2}+{\left({\varepsilon }^{\prime\prime} \left(\omega \right)\right)}^{2}}\end{eqnarray} \tag{ 13 }$$

Figure 10. Depict the frequency-dependent electric modulus M' and M'', respectively, of both unfilled epoxy and epoxy/SNPs composites as a function of frequency.

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Figure 10(a) illustrates the real part of the modulus. The epoxy with a 1% filler content exhibits a lower modulus value compared to the unfilled epoxy. The minimum modulus value is observed at a filler content of 3%. Thereafter, the modulus value exhibits a steady increase as the filler concentration escalates to 5%, culminating in its peak value at a filler concentration of 20%.

The imaginary part of the electric modulus spectra is shown in figure 10(b). Very clear relaxation peaks are seen in the M'' spectra for samples at 10⁶ Hz. Since ions are largely immobilized due to constrained chain segment motions at room temperature, ion polarization can be excluded. In addition, considering the fact that the relaxation also occurs in pure epoxy resin, Maxwell–Wagner interfacial polarization due to charge accumulation at heterogeneous contacts can be ruled out. Therefore, the relaxation process should be ascribed to the orientation of small polar groups such as those in side chains or side groups. The polar entities can be residual amines -NH2- and -NH-, hydroxyl, epoxide rings, and other possible dipolar species [44].

The significant increase in the M in epoxy/SNPs at 10⁶ Hz is attributed to the common effects of hopping conductance loss, dipole polarization loss and microscopic interface polarization loss [44]. This can be seen in samples of epoxy/10 wt% of SNPs and epoxy/15 wt% of SNPs due to the formation of nucleated immobilized nanolayers. In other words, the material becomes more insulating. Finally, a noteworthy reduction in M'', static dielectric interfacial polarizability, static dielectric dipolar polarizability, and hopping conductivity is observed upon the addition of both low concentration (epoxy/1 wt% and epoxy/3 wt% SNPs) and high concentration (epoxy/20 wt% SNPs) of SNPs. This observation can be attributed to the presence of space charges and the formation of conductive pathways, ultimately resulting in increased material conductivity.