#### 3.1. XRD Analysis

Figure 1 shows the X-ray diffraction (XRD) patterns of PEO, MC, and PEO:MC blend films. It can be observed that the XRD pattern of pure PEO (

Figure 1a) has two sharp Bragg peaks at 19.15° and 23.35°, which indicates the semicrystalline nature of this polymer [

28]. The XRD pattern of pure MC (

Figure 1f) shows a broad hump around 20.15°, which, according to the literature, indicates an amorphous phase with some order in the intermolecular structure of MC [

23].

From

Figure 1b–e, it can be seen that with incorporation of different concentrations of MC in PEO to form blending, the intensity of the semicrystalline peaks of PEO decreased, indicating the increase in the amorphous phase due to the destruction of the ordered arrangements of the PEO chains. The amorphous enhancement in the PEO:MC polymer blends system will affect the conductivity of the samples. The amorphous phase obtained causes a reduction in the energy barrier of polymer chain segmental motion. Thus, the conductivity increases with an increase in the amorphous domain of the sample [

29]. It can be predicted that the specimen with the maximum amorphous domain exhibits the highest electrical conductivity at room temperature [

30,

31]. To illustrate this enhancement, electrical conductivity analysis was performed on the samples.

This result demonstrates that the PEO:MC polymer blend films shows two-phase morphology, i.e., crystalline and amorphous states. To estimate the crystallinity for all samples and resolve the crystalline peaks, a combination of the scattered intensities can be used. In this method, the percentage of the degree of crystallinity

$\left({X}_{c}\right)$ was obtained from the ratios of the area under the crystalline peak and the corresponding amorphous halos. In order to separate the crystalline and amorphous peaks, the XRD pattern for all polymer blend compositions are deconvoluted using Fityk software (1.3.1, Warsaw, Poland, 2010) [

32], and according to the following equation [

33].

where

A_{c} and

A_{a} are, respectively, the area under crystalline peaks and amorphous halos.

Table 1 shows the center and the full width at half maximum (FWHM) for deconvoluted XRD patterns into Gaussian components for PEO:MC polymer blend films.

Figure 2 depicts deconvoluted and fitted XRD patterns for PEO:MC polymer blend films. It can be observed that the semicrystalline peaks are deconvoluted into four or five Gaussian peaks. The degrees of crystallinity of the films are calculated from the area under the deconvoluted peaks and are tabulated in

Table 1. It is observed that the

${X}_{c}$ value decreases gradually with increasing MC concentration until 40 wt.%, and then increases with further increasing MC concentration, achieving a minimum value of approximately 15.864%. It is clear that the PEO:MC polymer blend with a weight ratio of 60:40 exhibits a significant reduction in the crystalline phase, i.e., this composition has higher amorphicity.

#### 3.3. FTIR Spectroscopy Analysis

The chemical composition and the possible interactions between the functional groups in PEO:MC polymer blend films have been achieved by using FTIR spectroscopy. The complexation occurs between two polymers due to specific intramolecular and intermolecular interactions of polymer chains. The observed changes in the position, shape, and intensity of the IR absorption bands were used as a tool to detect all the materials interacting with each other [

25].

Figure 4 shows the recorded FTIR spectra for all samples in the wavenumber range from 400 to 4000 cm

^{−1}.

In the case of pure PEO, for the distinctive peaks between 800–1400 cm

^{−1} in the spectrum, the stretching vibration peak of C–O–C splits into three peaks at 1146, 1110, and 1062 cm

^{−1}, and the two bands appeared at 1344, and 1359 cm

^{−1} can be ascribed to the bending vibration of CH

_{2} [

35]. These results reveal the existence of high crystallinity in the PEO structure [

36]. However, when different amounts of MC were added to the PEO matrix, the triplet band corresponding to C–O–C stretching vibrations become broader and nearly combine into a single peak at 1067 cm

^{−1}, indicating a reduction of PEO crystallinity as shown in

Figure 5 [

35]. This observation agrees well with the results of XRD studies. From

Figure 4, it can also be noted that the O–C–O bending peaks in pure PEO at 529 cm

^{−1} will disappear with increasing MC; this is another indication of the existence of complexation between PEO and MC molecules [

37].

Figure 6 shows that the C–H aliphatic stretching band for PEO appears at 2889 cm

^{−1}, and this peak was shifted to lower wavenumbers upon blending with different ratios of MC. The observed changes in the position and intensity of the C–H band reveal the change in bond length; hence, complexation takes place between the chains of the two polymers [

25,

26].

The hydroxyl bands (O–H) in the IR spectrum of pure PEO film, pure MC, and their blend films are shown in

Figure 6. The O–H vibrational mode for pure PEO and pure MC are situated at 3520 and 3448 cm

^{−1}, respectively. The position of O–H band of two polymers is comparable with the previous works [

20,

38]. The O–H band of PEO:MC polymer blend films has shifted to 3436, 3437, 3434, 3448 cm

^{−1} for weight ratios 80:20, 60:40, 40:60, and 20:80, respectively. The change in the position and intensity of both O–H and C–H band indicate the formation of hydrogen bonds between the hydrogen atoms in PEO and oxygen atom in MC, or vice versa.

#### 3.4. Impedance Analysis

Impedance spectroscopy is a relatively new, nondestructive, and powerful technique for characterizing the electrical properties of electrolyte materials and their interfaces with conducting electrodes. The complex impedance planes (

${Z}^{\u2033}$ vs.

${Z}^{\prime}$) of the PEO:MC blend samples at different temperatures are shown in

Figure 7, which consist of a single semicircle arc starting from the origin and inclined at different angles to the real axis and the frequency increases from right to left on the arcs. In general, the impedance plots exhibit two noticeable regions: the high-frequency semicircular arc and low frequency tail. For a perfect Debye-type relaxation, a complete semicircle with its center overlapping with the

${Z}^{\prime}$ axis should be observed. The deviation from Debye-type behaviour was expected when detecting a depressed semicircle whose center is below the

${Z}^{\prime}$ axis [

11]. Thus, these plots separate in two regions, which correspond to the electrode polarization effect in the low frequency regions and the bulk material properties in the high frequency regions [

39,

40].

The nature of dielectric material in impedance spectra provides significant information about the contribution of electrode polarization phenomena (EP) (formation of electric double layer between electrodes surfaces and the dielectric material interface) and about the current carriers, whether they are electrons or ions [

40,

41].

From

Figure 7, it is observed that the large values of the imaginary part (

${Z}^{\u2033}$) as compared to the real part (

${Z}^{\prime}$) of the complex impedance confirm a high capacitive behavior of these films, owing to their low conductivity [

42]. Moreover, at low temperatures, all weight ratios of polymer blend samples exhibit nearly straight lines with large slope, suggesting the low conductivity of the samples. With increasing temperature, the curves bend toward the abscissa to form semicircular arcs, and the radii of semicircular arcs become smaller, indicating a higher value of conductivity at higher temperatures. This means that the hopping mechanism could be responsible for the electrical conduction in the present system [

43].

The semicircle arc in the complex impedance plane plots are commonly used to estimate the

DC bulk resistance

${R}_{b}$, of the dielectric material by extrapolating the intercept on the real axis

Z′, then finding the

${\mathsf{\sigma}}_{dc}$ values according to the following equation for all compositions [

41]:

where

$t$ (cm) is the thickness,

$A$ (cm

^{2}) is the electrode–electrolyte contact area, which is 3.14 cm

^{2}, and

${R}_{b}$ is the bulk resistance in ohms.

The total conductivity

${\sigma}_{\omega}$ spectra at different temperature for all samples are shown in

Figure 8, which are calculated by using the following relation [

44]:

According to

Figure 8, two distinct regions could be noted in the

${\sigma}_{\omega}$ spectra; a lower-frequency plateau region corresponding to DC conductivity, and a higher-frequency dispersion region corresponding to power law which has been defined by the Jonscher power law:

The first term (

${\sigma}_{dc})$ is the temperature-dependent (frequency-independent) DC conductivity and accounts for free charge resident in the bulk, while the second term (

${\sigma}_{ac})$ represents the frequency and temperature dependent ac conductivity and accounts for the bound and free charges.

$D$ is the dispersion parameter;

$\omega $ is angular frequency

$\left(\omega =2\mathsf{\pi}f\right)$, and

$s$ is the power law exponent which generally varies between 0 and 1 [

45].

The temperature dependence of conductivity for all complexes is in agreement with the theory founded by Croce et al. [

46], and it is observed that the conductivity increased directly with temperature. This is explained due to the fact that the segmental motion causes an increase in the free volume of the system, which facilitates the movement of charge carriers [

47,

48]. It is well established that the improvement of conductivity with increasing temperature indicates the formation of voids presented by the amorphous area of the polymer blend electrolyte [

49].

Increase in

${\sigma}_{ac}$ with frequency and temperature indicates that there may be charge carriers which are transported by hopping through the defect sites along the film structure [

50]. It suggests that the blending PEO with MC is helpful in improving the electrical conductivity. This phenomenon is explained by investigation of the temperature-dependent DC conductivity

$\left({\sigma}_{dc}\right)$ for all compositions.

In this study, the value of

${\mathsf{\sigma}}_{dc}$ has been attained by extrapolating of the plateau region of the total conductivity

${\sigma}_{\omega}$ in

Figure 8 to the zero frequency

$\left(f\to 0\right)$. The obtained values of

${\mathsf{\sigma}}_{dc}$ for all samples at various temperature ranges are presented in

Table 2. According to Aziz et al. [

24], the estimated

${\mathsf{\sigma}}_{dc}$ from the plateau region of

${\sigma}_{\omega}$ spectra are comparable to the calculated

${\sigma}_{dc}$ values from the bulk resistance

${R}_{b}$. The room temperature DC conductivity for pure PEO and pure MC (

Figure 9) are found to be respectively

$13\times {10}^{-10}S/cm$ and

$1\times {10}^{-10}S/cm$, which are compatible with the reported values in the literature [

39,

51,

52]. The PEO:MC polymer blend with the weight ratio of 60:40 shows the highest room temperature DC conductivity of

$6.55\times {10}^{-9}S/cm$ and this value increased to

$26\times {10}^{-6}S/cm$ at 373 K. It is quite interesting to note that the greatest value of DC conductivity was associated with the minimum degree of crystallinity. This result has been confirmed by XRD and POM analysis. According to Buraidah et al. [

53], increase in conductivity is due to more complexation sites provided by the blending of the two polymers, which is supported by the FTIR result. Hence, there will be more sites for carrier migration and exchange to take place in the amorphous phase of the polymer blend samples [

54].

#### 3.5. Dielectric Studies

Investigation of dielectric properties is another significant source of valuable information concerning electrical conduction processes; thus, the dielectric data for 60:40 weight ratio PEO:MC blend samples with different temperature can be analyzed using tangent loss (Dispersion factor D)

$\mathrm{tan}\text{}\delta $, and complex electric modulus

${M}^{*}$.

Figure 10 shows the variation of tangent loss

$(\mathrm{tan}\text{}\delta \text{}={\epsilon}^{\u2033}/{\epsilon}^{\prime}$) with frequency for PEO:MC blend sample with 60:40 weight ratio, at different temperatures between 303 and 373 K.

The single relaxation peak of

$\mathrm{tan}\text{}\delta $ spectra appeared in

Figure 10 can be used to determine the relaxation time (

${\tau}_{EP}=1/2\mathsf{\pi}{f}_{EP}$), where

${f}_{EP}$ is the relaxation frequency [

55]. The observed shift in the position of the relaxation peak towards the high-frequency side with increasing temperature indicates the decrease of relaxation time, which evidences the increase in electrical conductivity [

56]. Thus, the dominant charge transport mechanism in these samples is mostly hopping of charge carriers among the trap levels situated in the band gap which can be described by the following equation [

57]:

where

${\epsilon}_{o}$ is the permittivity for free space,

${\epsilon}^{\prime}$ is the real part of dielectric constant, and

$\omega $ is angular frequency (

$\omega =2\mathsf{\pi}f$). Pradhan et al. [

58] described that the peak shifting towards higher frequency causes reduction of the relaxation time due to an increase in carrier mobility. It is also obvious that the

$\mathrm{tan}\text{}\delta $ peak heights are increased due to increasing temperature. Parameswaran et al. [

49] reported that the increase in the peak intensity indicates the breaking of bond formation from the dipoles. The peak observed in the

$\mathrm{tan}\text{}\delta $ spectra can also be attributed to the fact that the hopping frequency of the charge carriers is approximately equal to the frequency of the external applied field [

59].

The mechanism of dielectric relaxation has been studied by the complex electric modulus (

${M}^{*}$), which is defined as the reciprocal of the complex permittivity (

${\epsilon}^{*}$) as given by Equation (6). The advantage of this formulation is that the effects of electrode polarization are suppressed so that the electric modulus spectrum mainly reflects the bulk electrical properties of the samples [

43]:

where

${M}^{\prime}$ and

${M}^{\u2033}$ are, respectively, real and imaginary parts of the complex electric modulus. The frequency dependence of real

${M}^{\prime}$ and imaginary parts

${M}^{\u2033}$ of the electrical modulus at different temperatures for the highest conducting sample are presented in the

Figure 11. Based on this plot,

${M}^{\prime}$ increased at the high-frequency end. This increasing trend at a higher frequency may be attributed to the bulk effect. At low frequency,

${M}^{\prime}$ approached zero, indicating that the contribution of electrode polarization is negligible [

24]. On the other hand, the reduction in

${M}^{\prime}$ with increasing temperature is related to the segmental chain motion due to an increase in free volume caused by thermal expansion [

60].

It is also evident from

Figure 11 that the observed dispersion of

${M}^{\prime}$ at higher frequency is accompanied by a loss peak in the

${M}^{\u2033}$ spectra. The asymmetric broadening in the

${M}^{\u2033}$ peak indicates the presence of non-Debye-type relaxation behavior in the present sample. The peak of

${M}^{\prime}\u2019$ can be further analyzed by using the relation shown in Equation (7). The change in peak position suggests temperature-dependent relaxation [

61]; it is clearly seen that with increasing temperature, the

${M}^{\u2033}$ peak shifts towards higher frequency, but the peak height does not significantly change with temperature. This trend could be due to a decrease in the capacitance of the film.

The relaxation function

$\phi \left(t\right)$, which describes the electric filed within the dielectric material, is related to relaxation time by the decay function, given as [

62]:

where

${\tau}_{m}$ is the most probable relaxation time, and

$\beta =1.14/\omega $ is the stretching exponent parameter. Here, ω is the full-width at half-maximum. The value of

$\beta $ is between 0 and 1, and for an ideal Debye relaxation,

$\beta =1$. The smaller the value of

$\beta $, the larger the deviation of relaxation with respect to Debye-type relaxation [

63]. The value of

$\beta $ at different temperatures was calculated from the

${M}^{\u2033}$ spectra in

Figure 11, and the values are tabulated in

Table 3. The obtained values of

$\beta <1$ reflect that the relaxations observed are a temperature-dependent non-Debye relaxation process [

61].