3.3. X-ray Diffraction (XRD) Analysis
The XRD patterns indicate that the MWCNTs are embedded into the PPy nanocomposite. Furthermore, no significant peak shifts were observed in the XRD patterns.
Figure 2 presents the pattern XRD for the experimental and simulated for PPy/MWCNTs composite. When spinning doped, the MWCNTs can be incorporated into the PPy crystal lattice. The XRD pattern obtained from the fabricated PPy/MWCNTs composites thin films. They were correlated to the isolated system matrix. The predicted crystallite size (D) and miller index (hkl) depend on the absolute values of full width at half maximum (FWHM) as given in
Table 2. The data in database code amcsd 0020475 corresponds well with the interplanar distances d spacing [
37]. The TDDFT-DFT and Crystal Sleuth Microsoft programs were used to designate peak lines calculated by diffraction that were close to the observed findings. The Debye–Scherrer formula was applied to assessed XRD for [PPy/MWCNTs]
^{0–3} thin films, the range of 5 ≤ 2θ ≤ 45 with
$1/dhkl=0.06{\u212b}^{-1}-0.74{\u212b}^{-1}$,
$\lambda =1.54\u212b$,
${I}_{2}/{I}_{1}=0.5$, polarization = 0.5, and Pesedo-Voigt function. From Scherer’s formula:
where λ is the X-ray wavelength (1.54 Å). As presented in
Table 2, for the fabricated [PPy/MWCNTs] composites thin films XRD data from the XRD pattern was used to examine factors and features such as FWHM, the crystallite size (D), hkl indices, d-spacing (d), and peak intensity. The crystallite size is
${D}_{av}=62.26$ nm was within the range of 32.49–144.87 nm. Polymorph calculated the theoretical X-ray diffraction models using content studio software (version 7.0) (See
Figure 2). Inset
Figure 2, the integrals were conducted on the Brillouin zone with 2 × 2 × 1 (Polymorph PPy/MWCNTs composites). For the corresponding experimental, a comparison was made between experimental X-rays structures and measured PXRD patterns for PPy/MWCNTs composites thin films. While both experimental and PXRD models the intensity and location of specific peaks vary only slightly, the emphasis here is mostly on their overall resemblance. Only the important comparison characteristics between the measured and the experimental data should therefore be evaluated. It is also known that instrumentation and data collection processes are only two of the many variables that can affect the experimental PXRD pattern. The simulated PPy/MWCNTs composites as isolated position in polycrystalline and provide a triclinic in the group P
$\overline{1}$. For PPy/MWCNTs composites thin films, the main peaks at hkl (1
$\overline{1}$1), hkl (021), hkl (004), and hkl (
$\overline{1}\overline{1}$2) at 2θ values of 17.54°, 18.30°, 20.04°, and 20.38°, respectively. A full assessment demonstrating a good agreement between the calculated PXRD patterns and the experimental patterns for PPy/MWCNTs composites thin films, validating the accuracy of the fabricated material’s PXRD patterns. As presented in
Figure 2, a combination of experimentally based diffraction and density functional theory calculations yields a great estimation of the atomic scale for PPy/MWCNTs composites thin films (2θ at hkl (1
$\overline{1}$1).
3.4. Geometric Study
For
Figure 3a–f, the similarity of physical-chemical properties of the gaseous phase of PPy/MWCNTs composites was investigated using electrostatic potential and electron density [
38,
39]. DFT concepts
Figure 3a,d, that use electron density as an essential operator for the assessment of isolated state of PPy/MWCNTs composites gas-phase electron systems, respectively.
Figure 3b,e explains potential diagrams demonstrating significant potential growth for PPy/MWCNTs composites gas-phase potential, respectively. It supports the possibility of electron transfer to PPy/MWCNTs composites in the gas phase to compute the electrostatic potential (MEP) according to its surface density.
Figure 3c,f showing 3D images of the active site of the MEP during the PPy/MWCNTs composites isolated molecules, respectively. The colors blue and red demonstrate the areas advantageous for nuclear and electrical attacks. In isolated molecule phase, the potential range [P] of the PPy/MWCNTs composites matrix is 2.436 ≥ [P] ≥ −1.046 × 10
^{−1} and 1.257 × 10
^{−1} ≥ [P] ≥ −1.997 × 10
^{−1} the color order: red < brown < blue [
40,
41]. The MEP diagram shows potential negative areas of positive potential for hydrogen atoms. The blue hue represents the most attraction, while the red color represents the most repulsion [
42,
43]. The single electronegative atom pair was aligned with negative V regions (r). The oxygen atoms of the anion of nitrogen were detected in the examined molecule in negative regions, while maximal positive regions in pyrazine2-one are local to protonated groups (–N(H)–C=C=C–N(CH)–), which may be regarded as possible nucleonic attack sites with a maximum value of +3.87 a.u. According to the following computations, the MEP map showed negative potential locations for N-atoms and positive potentials surrounding the H-atoms. These websites offer a valuable understanding of the intermolecular interactions of the chemical. The presence of intermolecular hydrogen bonding is, therefore, confirmed in
Figure 3c,f.
The measured
$\Delta {E}_{g}^{Opt}$ values were based on the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) theory discrepancy by utilizing the DMol
^{3}/DFT procedure as shown in insert
Figure S5.
The boundary molecular orbits in the molecular orbit (FMOs), also known as HOMO and LUMO, are important parameters in quantum chemical simulations for complex analysis (insert
Figure S4). The computed energy
${E}_{HOMO}$,
${E}_{LUMO}$ and
$\Delta {E}_{g}^{Opt}$ are presented in
Table 3. The following equations were used to compute the reported values of the chemical potential, global hardness, electronegativity, global softness, global electrophilicity index, softness, and the maximum quantity of electronic charge [
44].
The negative values of
${E}_{HOMO}$ and
${E}_{LUMO}$ energies can be ascribed to product stability for the [PPy/MWCNTs]
^{0–3} matrix. Coordination position simulation was considered for the highest magnitude molecular orbital coefficients. The electrophilicity index (t), which evaluates energy stability when the device receives an additional electronic charge, is a critical quantum chemical feature [
45].
3.5. Optical Properties
The observation of the absorption edge in the ultraviolet field will explain crystalline/non-crystalline materials’ optical transitions and electronic band structures.
Figure 4. demonstrates the PPy/MWCNTs composites thin films absorbance (a) which was computed for the normal incidence of light within a wavelength range 380 ≤ λ ≤ 1000 nm at room temperature (298 K). The relation between the absorption coefficient (α) and the transmittance (T) of a sample is
$\alpha =1/dln\left(1/T\right)$, where d is the thickness (d ≅ 75 ± 3 nm). The values of the absorption coefficient (α) for the [PPy/MWCNTs] composites are calculated by using the following equation:
where
A,
E_{g}_{,} and
n are a constant that is based on the transition probability, the band gap’s width and an index characterize the optical absorption processes in the PPy/MWCNTs composites thin films, respectively [
46]. Non-linear optical effects influence a new field that changes the point, λ(nm), amplitude, or other incident fields transmission as a result of the electromagnetic fields’ relationships with different media. Non-linear optical has an important role in new applications including networking, optical links, and signal processing as the main roles of optical interference. The UV-Vis spectra, at the wavelength range (λ) 300 ≤ λ ≤ 1200 nm of the PPy/MWCNTs composites nanocomposite thin films are illustrated in
Figure 4. For PPy/MWCNTs composites as-deposited thin films, in the first region, at a wavelength (λ) region 300 ≤ λ ≤ 705 nm the absorption bands are associated to n→π* electronic transition. The bands at 433, 57, 606, and 653 nm are associated with the electronic transitions from HOMO to LUMO for PPy/MWCNTs composite thin films, respectively. In the second region, at a wavelength range (λ) 705 ≤ λ ≤ 1200 nm, the absorption bands are associated with π→π* electronic transition. Likewise, the absorption bands at 775, 791, and 816 nm are associated with the electrons’ transition from valence orbital to conduct orbital for PPy/MWCNTs composites thin film as experimental parts. The UV-Vis spectra, at the wavelength range (λ) 550 ≤ λ ≤ 2900 nm of the [PPy/MWCNTs] in an isolated gaseous state as simulated part (DMOl
^{3}/DFT) is illustrated in
Figure S3. The results of the PPy/MWCNTs in an isolated gaseous state as simulated part (DMOl3/DFT) are in good agreement with PPy/MWCNTs composites thin film which is presented in
Figure 4.
The absorption spectrum curve Abs. (λ) was used to measure the band-gap energy of the [PPy/MWCNTs] composites nanocomposite thin film. Tauc’s interaction is used to evaluate the values of (
$\alpha h\nu {)}^{A}$ as
from Abs. (λ) curve, where
${\u03f5}_{E}^{Ind.}$ and
$h\nu $ are the energy-independent constant and the incident photons energy, respectively [
47]. The value A = ½ for indirect transitions (
${E}_{g}^{Dir})$ and 2 for direct allowed (
${E}_{g}^{Ind.}$) transitions. The expression
$\alpha =Abs./d$ was utilized to evaluate the coefficient of absorption (α), where
d is the thickness of the film. The
${E}_{g}^{Dir}$ and
${E}_{g}^{Ind.}$ transitions for the PPy/MWCNTs composites thin film were assessed by applying Tauc’s equation. Davis and Shilliday suggested that the direct transition (
${E}_{g}^{Dir})$ and indirect transition (
${E}_{g}^{Ind.}$) can be determined by plotting (
$\alpha h\nu {)}^{2}$ and (
$\alpha h\nu {)}^{0.5}$ as a function of photon energy (
$h\nu $) close in the Abs. (λ) curves to zero absorption, respectively. The indirect energy values are 2.413, 1.549, 1.502, and 1.475 eV for PPy/MWCNTs composites, whereas these values of PPy/MWCNTs composites nanocomposite thin films decreased from 2.413 eV to 1.475 eV with increasing the molar ratio of MWCNTs. This decrease in
${E}_{g}^{Ind.}$ is because of increased disruption, which allows the electrons transformation from the valence band to the conductive band. Adding the MWCNTs decreased the bandgap as shown in
Figure 5. As shown in inset
Figure S4, the value of
${E}_{g}^{Opt}=2.888eV$ was assessed by applying the DMol
^{3} process in DFT based on the discrepancy between HOMO and LUMO for free polypyrrole PPy. For
Figure S4, the direct energy values are 2.648, 1.553, 1.503, and 1.48 eV for the [PPy/MWCNTs] composites, whereas the value of energy gaps for PPy/MWCNTs composites thin film decreased from 2.648 eV to 1.480 eV with increasing the molar ratio of MWCNTs. This decrease in
${E}_{g}^{Dir.}$ is because of increased disruption, which allows the electrons transformation from the valence band to the conductive band. As shown in inset
Figure 5, the value of
${E}_{g}^{Opt}=1.58eV$ was assessed by applying the DMol
^{3} process in DFT based on the discrepancy between HOMO and LUMO for PPy/MWCNTs composites in an isolated state. The results of the simulations by using DFT/DMOl
^{3} and experimental data (
Figure 4 and
Figure 5) are well agreed. The equation of Tauc`s and the
${E}_{g}^{Opt}$ obtained can be used to evaluate electrical and energy transfer methods effectively.
The refractive index
n(λ) is an important physical factor for a microscopic atomic interaction, which is important for polymer solar cells as well. (
n) and (
k) values can be calculated by applying reflectance (
R) according to the following equations [
48]:
where (
n) is the real part of the refractive index.
Figure 6a–c reveals the dependence of
n(
λ) and
k(
λ)on photon energy (
hν). As shown in
Figure 6a at (
hν) = 1.52, 1.56, 1.59, and 2.88 eV, the maximum values are 1.82, 1.71, 1.66, and 1.49 for
n(
λ) behavior of PPy/MWCNTs composites, respectively. From the these results, it can be concluded that the refractive index (
n) is increased with increase the amounts of MWCNTs at the photon energy value (
hv) = 3.938 eV, then (
n) exhibited an increment again by increasing the wavelength until it reaches an approximate value of 1.94 at photon energy
$hv=1.52$ eV. The absorption index
k(
λ) exhibited the same behavior at the same photon energy value
$\left(hv\right)$, and four peaks were observed with a maximum value of
k(
λ) = 4.82 × 10
^{−8}, 2.99 × 10
^{−8}, 2.44 × 10
^{−8} and 2.88 × 10
^{−9} which corresponds to the π→π* benzenoid rings transition for [PPy/MWCNTs] composites, respectively. From the behavior of PPy/MWCNTs composites in
Figure 6b, the intensity of four peaks observed is increased with an increase in the molar ratio of CNTs, respectively. From the behavior of the simulated nanocomposite PPy/MWCNTs composites as the isolated state in
Figure 6c, the CASTEP/DFT computations were used to evaluate
n(
λ) and
k(
λ) values and compared to the experimental values, simulated values are close to those achieved by DFT with the CASTEP model.
According to the single oscillator model, the dispersion curve can be described by dispersion (
${E}_{d}$) and oscillating energy (
${E}_{0}$) [
49];
The
${\left({n}^{2}-1\right)}^{-1}$ is characterized as (
$h\nu $) (
Figure 7a).
Table 4 demonstrates typical dispersal parameters (
${E}_{d}$ and
${E}_{o}$), from both the slope and the linear fit of the high-frequency field. The high-frequency dielectric constant is related to the contribution produced by the electronic polarization process to [PPy/MWCNTs]
^{0–3} total dielectric reaction. The oscillator strength can be computed
$f={E}_{0}$ and demonstrated in
Table 4. The high-frequency dielectric constant can be computed as follows:
The relationship of
${n}^{2}$ vs.
${\lambda}^{2}$ is demonstrated in
Figure 7b. To measure both the ratio (
$N/{m}^{*}$) and
${\epsilon}_{\infty}$, the slope and extrapolate can be employed in the resulting linear fittings. In addition, two significant periods like the one-oscillator parameters
${M}_{-1}$ and
${M}_{-3}$ depend on
${E}_{0}$ and
${E}_{d}$ as the following formula [
50]:
and
To identify a single oscillator approximation to the dielectric response of the material and find the average bond strength, these moments are estimated. These optical moments are also compared to macroscopic numbers as the effective dielectric constant, effective value of electrons in the substance studied [
51]. The computed
${M}_{-1}$ and
${M}_{-3}$ values of [PPy/MWCNTs]
^{0–3} thin films are demonstrated in
Table 4. The low
${M}_{-1}$ and
${M}_{-3}$ values provide the signal for low polarization of the examined material. The averaged wavelength (λ
_{0}) of the interband oscillator and the average intensity of the oscillator (
S_{0}) can be estimated by a single Sellmeier oscillator at low energy:
since λ
_{0} and
${S}_{0}$ values can be achieved from the slope and intercept of plotting
${({n}^{2}-1)}^{-1}$ against
${\left(\lambda \right)}^{-1}$ curve as demonstrated in
Figure 7c and tabulated in
Table 4.
The difference between ε
_{1}(λ) and ε
_{2}(λ) as a function of photon energy (hν) exposes various correlations with electrons and photons observed in PPy/MWCNTs composites as-deposited thin film. For PPy/MWCNTs composites as the deposited thin film, the n(λ) values are determined to achieve the lattice constant of a dielectric as the following formulas:
and
where the coefficient of extinction k(λ) is gained from the relation:
The real ε
_{1}(λ) and ε
_{2}(λ) imaginary dielectric constants are used to illustrate the media’s response spectra to electromagnetic radiation incidents [
52]. Furthermore, for both status compositions, the computed ε
_{1}(λ) is higher than the computed ε
_{2}(λ). For PPy/MWCNTs composites, in the experimental part (
Figure 8), the ε
_{1} (λ) show the maximum values of 2.22, 3.33, 2.92, and 2.72 for PPy/MWCNTs composites at the photon energy value of 1.52, 1.56, 1.59 and 2.88 eV, respectively. The ε
_{2}(λ) show the maximum values of 1.74 × 10
^{−7}, 1.02 × 10
^{−7}, 8.13 × 10
^{−8} and 1.72 × 10
^{−8} for PPy/MWCNTs composites at the same photon energy value of ε
_{1} (λ), respectively. The high value of the computed ratio
${\epsilon}_{1}\left(\lambda \right)/{\epsilon}_{2}\left(\lambda \right)=1.91\times {10}^{7}$ indicates that ε
_{1} is predominated.
Using the CASTEP technique, the maximum value of ε
_{1}(λ) and ε
_{2}(λ) for PPy/MWCNTs composites in isolate state is ≅ 7.50 eV at photon energy (eV) ≅ 3.00 and 1.50, respectively as shown in
Figure 8b. For average values ε
_{1}(λ) and ε
_{2}(λ), resulted from the experimental and simulation dimensions are found within the photon energy range values of 1–53 eV. As demonstrated in this figure, one peak was observed in the dielectric constant parts performance of PPy/MWCNTs composites. From the behavior of the simulated composite PPy/MWCNTs as an isolated state in
Figure 8b, the CASTEP/DFT computations were used to evaluate ε
_{1}(λ) and ε
_{2}(λ)values and compared to the experimental values for PPy/MWCNTs composites thin films, simulated values are close to those achieved by DFT with the CASTEP model.
To obtain the spectrum of conductivity, ε
_{1}(λ) and ε
_{2}(λ) must be combined to the consequential relationship:
where the real part is
and the imaginary part is
fragments of the optical conductivity, (ω) and (ε
_{0}) are the frequency of angular and the constant of dielectric free space, respectively. The optical conductivity real and imaginary parts of PPy/MWCNTs composites thin film are shown in
Figure 9a. The σ
_{2} has a greater value than that of σ
_{1}.
For PPy/MWCNTs composites, in the experimental part (
Figure 9a), the σ
_{1} (λ) show the maximum values of 6.67 × 10
^{−6}_{,} 1.53 × 10
^{−5}, 2.09 × 10
^{−5}, and 3.57 × 10
^{−5} for PPy/MWCNTs composites at the photon energy values of 1.52, 1.56, 1.59 and 2.88 eV, respectively. The σ
_{2}(λ) show the maximum values of 869, 593, 615 and 668 for PPy/MWCNTs composites at the same photon energy value of σ
_{1} (λ), respectively. The high value of the computed ratio
${\sigma}_{1}\left(\lambda \right)/{\sigma}_{2}\left(\lambda \right)=5.34\times {10}^{-3}$ indicates that
${\sigma}_{2}$ is predominated. The σ
_{1}(λ) and σ
_{2}(λ) values of the PPy/MWCNTs as isolate state depends on (
$h\nu $) are demonstrated in
Figure 9b. In the CASTEP technique, for PPy/MWCNTs, the maximum values of σ
_{1}(λ) and σ
_{2}(λ) are ≅ 0.985 Ω
^{−1} m
^{−1} and 0.768 Ω
^{−1} m
^{−1} at photon energy ≅ 1.49 and 4.40 eV, respectively. The results obtained for σ
_{1}(λ) and σ
_{2}(λ) from the experimental method and the CASTEP technique are close.