The absorption spectra of pure PEO and PEO-based composites are demonstrated in
Figure 12. It is obvious that pure PEO does not show any absorption peak in the visible spectrum. The polymer film remains transparent at this spectral range as the incident light is incapable of establishing electronic transition. In contrast, the absorption of PEO composites increases due to the additives, which aid in reducing the OBG of PEO. In polymer composites photon energy is substantially absorbed by the materials in the ultraviolet and visible ranges; the absorption leads to electron transitions in the
σ,
π, and
n-orbitals to higher energy states [
21]. Since the vast majority of the optical transitions are caused by impurities that have energies lain throughout the visible spectrum, the defects are regarded as color centers [
77]. Because of the strong
π→
π* interactions, the absorption spectra of PEO:Zn-PPHNL solid films are more widened than those of Zn-PPHNL solutions. This kind of interaction is explained by the
π→
π* staking and packing effect under solid-state conditions [
67]. In addition, the presence of
π-delocalization along the polymer chain can be attributed to strong shifts towards longer wavelengths. This hypothesis is significantly confirmed by the absence of absorption peaks in a pure PEO film [
78,
79]. The absorption of PEO:Zn-PPHNL composite films begins in the near-infrared region and extends across the full UV–Vis region; the absorption maxima of a PEO:Zn-PPHNL film display a red shift, indicating the presence of interchain interactions in the solid structure [
66]. Materials with amendable absorbance in the lower–mid visible spectrum are important for applications such as optoelectronics and optical sensors.
Interband absorption is a well-known technique for investigating the transition of electrons between the solid bands. Fundamental absorption, which appears as a rapid change in the material spectrum, is referred to as the absorption edge. This is in strong association with either band-to-band or exciting transitions and is regarded as a suitable indicator of OBG energy. The absorption coefficient is expressed by
α(
υ), which measures how quickly the intensity of the incident light decreases in accordance to a medium length [
82,
83]. The Beer–Lambertequation is applied to calculate the
α(υ) from the absorbance spectra,
A(
υ), at the equivalent frequency (
v):
where
is incident beam intensity,
is transmitted beam intensity, and
d is sample thickness. The incident beam intensity
Io, equals the sum of the intensities of the reflected, absorbed, and transmitted beams (labeled as
IR,
IA, and
IT, respectively) when they hit the second medium surface, or as follows:
the above equation can be written as follows:
where
A,
T, and
R represent, respectively, the absorptivity,
IA/
Io, transmissivity,
IT/
Io, and reflectivity,
IR/
Io, or the fractions of incident radiation which are transmitted, absorbed, and reflected by a material. The
T value can be calculated using Beer’s equation (i.e.,
T = 10
−A), where
A is the raw absorption and reflectance,
R, is required for the calculation refractive index, determined from Equation (3). The study of optical absorption, particularly the absorption edge, is a key tool for understanding materials’ electronic structures and the existence of direct and indirect transitions [
13,
84].
Table 1 includes the values of absorption edges as well as the absorption edge values of polymer films computed by extrapolating the linear part of the ordinate to zero. It is clear that adding Zn-PPHNL causes the absorption edge to reduce remarkably for pure PEO, from 5.25 eV to 1.1 eV for PEO:Zn-PPHNL samples, shifting toward low photon energy (see
Figure 13). The substantial change in the absorption edge implies a significant change in theband structure polymer composites due to the creation of new localized states in the mobility gap [
85]. In other words, absorption edge data indicate that a polymer with wide band gap is converted into a narrow OBG, which plays a significant role in the development of organic solar cells and optoelectronic devices [
86,
87].
4.1. Refractive Index Study
The refractive index is strongly linked to the polarizability of ions and the local field inside the substance. The parameter is crucial for purposes of integrated optical devices, such as modulators, filters, and switches [
88]. Along with the optical dielectric constant, it is regarded as a significant characteristic in the design of new compounds for various optical electrical applications. When a beam of electromagnetic light transmits through a material, reflectance and absorption can be used to determine the refractive index of a material, which expresses as the following:
where
n* is the complex refractive index, the real part of the refractive index is
n, which is related to the actual velocity, and
k is the extinction coefficient. Fresnel formulae are helpful in calculating the refractive indices of pure PEO films and PEO films doped with Zn-PPHNL by using the values of reflectance,
R, and the optical extinction coefficient,
k =
αλ/4
πd;
α and
λ sequentially stand for the absorption coefficient and the wavelength, and d is the sample thickness [
89]:
When a light beam is guided through an optical medium, the refractive index
n(
λ) defines how transparent materials are. For materials that are entirely transparent
n(
λ) approaches zero, and positive values indicate that light is being absorbed. The dispersion curve of the refractive index,
n(
λ), for pure PEO and PEO doped with Zn-PPHNL is shown in
Figure 14. The doped samples exhibit larger
n values and display notable dispersion. The results indicate that adding a Zn-PPHNL complex to a PEO polymer increases the refractive index from 2.05 to about 2.27. This is most likely due to the space charge creation in the Zn-PPHNL complex. As previously mentioned, altering the
n value of materials in accordance with wavelength is important for changing their optical properties, with their dispersion being quite significant from an application viewpoint. The most significant optical materials have a refractive index,
n, between two and three, as visible light absorbs in the upper atomic layers of the material [
90,
91]. The refractive index value (typically > 1.65) for PEO/Zn-PPHNL metal complex composite films makes them suitable basic structures for photovoltaic and optical devices in applications such as Bragg gratings, solar cells, waveguide-based optical circuits, and photonic crystals [
92].
4.3. Optical Dielectric Constant Study
Regarding polymer composites, the optical transition mainly corresponds to changes in the optical dielectric constant, which characterizes the possibility that an electron could lose energy while passing through the surface of the bulk material [
96]. The dielectric constant of the materials (as expressed in Equation (7)) consists of a real part,
ԑr, and an imaginary part,
ԑi, where the real part represents the capacity of the material to reduce the speed of light and the imaginary part represents its capacity to efficiently absorb energy owing to polarization.
ԑr is determined from the refractive index,
n, of the media (
), and
ԑi is obtained from the extinction coefficient,
(
) [
10,
97].
From the point of view of the Spitzer–Fan model, the dielectric constant of the material at a low frequency (long wavelengths),
ԑ∞, is obtainable from correlations between the wavelength and refractive index [
98]:
where the charge of an electron is
e, the speed of light is denoted by
c,
ԑo stands for the dielectric constant of free space,
N is the localized density of a charge carrier, and
m* stands for effective mass; all of the values are shown in
Table 3 [
99,
100]. A straight-line result is obtained from plotting the values of
ԑr against
λ2 in the visible spectrum range, as seen in
Figure 16. The
ԑ∞ and
N/
m* values, sequentially from the slope and intercept of the line of
ԑr versus λ
2, are obtained using the constants listed in
Table 3. An illustration of the values of
ԑ∞ and
N/
m* that are gained from Equation (8) is presented in
Table 4.
The quantitative values in
Table 4 imply that as doping concentration increases the localized density of state
N/
m* for the pure PEO sample increases from 3.89 × 10
55 to 6.93 × 10
55 atoms/m
3, with the
ԑ∞value increasing from 4.54 to 5.4503, showing that the growing of free charge carriers has strongly contributed to the process of polarization. The values expected for the localized density of states
N/
m* in Equation (8) of the current research are equivalent with those reported in the literature [
54,
101,
102].
4.4. Tauc’s Approach for Band Gap Study
Broadband beams transmit through polymer films; band-to-band transitions occur by obeying particular selection rules and are characterized by a sharp increase in the fundamental absorption area [
103,
104]. According to the band structure of the materials, the transitions are divided into four different types [
104]. Regarding amorphous semiconductors with indirect transitions, there is no conservation of electronic momentum when moving from the valence to the conduction band [
105]. The following relationship provides the absorption coefficient for direct band gap materials [
106]:
where
hυ stands for photon energy,
B is a constant, and
Eg stands for the OBG energy, while the coefficient
n defines the type of electronic transitions that lead to absorption [
107]. Depending on the types of transition, the coefficient
n can be 2, 2/3,1/2, or 1/3, corresponding to direct allowed, direct forbidden, indirect allowed, and indirect forbidden transitions, respectively, as shown clearly in
Figure 17 [
96]. The intercept of linear portions of the (
of
Figure 18a–d against the axis of photon energy,
hυ, can be used to determine the value of
Eg. The determination of OBGs is crucial for comprehending the electrical behavior of a semiconductor and its practical interest [
104]. The values of the OBGs of both transitions, allowed direct (
n = 2) and forbidden direct (
n = 2/3), are shown in
Table 5. The materials of the amorphous phase and the band edges are influenced by the contribution of the various orbitals of both the metal complex and the ligand. As a consequence, the prediction as to whether the type of band is direct or indirect is a complicated task [
108]. Thus, depending on the choices of
n, many figures can be displayed by using the basic absorption equation (Equation (9)); however, only using Equation (9) makes it impossible to define the kind of electron transition. The complex dielectric function,
ɛ*, needs to be examined in order to correctly classify the kind of electron transition. In order to calculate band structure in a relatively precise manner, the spectra of optical dielectric loss have to be carefully compared with Tauc’s plots. From such a comparison, the optical transition types for each solid film can be determined. In addition, the evolution of disorder in the polymer samples that results from the modification of a polymer’s structure can also be used to explain the OBG reduction [
109,
110]. The reduction in OBG results from the creation of new localized energy states in the bandgap between the VB and the CB [
20]. Quantitatively, the declining of
Eg magnitudes as the Zn-PPHNL is increased is shown in
Table 5 and
Figure 19. By comparing the
Eg values in Tauc’s model (
Figure 18a–d) with the energies from the optical dielectric loss as can be seen in later section, the types of transitions can be determined, such that for PEOZn0 it is direct allowed (
n = 2), for PEOZn1 it is indirect allowed (
n = 1/2), and for PEOZn2 it is an indirect forbidden (
n =1/3) transition.
This study addresses creating polymer composites with small OBGs that close to semiconductor or conductive polymer materials. The reduction in the
Eg from 5.5 eV to 0.6 eV is achieved, verifying the hypothesis that green metal complexes can modify insulating polymers to semiconducting polymer composites. In general, polymer-based materials could show the property of declining OBGs by adding metal-based fillers.
Table 6 shows the OBGs of different types of polymer composites with different fillers and dopants. Furthermore, the metal complex causes a more remarkable drop in the OBG compared to other types of fillers. The metal–PPHNL complexes contain several N-H and O-H, which in turn leads to interactions between the functional groups of metal–PPHNL complexes, with the polymer chains causing a drop in the gap between the valence and conduction bands of the doped polymer material. Based on the results of band gap reduction in the current work, Zn-PPHNL may introduce tremendous localized densities of states into the band gap region, and thus they overlap and reduce the band gap region in which the electrons should transfer from the VB to the CB. Moreover, it can be concluded that Zn-PPHNL is more influential than irradiation and ceramic nanoparticles, NPs, to manipulate the optical band gap of weakly polar polymers, such as PEO. Extra research is required to establish the fact that metal–PPHNL complexes are outstanding in reducing the band gap of weakly polar polymers.
4.5. Dielectric Function Study
Fundamental optical behaviors are explained through the use of the transverse dielectric function, the latter based on the momentum transfer,
q, in the light–matter interaction and the transfer of energy. The total dielectric function is expressed as
, where
εr is the real part and depends on frequency [
119] while the imaginary part,
, describes how rapidly a medium absorbs electromagnetic waves [
120]. Band gap investigations need to consider the quantum state of a material properly in order to be described more accurately, particularly the evaluation of the complex dielectric function,
ɛ*. This parameter plays a crucial rule in the optical properties of matter and explains how a material’s electron density responds to the applied electromagnetic field [
121].
In fact, the microscopic theory of the dielectric function applies a semiclassical method to establish the Hamiltonian function, describing the interaction between an incident electromagnetic field and Bloch electrons inside optical media. The modern description of electrons is via quantum mechanical (Bloch) wave functions; contrarily, the electromagnetic field is treated classically. This method is implemented since it is not as difficult as a total quantum mechanical approach, where an electromagnetic wave is considered as being quantized into photons. Nonetheless, it is more comprehensible and avoids sophisticated method of calculation [
122]. The optical dielectric loss,
εi, is strongly associated with the electronic structure, in particular the localized density of states. Equation (10) is a fundamental relationship of the components of a matrix between the occupied and the unoccupied wave functions based on the selection rules [
121]. In particular, the formula that essentially links the imaginary part,
ɛi, with the band structure is yielded from the electron–radiation interaction of the Hamiltonian function,
HeR, which also describes how a charges move in the presence of an electromagnetic field inside a material [
121]:
where
A(
r,
t) is denoted as the vector potential and
P is expressed as the momentum that conjugates to the vector of position. For semiconductor materials the momentum matrix elements of the electron enter directly into the
K·P approach of band structure determination. There are various methods with which to find a semiconductor dielectric function from
. The most straightforward method is to assume that
A(
r,
t) is small enough that time-dependent perturbation theory can be used (as represented in Fermi’s golden rule) to determine the transition probability (R) per unit volume for an electron in the valence band state |
V⟩(with energy,
Ev, and wavevector,
kv) to the conduction band
|C⟩ (with equivalent energy,
Ec, and wavevector,
kc). The electric dipole transition probability, R, for absorption photon per unit of time is expressed as follows:
In the above, the symbols for the incident photon frequency, Planck’s constant, effective mass, and electron charge are, respectively, ω, ℏ, m, and e.
Multiplying the transition probability per unit volume by the photon energy yields the power loss,
P, by the field due to the medium absorption:
The power loss can alternatively be stated in terms of the medium (absorption coefficient),
α, or
ɛi by considering that the rate of the declining energy of incident beam per unit volume is given by
dI/
dt;
I denotes the incident beam intensity:
The density of energy,
I, is linked to the amplitude of field as follows:
Then, we can obtain the following:
where
ω expressed the incident photon,
εₒ is the permittivity of the vacuum, and
e is the electron charge. From a quantum mechanics point of view, Equation (15) indicates that the imaginary part’s optical dielectric function,
ɛi, is related to the band structure
, the delta function obtained in Fermi’s golden rule. This outcome articulates the fact that the electron absorbs the photon energy and is excited from the valence band into the conduction band [
121]. The fundamental theory of an optical dielectric constant originates from a complex frequency function; it requires large-scale computation to determine dielectric constants [
96,
123]. The following equation illustrates how utilizing the extinction coefficient and refractive index in the calculation makes it simple to experimentally estimate the optical dielectric loss,
εi [
13]:
It is challenging to determine whether the band will be direct or indirect when using Tauc’s model [
108]. According to earlier theoretical investigations, there is a close connection between the optical dielectric function,
, and the band structure of semiconductor and insulating materials [
124,
125]. After the extrapolation of the linear component of the plot of
εi against photon energy,
hv, the intercept is a useful way for calculating the OBG [
111]. In reality,
ε* shows the properties of the medium and how it responds to electromagnetic waves passing through it. The dielectric loss characterizes actual transitions between the occupied and unoccupied wave functions (electronic states) [
124,
126].
Simple equations can be used to calculate
ɛ*, which is connected to the refractive index and extinction coefficient.
Figure 20 illustrates the optical dielectric loss against photon energy for PEO samples.
Previous research established that the appearance of peaks in the dielectric loss,
εi, are closely linked to interband transitions [
127,
128]. It has been noted that in amorphous or semicrystalline substances the band edges encompass associations from the various orbitals of the metal complex and the ligand, making it harder to identify if the band will be direct or indirect [
120]. In order to accurately identify the sort of electronic transition, this work uses optical dielectric loss. Moreover, it has been proven that optical dielectric loss accurately depicts how an incident photon reacts to electronic transition [
17,
113]; therefore, the excitation energy of an electron from the valence to the conduction bands is determined from the extrapolation of the linear part of optical dielectric loss on the axis of photon energy. Additionally, the band gap is actually represented from this energy. In Tauc’s semiempirical approach, the transition process is represented by
n, which can have one of the following values: 1/2, 3, 3/2, or 2, dependent on how the transitions of electrons are made from the valence band to the conduction band [
108]. The kinds of electronic transition be assumed if the band gap calculated using Tauc’s model agrees with the one calculated by optical dielectric loss. This method for ascertaining materials’ band gap and kind of electronic transition is time-consuming, but it includes significant physics information. The electronic transition types can be identified from comparisons of the plots using Tauc’s equation (
Figure 18,
Figure 19 and
Figure 20) of optical dielectric loss. From the comparisons it is convenient to argue that the kind of electronic transition in PEOZn0 is direct allowed (
n = 2), for PEOZn1 it is indirect allowed
(n = 1/2), and for PEOZn2 it is an indirect forbidden
(n = 1/3) transition, which implies that the optical dielectric function is an efficient technique for examining the band structures of materials. The design of a polymer composite with a low cost and improved optical properties is a topic of great interest. In this domain, wide-band-gap PEO is one of the noteworthy and commonly used thermoplastic polymers; in comparison with conductive polymers it is cheap and stable. In neat PEO the crystalline state is what explains why the direct transitions are most likely to occur. In crystalline materials the top of the VB coincides with the bottom of the CB, while in amorphous materials this would not happen. In neat PEO the crystalline domains which are higher than amorphous phases may be responsible for the dominancy of direct transition. In the XRD section it was found that the amorphous phase increased in PEO: Zn-PPHNL composites compared to pure PEO. The optical micrograph (see
Figure 10) clearly showed that neat PEO exhibits spherulites with big sizes, ascribed to the crystalline structure, while these spherulites were destroyed to small sizes and dark regions attributed to amorphous domains were dominant. In amorphous materials it is difficult to observe direct transition due to the disorder distribution of the valence and conduction bands. Su and Zhou observed the impact of crystallization on the enhancement of the optical and mechanical properties of PCCE polymer [
129]. From the above discussion it can be emphasized that materials’ structures will greatly affect the optical and electrical properties.