3.1. The X-ray diffraction (XRD)
Figure 1 shows the XRD of PVDF and PVDF incorporated with different weight percentages of LiZnVO4. PVDF has diffraction peaks at 2θ = 19.1º, 20.7º and 39.7º [27–29]. According to JCPDS Card No. 38-1332, XRD spectrum of LiZnVO4 shows the rhombohedral structure. Scherer's equation was used to determine the crystallite size of LiZnVO4. This equation has the form C= [(K𝜆)/( 𝛽cosθ ), where C is the crystallite size, K is constant equal 0.9 and 𝜆 is the X-ray wavelength. θ is the diffraction angle and 𝛽 is the full width at half maximum of a diffraction peak. For the purpose of computing the mean crystallite size, intense diffraction peaks were chosen, and the result was determined to be 83 nm.
The interaction between PVDF and LiZnVO4 NPs is confirmed by shifting the diffraction peak of PVDF at 2θ = 20.7º with a variation in its broadening and intensity. The diffraction peaks of LiZnVO4 begin to appear and their intensities increase with increasing the weight percentage of LiZnVO4 NPs with shifting in their position that is related to LiZnVO4 NPs. This indicates the interaction between PVDF and LiZnVO4 NPs.
3.3. Ultraviolet-Visible measurement
Figure 3 shows UV-Visible spectra of pure PVDF and PVDF incorporated with a different weight percentage of LiZnVO4 in the wavelength range of 190–800 nm. The optical absorption edge can be described using these spectra. All spectra have an intense absorption band at 237 nm. The intensity of this band at 237 nm is increased and the broadening decreases with increasing the weight percentage of LiZnVO4 which indicated that there is an interaction between PVDF and LiZnVO4.
Direct and indirect band gaps are the parameters that categorize polymers with doped fillers. The highest point of the valence band and the lowest point of the conduction band both lie at zero crystal momentum in the case of a direct band gap. Indirect conduction is referred to as conduction in which the bottom of the conduction band does not relate to zero crystal momentum. While in materials with an indirect band gap, the transition from the valence band to the conduction band should be coupled with phonons that have the appropriate magnitude of crystal momentum. Near the fundamental band edge plotting the relations between (αhʋ)2 and (αhʋ)1/2 against photon energy h𝜐 will allow to determine whether a transition is direct or indirect according to the following relation [32].
(αhʋ) = B (hʋ− Eg)1/n (1)
where Eg is the band gap energy and B is constant. α is the absorption coefficient calculated from 2.303A/d where A is the absorbance and d is the thickness of the prepared films. Plotting α against h𝜐 gives the value of absorption edge as seen in Fig. 4. n has a different value of 2 or 1/2 according to the type of transition [32–34].
(αhʋ) = B (hʋ − Egin) 2 (2) for allowed indirect transition
(αhʋ) = B (hʋ − Egd) 1/2 (3) for allowed direct transition
Figure 5 represents the relation between (αhʋ)2 and (αhʋ)1/2 against photon energy h𝜐. The value of the optical band gap energy can be determined by finding the intercept of the extension of the linear component of these curves to zero absorption on the axis. It is observed that band gap energies are decreased with increasing LiZnVO4. New energy levels (traps) have been created between the HOMO and LOMO, which has led to a fall in values. This is a consequence of the formation of disorder. As a result, the density of the localized states in the mobility band gap of the PVDF is increased.
3.4.1 Dielectric permittivity analysis
As a function of the frequency and temperature, the dielectric behavior of the PVDF polymer filled with different weight percentages of LiZnVO4 is investigated. The frequency ranged from 0.1 Hz to 7 MHz, and the temperature varied between 30 and 120°C. The following formula is used to represent the real (\({{\epsilon }}^{{\prime }}\)) and imaginary (\({{\epsilon }}^{{\prime }{\prime }}\)) components of the dielectric permittivity [35–38];
$${{\epsilon }}^{{\prime }}=\frac{{\text{C}}_{\text{e}}\text{d}}{{{\epsilon }}_{\text{o}}\text{A}}$$
4
$${{\epsilon }}^{{\prime }{\prime }}=\frac{{\sigma }}{2{\pi }\text{f}{{\epsilon }}_{\text{o}}}$$
5
where Ce is the capacitance experimentally obtained for a sample under investigation, d is the sample thickness A is the cross-sectional area of the used electrode, and εo is the permittivity of free space.
Over the above ranges, Figs. 6 and 7 show the ε' and ε" curves as a function of frequency. At low frequencies, both parameters (ε' and ε") had their maximum values and began to decrease as the frequency increased. It is clear that both ε' and ε" are temperature-dependent parameters since their values have improved as the applied temperature increased.
It is worth mentioning that the high ε' values achieved for frequencies lower than 102 Hz have been ascribed to the induced dipoles' ability to follow the periodic change in the field direction employed. This alteration is slow; thus, it provides the current dipoles sufficient time to align themselves against/with the applied field direction. This reaction gave rise to a significant increase in interfacial polarization (also known as the Maxwell-Wagner-Sillars polarization), which resulted in the current nanocomposite films having excellent dielectric characteristics.
On the other hand, the substantial drop in the ε' values in the high-frequency region was attributed to charge carriers' inability to alter their direction in response to the applied field, leading to the gradual accumulation of ions at the interfacial areas between PVDF and LiZnVO4, hence reducing the interfacial polarization. Thus, we can conclude that the minor fluctuations in the ε' and ε" values with frequency, seen in Figs. 6 and 7, are owing to the minimal effective impact of ionic polarization combined with the low contribution of electronic polarization. Additionally, this negligible variation is responsible for the dielectric relaxation processes occurring inside the current host matrix [39–41]. So, the introduction of LiZnVO4 nanofiller into the PVDF host matrix improved the dielectric properties of all samples, particularly the sample with 5 wt% of LiZnVO4, which confirms the XRD findings.
The minimum dielectric loss is due to the existence of thin layers of PVDF that function as a protective covering for the Li-ions. This coverage minimizes current leakage caused by direct contact with Li-ions, while also confirming the reasonable compatibility between the LiZnVO4 and the PVDF matrix. PVDF is a dielectric substance, whereas LiZnVO4 is a conductive material. Therefore, filling PVDF with the nanofiller resulted in the formation of micro-capacitors inside the current host matrix.
3.4.2. Dielectric relaxation analysis
The variation of loss tangent (tan δ) of the PVDF/ LiZnVO4 films as a function of the frequency at 30°C is demonstrated in Fig. 8. A careful examination of this dependency provides a deeper insight into the dielectric relaxation processes occurring inside the PVDF-based system. Loss tangent value is governed by the ratio of dissipated energy (ε") to energy stored (ε') by the nanocomposite film under study. This figure is distinguished by the presence of intense relaxation peaks, especially for the samples containing Li-ions at high temperatures. These peaks are attributed to dipolar relaxation responses of the polymeric segments as a consequence of ion-dipole complexation. The appearance of this peak verifies the semicrystalline structure of the PVDF and suggests that ionic conduction dominates within doped with LiZnVO4. It has located in the low-frequency region as a result of the α-relaxation process accompanied by the rotational motion of lateral functional groups distributed around the central chain axis inside the polymeric matrix. Further, the observed shift in the peak position toward higher frequencies with increasing temperature is attributed to the dominance of amorphous regions inside the PVDF host matrix. In other words, the distinct shift in the peak’s position towards the high-frequency region indicates that the relaxation time (τ) value decreased as the LiZnVO4 percentage increased. Thus, the incorporation of conductive lithium ions into the dielectric PVDF produced an interfacial polarization, which resulted from the formation of interfacial areas between the PVDF and the nanofiller. Furthermore, this reduction in the τ value is attributable to the decrease in free volumes within the host matrix upon increasing the LiZnVO4 concentration giving rise to the accumulation of Li+ ions in these interfacial regions.
The increase in tan δ value with frequency in the low-frequency region is due to the Ohmic elements' dominance over the nanocomposite samples' capacitive nature. tan δ increased with increasing frequency and subsequently progressively dropped owing to the increase in capacitive components inside the synthesized samples at 90 and 120°C. This finding leads to shorter relaxation times at higher temperatures, where lithium ions have higher energy. The best value of tan δ has attained for the nanocomposite containing 5 wt% of LiZnVO4, indicating that the nanofiller was well incorporated into the PVDF, and this confirms the XRD and FT-IR results. This sample shows the greatest improvement in amorphous regions and is recommended for use in the manufacture of lithium solid batteries.
3.4.3. Electric moduli formalism
The electric modulus formalism is mainly used to suppress the contribution of electrode polarization. The dielectric real and imaginary moduli denoted by M' and M", respectively were determined by the well-known formulas [42–45]:
$${\text{M}}^{{\prime }}=\frac{{{\epsilon }}^{{\prime }}}{{{\epsilon }}^{{{\prime }}^{2}}+{{\epsilon }}^{{{\prime }{\prime }}^{2}}}$$
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$${\text{M}}^{{\prime }{\prime }}=\frac{{{\epsilon }}^{{\prime }{\prime }}}{{{\epsilon }}^{{{\prime }}^{2}}+{{\epsilon }}^{{{\prime }{\prime }}^{2}}}$$
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The dependence of M' values on the frequency at 30°C for the PVDF doped with various concentrations of LiZnVO4 is exhibited in Fig. 9. The spectra in this figure are characterized by the presence of long-tail lies in the frequency range of 10 Hz − 5 MHz. The presence of such a long tail indicates that the electrode polarization contribution has been completely eliminated. This finding also implies that the PVDF-based nanocomposite films have a remarkable capacitive feature.
The observed reduction in M' values with increasing the LiZnVO4 contents up to the concentration 5 wt % means that generated ions hop across locations, which indicates that hopping is the dominant conduction mechanism in the current nanocomposite films. The variation of M'' values with frequency recorded at 30°C for the nanocomposite samples is displayed in Fig. 10. The M'' curves exhibit two distinct loss peaks caused by the migration of induced charge carriers (Li+ and H+ ions), implying that the host matrix main chain has been relaxed. The obvious change in the peaks intensities with the increase in the nanofiller percentage refers to the non-Debye behavior of the present nanocomposite films. This change is also largely in agreement with the dielectric relaxation stemming from Maxwell-Wagner-Sillars (MWS) polarization effect. The shift observed in the first characteristic relaxation peak toward the higher frequencies is a good indication of the decrease in relaxation time with the increase of LiZnVO4 percentage.
The variation of M" versus M' for the PVDF/ x wt% LiZnVO4 samples are exhibited in Fig. 11. The Cole-Cole plot is generally divided into three frequency-dependent regions; low, middle, and high-frequency regions. These three regions are ascribed to the grain boundary effect, the participation of grains, and the bulk conduction relaxation process, respectively. The present spectra are characterized by a single semicircular arc attributed to the grain boundary effect and surface polarization, while the observed peak is assigned to the bulk conduction response [38, 46]. The asymmetrical behavior of this relaxation peak verifies the non-Debye dielectric relaxation response. The relaxation peak frequencies are governed by the following equation:
$${\text{f}}_{\text{m}\text{a}\text{x}}\approx \frac{1}{2{\pi }\text{R}\text{C}}$$
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According to this equation, the peak frequency is inversely proportional to the capacitance of the geometrical capacitor. Compared to the observed shift in the fmax toward the lower frequency region, the PVDF/ 5wt% LiZnVO4 nanocomposite sample has achieved the highest capacitance, recommending it to be used in designing Li-ion batteries. Further, this shift is a clear indication of the small contribution of the grain boundary to the electrical conduction mechanism inside the PVDF host matrix. This performance is attributed to the rotation of the dipoles, which supports the capacitive nature of the present nanocomposite film on resistive behavior and gives it valuable comparative advantages over other composites.
3.5. Electrical conduction behavior
Figure 12 shows the dependency of AC conductivity (σac) on frequency for the above-described nanocomposite samples recorded at 30°C. As the concentration of LiZnVO4 increased, amorphous areas became more dominant over crystalline regions, thus facilitating the transit of induced ions over short-range distances, giving rise to the detected increase in σac values. The relaxation of ions via bouncing back and forth across localized sites increased with increasing frequency, resulting in the enhancement of electrical conductivity. This improvement is attributed to the shift in hopping behavior from long-range to short-range distances.
The σac curves have been divided into three main parts; the first part located in the low-frequency region (region I) represents the DC conductivity (σdc), whereas the second part (region II) reveals the dispersive region and is located at 100 Hz − 5 MHz. The third segment (region III) is located at f < 5 MHz, where the induced ions cannot follow the rapid rotation of the direction of the applied field, forming ion-pairs and ion-triplets, which affects their mobility and thus reduces the AC conductivity at this stage.
The three parts of σac curves can be elucidated using the jump relaxation model. This model is based on the ratio between successful hops getting back to their original site to unsuccessful hops (i.e., it gets back to their original site). The variation in this ratio between successful and unsuccessful hops has resulted in the observed difference in the σac values over the considered range of frequency for the PVDF-based nanocomposite samples. Thus, the universal power-law set by Jonscher is the relevant law for describing the electrical conduction in the nanocomposite samples, and is represented as follows [37, 39, 40];
$${\sigma }={{\sigma }}_{\text{d}\text{c}}+{\text{A}{\omega }}^{\text{S}}$$
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where A is a factor that depends on temperature. S is a frequency exponent, which affects by the translational movement of the induced ions during the electrical conduction process inside the PVDF/ LiZnVO4 nanocomposite samples.
The variation of σac with frequency curves of the sample containing 5 wt% of LiZnVO4 (the optimized percentage) at different temperatures is demonstrated in Fig. 13. Similar behavior has been reported in the literature. This figure shows that as the temperature applied to the sample increases, so the σac values, emphasizing the thermally activated behavior of the induced ions inside the nanocomposite matrix. The behavior of S values for the PVDF/5% LiZnVO4 sample studied in the temperature range 30°C-120°C is exhibited in Fig. 14, where a decrease in S values with the continuous increase in temperature is observed. This result indicates that the most appropriate model for elucidating and describing the behavior of ions during the conduction process inside the current nanocomposite samples is the correlated barrier hopping model, confirming the above findings. According to Laumann et al. research, these results may be ascribed to the low-temperature diffusion of lithium ions mainly through the path Li (8a) → V(16c) → V(8a), where these sites are thought to be metastable for the migration of lithium ions. These findings reveal that the studied films filled with LiZnVO4 have advantageous features, indicating their suitability as a qualified base material for designing and developing promising energy storage devices and lithium batteries.