1. Introduction
Optical properties of materials allow one to understand where they can be applied and, at the same time, how these materials can be tuned, with the objective of matching specific requirements. In particular, the optical properties of a material define how the material interacts with light. Different types of analysis based on light can be used for studying the properties of a material, for example, IR and UV-Vis spectroscopies. In modern materials science, the use of UV-Vis spectroscopy allows one to obtain information regarding the chemical composition of an analyte. Among the uses of this technique is the determination of the band-gap of a sample, absorption coefficient, optical conductivity, and dielectric constant.
The use of UV-Vis spectroscopy allows one to study the presence of chemical species in zeolites. In particular, after preparing mononuclear titanium oxide species in faujasites with a variation of Si/Al ration, the use of UV-Vis diffuse reflectance spectra, Raman spectroscopy, and XRD showed the presence of three different species of titanium oxide [
1]. Hamidouche et al. [
2] synthesized a composite material based on zeolite HY/polypyrrole; in particular, the zeolite HY is obtained after a process of ammonium ion exchange in NaY zeolite [
3]. The material was studied using UV-Vis spectroscopy, and it was determined that the band-gap energy of the composite was lower than the values of its precursor components.
Although UV-Vis spectroscopy is an experimental technique that requires the physical analysis of the sample, in the last years and with the advance of computational technology, theoretical advancements have made the study of theoretically generated UV-Vis spectra available. For instance, Fois et al. [
4] studied the red shift that is attributed to the ligand-to-metal-charge-transfer electronic transitions detected by UV-Vis studies, after the use of density functional theory (DFT), where the periodicity of crystalline phase is considered.
While there are reports of studies related either to optical or to electrical properties of zeolites, a clear link between the phenomena associated during the analysis is not presented. In particular, relative permittivity is frequency dependent and at low frequencies, it is obtained from electrical measurements, while optical measurements yield relative permittivity at high frequencies. For this reason, calculating the relative permittivity in a wide frequency range allows one to understand the physical properties of a material under analysis. Hence, it is known that the permittivity of a material is related to the dielectric absorptivity, and it is a complex parameter. In the case of the real part of permittivity, it describes the field-induced charge separation, while the imaginary part defines the absorbed energy that is converted into heat [
5]. There are diverse applications where the relative permittivity of a material is of interest. For example, the absorption of electromagnetic energy can be adjusted through the permittivity and permeability of a material [
6]. The relative permittivity of zeolites allows one to use them as sensors. This is possible because if the zeolite is used as a “dielectric”, there is a change of its relative permittivity when there is the presence of gases [
7,
8]. It is also known that the conductivity and dielectric permittivity are used in the study of catalytic activity [
9].
Even though the importance of studying optical and electrical properties of materials is undeniable, the literature is scarce when dealing with frequency analysis in the electrical and optical spectrum. One example of this kind of study is reported by Saad et al. [
10]. In the case of zeolites, to our knowledge, there is no similar study regarding zeolites.
In this work, the optical and electrical properties of synthetic zeolites with codes—provided by the International Zeolite Association (IZA) [
11]—LTA, FAU and MFI are studied. This is after the study of optical data generated from UV-Vis spectroscopy and the frequency response analysis using electrochemical impedance spectroscopy. Finally, the results of data analysis are compared, and the relationship between electrical and optical processes is presented.
3. Scanning Electron Microscopy and X-ray Diffraction Analysis
The micrographs of each zeolite were obtained after the use of scanning electron microscopy (SEM) on a JEOL JIB-4500 (Peabody, MA, USA) microscope equipped with an EDS detector. Characteristic micrographs are presented in
Figure 1. As is observed, the zeolites MFI and FAU show quite small particles in comparison to LTA crystals. However, energy dispersive spectrometry (EDS) allows for study of chemical elements present in each sample; in
Figure 2, the normalized data of EDS spectra are presented.
From
Figure 2, it can be noted that all the samples have the characteristic elements expected on these zeolites, namely, oxygen, sodium, aluminum, and silicon. Moreover, the relative amount of each element can be correlated. As expected for zeolite, LTA and FAU, with a theoretical Si/Al ratio of 1 and 1.2, respectively [
11], both of them exhibit a similar amount of Si and Al atoms. In the case of zeolite MFI, the theoretical Si/Al ratio is 13.28, which is similar to that presented in experimental data.
In order to study the crystalline characteristics of samples, all powders were studied using X-ray diffraction (XRD) by using Aeris Panalytical (Malvern, UK) equipment with Cu K alpha monochromatic radiation (l = 0.154056 nm, 40 kV, 15 mA). The results are presented in
Figure 3. Theoretical diffractograms were retrieved from IZA (International Zeolite Association) [
11], and they are identified with -r (FAU-r, LTA-r, MFI-r) as reference. For comparison purposes, the intensity of all diffractograms was normalized. When the experimental and theoretical data are compared, it can be noted in each case how the position of theoretical peaks coincides with those of peaks from experimental data.
In particular, for FAU-r and FAU, the relative intensity shows variations, and also, there is a displacement in
, which indicates a variation in the call parameter. In the case of LTA-r and LTA, there are no observable variations in the angular position of peaks. Finally, for zeolite MFI, when comparing theoretical (MFI-r) and experimental (MFI) data, the peaks are located at almost the sample angles, but also, in the case of experimental data, the narrowest peaks are masked. From the SEM, EDS and XRD data, it is confirmed that the characteristics of the materials correspond to the target zeolites. Furthermore, from the Scherrer Equation, the average crystallite sizes are calculated as 19, 58 and 8 nm for MFI, LTA and FAU zeolites, respectively. Based on the micrographs in
Figure 1, the particle size of MFI and FAU zeolites is smaller than LTA crystals. This is confirmed by the average particle size calculated from XRD, and it was found that the average particle size of FAU is smaller than MFI zeolites.
4. UV-Vis Analysis
UV-Vis spectroscopy data were obtained through the use of a UV-Vis NIR Cary 5000 (Santa Clarita, CA, USA) spectrophotometer. From the UV-Vis data, plenty of information can be obtained. In this regard, relative permittivity real part
is given by
and the imaginary part
can be calculated from
where
and
are the refractive index and extinction coefficient, respectively.
Considering the percent transmittance
and the absorbance
in arbitrary units (a.u.),
Then
and from the wavelength λ and absorption coefficient α can be calculated from the thickness of the film in cm as
. As a result, the extinction coefficient
is given by
Given the speed of light as
m/s, the optical conductivity is given by
In addition to these parameters, the band-gap can be estimated from the UV-Vis data. In this case, the Tauc model, which is a general formula for absorption in material [
13], can be used
From direct measurements, the UV-Vis absorption spectra were obtained. As is presented in
Figure 2, zeolites FAU and LTA have a similar Si/Al ratio, which leads to a similar presence of Al
2O
3. This can be observed in the evident similarity of their UV-Vis absorption spectra (
Figure 4a). In the case of MFI zeolite, there is a greater Si/Al ratio than in FAU and LTA zeolites [
14,
15], which is observed in
Figure 1 and in the absorbance (
Figure 4a). In addition, the data of
Figure 4a can be evaluated through CIE lab space [
16].
Color spaces are widely recognized as a means of describing colors, including absorbance, through descriptors such as numerical values. In this context, the CIE Lab color space is particularly employed due to its ability to establish a correlation between numeric values and human visual perception. In this sense, L, A and B refer to luminosity, red/green coordinates, and yellow/blue coordinates, respectively.
As shown in
Figure 4b, according to the absorption presented by each zeolite, a color is assigned in the CIE lab space. As a result, we can compare the colors associated with each zeolite. As can be observed, the greatest variation exists when the color of LTA is compared with FAU, and also FAU and MFI are closer among them.
As stated before, from the UV-Vis absorption spectra, a plethora of parameters can be obtained. In the case of the band-gap, after the use of Equation (7) and considering
for direct allowed transitions (direct band-gap), the Tauc plot for each zeolite was obtained (
Figure 5). As is observed, zeolites FAU and LTA have a close band gap among them, but the MFI zeolite exhibits the widest forbidden band energy. This can be attributed to the chemical composition of zeolites. This includes the location of Al, Na atoms in the zeolitic matrix [
17,
18,
19], as well as the inclusion of novel chemical species into the crystalline array [
14,
20].
In addition, after the use of Equations (1) and (2), the optical relative permittivity can be calculated. These results are presented in
Figure 6a–c. As discussed by Sebastian et al. [
21], the relative permittivity of a material shows its energy storing capacity when a potential is applied across it. It is related to the macroscopic properties, such as polarization or capacitance.
In this sense, each material presented in
Figure 6 exhibits a particular behavior of its complex relative permittivity, which is defined by the nature of the sample and also by the frequency range where the analysis has been carried out. At has been discussed elsewhere [
22], the UV-Vis range shows us the electronic processes that are taking place in the sample under study. Hence, the behavior of real and imaginary parts of relative permittivity follows the expected behavior, which is that, after an increase in frequency, there is an increment of the real part, and there is a decrement of the imaginary part.
In the case of the optical conductivity, it can be calculated after Equation (6). This leads to a plot (
Figure 7) similar to
Figure 4a, but in this case, we have the magnitude corresponding to the conductivity in S/m. Since the optical conductivity shows the relationship between the magnitude of the induced electric field for arbitrary frequencies and the induced current density in the material, it is clear from
Figure 4 that the MFI zeolite has the greatest optical conductivity at the highest frequencies or wavelengths. In contrast, between 200 and 300 nm, the LTA zeolite is the best conductor.
Since the data from UV-Vis allows us to calculate the real and imaginary parts of relative permittivity, we can say that this process works as a “sort” of optical impedance, where the dissipation factor can be calculated as a function of frequency. Therefore, the relative optical permittivity demonstrated in
Figure 6a–c can be effectively utilized with data obtained from electrochemical impedance spectroscopy. This combined approach enables a deeper comprehension of the dielectric processes occurring within zeolites.
5. Electrochemical Impedance Spectroscopy
For this study, the methodology described was used. Each sample was ground and compressed into a pellet with a diameter of 1 cm and a thickness of 1 mm; the pellet was then placed between two polished copper electrodes, which were connected to an E4980A Precision LCR Meter. As a result, for each sample, a data set was obtained corresponding to the magnitude of the total impedance in ohms, phase angle in arc degrees, and frequency of interrogation signal in hertz.
As is well known, the complex impedance is given in terms of the real
and imaginary part
of
,
and the phase angle is given by
The electrical conductivity
of the sample is given in terms of AC conductivity
and DC conductivity
,
From the data obtained during the frequency interrogation process and using Equations (8) and (9), the real and imaginary parts of impedance were calculated. The results are presented in
Figure 1. As can be noted, all zeolites have a Nyquist plot that shows an “arc”-like behavior. This can be attributed to electric interactions inside the zeolitic matrix and how the ionic conductivity is taking place. A greater magnitude of
is caused by an increase in the energy storage processes of the material, which is caused by the morphology of the crystals. In this sense, it is clear that all zeolites exhibit variations in the electrical processes that are taking place. Although there is no linear relationship between
and
, there are zones where such behavior could be apparent, for example, the inset in
Figure 8. In the case of
being equal to
, this indicates that a purely reactive impedance exists. This means that the reactive and resistive components of impedance have the same component, but they are out of phase by 90°. As a consequence, the impedance has, in its parts, equal amounts of resistance and reactance, and impedance is frequency dependent, which occurs at specific frequency values. Therefore, if
, this suggests that the electrical model is neither purely resistive nor purely reactive but lies somewhere in between. This depends on the values and types of electrical elements in the electrical model.
After examining the data in
Figure 8, two electrical models can be used to describe the observed behavior. FAU and MFI zeolites exhibit an electrical response corresponding to a circuit of the form
, and in the case of LTA, there is a circuit of the form
. These circuits are presented in
Figure 9. After using ZView software, the parameters of the elements in the proposed circuits are fitted. These values are presented in
Table 1 and
Table 2.
As described elsewhere [
23,
24], the grain boundary and the particle size define how the conductivity takes place in ionic conductors. In this sense, the synergic effects of these characteristics define the system dynamics and, as a consequence, the electrical model that describes such a system. As is shown by the XRD data, the average particle size of MFI is almost twice that FAU. This allows us to understand why the
value of MFI is almost twice that presented by FAU zeolite, and this parameter can be proposed as the electrical effects between grains. At the same time, since they have a different morphology and chemical composition, the
and
parameters follow a non-linear variation. Since the
parameter approaches 1, we conclude that reactance takes place due to capacitive effects [
25], and while the capacitance
of MFI and CPE is almost the same, the
value in FAU is almost two orders of magnitude above MFI. In the case of LTA zeolite, there are two branches that contribute to the observed impedance, each one with reactive effects. Like in the data of
Table 1,
and
approaches 1, which shows that reactive effects are due to a capacitive behavior. In addition, branch 1 models the interparticle effects, while branch 2 models the effects that take place inside the particles.
The total conductivity for all samples is presented in
Figure 10. Three characteristic zones are found. The first one corresponds to DC conductivity, the second one is the transition from DC to AC conductivity, and finally the third zone corresponds to AC conductivity.
As observed, the conductivity is almost constant at low frequencies, which coincides with the Nyquist plot. In the case of high frequencies, the conductivity has a greater slope than the DC conductivity. The transition zone defines what kind of conductivity is taking place, and as has been shown elsewhere, after the use of Jonscher power law, it is found that we are dealing with ionic conductors. This is characteristic of these materials examined within the frequency range presented in
Figure 10.
From electrical impedance data, the electrical complex relative permittivity can be obtained [
26]. With the aim of comparing the electrical data with the optical data, the relative electrical permittivity is presented in
Figure 6d–f. As is observed, for each case, both real and imaginary parts have almost constant values. This is expected for ionic conductors that are interrogated with frequencies below microwaves. In general terms, the electric permittivity decreases as the frequency increases; this fact can be appreciated if the optical relative permittivity is observed after the electrical relative permittivity.