Incorporation of NiO into SiO2, TiO2, Al2O3, and Na4.2Ca2.8(Si6O18) Matrices: Medium Effect on the Optical Properties and Catalytic Degradation of Methylene Blue

The medium effect of the optical and catalytic degradation of methylene blue was studied in the NiO/SiO2, NiO/TiO2, NiO/Al2O3, and NiO/Na4.2Ca2.8(Si6O18) composites, which were prepared by a solid-state method. The new composites were characterized by XRD (X-ray diffraction of powder), SEM/EDS, TEM, and HR-TEM. The size of the NiO nanoparticles obtained from the PSP-4-PVP (polyvinylpyrrolidone) precursors inside the different matrices follow the order of SiO2 > TiO2 > Al2O3. However, NiO nanoparticles obtained from the chitosan precursor does not present an effect on the particle size. It was found that the medium effect of the matrices (SiO2, TiO2, Al2O3, and Na4.2Ca2.8(Si6O18)) on the photocatalytic methylene blue degradation, can be described as a specific interaction of the NiO material acting as a semiconductor with the MxOy materials through a possible p-n junction. The highest catalytic activity was found for the TiO2 and glass composites where a favorable p-n junction was formed. The isolating character of Al2O3 and SiO2 and their non-semiconductor behavior preclude this interaction to form a p-n junction, and thus a lower catalytic activity. NiO/SiO2 and NiO/Na4.2Ca2.8(Si6O18) showed a similar photocatalytic behavior. On the other hand, the effect of the matrix on the optical properties for the NiO/SiO2, NiO/TiO2, NiO/Al2O3, and NiO/Na4.2Ca2.8(Si6O18) composites can be described by the different dielectric constants of the SiO2, TiO2, Al2O3, Na4.2Ca2.8(Si6O18) matrices. The maxima absorption of the composites (λmax) exhibit a direct relationship with the dielectric constants, while their semiconductor bandgap (Eg) present an inverse relationship with the dielectric constants. A direct relationship between λmax and Eg was found from these correlations. The effect of the polymer precursor on the particle size can explain some deviations from this relationship, as the correlation between the particle size and absorption is well known. Finally, the NiO/Na4.2Ca2.8(Si6O18) composite was reported in this work for the first time.


Introduction
Metal oxide nanoparticles are widely used in many applications such as coatings, catalysis, electrode materials, or sensors [1]. It is important to remark that their physical and chemical properties are strongly influenced by their agglomeration [2]. In this sense, it is well known that the incorporation of metal oxides onto inert support materials with high surface areas could help prevent particle agglomeration and also improve their reactivity and stability [3,4].
NiO is a p-type semiconductor with EG = 3.5 eV presenting multiple practical applications [4][5][6]. However, their band gap can be modified by doping with other metal oxide semiconductors, and thus changing their photocatalytic properties [5,6]. NiO has been widely used in catalysis, battery cathodes, fuel cell electrodes, electrochromic films, electrochemical supercapacitors, or magnetic materials [4][5][6]. In this sense, Bonomo et al. [7] recently reported on the electrochemical and opto-electrochemical properties of nanostructured NiO for photoconversion applications. Although these applications are determined by their band-gap, which depend on the environment [8,9], no systematic studies have been reported regarding the effect of the medium on the band-gap behavior [10][11][12]. In this sense, it is well known that the dielectric medium affects the optical properties of nanoparticles, as previously observed for Au and Ag systems [10]. The optical properties of Au nanoparticles embedded into TiO2, ZrO2, and Al2O3 have been also studied qualitatively [10]. In addition, the effect of SiO2, TiO2, and ZrO2 supports was recently analyzed showing that MoO3/SiO2 is the most efficient epoxidation catalyst [12].
In previous works, we have reported a method to prepare metal and metal oxide nanostructured materials from a thermal treatment of the Chitosan (MLn)x and PS-co-4-PVP (MLn)x macromolecular complexes [16][17][18]. The method consists of two steps: (1) Formation of both macromolecular complexes by a solvent assisted reaction between the respective polymer and the metallic salt; and (2) a thermal process of the solid under air atmosphere.
In addition, the effect of the different matrices on the optical properties will also be studied and discussed.  In addition, the effect of the different matrices on the optical properties will also be studied and discussed.

Preparation of the Precursors
The coordination of the polymer was confirmed by IR analysis, as the broad ν(OH)+ ν(NH) band observed at 3448 cm −1 for free chitosan becomes unfolded upon coordination, shifting in the range of 3345-3393 cm −1 . On the other hand, the ν(py) band is shifting to high frequencies upon coordination [16][17][18].
Finally, polymer-metal complexes were placed into a box furnace (lab tech) using a pyrolysis temperature of 180 • C for the precursor complexes and 800 • C for the polymer complexes. Additional experimental conditions are summarized in Table 1.

Characterization
IR spectra were recorded with a FT-IR Jasco 4600 spectrophotometer (Jasco Inc., Easton, MD, USA). Scanning electron microscopy (SEM) was performed on a JEOL 5410 scanning electron microscope (JEOL Ltd., Tokyo, Japan). Elemental microanalysis was performed by energy dispersive X-ray (EDS) analysis using a NORAN Instrument micro-probe attached to the SEM (Thermo Scientific, Waltham, MA, USA). High-resolution transmission electron microscopy (HR-TEM) was performed using a JEOL 2000FX TEM microscope (JEOL Ltd., Tokyo, Japan)at 200 kV to characterize the average particle size, distribution, and elemental and crystal composition. EDS analysis was performed in individual particles in order to discriminate NiO from the matrix. Average particle sizes were calculated using the Digital Micrograph software (Gatan, Inc., Pleasanton, CA, US). Methylene blue (MB) was used as a model compound to test the photocatalytic properties at 655 nm under UV-Vis illumination (Shimadzu UV-2600 spectrophotometer, Shimadzu Coorporation, Kyoto, Japan) using a xenon lamp (150 W) positioned 20 cm away from the photoreactor in a 330-680 nm range at room temperature, to avoid the self-degradation and thermal catalytic effects of cationic dye. Suspensions were stirred in the dark for 60 min to establish an adsorption/desorption equilibrium, after which the photocatalytic discoloration of MB was initiated.

Composite NiO/SiO 2
The X-ray diffraction pattern of the as-synthesized NiO/SiO 2 composite for the material from the chitosan precursor is shown in Figure 2a. All the reflection peaks of the XRD pattern can be indexed to NiO and SiO 2 phases [19] (JPDS no. 03-065-2901 for NiO and JPDS no. 01-088-1535 for SiO 2 ). The broad feature appearing at 22 • corresponds to amorphous silica [19]. Similar X-ray diffraction patterns for NiO from the PVP precursor were obtained.
The SEM analysis (Figure 2b) shows irregular particle agglomerates, as typically observed from the preparation of nanoparticles using the solid-state thermal route [30]. From the TEM analysis, the agglomeration of NiO nanoparticles embedded into a mesh of SiO 2 can be observed in Figure 2c, where these agglomerates are composed of fused NiO nanoparticles. The size of these nanoparticles are in the range of 14 nm with a mean size of 25 nm (Figure 2c). Detailed HR-TEM images in Figure 2e,f show a homogeneous dispersion of NiO over the silica network. However, it was not possible to acquire high resolution images in order to study the interfaces between NiO and the different matrices. In any case, as also confirmed by SEM-EDS mapping (Figure 2g), there is a uniform distribution of NiO and SiO 2 particles. Similar results were observed for NiO obtained from the PVP precursor (see Supplementary Materials, Figure S1). The only difference is that NiO particles are bigger in size ca. 100 nm. The SEM analysis (Figure 2b) shows irregular particle agglomerates, as typically observed from the preparation of nanoparticles using the solid-state thermal route [30]. From the TEM analysis, the agglomeration of NiO nanoparticles embedded into a mesh of SiO2 can be observed in Figure 2c, where these agglomerates are composed of fused NiO nanoparticles. The size of these nanoparticles are in the range of 14 nm with a mean size of 25 nm (Figure 2c). Detailed HR-TEM images in Figure  2e,f show a homogeneous dispersion of NiO over the silica network. However, it was not possible to acquire high resolution images in order to study the interfaces between NiO and the different matrices. In any case, as also confirmed by SEM-EDS mapping (Figure 2g), there is a uniform distribution of NiO and SiO2 particles. Similar results were observed for NiO obtained from the PVP  Figure 3 shows the XRD pattern of the NiO/TiO 2 nanocomposite from the chitosan precursor, where the anatase phase and NiO are observed as single phases. Using this method, the pure TiO 2 anatase phase was obtained, in contrast with other solution methods, where a mixture of anatase and rutile in the NiO/TiO 2 composite was obtained [22]. The NiO/TiO 2 composite shows a "cotton" type morphology from the chitosan precursor (Figure 3b), whereas the morphology from the PVP precursor presents a more densified structure, as shown in Figure 3c. The SEM-EDS mapping, shown in  Figure S2). rutile in the NiO/TiO2 composite was obtained [22]. The NiO/TiO2 composite shows a "cotton" type morphology from the chitosan precursor (Figure 3b), whereas the morphology from the PVP precursor presents a more densified structure, as shown in Figure 3c. The SEM-EDS mapping, shown in Figure 2g, indicates an homogeneous distribution of NiO and TiO2. Similar results were obtained for the NiO/TiO2 from the PVP precursor (see Supplementary Materials, Figure S2).

NiO/TiO 2
The TEM analysis (Figure 3d,e) presents a "spider web" TiO2 network where the NiO nucleates forming agglomerated nanoparticles. They present a mean particle size of 25 nm (Figure 2f). A similar TEM analysis was observed for NiO/TiO2 obtained from the PVP precursor ( Figure S1b and Supplementary Materials, Figure S2).  The TEM analysis (Figure 3d,e) presents a "spider web" TiO 2 network where the NiO nucleates forming agglomerated nanoparticles. They present a mean particle size of 25 nm (Figure 2f). A similar TEM analysis was observed for NiO/TiO 2 obtained from the PVP precursor (Figure 3b and Supplementary Materials, Figure S2).   The effect of the polymer template on the morphology can be observed in Figure 4b,c. The chitosan precursor induces a "cotton" type morphology, while the PVP precursor also combines dense and Nanomaterials 2020, 10, 2470 8 of 17 irregular zones. Figure 4f shows an elemental mapping image demonstrating that NiO is well dispersed inside Al 2 O 3 . A complete characterization is shown in Supplementary Materials, Figure S3.
As observed for the NiO/TiO 2 system, the TEM analysis ( Figure 4e) shows a "spider web" network of Al 2 O 3 where the NiO nucleates form agglomerates. The histogram (Supplementary Materials, Figure S3) shows a particle mean size of 17 nm. The HRTEM image of the NiO/Al 2 O 3 from the PVP precursor is shown in Supplementary Materials, Figure 3c, where it can be observed that the medium particle size is 32 nm.
The XRD pattern of the NiO/Na 4.2 Ca 2.8 (Si 6 O 18 ) composite prepared from the chitosan precursor indicates the formation of NiO inside the glass Na 4.2 Ca 2.8 (Si 6 O 18 ) (see Figure 5a). The XRD pattern is in agreement with those reported in the literature [13][14][15]. The observed morphology is similar to the one previously reported [13][14][15] (see Figure 5b,c), also presenting a uniform distribution of NiO inside the Na 4.2 Ca 2.8 (Si 6 O 18 ) (Figure 5d). Similar conclusions can be deduced for the PVP precursor (see Supplementary Materials, Figure S4). Nanomaterials 2020, 10, x FOR PEER REVIEW 8 of 17 The effect of the polymer template on the morphology can be observed in Figure 4b,c. The chitosan precursor induces a "cotton" type morphology, while the PVP precursor also combines dense and irregular zones. Figure 4f shows an elemental mapping image demonstrating that NiO is well dispersed inside Al2O3. A complete characterization is shown in Supplementary Materials, Figure S3.
As observed for the NiO/TiO2 system, the TEM analysis ( Figure 4e) shows a "spider web" network of Al2O3 where the NiO nucleates form agglomerates. The histogram (Supplementary Material, Figure S3) shows a particle mean size of 17 nm. The HRTEM image of the NiO/Al2O3 from the PVP precursor is shown in Supplementary Materials, Figure 3c, where it can be observed that the medium particle size is 32 nm.
The XRD pattern of the NiO/Na4.2Ca2.8(Si6O18) composite prepared from the chitosan precursor indicates the formation of NiO inside the glass Na4.2Ca2.8(Si6O18) (see Figure 5a). The XRD pattern is in agreement with those reported in the literature [13][14][15]. The observed morphology is similar to the one previously reported [13][14][15] (see Figure 5b,c), also presenting a uniform distribution of NiO inside the Na4.2Ca2.8(Si6O18) (Figure 5d). Similar conclusions can be deduced for the PVP precursor (see Supplementary Materials, Figure S4).   A summary of the medium particle sizes for NiO included into the different matrices is presented in Table 2, where the effect of the matrix and that of the polymer precursors on the final particle sizes can be observed. The nanoparticle size of NiO obtained from the PVP precursor inside the matrices follow the order of SiO 2 > TiO 2 > Al 2 O 3 , while that for the NiO from the chitosan precursor does not present a significant effect on the nanoparticle size.

Photocatalytic Behavior
Although the main applied property of NiO is in the field of electrochemistry as Li-ion batteries [32] and supercapacitors applications, [33] its application as a photocatalytic activity toward organic dyes have also been suggested [34]. In any case, reports on the photocatalytic activity toward organic dyes using NiO/matrices are scarce. Yu et al. [6] found a higher photocatalytic activity for NiO/TiO 2 than for pure NiO, towards the photodegradation of p-chlorophenol. Regarding the photocatalytic efficiency when using composites, important parameters to be considered include the formation of hierarchical porous structures, the dispersion of the catalytic semiconductor on the matrix surface, and the p-n junction in a NiO/M x O y composite, where a new band gap will be formed with a most favorable value for the photodegradation chemical processes.

NiO
Methylene blue (MB) is extensively used as an organic dye in coloring paper, temporary hair colorant, dyeing cottons, and coating for paper stock [35]. The removal of this hazardous dye is considered as one of the growing requirements in recent years. The photocatalytic experiments were carried on the sample with definite dye concentration under dark conditions and UV irradiation. The band-gap of the NiO is 5.0 and 5.2 eV, when it is prepared from chitosan and PVP precursors, respectively. For the semiconductor metal oxides, their band gap value dictates their photocatalytic activity [35,36]. For this reason, the band gap of the C 3 -C 8 composites was determined. These values are: 5.0, 5.2, and 5.4 eV for the NiO/SiO 2 , NiO/TiO 2 , NiO/Al 2 O 3 composites, respectively, all obtained from the chitosan precursors. The values for the PVP precursor are: 5.5 eV, 5.2 eV for the NiO/SiO 2 , NiO/TiO 2 composites, respectively. Those values do not change significantly, and are slightly higher than those reported previously, which can be due to their bigger particle sizes [34] (see Supplementary Materials, Figure S5).
The changes in the absorption spectra of the MB aqueous solution exposed to UV light for various times in the presence of NiO are shown in Supplementary Materials, Figure S6. The peak at 655 nm is characteristic of methylene blue and decreases with the irradiation time. Figure 6 shows the plot of time vs. concentration of methylene blue measured as C/C o for NiO arising from both precursors, obtaining a catalytic efficiency of~68% and~71% of degradation in 5 h (see Figure 6c). Both degradation processes follow a zero order, as shown in Figure 6b,d. As previously mentioned, only a few photodegradation studies for NiO have been reported. For example, using 3 nm NiO nanoparticles [34] and NiO nanofibers [5], a moderated catalytic activity towards Rhodamine B was observed. In both cases, the degradation kinetic was zero order, which means that the rate of degradation does not depend on the MB concentration. This type of model is normally observed when the surface of the photocatalyst is saturated with the dye, so that the degradation rate remains relatively constant, depending only on the generation of photo-induced charges in the catalyst. Nanomaterials 2020, 10, x FOR PEER REVIEW 10 of 17 nanoparticles [34] and NiO nanofibers [5], a moderated catalytic activity towards Rhodamine B was observed. In both cases, the degradation kinetic was zero order, which means that the rate of degradation does not depend on the MB concentration. This type of model is normally observed when the surface of the photocatalyst is saturated with the dye, so that the degradation rate remains relatively constant, depending only on the generation of photo-induced charges in the catalyst.

NiO in Matrices
The photocatalytic activity towards MB degradation for the NiO composite using different matrices is shown in Figure 7. The degradation rate of the NiO/TiO2 composite is shown for comparison. In any case, the photocatalytic activity of these NiO compounds is still far from the pure TiO2 standard phase [37]. For example, we have recently reported a 98% discoloration rate in only 25 min for TiO2 nanostructures using similar synthetic routes, and the degradation of commercial TiO2 (Degussa P25) is about 75% of MB under the same experimental conditions [38]. A representative plot of MB absorption at 655 nm vs. time is given in Supplementary Materials, Figure S6. A summary of the kinetic degradation data is also displayed in Table 3.

NiO in Matrices
The photocatalytic activity towards MB degradation for the NiO composite using different matrices is shown in Figure 7. The degradation rate of the NiO/TiO 2 composite is shown for comparison. In any case, the photocatalytic activity of these NiO compounds is still far from the pure TiO 2 standard phase [37]. For example, we have recently reported a 98% discoloration rate in only 25 min for TiO 2 nanostructures using similar synthetic routes, and the degradation of commercial TiO 2 (Degussa P25) is about 75% of MB under the same experimental conditions [38]. A representative plot of MB absorption at 655 nm vs. time is given in Supplementary Materials, Figure S6. A summary of the kinetic degradation data is also displayed in Table 3. Nanomaterials 2020, 10, x FOR PEER REVIEW 12 of 17

Photocatalytic Activity of the NiO/Na4.2Ca2.8(Si6O18) Composite
The photocatalytic activity of the NiO/Na4.2Ca2.8(Si6O18) composite obtained from the chitosan precursor is shown in Figure 7 and the kinetic data is also shown in Table 2. It is observed that the photocatalytic activity is higher than that of NiO, NiO/SiO2, and NiO/Al2O3 but lower than of NiO/TiO2. It is concluded that the Na4.2Ca2.8(Si6O18) sample presents a similar behavior to those of the SiO2 sample.  Figure S9. The band-gap values were estimated from these spectra using the Tauc procedure (Supplementary Materials, Figure S9). Considering that the static dielectric constants (K) for the matrices are: SiO2 3.9; TiO2 80, and Al2O3 8.8 [43], both Eg and λmax could be related to the dielectric constant of the matrix. Unfortunately, there is no available data for Na4.2Ca2.8(Si6O18). The dependence of Eg with the dielectric constant ε is not totally understood, where several relationships have been previously found [43][44][45]. The shape of the experimental or theoretical expression depends, among others, on the type of materials. On the other hand, the relationship of λmax with ε and the refractive index n is known for metallic nanoparticles [8]:   As seen in Figure 6, the NiO from the chitosan precursor produces a higher activity than that arising from the PVP precursor. These results also apply for both SiO 2 and TiO 2 matrices. Interestingly, the most efficient photocatalytic activity was observed for the NiO/TiO 2 composite with a 91% degradation of methylene blue in 5 h. This can be probably related with a matrix effect of SiO 2 , TiO 2 , and Al 2 O 3 .

Effect of the Matrices on λmax and Eg
Our results of catalytic degradation for the NiO//TiO 2 composite (about 91%) are similar or slightly higher than those reported in the literature. Ahmed claimed 90% of catalytic degradation efficiency on the NiO//TiO 2 composite prepared from titanium chloride and nickel acetylacetonate [39]. Faisal et al. obtained a similar catalytic degradation efficiency using an ultrasonication method [40]. Sim et al. reported 86% of the degradation efficiency using plasma enhanced chemical vapor deposition (PECVD) with hydro-oxygenated amorphous titanium dioxide obtained from titanium tetra-isopropoxide [Ti(OC3H7)4, TTIP] liquid as a precursor [41]. Finally, Chen et al. reported 86% catalytic degradation of MB using a method that involves incipient wet impregnation of the nickel oxide (NiO) nanoparticles over previously prepared TiO 2 nanotubes [24].
It is suggested that for the most catalytically active TiO 2 as the matrix, a p-n junction can be formed acting NiO as p-NiO and TiO 2 as n-TiO 2 , see Supplementary Materials, Figure S7, leading to a reduction of the recombination rate of photogenerated electron-hole pairs, which is known to enhance the photocatalytic activity of TiO 2 . A detailed description of the mechanism can be found on Supplementary Materials, Figure S8. Therefore, it seems that the matrix is playing a crucial role for the NiO/TiO 2 composite and in this case, the NiO acts as the matrix rather than an active semiconductor.
On the other hand, the less efficient photocatalyst toward MB degradation arises probably from an insulating Al 2 O 3 effect [28,42], which preclude the p-NiO behavior. This is in agreement with the observed photocatalytic decrease for the TiO 2 /SiO 2 composite in comparison with pure TiO 2 . In the case of the NiO/SiO 2 composite, the lower photocatalytic activity is probably a consequence of the high porous morphology which is induced by the SiO 2 matrix. All the photodegradation processes of MB with NiO/SiO2, NiO/TiO 2 , NiO/Al 2 O 3 , and NiO/Na 4.2 Ca 2.8 (Si 6 O 18 ) composites exhibited a zero order kinetic law, as shown in Supplementary Materials, Figure S9. The photocatalytic activity of the NiO/Na 4.2 Ca 2.8 (Si 6 O 18 ) composite obtained from the chitosan precursor is shown in Figure 7 and the kinetic data is also shown in Table 2. It is observed that the photocatalytic activity is higher than that of NiO, NiO/SiO 2 , and NiO/Al 2 O 3 but lower than of NiO/TiO 2 . It is concluded that the Na 4.2 Ca 2.8 (Si 6 O 18 ) sample presents a similar behavior to those of the SiO 2 sample.
3.9. Effect of the Matrices on λ max and E g Figure 8 shows the variation of both E g and λ max for the different matrices. The respective UV-Vis absorption spectra of the composites are shown in Supplementary Materials, Figure S9. The band-gap values were estimated from these spectra using the Tauc procedure (Supplementary Materials, Figure S9). Considering that the static dielectric constants (K) for the matrices are: SiO 2 3.9; TiO 2 80, and Al 2 O 3 8.8 [43], both E g and λ max could be related to the dielectric constant of the matrix. Unfortunately, there is no available data for Na 4.2 Ca 2.8 (Si 6 O 18 ). The dependence of E g with the dielectric constant ε is not totally understood, where several relationships have been previously found [43][44][45]. The shape of the experimental or theoretical expression depends, among others, on the type of materials. On the other hand, the relationship of λ max with ε and the refractive index n is known for metallic nanoparticles [8]:

Photocatalytic Activity of the NiO/Na4.2Ca2.8(Si6O18) Composite
The photocatalytic activity of the NiO/Na4.2Ca2.8(Si6O18) composite obtained from the chitosan precursor is shown in Figure 7 and the kinetic data is also shown in Table 2. It is observed that the photocatalytic activity is higher than that of NiO, NiO/SiO2, and NiO/Al2O3 but lower than of NiO/TiO2. It is concluded that the Na4.2Ca2.8(Si6O18) sample presents a similar behavior to those of the SiO2 sample.  Figure S9. The band-gap values were estimated from these spectra using the Tauc procedure (Supplementary Materials, Figure S9). Considering that the static dielectric constants (K) for the matrices are: SiO2 3.9; TiO2 80, and Al2O3 8.8 [43], both Eg and λmax could be related to the dielectric constant of the matrix. Unfortunately, there is no available data for Na4.2Ca2.8(Si6O18). The dependence of Eg with the dielectric constant ε is not totally understood, where several relationships have been previously found [43][44][45]. The shape of the experimental or theoretical expression depends, among others, on the type of materials. On the other hand, the relationship of λmax with ε and the refractive index n is known for metallic nanoparticles [8]:

Effect of the Matrices on λmax and Eg
λmax α λp√2 + 1≅ √2 λp n (1)  However, the analogue relationship for metal oxides is not completely understood. The plot of λ max for the NiO vs. the refractive index [46,47] for the SiO 2 , TiO 2 , and Al 2 O 3 matrices shows an inverse and irregular relationship (see Supplementary Materials, Figure S10). Then, according to Figure 8, the variations of E g and λ max can be explained by a physical effect of the medium reflected in their dielectric constant of the different matrices. A close inspection of Figure 8 suggests the presence of three linear trends. In Figure 8, it can be observed that λmax varied inversely with the properties of the matrices (i.e., dielectric constant for instance) for the NiO obtained from both polymers in an approximate linear behavior. The composite C 8 having a "silica like" matrix does not follow this trend due to an unknown effect. Although the dependence of λmax with the dielectric or refractive index given by Equation (1) indicates a direct linear dependence, our results show an inverse linear trend. Then, the Equation (1) may not be valid for metallic oxides. A new equation is proposed (Equation (2), curve a in Figure 8), which could arise from the general trends for nanostructured metallic oxides. This is consistent with the fact observed in Supplementary Materials, Figure S9, where an inverse relationship of λmax with n is shown.
In addition, Eg values vary in a direct or inverse way depending on the NiO polymer precursor (direct behavior for the chitosan; curve b, Equation (3) or inverse for the PVP precursor; curve c, Equation (4)). As previously mentioned, the dependence of E g with the dielectric constant ε is not totally understood, and this is a matter of controversy in the literature. The inverse relationship (curve c) is in agreement with the results reported by Hervé and Vandamme [48], while the direct relationship (curve b) shows a similar trend to that shown by Kumar and Singh [49]. In any case, we do not have any clear explanation of the different dependencies of Eg with n and ε when using the different polymer precursors.
From the plot shown in Figure 8, the following equations can be established: λ max = a/(ε,n); valid for NiO from chitosan and PVP (2) Eg = b/(ε,n); valid for NiO from chitosan (3) Eg = c/(ε,n); valid for NiO from PVP (4) The following equations are then obtained by combining both expressions: Eg = ab/λ max ; valid for NiO from chitosan (5) Eg = cλ max /a; valid for NiO from PVP (6) In agreement with these new expressions, we can explain the effect of the physical properties of the matrices on the band gap with the refraction index or the dielectric constant. The experimental data fits into these equations, as seen in Figure 9 plots d (Equation (5)) and e (Equation (6)). These equations describing the effect of the medium modulated by various solid matrices on the band gap and the maximum absorption could be valid for other nanostructured metal oxides included in solid matrices. In order to validate this, additional experiments with other systems are being carried out.

Conclusions
NiO/SiO2, NiO/TiO2, NiO/Al2O3, and NiO/glass composites were satisfactorily prepared by a solid-state synthesis from the chitosan and PVP precursors. XRD, SEM/EDS, and HR-TEM were used to characterize the new formed composites. It was concluded that the nature of the precursor Experiments linking the band gap with the size and the maxima absorption of nanoparticles have been performed for other metal oxides such as ZnO [50,51], as well as for noble metal nanoparticles such as Au [52], Ag [32], and Pt [53]. However, there are no studies in the literature about the medium expressed by solid matrices on nanostructured metallic oxides.

Conclusions
NiO/SiO 2 , NiO/TiO 2 , NiO/Al 2 O 3 , and NiO/glass composites were satisfactorily prepared by a solid-state synthesis from the chitosan and PVP precursors. XRD, SEM/EDS, and HR-TEM were used to characterize the new formed composites. It was concluded that the nature of the precursor polymer influences the morphology, as well as the size of the obtained nanoparticles. The chitosan precursor induces the smallest NiO nanoparticles and also their respective nanocomposites. In addition, the nature of the matrix influences the NiO nanoparticle size, following the order of SiO 2 > TiO 2 > Al 2 O 3 for the PVP precursor. However, no relationship on the particle size was observed for the NiO obtained from the chitosan precursor.
The efficiency on the photocatalytic activity depends on the formation of a p-n junction between NiO acting as p-NiO and the metal oxide matrix acting as n-metal oxide. TiO 2 presents the most effective p-NiO//n-TiO 2 junction. On the other hand, the optical parameters Eg and λ max depends on the dielectric constant and the refractive index of the matrix medium in a manner which depends on the preparation procedure. The "silica like" Na 4.2 Ca 2.8 (Si 6 O 18 ) matrix does not follow these correlations. New equations describing the effect of the physical properties (dielectric constant and the refractive index) are proposed, which could be used for other metal oxides included in solid matrices.