TiO 2 @lipophilic Porphyrin Composites: New Insights into Tuning the Photoreduction of Cr(VI) to Cr(III) in Aqueous Phase

: Metal-free and Cu(II)-lipophilic porphyrins [H 2 Pp and Cu(II)Pp] loaded on titanium dioxide in the anatase phase (TiO 2 ) were prepared and used as a heterogeneous catalyst for the photoreduction of Cr(VI) to Cr(III) in aqueous suspensions under UV–Vis light irradiation. TiO 2 impregnated with copper(II) porphyrin [TiO 2 @Cu(II)Pp] was the most e ﬀ ective in photocatalyst reduction of toxic chromate Cr(VI) to non-toxic chromium Cr(III). We further evaluated an experimental design with the scope of fast optimization of the process conditions related to the use of TiO 2 or TiO 2 -porphyrin based photocatalysts. A full factorial design as a chemometric tool was successfully employed for screening the a ﬀ ecting factors involved in photoconversion catalysis, with the modiﬁcation of TiO 2 both with porphyrin H 2 Pp and Cu(II)Pp. The studied experimental factors were the catalyst amount, the concentration of Cr(VI) ions, and the pH of the medium. The performed multivariate approach was successfully used for fast ﬁtting and better evaluation of signiﬁcant factors a ﬀ ecting the experimental responses, with the advantage of reducing the number of available experiments. Thus, the stability of the optimized TiO 2 embedded Cu(II)Pp was investigated, conﬁrming the high reproducibility and suitability for environmental purposes.


Introduction
Heavy metals represent a cause of environmental contamination that affects the quality of the different matrices, thus, monitoring is nowadays strictly required. Even in trace concentrations, heavy metals can accumulate at different levels in trophic pathways and the toxicity of specific metal ions is largely known. The species of metal ions usually monitored because of their toxicity are also explicated at trace concentrations such as Hg, Cd, Pb, As, and Cr. Generally, the common persistent species of chromium present in the environment are represented by the trivalent and hexavalent form (Cr(III) and Cr(VI), respectively). Basically, Cr(III) is relatively non-toxic and can be found in trace amounts as 2 of 12 an essential nutrient in various biological pathways, whereas Cr(VI) is related to highly toxic effects on health and the environment [1]. Chemically, the chromate species are strong oxidants and act as carcinogens, mutagens, and teratogens. Considering the use of hexavalent chromium in dyeing, wood, textile, metallurgy, and tanning industries and its toxic nature, the development of an eco-friendly and low-cost process to remove Cr(VI) from sensitive stores is a great challenge for the wastewater and process waste industries [2].
Currently, the most commonly employed processes for the removal of Cr(VI) are adsorption, biosorption [3,4], electrocoagulation, ion exchange, reverse osmosis, liquid-liquid extraction, precipitation, photocatalytical reduction [5,6], and electrochemistry [7,8]. In particular, the photocatalytical reduction of chromate ions mostly employs titanium dioxide (TiO 2 ) as the catalyst [3,5,[9][10][11][12][13]. Basically, the photocatalysis of TiO 2 structures mainly hinges on the excitations of electrons from the semiconductor's valence band (VB) to the conduction band (CB), which are thus involved in redox processes. The photogenerated electrons are also responsible for the highly reductive properties of photocatalyst reactions [14]. Moreover, the advantages of using TiO 2 as photocatalysts include the lower synthesis cost, eco-friendly application, and their photo resistance, which reveal their suitability as composite materials for different purposes.
Titanium dioxide catalysts opportunely sensitized with lipophilic porphyrins or phthalocyanines have been particularly used both in the degradation of organic compounds [15] and in photoreduction reactions of CO 2 to formic acid [16]. Additionally, the application of TiO 2 and Cu/TiO 2 structures for the photoreduction of CO 2 to methanol has been reported in the literature [17]. Enzyme modified TiO 2 has also been studied for efficient and clean photoreduction to CO under visible light [18]. Furthermore, in order to improve the photocatalytic performances of TiO 2 , dyes and pigments as impregnated nanomaterials have been successfully proposed. For example, dye-sensitized TiO 2 has been applied for solar energy conversion, photocatalysis, and related processes, with the advantage of involving low cost technologies, decreasing the negative impact on the environment and enhancing power conversion at the same time. Porphyrins are among the most interesting sensitizers capable of enhancing the photocatalytic activity of TiO 2 in the visible light region [15,19,20]. In fact, the presence of porphyrin structures increased the photocatalytic reactions due to the position and spacer length of peripherally substituted groups on porphyrin, the strength of the other involved polar groups, and the electroactivity of the atoms [20]. Recently, among these sensitizers, various Cu(II) porphyrins-TiO 2 have been proposed for the photodegradation of organics [21,22] and hydrogen production [23]. In light of these considerations, the possibility of promoting light induced photocatalysis can be considered as a promising approach for the fabrication of novel composites with unique physical-chemical properties with the scope to transform Cr(VI) to Cr(III) in water matrices [24].
With the aim to remove toxic compounds from the environment, an effective green method is highly desirable. In this respect, the favorable operation conditions of photocatalyst composites represent a promising and alternative approach for practical applications when compared with conventional methods. In light of this, this work relies on the application of our previously prepared catalyst [25] impregnated with a renewable and natural meso-tetraarylporphyrin with metal-free and metal complexes (with Cu 2+ ) for the photocatalyst reduction of Cr(VI) ions. From the application point of view, the stability of catalysts plays an important role and their performances can be faster evaluated by using condensed methods. The investigation of catalyst performances most commonly follows the univariate one-factor-at-time (OFAT) approach, where parameters are subsequently treated and screened as independent of each other. In contrast, multivariate evaluation of parameters by design of experiments (DOE) offers a statistically significant model of a phenomenon by performing a minimum set of experiments [26,27]. The advantage consists of obtaining a model suited for describing the importance of each variable and the interaction effects between them. Moreover, the multivariate analysis allows for the reduction in cost and time of operation processes, which is highly required for real contexts.
In this work, TiO 2 powders were impregnated with a lipophilic metal-free porphyrin [H 2 Pp] and copper porphyrin [Cu(II)Pp], respectively, according to a procedure developed by Mele and co-workers [12]. To the best of our knowledge, this is the first time that the composites, listed as TiO 2 @Cu(II)Pp and TiO 2 @H 2 Pp, have been used as heterogeneous catalysts for the photoreduction of Cr(VI) to Cr(III) in aqueous suspensions under UV-Vis light irradiation, and their activity was compared with the pristine TiO 2 . We successfully adopted a DOE as a key-tool to assess and quickly compare the performances of the TiO 2 , TiO 2 @H 2 Pp, and TiO 2 @Cu(II)Pp composites. Thus, the effects of (i) pH, (ii) Cr(VI) ion concentration, and (iii) catalyst amount were simultaneously investigated with respect to the photoreduction efficiency of Cr(VI) to Cr(III) ions under UV-Vis light. The experimental design was successfully applied for faster evaluation of the performances of these kinds of catalysts. Upon the selected conditions, the reproducibility and reusability of the catalysts were studied and finally proposed for the photoreduction of Cr(VI) ions in water suspension.

Chemicals
Titanium dioxide of a high degree of purity in the crystalline form of anatase (specific surface area 8 m 2 g −1 ) was provided by Huntsman Tioxide (Varese, Italy). H 2 SO 4 (98%), CuCl 2 , K 2 Cr 2 O 7 , and 1,5-diphenylacarbazide were purchased from Sigma-Aldrich (Milano, Italy). Ultrapure water (Millipore System) was used as the solvent. The porphyrins employed in this work, opportunely functionalized with lipophilic (3-(pentadeca-8-enyl)-phenol) chains derived of a natural origin, were prepared for the first time as previously reported [25]. H 2 Pp and Cu(II)Pp were successively impregnated onto the TiO 2 surface and the related composites TiO 2 @H 2 Pp and TiO 2 @Cu(II)Pp were produced according to the previously described procedure [12]. All other chemicals used in this work were of analytical grade and were used without any purification.

Photocatalytic Activity
The photocatalytic activity of different catalysts (TiO 2 , TiO 2 @H 2 Pp and TiO 2 @Cu(II)Pp) were investigated by observing the efficiency of the photocatalytic conversion of Cr(VI) ions in water. Briefly, the experimental setup consisted of a batch photoreactor containing 50 mL of the catalyst dispersion and a solution of Cr(VI) in water. The mixture was magnetically stirred at 1000 rpm and irradiated using a Osram UltraVitalux UV-Vis lamp (OSRAM, Milano, Italy) at the distance of 15 cm from the batch solution. The emission spectrum of the lamp is shown in Figure 1. TiO2@Cu(II)Pp and TiO2@H2Pp, have been used as heterogeneous catalysts for the photoreduction of Cr(VI) to Cr(III) in aqueous suspensions under UV-Vis light irradiation, and their activity was compared with the pristine TiO2. We successfully adopted a DOE as a key-tool to assess and quickly compare the performances of the TiO2, TiO2@H2Pp, and TiO2@Cu(II)Pp composites. Thus, the effects of (i) pH, (ii) Cr(VI) ion concentration, and (iii) catalyst amount were simultaneously investigated with respect to the photoreduction efficiency of Cr(VI) to Cr(III) ions under UV-Vis light. The experimental design was successfully applied for faster evaluation of the performances of these kinds of catalysts. Upon the selected conditions, the reproducibility and reusability of the catalysts were studied and finally proposed for the photoreduction of Cr(VI) ions in water suspension.

Chemicals
Titanium dioxide of a high degree of purity in the crystalline form of anatase (specific surface area 8 m 2 g -1 ) was provided by Huntsman Tioxide (Varese, Italy). H2SO4 (98%), CuCl2, K2Cr2O7, and 1,5-diphenylacarbazide were purchased from Sigma-Aldrich (Milano, Italy). Ultrapure water (Millipore System) was used as the solvent. The porphyrins employed in this work, opportunely functionalized with lipophilic (3-(pentadeca-8-enyl)-phenol) chains derived of a natural origin, were prepared for the first time as previously reported [25]. H2Pp and Cu(II)Pp were successively impregnated onto the TiO2 surface and the related composites TiO2@H2Pp and TiO2@Cu(II)Pp were produced according to the previously described procedure [12]. All other chemicals used in this work were of analytical grade and were used without any purification.

Photocatalytic Activity
The photocatalytic activity of different catalysts (TiO2, TiO2@H2Pp and TiO2@Cu(II)Pp) were investigated by observing the efficiency of the photocatalytic conversion of Cr(VI) ions in water. Briefly, the experimental setup consisted of a batch photoreactor containing 50 mL of the catalyst dispersion and a solution of Cr(VI) in water. The mixture was magnetically stirred at 1000 rpm and irradiated using a Osram UltraVitalux UV-Vis lamp (OSRAM, Milano, Italy) at the distance of 15 cm from the batch solution. The emission spectrum of the lamp is shown in Figure 1. During the photoreaction, samples (1 mL) were taken out at specific time intervals (15,30, and 60 min) and filtered to remove the catalyst dispersion. The residual concentration of Cr(VI) ions in solution was determined by using the UV-Vis spectrophotometer with the standardized colorimetric method of 1,5-diphenyl carbazide (DPC, ʎ = 540 nm) [28]. The photoreduction efficiency (PE) of the catalysts was estimated from Equation (1): where C0 and Ct were the initial concentration and the residual concentration at the irradiation time t, respectively. A schematic diagram of the experimental setup is presented in Scheme 1. During the photoreaction, samples (1 mL) were taken out at specific time intervals (15,30, and 60 min) and filtered to remove the catalyst dispersion. The residual concentration of Cr(VI) ions in solution was determined by using the UV-Vis spectrophotometer with the standardized colorimetric method of 1,5-diphenyl carbazide (DPC, TiO2@Cu(II)Pp and TiO2@H2Pp, have been used as heterogeneous catalysts for the photoreduction of Cr(VI) to Cr(III) in aqueous suspensions under UV-Vis light irradiation, and their activity was compared with the pristine TiO2. We successfully adopted a DOE as a key-tool to assess and quickly compare the performances of the TiO2, TiO2@H2Pp, and TiO2@Cu(II)Pp composites. Thus, the effects of (i) pH, (ii) Cr(VI) ion concentration, and (iii) catalyst amount were simultaneously investigated with respect to the photoreduction efficiency of Cr(VI) to Cr(III) ions under UV-Vis light. The experimental design was successfully applied for faster evaluation of the performances of these kinds of catalysts. Upon the selected conditions, the reproducibility and reusability of the catalysts were studied and finally proposed for the photoreduction of Cr(VI) ions in water suspension.

Chemicals
Titanium dioxide of a high degree of purity in the crystalline form of anatase (specific surface area 8 m 2 g -1 ) was provided by Huntsman Tioxide (Varese, Italy). H2SO4 (98%), CuCl2, K2Cr2O7, and 1,5-diphenylacarbazide were purchased from Sigma-Aldrich (Milano, Italy). Ultrapure water (Millipore System) was used as the solvent. The porphyrins employed in this work, opportunely functionalized with lipophilic (3-(pentadeca-8-enyl)-phenol) chains derived of a natural origin, were prepared for the first time as previously reported [25]. H2Pp and Cu(II)Pp were successively impregnated onto the TiO2 surface and the related composites TiO2@H2Pp and TiO2@Cu(II)Pp were produced according to the previously described procedure [12]. All other chemicals used in this work were of analytical grade and were used without any purification.

Photocatalytic Activity
The photocatalytic activity of different catalysts (TiO2, TiO2@H2Pp and TiO2@Cu(II)Pp) were investigated by observing the efficiency of the photocatalytic conversion of Cr(VI) ions in water. Briefly, the experimental setup consisted of a batch photoreactor containing 50 mL of the catalyst dispersion and a solution of Cr(VI) in water. The mixture was magnetically stirred at 1000 rpm and irradiated using a Osram UltraVitalux UV-Vis lamp (OSRAM, Milano, Italy) at the distance of 15 cm from the batch solution. The emission spectrum of the lamp is shown in Figure 1. During the photoreaction, samples (1 mL) were taken out at specific time intervals (15,30, and 60 min) and filtered to remove the catalyst dispersion. The residual concentration of Cr(VI) ions in solution was determined by using the UV-Vis spectrophotometer with the standardized colorimetric method of 1,5-diphenyl carbazide (DPC, ʎ = 540 nm) [28]. The photoreduction efficiency (PE) of the catalysts was estimated from Equation (1): where C0 and Ct were the initial concentration and the residual concentration at the irradiation time t, respectively. A schematic diagram of the experimental setup is presented in Scheme 1.
= 540 nm) [28]. The photoreduction efficiency (PE) of the catalysts was estimated from Equation (1): where C 0 and C t were the initial concentration and the residual concentration at the irradiation time t, respectively. A schematic diagram of the experimental setup is presented in Scheme 1.
J. Compos. Sci. 2020, 4, x FOR PEER REVIEW 4 of 12 Scheme 1. Schematic diagram for the adopted experimental setup and analytical responses obtained for the conversion of Cr(V) ions by using TiO2 or TiO2-porphyrin based photocatalysts.

Experimental Design
Multivariate analysis was conducted to investigate the variables on the photoreduction efficiency and covered all interactions between parameters. Basically, the experimental design was a full factorial, with three replicated central points (2 k , k = 3; central points: 3). The pH, Cr(VI) concentration, and the amount of catalyst were selected as variables. A total of 11 experiments were conducted randomly to avoid the occurrence of unwanted systematic effects. The responses of the unmodified catalyst (TiO2), the TiO2@H2Pp, and the TiO2@Cu(II)Pp were compared and all the results were analyzed using MODDE 12.1 software (Umetrics, Umea, Sweden). The selected factors were studied in two levels, as reported in Table 1. mg L −1 500 1500 As previously reported by our group [16], the optimized ratio between Cu(II)Pp and TiO2 composite was found to be 6.65 µmol/g per TiO2 and thus selected for further investigation. The level of each factor agreed with those reported in the literature. In particular, the levels of pH were chosen according to the observed enhanced catalytical efficiency of TiO2 at lower pH [29]. A solution of sulfuric acid (0.1 N) was used to bring the desiderated pH within 2 and 5. The concentration of Cr(VI) and the amount of catalyst were studied in the range between 5-15 mg L -1 and 500-1500 mg L -1 , respectively. The polynomial equation for 2 3 factors containing coefficients weighting both linear terms and their interactions is reported in Equation (2): where b0, bi, and bij represent the coefficient related to the constant, linear, and interaction terms, respectively.

Raman Spectroscopy Characterization
The Micro-Raman measurements were carried out with a Renishaw inVia instrument, equipped with two laser sources, a diode and a He-Cd laser with excitation wavelengths of 785 nm and 442 nm, respectively, edge filters for both laser lines, and a Leica DMLM microscope [30,31] (Leica, Solms, Germany) with motorized xyz stage and objectives up to 50x with a spatial resolution of about 2 µm. Neutral density filters were employed to keep the laser power at a low level (0.5-2 mW) on the samples to avoid undesired heating effects. The spectra were collected with repeated acquisitions (3-5) each of 10 s. The wavelength scale was calibrated using a Si(111) standard (520.5 cm −1 ). The catalyst, the porphyrin structures, and the modified catalyst free metal and metal chelated one were compared, and the obtained spectra were identified with that reported in the literature.

Experimental Design
Multivariate analysis was conducted to investigate the variables on the photoreduction efficiency and covered all interactions between parameters. Basically, the experimental design was a full factorial, with three replicated central points (2 k , k = 3; central points: 3). The pH, Cr(VI) concentration, and the amount of catalyst were selected as variables. A total of 11 experiments were conducted randomly to avoid the occurrence of unwanted systematic effects. The responses of the unmodified catalyst (TiO 2 ), the TiO 2 @H 2 Pp, and the TiO 2 @Cu(II)Pp were compared and all the results were analyzed using MODDE 12.1 software (Umetrics, Umea, Sweden). The selected factors were studied in two levels, as reported in Table 1. As previously reported by our group [16], the optimized ratio between Cu(II)Pp and TiO 2 composite was found to be 6.65 µmol/g per TiO 2 and thus selected for further investigation. The level of each factor agreed with those reported in the literature. In particular, the levels of pH were chosen according to the observed enhanced catalytical efficiency of TiO 2 at lower pH [29]. A solution of sulfuric acid (0.1 N) was used to bring the desiderated pH within 2 and 5. The concentration of Cr(VI) and the amount of catalyst were studied in the range between 5-15 mg L −1 and 500-1500 mg L −1 , respectively. The polynomial equation for 2 3 factors containing coefficients weighting both linear terms and their interactions is reported in Equation (2): where b 0 , b i , and b ij represent the coefficient related to the constant, linear, and interaction terms, respectively.

Raman Spectroscopy Characterization
The Micro-Raman measurements were carried out with a Renishaw inVia instrument, equipped with two laser sources, a diode and a He-Cd laser with excitation wavelengths of 785 nm and 442 nm, respectively, edge filters for both laser lines, and a Leica DMLM microscope [30,31] (Leica, Solms, Germany) with motorized xyz stage and objectives up to 50x with a spatial resolution of about 2 µm. Neutral density filters were employed to keep the laser power at a low level (0.5-2 mW) on the samples to avoid undesired heating effects. The spectra were collected with repeated acquisitions (3)(4)(5) each of 10 s. The wavelength scale was calibrated using a Si(111) standard (520.5 cm −1 ). The catalyst, the porphyrin structures, and the modified catalyst free metal and metal chelated one were compared, and the obtained spectra were identified with that reported in the literature.

Full Factorial Design
In this work, the multivariate analysis conducted by MODDE software permitted us to elucidate (i) the distribution of the experimental data; (ii) the significance of factors; and (iii) the model fitting the experimental values, confirmed by the reproducibility and validity of the model. Table 2 shows the experimental matrix and the relative responses (Y, photoreduction efficiency) in the case of TiO 2 , TiO 2 @H 2 Pp, and TiO 2 @Cu(II)Pp, respectively.  2  7  5  5  500  21  18  23  3  6  2  15  500  17  16  31  4  5  5  15  500  12  14  16  5  4  2  5  1500  41  67  88  6  9  5  5  1500  38  28  48  7  2  2  15  1500  47  28  50  8  8  5  15  1500  17  15  22  9  3  3.5  10  1000  25  23  28  10  10  3.5  10  1000  27  28  32  11  11 3.5 10 1000 29 30 30 As a preliminary note, the TiO 2 @Cu(II)Pp catalyst had the highest photoconversion efficiency compared to the others. In particular, experiment no. 5 showed the highest achieved differences in photoreduction efficiency, whereas slight photocatalytical activity was observed in the other cases. Under the experimental conditions of experiment no. 5, TiO 2 @Cu(II)Pp revealed the maximum photoreduction efficiency of Cr(VI), as expected. In fact, the increased activity can be easily ascribed to the presence of metal porphyrin, which leads to the enhanced electron transport into TiO 2 networks. In fact, we have already demonstrated that the presence of copper into the coordination of macrocycles plays a favorable role in photoreaction processes [15]. The mechanism for the enhanced photoactivity of TiO 2 @Cu(II)Pp is schematically described in Scheme 2.

Full Factorial Design
In this work, the multivariate analysis conducted by MODDE software permitted us to elucidate (i) the distribution of the experimental data; (ii) the significance of factors; and (iii) the model fitting the experimental values, confirmed by the reproducibility and validity of the model. Table 2 shows the experimental matrix and the relative responses (Y, photoreduction efficiency) in the case of TiO2, TiO2@H2Pp, and TiO2@Cu(II)Pp, respectively. As a preliminary note, the TiO2@Cu(II)Pp catalyst had the highest photoconversion efficiency compared to the others. In particular, experiment no. 5 showed the highest achieved differences in photoreduction efficiency, whereas slight photocatalytical activity was observed in the other cases. Under the experimental conditions of experiment no. 5, TiO2@Cu(II)Pp revealed the maximum photoreduction efficiency of Cr(VI), as expected. In fact, the increased activity can be easily ascribed to the presence of metal porphyrin, which leads to the enhanced electron transport into TiO2 networks. In fact, we have already demonstrated that the presence of copper into the coordination of macrocycles plays a favorable role in photoreaction processes [15]. The mechanism for the enhanced photoactivity of TiO2@Cu(II)Pp is schematically described in Scheme 2.

Scheme 2.
Mechanism of electron transport of the catalyst in the presence of CuPp.
As described in Scheme 2, the higher performances of TiO2 in the presence of Cu(II)Pp is due to the electron and hole transfer between the catalyst structures. In particular, Cu-Pp caused the edge shift responsible for the electron transport [23]. In the presence of UV light irradiation, the photogenerated electrons can be attracted by Cu(II)Pp, leading to the lower charge recombination. In Scheme 2. Mechanism of electron transport of the catalyst in the presence of CuPp.
As described in Scheme 2, the higher performances of TiO 2 in the presence of Cu(II)Pp is due to the electron and hole transfer between the catalyst structures. In particular, Cu-Pp caused the edge shift responsible for the electron transport [23]. In the presence of UV light irradiation, the photogenerated electrons can be attracted by Cu(II)Pp, leading to the lower charge recombination. In addition, the photoinduced electrons of Cu(II)Pp are transferred to the conduction band of TiO 2 , confirming the synergic effects between the catalyst and the proposed metal chelated porphyrin. Therefore, in the presence of visible light, the improvement of photocatalytical effect is mainly due to the presence of Cu(II)Pp. The variability of the collected experimental data was higher than that obtained in the case of the replicated points. The high reproducibility of the system in the whole experimental domain was demonstrated by the low variability of the response at central points. Non-normality of data distribution required a normalization by a logarithmic transformation.

Significance of Factors (Coefficients)
The normalized responses were modeled based on Equation (2) and significant coefficients were plotted in Figure 3.  The variability of the collected experimental data was higher than that obtained in the case of the replicated points. The high reproducibility of the system in the whole experimental domain was demonstrated by the low variability of the response at central points. Non-normality of data distribution required a normalization by a logarithmic transformation.

Significance of Factors (Coefficients)
The normalized responses were modeled based on Equation (2) and significant coefficients were plotted in Figure 3. The variability of the collected experimental data was higher than that obtained in the case of the replicated points. The high reproducibility of the system in the whole experimental domain was demonstrated by the low variability of the response at central points. Non-normality of data distribution required a normalization by a logarithmic transformation.

Significance of Factors (Coefficients)
The normalized responses were modeled based on Equation (2) and significant coefficients were plotted in Figure 3.  The regression equations for normalized responses were obtained in the case of using TiO 2 , TiO 2 @H 2 Pp, and TiO 2 @Cu(II)Pp catalysts: logPE H2PpTiO2 = 1.39 − 0.12 X 1 − 0.14 X 2 + 0.09 X 3 (4) logPE Cu(II)PpTiO2 = 1.52 − 0.14X 1 − 0.10X 2 + 0.12 X 3 (5) where X 1 , X 2 ,and X 3 were the pH, the Cr(V) concentration, and the amount of catalyst, respectively. It was found that the significant coefficients were linked to the linear terms of the three studied factors. As a result of Equations (3)-(5), the weight of coefficients related to pH and the concentration of Cr(VI) was negative, as expected. This means that the lower levels of pH and concentration of Cr(VI) allowed for higher photocatalytic conversion. Moreover, the pH of the solution strictly induces modifications of the surface properties of the catalyst, also influencing the ionic forms of chromium [32][33][34]. Normally, the electrostatic interactions between the hydroxyl groups of TiO 2  to adsorb onto the surface of the catalysts via an electrostatic interaction [35]. Alternatively, at high pH, the surface of the catalyst becomes negative, with the subsequent repulsion of Cr 2 O 7 2− ions, reducing the photocatalytical efficiency [36]. It has also been reported that the high concentration of Cr(VI) generally blocks the activity of the catalyst, decreasing the interaction with the functional groups on the catalyst. Alternatively, the catalyst showed high catalytical conversion at any concentration below 5 mg/L; therefore, the concentration of Cr(VI) ions was investigated below those values. On the other hand, the amount of catalyst positively affected the efficiency of the photocatalytic reaction because of the higher specific surface area of the catalyst. However, an excessive concentration of the catalyst might induce particle aggregation [37] with a loss of overall performance.

Plots of Residual
The estimation of residuals is reported in Figure 4.
where X1, X2,and X3 were the pH, the Cr(V) concentration, and the amount of catalyst, respectively. It was found that the significant coefficients were linked to the linear terms of the three studied factors. As a result of Equations (3)-(5), the weight of coefficients related to pH and the concentration of Cr(VI) was negative, as expected. This means that the lower levels of pH and concentration of Cr(VI) allowed for higher photocatalytic conversion. Moreover, the pH of the solution strictly induces modifications of the surface properties of the catalyst, also influencing the ionic forms of chromium [32][33][34]. Normally, the electrostatic interactions between the hydroxyl groups of TiO2 and Cr(VI) occur under acidic conditions (pH around 2 or 3) [35]. At pH = 2.5, chromate ions are present as HCrO4 − , CrO4 2− , or Cr2O7 2− ions, whereas the active sites of the catalyst are highly protonated, leading Cr(VI) species to adsorb onto the surface of the catalysts via an electrostatic interaction [35]. Alternatively, at high pH, the surface of the catalyst becomes negative, with the subsequent repulsion of Cr2O7 2− ions, reducing the photocatalytical efficiency [36]. It has also been reported that the high concentration of Cr(VI) generally blocks the activity of the catalyst, decreasing the interaction with the functional groups on the catalyst. Alternatively, the catalyst showed high catalytical conversion at any concentration below 5 mg/L; therefore, the concentration of Cr(VI) ions was investigated below those values. On the other hand, the amount of catalyst positively affected the efficiency of the photocatalytic reaction because of the higher specific surface area of the catalyst. However, an excessive concentration of the catalyst might induce particle aggregation [37] with a loss of overall performance.

Plots of Residual
The estimation of residuals is reported in Figure 4.  The results show that the residuals were normally distributed and the points on the probability plot followed close to a straight line. In addition, these results confirmed the great quality of the model, allowing it to be easily used to perform the screening of significant factors by reducing the number of experiments. Figure 5 clearly shows the validity and reproducibility of the proposed mathematical model. The evaluated parameters elucidating the goodness of the model and its practicability to screen and predict the efficiency of chemical reactions were the R 2 , Q 2 , model validity, and the reproducibility. R 2 is the ability of the model in fitting row data variability, while Q 2 describes the ability of the model to predict the responses. Higher values of R 2 and Q 2 are substantially related to the goodness of the The results show that the residuals were normally distributed and the points on the probability plot followed close to a straight line. In addition, these results confirmed the great quality of the model, allowing it to be easily used to perform the screening of significant factors by reducing the number of experiments. Figure 5 clearly shows the validity and reproducibility of the proposed mathematical model. The evaluated parameters elucidating the goodness of the model and its practicability to screen and predict the efficiency of chemical reactions were the R 2 , Q 2 , model validity, and the reproducibility. R 2 is the ability of the model in fitting row data variability, while Q 2 describes the ability of the model to predict the responses. Higher values of R 2 and Q 2 are substantially related to the goodness of the model. As shown in Figure 5, the selected mathematical model could explain the overall variability of the studied reaction, confirmed by the high correlated values of R 2 , Q 2 , and the reproducibility around the three investigated central points ( Figure 5). As also reported in this latter case, the mathematical model was able to predict the overall behavior of the catalytical reaction by highlighting the importance to consider all the interactions existing between factors. Additionally, it appears that the prediction and validity of the model toward the experimental data were higher than that reported for the responses collected on TiO2 catalyst. As these parameters were directly correlated to the overall variability observed between the experimental results, it seems that the functionalization of porphyrin on the TiO2 structure positively influences the efficiency of the catalyst activity.

Design of Experiments (DOE) through the Time of Irradiation
The experimental data collected at 15 and 30 minutes of irradiation were additionally analyzed by MODDE software. Results for the TiO2 catalyst showed no effect of factors on the achieved responses in both the tested aliquots. In addition, the validity and reproducibility of the model appeared to be poor. In the case of the TiO2@H2Pp catalyst, the studied factors affected the response when the photocatalytical reaction reached 30 minutes. The further modification of the nanocomposite with Cu 2+ ions improved the photocatalytical efficiency of the catalyst. In fact, indicators like residual distribution, significant factors, and R 2 were high, indicating that the optimal photocatalytic conversion could be achieved after the modification of the catalyst with metal chelated porphyrin. Figure 6 shows the Raman spectra recorded for TiO2, H2Pp, TiO2@H2Pp, and TiO2@Cu(II)Pp, respectively. The spectra are reported as acquired and were not baseline subtracted. Additionally, it appears that the prediction and validity of the model toward the experimental data were higher than that reported for the responses collected on TiO 2 catalyst. As these parameters were directly correlated to the overall variability observed between the experimental results, it seems that the functionalization of porphyrin on the TiO 2 structure positively influences the efficiency of the catalyst activity.

Design of Experiments (DOE) through the Time of Irradiation
The experimental data collected at 15 and 30 minutes of irradiation were additionally analyzed by MODDE software. Results for the TiO 2 catalyst showed no effect of factors on the achieved responses in both the tested aliquots. In addition, the validity and reproducibility of the model appeared to be poor. In the case of the TiO 2 @H 2 Pp catalyst, the studied factors affected the response when the photocatalytical reaction reached 30 minutes. The further modification of the nanocomposite with Cu 2+ ions improved the photocatalytical efficiency of the catalyst. In fact, indicators like residual distribution, significant factors, and R 2 were high, indicating that the optimal photocatalytic conversion could be achieved after the modification of the catalyst with metal chelated porphyrin. Figure 6 shows the Raman spectra recorded for TiO 2 , H 2 Pp, TiO 2 @H 2 Pp, and TiO 2 @Cu(II)Pp, respectively. The spectra are reported as acquired and were not baseline subtracted. Figure 6 shows the Raman spectra recorded for TiO2, H2Pp, TiO2@H2Pp, and TiO2@Cu(II)Pp, respectively. The spectra are reported as acquired and were not baseline subtracted.  The observed Raman frequencies for the bare TiO 2 structure were 144, 192, 395, 515, and 635 cm −1 , as reported in the literature in the case of anatase [38]. When the substrate was treated with either H 2 Pp or Cu(II)Pp, the intensity of these peaks was clearly reduced, whereas the onset of a fluorescence background was observed. This is good evidence, although indirect, of the adsorption of H 2 Pp or Cu(II)Pp on the TiO 2 catalyst. The same spectra were recorded on TiO 2 @Cu(II)Pp after the catalytic experiments.

Stability of TiO 2 @Cu(II)Pp Nanocomposite
Reusability of a photocatalyst is one of the most important keys in catalysis research for its utilization to be cost effective and practical. Our optimized catalyst may be promising for Cr(VI) removal from wastewater. The major sources of Cr(VI) include chemical industrial processes, plastic products, manufacturers of pharmaceuticals, and so on, which contribute to the emission of Cr(VI) in wastewater matrices in the concentration range between 0.1 and 200 mg L −1 . Moreover, the catalyst can also be proposed for underground water monitoring of Cr(VI) thanks to its operation in a more environmentally-friendly pH (nearby 5), which appears particularly favorable in obtaining higher retentions of chromium complex in abyssal water (pH = 6) [39]. Accordingly, the further re-usage measurements were conducted by selecting 1500 mg L −1 of catalyst and 1 mg L −1 as the initial concentration of Cr(VI) at pH = 5. Therefore, the stability of the TiO 2 @Cu(II)Pp catalyst was evaluated by measuring the photocatalytical efficiency after six repeated cycles of measurements over 180 min of reaction time (Figure 7a,b).
J. Compos. Sci. 2020, 4, x FOR PEER REVIEW 9 of 12 The observed Raman frequencies for the bare TiO2 structure were 144, 192, 395, 515, and 635 cm -1 , as reported in the literature in the case of anatase [38]. When the substrate was treated with either H2Pp or Cu(II)Pp, the intensity of these peaks was clearly reduced, whereas the onset of a fluorescence background was observed. This is good evidence, although indirect, of the adsorption of H2Pp or Cu(II)Pp on the TiO2 catalyst. The same spectra were recorded on TiO2@Cu(II)Pp after the catalytic experiments.

Stability of TiO2@Cu(II)Pp Nanocomposite
Reusability of a photocatalyst is one of the most important keys in catalysis research for its utilization to be cost effective and practical. Our optimized catalyst may be promising for Cr(VI) removal from wastewater. The major sources of Cr(VI) include chemical industrial processes, plastic products, manufacturers of pharmaceuticals, and so on, which contribute to the emission of Cr(VI) in wastewater matrices in the concentration range between 0.1 and 200 mg L -1 . Moreover, the catalyst can also be proposed for underground water monitoring of Cr(VI) thanks to its operation in a more environmentally-friendly pH (nearby 5), which appears particularly favorable in obtaining higher retentions of chromium complex in abyssal water (pH = 6) [39]. Accordingly, the further re-usage measurements were conducted by selecting 1500 mg L -1 of catalyst and 1 mg L -1 as the initial concentration of Cr(VI) at pH = 5. Therefore, the stability of the TiO2@Cu(II)Pp catalyst was evaluated by measuring the photocatalytical efficiency after six repeated cycles of measurements over 180 min of reaction time (Figure 7a,b). Photocatalytic efficiency as a function of time is presented in Figure 7a. The results show the increase in photocatalytic efficiency from 0 to 180 min of reaction time. The only slight decrease in photocatalytic efficiency was noticeable after five repetitive measurements, which revealed the high reliability of the proposed composite. Moreover, after 120 min of reaction time, the photocatalysis reached maximus percentage in all cases. Figure 7 also confirms the observed high reproducibility of the TiO2@Cu(II)Pp catalyst, revealing it as promising for future environmental applications.

Conclusions
In this work, a multivariate experimental design was adopted to perform the screening of Photocatalytic efficiency as a function of time is presented in Figure 7a. The results show the increase in photocatalytic efficiency from 0 to 180 min of reaction time. The only slight decrease in photocatalytic efficiency was noticeable after five repetitive measurements, which revealed the high reliability of the proposed composite. Moreover, after 120 min of reaction time, the photocatalysis reached maximus percentage in all cases. Figure 7 also confirms the observed high reproducibility of the TiO 2 @Cu(II)Pp catalyst, revealing it as promising for future environmental applications.

Conclusions
In this work, a multivariate experimental design was adopted to perform the screening of affecting variables on the photocatalytical conversion of Cr(VI) in water by the TiO 2 @Cu(II)Pp catalyst. The approach was successfully used to avoid the high number of experiments needed to perform a univariate operative work. Additionally, the experimental design allowed us to identify all the significant factors to be considered in the optimization processes, based on an accurate statistical analysis. The proposed model was also able to describe the physics of the processes and its statistical validation allowed us to predict the responses under defined conditions. As a result, the catalyst's efficiency of conversion was maximized by Cu(II) ion-based composite materials. Finally, the synergy between porphyrins and titanium dioxide in photocatalytic reactions and their flexibility also demonstrated their effectiveness for real-practical Cr(VI) reduction in polluted water matrices.