P-Doped Titania Xerogels as Eﬀicient UV-Visible Photocatalysts

In the present study, sol-gel process is used to synthesize P-doped TiO 2 xerogels by the cogelation method of a functionalized P alkoxide, (NH 2 -(CH 2 ) 2 -NH-(CH 2 ) 2 -P(O)-(OC 2 H 5 ) 2 ) with Ti(OC 3 H 7 ) 4 in either 2-methoxyethanol or isopropanol. The phosphorus-doping improved the thermal stability of titania and decreased the phase transformation of anatase into rutile. This modification by phosphorus shifted the absorption edge of titania to the visible region as proved by Diffuse reflectance measurements, and thus offers the possibility to produce visible light effective TiO 2 photo-catalyst. The excellent photocatalytic activity of P-doped TiO 2 xerogels compared to pure TiO 2 could be explained by its high surface area and small TiO 2 -anatase crystallite size. From these results, it was proved by using three different models that phosphorus intrinsically influences the photocatalytic activity.


Introduction
TiO 2 heterogeneous photocatalysis is an attractive technique for the complete destruction of undesirable contaminants either in aqueous or gaseous phase by using solar or artificial light illumination [1]- [3]. Upon band gap excitation of TiO 2 , the photoinduced electrons and positively charged holes can reduce and oxidize the species adsorbed on the TiO 2 particles. However TiO 2 has several drawbacks among which it can only be activated by

Sample Preparation
Four gels were synthesized from TTIP (Ti(OC 3 H 7 ) 4 ), EDAP (NH 2 -(CH 2 ) 2 -NH-(CH 2 ) 2 -P(O)-(OC 2 H 5 ) 2 ) in either 2-methoxyethanol or isopropanol as solvent. The synthesis operating variables are presented in Table 1 , were fixed to 20 and 2 respectively for all the samples. For each sample, Met or Iso denotes the solvent used for the synthesis, respectively 2-methoxyethanol and isopropanol; TiP/X denotes TiO 2 xerogels synthesized with EDAP and for which, X is the molar [EDAP]/[TTIP] ratio. Pure TiO 2 xerogel synthesized in 2-methoxyethanol is denoted Met-TiO 2 and was synthesized as blank material for comparison with the P-doped xerogels.
All the syntheses were performed under inert atmosphere (N 2 ) according to the following steps: 1) after mixing EDAP in half of the total volume of solvent, the slurry was stirred at room temperature for 10 min; 2) then the mixture of TTIP and water in the remaining half of the total ethanol volume was slowly added to the EDAP mixture under vigorous stirring. The volume of the final solutions was 125 mL. The vessel was then tightly closed and heated up to 60˚C for 24 h (gelling and ageing [17]).
Gel time (t g ) is the time elapsed from the introduction of the last reactant in the solution until gelation occured and was performed in an oven at 60˚C. Gelation is defined as the point when the liquid does not flow anymore when the flask is tipped at an angle of 45˚. The wet gels were dried under vacuum according to the following procedure: the flasks were opened and placed into a drying oven at 60˚C, and the pressure was slowly decreased (to prevent gel bursting) to the minimum value of 1200 Pa after 48 h. The drying oven was then heated at 150˚C for 24 h leading to xerogels [17].
Each sample is divided in four parts with the same mass. Each part is calcined at a different temperature, i.e. 350˚C, 450˚C, 550˚C and 650˚C, as follows: the sample was heated up to the desired temperature at a rate of 150˚C/h under flowing air (0.0074 mol•s −1 ); this temperature was maintained for 5 h in air (flow rate: 0.02 mol•s −1 ). Calcined samples are denoted Met-TiP/X-T or Iso-TiP/X-T, where T is the calcination temperature of the sample. For example, Met TiP/0.1-550 is a P-doped TiO 2 xerogel synthesized in 2-methoxyethanol, with a molar [EDAP]/[TTIP] ratio = 0.1, and calcined at 550˚C under air for 5 h.

Sample Characterization
Inductively coupled plasma-atomic emission spectroscopy (ICP-AES), equipped with an ICAP 6500 THERMO Scientific device was used to determine the molar [EDAP]/[TTIP] ratio of the dried and calcined samples of P-doped TiO 2 xerogels. Solutions for analysis were prepared as follows: 1) 2 g of Na 2 O 2 , 1 g of NaOH and 0.1 g of sample were mixed in a vitreous carbon crucible; 2) the mixture was heated beyond the melting point (up to 950˚C); 3) after cooling and solidification, the mixture was digested in 30 mL of HNO 3 (65%); 4) the solution was then transferred into a 500 mL calibrated flask that was finally filled with deionized water. The measured molar [EDAP]/[TTIP] ratio for dried P-doped TiO 2 xerogels are given in Table 1 and the measured molar [EDAP]/[TTIP] ratio for calcined P-doped TiO 2 xerogels are given in Table 2.
TG-DSC measurements were realized under helium between 40˚C and 700˚C, with a heating rate of 0.16˚C•s −1 , using a Setaram TG-DSC 111 device, according to the following procedure: 1) a precise amount of sample was placed into a platinum crucible; 2) the sample was heated under helium from 40˚C to 700˚C; 3) the sample was cooled and was weighed again.
X-ray diffraction (XRD) patterns were recorded with a Siemens D5000 powder diffractometer (Cu-K α radiation) between 20˚ and 65˚ (2θ). The size of TiO 2 -anatase particles, d a , was estimated from X-ray peak broadening by the Scherrer method [18].
Nitrogen adsorption-desorption isotherms were measured at −196˚C on a Fisons Sorptomatic 1990 after outgassing (10 −5 Pa) for 24 h at room temperature.
Diffuse reflectance measurements in the UV/Vis region (250 -800 nm) (DR-UV/Vis) were performed on a Varian Cary 5000 UV/Vis/NIR spectrophotometer, equipped with a Varian External DRA-2500 integrating sphere, using BaSO 4 as reference. Samples have been prepared by immobilizing the powder between a PVC support and a quartz glass. UV/Vis spectra were recorded in diffuse reflectance mode (R = reflection intensity) and transformed to the absorbance coefficient (F(R)) by the Kubelka-Munk function [19], ( ) ( ) The illuminated surface is the same for all samples. For the sake of comparison, all spectra were arbitrary normalized in intensity to 1.0 by dividing each spectrum by their maximum. The band gap has been determined from the Tauc plot [20] ( ) ( )

Photocatalytic Tests
The photoactivity of the xerogels was compared by evaluating the relative residual concentration of p-nitro- In a typical experiment, the catalyst was added to 15 mL aqueous solution of PN (Initial concentration, C i , is equal to 10 −4 mol•L −1 ) to reach a concentration of 1 g•L −1 . To degrade only the protonated form of PN (pK a = 7.2), the solution pH was fixed at 3.5 by adding a few µL of 1 N HCl aqueous solution. The shaking of the suspension was controlled during the photocatalytic test to ensure that the suspension was homogeneous. Time 0 corresponds to the switching on of the lamp. After 6 h, 2 mL of each suspension were sampled with a syringe and filtered in order to separate the xerogel powder from the p-nitrophenol solution. In those experimental conditions, the pH of the filtered p-nitrophenol solution was equal to 4. Therefore, only the protonated form of pnitrophenol was present in the solution. The final concentration of that protonated form of p-nitrophenol, C f , was measured by UV/Vis spectroscopy (Genesys 10S UV-Vis, Thermo Scientific) at 318 nm. The photocatalytic activity of samples was calculated from the percentage of PN degraded after 6 h, A, and given by Equation (1): where C i is the initial PN concentration and C f is the final PN concentration after 6 h. The same experimental protocol was applied to a solution containing PN only, that is without xerogel under light and to PN solution containing each xerogel successively but without light to ensure that the relative residual concentration obtained corresponds really only to the photodegradation of PN by pure TiO 2 and P-doped TiO 2 xerogels under halogen lamp. Each measurement was repeated three times.

Parameters Estimation and Statistical Testing of Models
The fitting of kinetic models was performed by applying the Gauss-Newton optimization method by using a statistical Fisher F-test [21] [22]. NLPE software, Non Linear Parameter Estimation, from IBM was used [23].

Thermogravimetric Behaviour of Pure TiO2 and P-Doped TiO2 Xerogels
In Figure 1 to a large endothermic peak is observed between 50˚C and 250˚C, corresponding to the evaporation of 2-methoxyethanol and water. The weight loss (for a total of about 28%) extends to 450˚C with two exothermic phenomena at 300˚C and 385˚C. In that temperature range it is known that the condensation reactions occur in the solid and thus these exothermic phenomena can be attributed to the condensation between hydroxyl groups or between hydroxyl groups and remaining alkoxy groups associated to the formation of water or alcohol and to the weight losses [24]. Moreover, the cristallization of amorphous TiO 2 into anatase is also an exothermic phenomenon which occurs at around 373˚C [7]. The peak corresponding to this transformation probably overlaps with the second peak at 385˚C and associated to one of the condensation reactions. A weight loss of about 20% associated to a large endothermic peak is observed between 30˚C and 210˚C, corresponding to the evaporation of 2-methoxyethanol and water. The weight loss (for a total of about 32%) extends to 500˚C with one endothermic peak at 250˚C following by two exothermic phenomena at 300˚C and 410˚C. The endothermic peak at 250˚C could correspond to residual 2-methoxyethanol pyrolysis. As in the former case, both exothermic peaks are attributed to the condensation reactions [25]. Nevertheless, the first exothermic peak at 300˚C is smaller in Figure 1(b) than in Figure 1(a). This peak mitigation could correspond to the formation of P 2 O 5 species from EDAP, which sublimes at around 300˚C and which is an endothermic phenomenon [24]. Moreover, the second exothermic peak at 420˚C could correspond to the cristallization of amorphous TiO 2 into anatase, but with a delay of about 40˚C.
Both samples Met-TiP/0.1 and Iso-TiP/0.1 (curves not shown) exhibit similar TG-DSC curves under He as sample Met-TiP/0.01. Nevertheless, the second exothermic peak appears at markedly higher temperature (550˚C) instead of 420˚C for sample Met-TiP/0.01 and instead of 385˚C for sample Met-TiO 2 . We may thus conclude that the presence of phosphorus into TiO 2 matrix delays the crystallization of amorphous TiO 2 into anatase, an incremental crystallization delay being observed with increasing phosphorus loading.

X-Ray Diffraction of Pure TiO2 and P-Doped TiO2 Xerogels
The effect of calcination temperature on sample crystallinity was investigated by X-ray diffraction.  [15].
The XRD patterns of sample Met-TiP/0.01 calcined at 350˚C, 450˚C, 550˚C and 650˚C are presented in Figure 2 and exemplifies those of samples Met-TiP/0.01, Met-TiP/0.1 and Iso-TiP/0.1 which follow the same trend. After calcination at 350˚C and 450˚C, the sample Met-TiP/0.01 is always amorphous. When the calcination temperature is ≥550˚C, the characteristic peaks of anatase structure appear on the patterns. Nevertheless, even after a calcination at 650˚C for 5 h, no rutile structure appears on the patterns of samples Met-TiP/0.01, Met-TiP/0.1 and Iso-TiP/0.1.
The TiO 2 anatase crystallite sizes, d a , calculated by the Scherrer equation from peak broadening [18] are presented in Table 3 for all the samples. It is observed that d a increases with the calcination temperature. Interestingly, by comparing samples Met-TiP/0.01 with Met-TiP/0.1, it is obvious that the nanoparticle size, d a , increases more slowly, and thus the cristallization of amorphous TiO 2 into anatase structure is more delayed in the latter case with a higher phosphorus loading increases. This is confirmed with sample Iso-TiP/0.1 which exhibits similar sizes as Met-TiP/0.1.

Nitrogen Adsorption-Desorption Isotherms of P-Doped TiO2 Xerogels
The textural properties of P-doped TiO 2 xerogels are reported in Table 4. Those of sample Met-TiO 2 are not given in this table because it is not porous (S BET < 5 m 2 •g −1 ) whichever the calcination temperature (350˚C, 450˚C, 550˚C and 650˚C).
In Figure 3(a), nitrogen adsorption-desorption isotherms of sample Met-TiP/0.01 dried and calcined at 350˚C, 450˚C, 550˚C and 650˚C are presented. Like sample Met-TiO 2 , the dried sample Met-TiP/0.01 is not porous. One reason could be the presence of the organic aminoethylaminopropyl chain of EDAP in the pores thus reducing accessibility to the latter ones and this is also shown in Table 4 with a specific surface area, S BET , of <5 m 2 •g −1 . After calcination under air at 350˚C, the isotherm of the resulting sample Met-TiP/0.01-350 exhibits a narrow adsorption-desorption hysteresis loop for p/p 0 values between 0.4 and 0.6 characteristic of capillary condensation in small mesopores (2 -10 nm) [26]. Indeed, in Table 4, the specific surface area obtained from the Broekhoff-de-Boer theory and characteristic of the presence of mesopores, S BdB , is equal to 90 m 2 •g −1 , while S BET of this sample is equal to 115 m 2 •g −1 showing that sample Met-TiP/0.01-350 is essentially mesoporous. Nevertheless, this sample is also slightly microporous because the microporous volume calculated from the Dubinin-Raduskevitch theory, V DR , is equal to 0.04 cm 3 •g −1 . Upon calcination under air at 450˚C (Figure 3(a)), the adsorption-desorption hysteresis loop is shifted towards higher p/p 0 values, resulting from an increase of the size of the mesopores [26]. In Table 4     and 55 m 2 •g −1 respectively. Their decrease could be due to the beginning of the crystallization of amorphous TiO 2 into anatase (Figure 2) [15]. After calcination at 550˚C and 650˚C, mesoporosity is partly maintained but microporosity disappears with similar values of S BET and S BdB ( Table 4). These samples still present S BET values around 35 -40 m 2 •g −1 .
The data from Table 4, show that samples of dried Met-TiP/0.1 and Met-TiP/0.1-350 are not porous (S BET < 5 m 2 •g −1 ). After calcination at 450˚C, porosity appears within the sample with S BET and S BdB reaching 70 m 2 •g −1 and 55 m 2 •g −1 respectively. Further calcination to 550˚C, results in an increase of S BET and S BdB to 105 m 2 •g −1 and 85 m 2 •g −1 respectively. At this temperature, the anatase structure is not yet well developed ( Table 3, in which d a is equal to 8 nm). Upon calcination at 650˚C, S BET and S BdB slightly decrease to 90 -95 m 2 •g −1 . Indeed, in Table 3, d a gradually increases because the crystallization of amorphous TiO 2 into anatase structure starts at this stage. The comparison between samples Met-TiP/0.01 and Met-TiP/0.1 shows that the crystallization of amorphous TiO 2 into anatase structure is shifted towards higher temperatures when the phosphorus loading increases, and correlate with the TG-DSC measurements (see 3.1).
In Figure 3(b), nitrogen adsorption-desorption isotherms of samples Iso-TiP/0.1 dried and calcined at 350˚C, 450˚C, 550˚C and 650˚C are presented. The dried sample Iso-TiP/0.1 presents at low relative pressure, a sharp increase of the adsorbed volume, followed by a plateau which corresponds to type I isotherm according to BDDT classification [26], which is characteristic of microporous adsorbents. Compared with samples Met-TiP/0.01 and Met-TiP/0.1, the specific surface area, S BET , of the dried sample Iso-TiP/0.1 ( Table 4) is significantly high (340 m 2 •g −1 ). Nevertheless, after calcination at 350˚C, S BET , S BdB , and V DR strongly decrease and the calcination at 450˚C induces the collapse of the texture of the sample with very low surface area (S BET < 5 m 2 •g −1 ). After calcination at 550˚C and 650˚C, amorphous TiO 2 crystallizes into anatase structure with d a equal to 9 and 11 nm respectively ( Table 3). In this case, S BET of samples Iso-TiP/0.1-550 and Iso-TiP/0.1-650 is equal to around 40 -45 m 2 •g −1 , and the isotherms exhibit similar narrow adsorption-desorption hysteresis loop for p/p 0 values between 0.4 and 0.6. This hysteresis is characteristic of capillary condensation in small mesopores (2 -10 nm) [26], located between TiO 2 crystallites [15].

UV/Vis Diffuse Reflectance (DR-UV/Vis) of Pure TiO2 and P-Doped TiO2 Xerogels
The DR-UV/Vis spectra of some calcined samples (Met-TiO 2 -650, Met-TiP/0.01-550, Met-TiP/0.1-550 and Met-TiP/0.1-650) are given in Figure 4: the other samples calcined at 550˚C and 650˚C are not shown as they are very similar. The DR-UV/Vis spectra of those samples of Met-TiO 2 , Met-TiP/0.01, Met-TiP/0.1 and Iso-TiP/0.1 calcined at 350˚C and 450˚C are not considered since they still contain a lot of organic moieties as illustrated by their coloured feature. Thus, it is difficult to analyze the DR-UV/Vis spectra of these samples because their absorption in the visible range is higher than the samples calcined at 550˚C and 650˚C [27].

Photocatalytic Tests with Pure TiO2 and P-Doped TiO2 Xerogels
The photocatalytic activity of the TiO 2 xerogels (pure and P-doped) examined for the PN degradation is presented in Figure 5 which firstly shows that all dried samples are inactive. With calcination the efficiency of the resulting materials highly increases reaching a maximum of 57% in the case of sample Met-TiP/0.1-650. It also appears that phosphorus has a strong influence on the photocatatytic activity.

Thermal Evolution of Pure TiO2 and P-Doped TiO2 Xerogels
From TG-DSC measurements, the thermogravimetric behaviour of pure TiO 2 and P-doped TiO 2 xerogels was studied and allowed to define the different temperatures of calcination for samples. Nevertheless, since the operating variables between TG-DSC measurements and calcination are not strictly the same (heating rate, length of the temperature bearing, He for TG-DSC and air for calcination), the temperatures, for which thermal behaviours are examined, can be different for both cases [28].
For the blank Phophorus-free sample Met-TiO 2 , the TG-DSC and XRD measurements show three successive thermal behaviours: 1) the solvent and water, which are always present inside the pores of this sample even after drying under vacuum at 150˚C for 24 h, are evaporated below 250˚C, which corresponds to an important weight loss of sample (about 20%); 2) the crystallization of amorphous TiO 2 into anatase occurs at around 380˚C [7] [15]; 3) the crystallization of anatase into rutile seems likely to occur between 550˚C and 650˚C [15]. Furthermore, two exothermic peaks at 300˚C and 385˚C (overlapping with the peak of crystallization of amorphous TiO 2 into anatase) are present in Figure 1(a). These peaks are assigned to condensation reactions between hydroxyl groups or between hydroxyl groups and alkoxy groups [24]. The condensation in the gel is therefore not complete after 24 h at 60˚C (gelling and aging [17]). Indeed, Bodson et al. [16], showed that 2-methoxyethanol used as solvent, can also act as a chelating ligand and hence the formation of chelated Ti-species by ligand exchange (Equation (2)) is expected. These are less reactive towards hydrolysis and condensation reactions.    Considering the P-doped samples (Met-TiP/0.01, Met-TiP/0.1 and Iso-TiP/0.1), the introduction of phosphorus modifies the crystallization temperatures of TiO 2 (Figure 1(b) and Figure 2): 1) the exothermic peak corresponding to the crystallization of amorphous TiO 2 into anatase, appears at significantly high temperature (550˚C) for the samples with higher phosphorus content (Met-TiP/0.1 and Iso-TiP/0.1); this crystallization temperature decreases to 420˚C for sample Met-TiP/0.01 and is even lower (385˚C) for the P-free sample Met-TiO 2 . It is clear that the presence of phosphorus in the TiO 2 matrix delays the transformation of amorphous TiO 2 into crystalline anatase. A longer crystallization delay is observed on increasing the phosphorus loading [5] [27]. Nevertheless, the nature of solvent (2-methoxyethanol or isopropanol) has no influence on the TiO 2 crystalliza- tion temperature; 2) even after calcination at 650˚C, no rutile phase is detected in P-doped TiO 2 xerogels, contrarily to the sample Met-TiO 2 , for which the rutile phase is detected when calcined at 650˚C [15]. These results were also observed by Körösi et al. [28] for P-doped TiO 2 materials with molar P/Ti ratios = 0.01 and 0.1. The presence of phosphorus stabilizes the anatase structure, which is very interesting since anatase is the most effective structure of TiO 2 in photocatalysis. Previously, H 3 PO 4 -doped TiO 2 xerogels were reported and in this case, the rutile structure is obtained for temperatures > 900˚C with a molar P/Ti ratio of 0.05, and >1000˚C with a molar P/Ti ratio of 0.1 to 0.5 [29].
Myller et al. [30] showed that [2-(aminoethyl)dihydrogeno]phosphate and [2-(aminoethyl)hydrogenoammonium]phosphate, two similar molecules to EDAP, are decomposed around 300˚C -350˚C in P-doped TiO 2 materials when these molecules are free and not bonded to TiO 2 . In Bodson et al. [16], it was shown by Raman and Solid 31 P NMR spectroscopies, that the EDAP fragment is maintained within the TiO 2 structure, either by complexation of titanium atoms with the ethylenediamine fragment of EDAP, or by covalent linkage through P-O-Ti bonds. So EDAP molecules only complexed to titanium atoms can sublimate when temperature increases. These results are confirmed by ICP-AES measurements ( Table 2), for which a loss of phosphorus is observed for all P-doped TiO 2 xerogels when the calcination temperature increases.
It is observed that the size of TiO 2 -anatase crystallites, d a , increases with the calcination temperature for all the samples ( Table 3). But the growth of TiO 2 -anatase crystallites slows down when the molar P/Ti ratio increases [31]. Indeed, after calcination at 650˚C, d a is equal to 19 nm for the sample Met-TiP/0.01-650, while d a is around 10 nm for the samples Met-TiP/0.1-650 and Iso-TiP/0.1-650.
In opposite to the nitrogen adsorption-desorption measurements for dried P-doped TiO 2 xerogels [15], the nature of solvent (2-methoxyethanol or isopropanol) is not the key factor, which influences the porous texture of xerogels ( Table 4). In this work, it seems that the molar P/Ti ratio is the more important factor. Such an influence can be due to either to the influence of phosphorus on surface area, crystallite anatase size, and/or intrinsic influence of Ti-O-P bond formation. To distinguish between both effects, three models are developed below to find any correlations between activity and physico-chemical properties.

Parameter Adjustment
After examination of Figure 5 representing the activity of pure TiO 2 and P-doped TiO 2 xerogels for the PN degradation, it is not possible to determine what are the physico-chemical properties-the phosphor rate, the anatase crystallite size and the specific area-that intrinsically influence the phosphor doped TiO 2 xerogel activity. In order to establish correlations between the phosphor rate, the anatase crystallite size, the specific area and the photocatalytic activity, parameter adjustments and a statistical data treatment were performed on TiO 2 -anatase xerogel samples calcinated at 550˚C and 650˚C. The considered samples are listed in Table 6 with their photocatalytic activity and their physico-chemical properties.
The main question is to determine if the photocatalytic activity of the TiO 2 xerogels doped with phosphor only depends on the particle size and on the specific area varying with amount of EDAP used during synthesis, or if the phosphor rate intrinsically influences the photocatalytic activity. In order to answer the question of the phosphor influence, three models have been adjusted on experimental data. The first model, named Model 1, describes the photocatalytic activity, A, as a function of the molar ratio P/Ti, P, only. The second model, named Model 2, describes A as a function of the particle size, d a , and of the specific area, S BET . The last model, named where a 0 , a 1 , a 2 are the parameters of Model 1, b 0 , b 1 , b 2 are the parameters of Model 2 and c 0 , c 1 , c 2 , c 3 are the parameters of Model 3.
In order to determine which model better fits on experimental data, a statistical Fisher F-test was performed with a 75% confidence interval. Models 1 and 2 include 3 parameters, while Model 3 includes 4 parameters. So the number of degrees of freedom of Models 1 and 2 and of Model 3 is respectively equal to 4 and 3 because 7 experimental points have been used for parameter adjustment. The estimators of the residual variance are equal to 68, 126 and 49 for Models 1, 2 and 3 respectively. The ratio between the estimators of the residual variance of Models 1 and 3 is equal to 1.39 and the ratio between the estimators of the residual variance of Models 2 and 3 is equal to 2.57. However, the Fischer variable F(0. 25,4,3) is equal to 2.4, which is greater than 1.39 and smaller than 2.57, meaning that Model 2 can be rejected while Models 1 and 3 cannot be discriminated. Figure 6 compares the photocatalytic activity calculated with models 1, 2 and 3 with the experimental photocatalytic activity. Points corresponding to Models 1 and 3 are better aligned along the bisector than points corresponding to Model 2, in agreement with the statistical Fischer F-test. So because Model 2 describes A as a function of d a and of S BET only, it can be stated that phosphor intrinsically influences the photocatalytic activity, probably by extending the light adsorption to the visible range.
One last question remains till in mind: why Model 1 depending on P only, and Model 3 depending on P, d a and S BET simultaneously, are not statistically discriminatory. The explanation comes from the dependence of d a and S BET on P. Figure 7 represents the experimental photocatalytic activity A as a function of P. A second degree expression corresponding to Model 1 and passing through a maximum is adjusted. According to Yu et al. [29], the maximum can be explained by the fact that a too high P value improves the formation of TiP 2 O 7 species inhibiting the TiO 2 photocatalytic activity.
Because Model 1, depending on P only, and Model 3, depending on P, d a and S BET , are not statistically different, it seems that d a and S BET only depends on P. Figure 8 represents the anatase particle size d a as a function of P and the relation between d a and P is modelled by: where d 0 , d 1 , d 2 are the coefficients of the equation. The particle size d a increases when P increases, reaches a maximum for a P value around 0.07 before decreasing for higher P values. The optimal P value of 0.07 corresponds to the maximum photocatalytic activity observed in Figure 7. Those results are in agreement with Zheng et al. observations that highlighted that above P equal to 0.08, the increase of P inhibits the particle growth [31]. Figure 9 represents the specific surface area, S BET , as a function of P and the relation between S BET and P is modelled by: where e 0 e 1 , e 2 are the coefficients of the Equation (7). The specific surface area, S BET , increases when P increases, reaches a maximum for a P value of around 0.06 before decreasing for higher P values. The optimal P value of 0.06 approximately corresponds to the maximum photocatalytic activity observed in Figure 7. Those results are in agreement with literature that places the optimal P value between 0.05 and 0.1 [29] [31]. So Equation (6) and Equation (7) describe d a and S BET as a function of P only, according to a second degree relation. Furthermore, Model 3 is linear with P, d a and S BET , meaning that Model 3 can be assimilated to a second degree equation as a function of P. This explains why Models 1 and 3 are not statistically discriminatory and proves that phosphor intrinsically influences the photocatalytic activity.

Conclusions
The TiO 2 -anatase structure in P-doped TiO 2 xerogels appears after calcination at 550˚C and is always present af-  Points correspond to experimental data, the line corresponds to parameter adjustment and numbers correspond to samples listed in Table 6.
In this study, it was established that the relations between the physico-chemical properties and the photocatalytic activity of P-doped TiO 2 xerogels strongly depend of the molar P/Ti ratio. The photocatalytic activity also depends to the size of TiO 2 -anatase crystallites and to the specific surface area of xerogels: xerogels are even more active for the p-nitrophenol degradation that the size of TiO 2 -anatase crystallites is small and the specific surface area is high.  Table 6. Figure 9. Specific surface area, S BET , of TiO 2 -anatase crystallites as a function of P. Points correspond to experimental data, the line corresponds to parameter adjustment and numbers correspond to samples listed in Table 6.