Preparation and Photocatalytic Performance of Nano-TiO2 Codoped with Iron III and Lanthanum III

Nanoscale titanium dioxide (nano-TiO 2 ) was modified via metal doping to improve its photocatalytic activity and utilization of visible light. Nano-TiO 2 doped with iron III (Fe) only, lanthanum III (La) only, and both Fe/La was prepared using the sol-gel method.The photocatalytic activities of the three forms of doped nano-TiO 2 were evaluated. Metal codoping limited crystal growth of crystal, and the sol-gel method was shown to be an effective technique for doping the lattice of TiO 2 with Fe and La. Codoping of nano-TiO 2 with the tombarthite metal mixture had a synergistic effect of the photocatalytic performance, with the codoped nano-TiO 2 exhibiting a performance greater than the sum of those of the single-doped nano-TiO 2 samples. Kinetic studies showed that the photodegradation reaction of methyl orange by nano-TiO 2 follows the Langmuir-Hinshelwood first order mechanism.


Introduction
Global environmental pollution and energy shortages are becoming increasingly serious problems [1,2].The control of environmental pollution has become a major and urgent topic of concern.In 1972, Fujishima and Honda published the first article in Nature declaring that the semiconductor titanium dioxide crystal electrode has the ability to photocatalytically split water to produce hydrogen [3,4].This discovery signaled the beginning of heterogeneous photocatalysis research in the area of semiconductors.Photocatalysis technology, as a representative of green chemistry, is widely applied in many areas, such as wastewater treatment, air purification, and solar energy transfer and storage [5][6][7].
Nanoscale titanium dioxide (nano-TiO 2 ) has become a preferred material for these applications due to its high catalytic activity and stable chemical properties and because it is cheap and nontoxic [8][9][10].However, there are some disadvantages of using nano-TiO 2 , such as the high recombination rate of photoproduced electron-hole pairs, low quantum efficiency, and poor photocatalytic performance [9][10][11][12].Nano-TiO 2 can only use the ultraviolet portion of the solar spectrum range (only 3-5% of the total range) due to a wide band gap (3.2 eV), which leads to low effective utilization of sunlight [13][14][15].Researchers have used a variety of methods to modify nano-TiO 2 , including noble metal modification, compound semiconductor, dye sensitization, metal ion doping, and others [16][17][18][19].With these modification methods, the recombination rate of photogenerated electron-hole pairs of nano-TiO 2 photocatalyst is decreased, and the photocatalysis efficiency and range of visible light that generates a response are increased [20][21][22][23].Our research group found that modification by codoping with two elements can increase the visible light photocatalytic activity of nano-TiO 2 .
The main aim of the present study was to increase the visible light photocatalytic activity of nano-TiO 2 .The originality and significance of this study are described as follows.

Experimental Section
2.1.Preparation of Nano-TiO 2 Photocatalysts.The preparation process for nano-TiO 2 photocatalysts is shown in Figure 1.First, 100 mL absolute ethanol and 5 mL glacial acetic acid were added to a 250 mL beaker.After magnetic stirring for 30 min, the pH value of the solution was adjusted to 2 using nitric acid.The obtained mixture was designated solution A. Then, 15 mL ethanol and different doses (doping percentage is described as mole ratio) of modifier (Fe 3+ and/or La 3+ ) were added to a separate beaker to obtain solution B. Solution B was then added to solution A to obtain solution C.Then, 20 mL tetrabutyl titanate was added to the mixed solution C, followed by the addition of 5 mL distilled water.This solution was then stirred for 4 h.Sol TiO 2 was obtained after sealing the container for 2 days.The sol TiO 2 gradually formed nano-TiO 2 upon drying, grinding, and heat treatment.

Characterization of Photocatalysts.
The phase of the asprepared samples was analyzed using a Shimazu XRD-6000 X-ray diffractometer with a copper target (Cu K,  = 0.15406 nm), a voltage of 40.0 KV, and a current of 30.0 mA.Surface charge analysis was conducted using a British Kratos XPSAM800 multifunctional surface analysis electron spectrometer, with an Al target (1486.6ev) X-ray gun operating under 12 kv × 15 ma power.The analysis chamber background vacuum was 2 × 10 −7 Pa, adopting FAT working style.The spectrometer was operated with Cu2P3/2 (932.67 ev), Ag3d5 (368.30ev), and Au4f7/2 (84.00 ev) prototype correction, and data were corrected using carbon pollution Cls (284.8 ev).
The compounds produced in photocatalyzed reactions were identified using UV-Vis absorption spectroscopic analysis.This study used a Shimadzu UV-Vis 2550 spectrophotometer (integrating sphere method) for fixed UV-Vis spectroscopy.A fixed amount of photocatalyst powder was placed in a quartz ware, using standard BaSO 4 powder as a reference.Spectra were collected with a sweep rate of 1800 nm/min and a scanning range of 300-650 nm.
The molecular structures of reaction produces were analyzed by fluorescence spectroscopy (FS).This study used solid form testing with a fixed fluorescence intensity at a certain incident light wavelength (275 nm), and the results were combined with the experimentally determined photocatalytic activity to analyze the fluorescent light characteristics of the photocatalysts.

Target Compounds.
This study used methyl orange (chemical name, dimethylamino azo benzene sulfonic acid sodium), which is produced by nitriding aminobenzene sulfonic acid via N, N-dimethylaniline coupling, as the target compound for assessing photocatalyst activity.The molecular formula of methyl orange is C 14 H 14 O 3 N 3 SNa.Its molecular weight is 327.34Da, and its molecular structural contains a benzene group and N and S heteroatoms as shown in Scheme 1 [24].
Its molecular structure has certain representativeness.Remediation of methyl orange is a widespread problem, because this material is widely used as an industrial dye and is harmful to the aquatic environment.Methyl orange shows obvious absorption of visible light, as its absorbance and concentration have a linear relationship within a certain range, according to the Lambert-Beer law.In the continual degradation process of methyl orange, the maximum absorption wavelength has been at near 465 nm, almost without deviation.The UV-Vis absorption spectra of methyl orange solution undergoing degradation with TiO 2 photocatalyst is shown in Figure 1.

Photocatalytic Reaction Experiment.
In a typical photocatalytic experiment, with a 30-W UV lamp and 35-W xenon lamp as light sources, 100 mL methyl orange solution (10 mg/L) and photocatalyst were added to five 300 mL beakers to form separate mixed suspensions.Prior to illumination, these mixed suspensions were stirred using a magnetic stirrer for 30 min.Then, the mixed suspensions were illuminated (the distance from the liquid level to the UV lamp was 10 cm) for 180 min.The mixtures obtained after illumination were separated by centrifugation for 20 min.

Photocatalytic Activity Experiment.
The photocatalytic activity of the as-prepared TiO 2 samples was evaluated according to the decolorization rate of methyl orange solution.First, 100 mL methyl orange solution and a specified amount of TiO 2 photocatalyst were placed in a homemade photocatalytic reaction container.After 30 min of magnetic stirring, the reaction mixture was illuminated using the UV lamp and xenon lamp.By measuring the absorbance of the solution at the maximum absorption wavelength of methyl orange ( max = 465 nm), the decoloring rate can be calculated as follows: where  is the decoloring rate,  0 is the initial absorbance before illumination, and   is the absorbance after illumination time, .

Results and Discussion
3.1.Phase Distribution, Particle Size, and Lattice Distortion of the Prepared Nano-TiO 2 Photocatalysts.Figure 2 shows the XRD spectra for the different types of nano-TiO 2 photocatalyst treated at 500 ∘ C for 2 h.Compared to the standard X-ray spectrum of TiO 2 , it can be seen that the nano-TiO 2 powders and Fe 3+ /La 3+ co-doped nano-TiO 2 powders were anatase phase.As shown in Figure 2, the peak shapes of (101), (004), and (200) crystal plane diffraction was sharp, indicating that anatase phase had completely developed.Due to the small amounts of iron and lanthanide used for doping, no metal oxide diffraction peaks were observed corresponding to Fe 3+ or La 3+ .According to previous reports, in the La 3+doped nano-TiO 2 , La 3+ ions on the surface of nano-TiO 2 are oxidized and form a single layer of lanthanide oxide, which is difficult to detect by XRD.According to the solid physical band theory, in the nano-TiO 2 crystal, the ionic radius of Ti 4+ is 0.074 nm, and the ionic radius of Fe 3+ is 0.069 nm.Thus, Fe 3+ can easily spread into the nano-TiO 2 lattice and replace Ti 4+ in the nano-TiO 2 lattice.The ionic sizes of Fe 3+ and Ti 4+ ions are different, leading to nano-scale TiO 2 crystal lattice deformation.Upon La 3+ doping onto nano-TiO 2 , La 3+ replaces the lattice Ti 4+ .The ionic radius of La 3+ is 0.115 nm, which is larger than that of Ti 4+ .Thus, the substitution of La 3+ for Ti 4+ will cause distortion and inflation of the nano-TiO 2 crystal lattice, which will improve the photocatalytic activity of the material.The size of the nanoscale grain obtained using this formula, that is, the first particle size of oriented crystal growth, cannot reflect particle agglomeration.The calculation results are shown in Table 1.
The calculation results show that the average particle size of Fe 3+ /La 3+ codoped nano-TiO 2 was lower than that of pure TiO 2 .The particle size of 0.01% Fe 3+ /0.6% La 3+ -doped TiO 2 was the smallest among those tested (6.1 nm).According to the results of photocatalytic degradation of methyl orange solution, the photocatalytic activity of 0.01% Fe 3+ /0.6% La 3+doped TiO 2 was the best among the photocatalysts tested.The average grain size of tombarthite-doped TiO 2 was smaller Table 1: XRD analysis results (A: anatase).
than that of pure TiO 2 , indicating that the mixture of tombarthite ions inhibited the growth of the nanocrystalline phase.The average grain size of nano-TiO 2 codoped with tombarthite ions and transition metal ions was smaller, indicating that doping improved this inhibition.Doping with metal ions will affect the phase transition temperature, grain size, and other parameters and cause lattice distortion.Fe 3+ partly replaced lattice Ti 4+ , inevitably causing oxygen defects, and the existence of oxygen vacancies is thought to promote grain growth of the rutile phase.Therefore, Fe 3+ doping has a beneficial effect on the transformation of nano-TiO 2 from anatase to rutile type.Doping with La 3+ can inhibit the transformation of TiO 2 from anatase to rutile and thereby increase the content of the highly photocatalytic anatase phase, causing the grain size of nano-TiO 2 to decrease and thus the quantization effect to increase.Therefore, the synergistic effect of codoping with Fe 3+ and La 3+ makes the photocatalyst activity higher than the sum of the activities with single ion doping.According to Figure 2, upon doping with a small amount of Fe 3+ and La 3+ , the diffraction peaks of nano-TiO 2 shift towards the low angle direction, indicating that the diffraction peaks of Fe 3+ /La 3+ codoped nano-TiO 2 catalyst are wider than those of pure TiO 2 .Compared with pure nano-TiO 2 , the particle size of doped nano-TiO 2 was reduced.This is because a certain amount Fe 3+ and La 3+ penetrates the nano-TiO 2 crystal lattice, restricting the transfer and rearrangement of Ti and O ions, inhibiting the growth of nano-TiO 2 crystals and decreasing the particle size.).This is due to doping with Fe 3+ and La 3+ .In the Fe 3+ /La 3+ codoped TiO 2 , these two peaks shift 0.5 eV toward the higher energy direction, indicating that the effective positive charge of Ti was increased.Upon doping with elemental Fe and La, on the surface or in the lattice of nano-TiO 2 , electronic redistribution occurs and leads to a decrease in the Ti outer electron density, a reduction in the shielding effect, and an increase in the electron binding energy.These effects are beneficial for increasing photocatalytic activity.The binding energy difference between catalyst Ti2p and O1s is 71.3 eV, which indicates that Ti in the three prepared catalysts is in the tetravalent form (TiO 2 ).According to Figures 3(a)-3(c), the peaks at 529.6-529.8eV in the O1s high-resolution XPS patterns are mostly related to Ti, and the surface hydroxyl or oxygen in oxide defects is the key.Hydroxyl groups on the surface of the catalyst are considered to be an important factor affecting photocatalytic activity.A hydroxyl group on the nano-TiO 2 catalyst surface can capture light and generate an ⋅OH free radical, which has strong oxidation ability.The ⋅OH free radical is the main strong oxidizer in the photocatalytic reaction.Therefore, as the hydroxyl content on the surface of nano-TiO 2 catalyst increases, the surface becomes more conducive to the generation of ⋅OH free radicals and the quantization efficiency is further improved, thereby effectively improving the catalytic activity of the nano-TiO 2 catalyst.

Elemental Analysis of the Prepared Nano-
According to Figures 3(a) and 8(b), in the Fe2p highresolution XPS patterns for 0.01% Fe 3+ doped nano-TiO 2 and 0.01% Fe 3+ /0.6% La 3+ doped nano-TiO 2 , Fe2p peaks appear at 710.68 eV and 710.98 eV.This is trivalent iron, indicating that iron doped on TiO 2 is in the form of Fe 2 O 3 .In addition, as shown in Figure 3(c), no Fe2p peak appears in the TiO 2 XPS spectrum, indicating that elemental Fe exists only in crystalline Fe 3+ /La 3+ doped nano-TiO 2 .Elemental Fe in the three prepared catalysts is in the tetravalent form.
According to Figures 3(a) and 3(c), in the La3d highresolution XPS patterns of 0.6% La 3+ doped nano-TiO 2 and 0.01% Fe 3+ /0.6% La 3+ doped nano-TiO 2 , La3d peaks appear at 835.75 eV and 836.20 eV.In Figure 3(d), no La3d peaks appear in the TiO 2 XPS spectrum at these positions, confirming that elemental La was present only in La 3+ doped nano-TiO 2 and Fe 3+ /La 3+ codoped nano-TiO 2 powders.The difference in the binding energies of La 3+ doped nano-TiO 2 and Fe 3+ /La 3+ codoped nano-TiO 2 is 0.5 eV.This suggests that La 3+ doping changed the electronic distribution on the nano-TiO 2 surface or lattice, thus improving photocatalytic performance.In the La3d spectrum, two peaks appear for La3d 3/2 and La3d 5/2 .According to previous reports, La exists in the form of La 2 O 3 [25,26].Thus, La 3+ ions did not enter into the lattice of TiO 2 .This is because the ionic radius of La 3+ ions is bigger than that of Ti 4+ ions, and thus, La 3+ ions cannot enter into the lattice of TiO 2 .

FS Analysis of the Prepared Nano-TiO 2 Photocatalyst.
Figure 4 shows the fluorescence spectra of TiO 2 and the three prepared nano-TiO 2 photocatalysts.According to Figure 4(a)(A-D), the fluorescence spectra for Fe 3+ /La 3+ codoped nano-TiO 2 and pure TiO 2 have a fluorescence peak at 417 nm.The intensity of this peak for Fe 3+ /La 3+ codoped nano-TiO 2 is lower than that in the spectra for nano-TiO 2 doped with either metal or pure TiO 2 .Combined with the experimental results for methyl orange solution decolorization, this decrease in fluorescence intensity indicates a reduced recombination rate of photo-produced electronhole pairs, and thus, an increased photocatalytic activity.The above results show that the improvement in visible light catalytic activity is due to the reduction of the light carrier recombination rate by doping.
Figure 4(b) shows the fluorescence spectra of nano-TiO 2 doped with different amounts of La 3+ .Figure 4(c) shows the fluorescence spectra of nano-TiO 2 doped with different amounts of Fe 3+ .Figure 4(d) shows the fluorescence spectra of nano-TiO 2 doped with different amounts of Fe 3+ and La 3+ .According to these spectra, TiO 2 shows a strong peak at 417 nm, and the position of this peak is not affected by doping of the nano-TiO 2 with any amount of Fe 3+ and/or La 3+ .The intensity of this peak is weaker in the spectra for Fe 3+ /La 3+ codoped nano-TiO 2 .La and Fe exist in the form of La 2 O 3 and Fe 2 O 3 , respectively, and these metal oxides can function as agents to capture photo-produced electrons.After capture of a photo-produced electron, it is difficult for the electron to recombine with a hole.Together with the results of the methyl orange decolorization experiments, these results showing that the fluorescence intensity of codoped samples is smaller indicate that their photocatalytic activity is better.Codoping with Fe 3+ and La 3+ reduces the recombination rate of photo-produced electron-hole pair and improves the quantum efficiency, thus leading to improvement in the photocatalytic efficiency.Relative to the absorption spectra of pure TiO 2 , the absorption band edge of Fe 3+ doped nano-TiO 2 shows an obvious red-shift.The obviously enhanced absorption strength in the visible area is beneficial for improving the utilization of sunlight and the photocatalytic efficiency.The main reason for this improvement is that the radius of Fe 3+ (0.064 nm) is similar to that of Ti 4+ (0.068 nm), and thus, Fe 3+ can replace some Ti 4+ in the lattice and create lattice defects.Impurity level formed in nano-TiO 2 band gap, and the energy of semiconductor optical electronic transiting to guide reduced, smaller energy photoproduction electronic can also transit, so the spectrum redshift, light response range extended.
Figure 6 shows the UV-Vis absorption spectra for singleand codoped nano-TiO 2 photocatalysts.The absorption bands for these nano-TiO 2 catalysts shifted to the visible light region at varying degrees.For catalyst doped with La 3+ and Fe 3+ individually, the absorption edge moved 35 nm and 41 nm toward the visible light region, respectively.That for nano-TiO 2 photocatalyst codoped with 0.01% Fe 3+ and 0.6% La 3+ moved 49 nm toward the visible light region.Therefore, the absorption sideband of Fe/La codoped nano-TiO 2 red-shifted more than that for the Fe 3+ or La 3+ singledoped nano-TiO 2 , and the absorption of visible light by the codoped catalyst is stronger than that by the singledoped catalysts.This indicated that the codoping with both elements has a synergistic effect.The main reasons are as follows: the 3d orbital of Fe 3+ is above the valence band of nano-TiO 2 .Electrons on the 3d orbital can absorb 415 nm visible light and transit it to nano-TiO 2 to create Fe 4+ , and thus, Fe 3+ acts as an electron trap.The vacant 5d orbital of La 3+ serves as a good electron transfer orbital.This orbital can be used to transfer the photo-produced electrons in the TiO 2 photocatalytic reaction, and thus, La 3+ also acts as an electron trap.Therefore, codoping with Fe 3+ and La 3+ inhibited recombination of photo-produced electrons and holes, and thereby improved the quantum efficiency of photoproduction.

Influence of Doping Amount on
the Photocatalytic Activity of Nano-TiO 2

Influence of Doping with Fe 3+
or La 3+ on the Photocatalytic Activity of Nano-TiO 2 .Figure 7(a) demonstrates the influence of Fe 3+ doping concentration on the photocatalytic activity of nano-TiO 2 .According to Figure 7(a), the optimum doping amount of Fe 3+ is 0.01%, which gives methyl orange decolorization rates of 93.5% with 3 h of UV illumination (versus 56.88% for pure TiO 2 ) and 29.8% with 5 h of visible light illumination (versus 4.2% for pure TiO 2 ).Doping with Fe 3+ causes the nano-TiO 2 to not only be able to capture electrons, but also to capture holes and the carrier is easily released.Thus, doping with Fe 3+ can increase the photocatalytic activity of the nano-TiO 2 catalyst.Doping with a small amount of Fe 3+ can reduce the recombination rate of electrons and holes and enhance the photocatalytic activity of nano-TiO 2 in the visible region, by improving the visible light utilization efficiency.At a low doping concentration, Fe 3+ can play a dual role as an electron and a hole trap, and thereby improve the photocatalytic activity of the catalyst.At a high doping concentration, Fe 3+ can reduce the quantum efficiency of photo-produced electrons and holes, leading to a decrease in the photocatalytic activity of the catalyst.This also can explain the influence of the doping amount on the photocatalytic activity via the process of capturing electrons and holes crossing the barrier.The recombination rate depends on the distance, , of separation between the electron and hole [27]: where  composite is the recombination rate constant,  0 is the capture carrier hydrogen-like wave equation, and  is the distance of separation between the electron and hole.
According to the formula above, when the doping concentration is less than the optimum value, the semiconductor does not have enough traps to catch carriers.When the doping concentration is larger than the optimum value, due to the reduction in the average distance between the electrons and traps, the recombination rate  grows exponentially as the doping concentration is increased.Thus, use of the optimum doping amount of transition metal ions is critical.
Figure 7(b) shows the influence of La 3+ doping concentration on the photocatalytic activity of nano-TiO 2 .As shown in Figure 7(b), doping with tombarthite element La 3+ improved the photocatalytic activity of nano-TiO 2 .The methyl orange degradation rate under visible light illumination is greatly improved by La doping.The methyl orange decolorization rate increased as the doping amount of La 3+ increased.The highest photocatalytic activity was observed for a doping concentration of La 3+ of 0.6%.The methyl orange decolorization rate was 88.1% with 3 h of UV irradiation (pure TiO 2 ) and 27.4% with 5 h of visible light irradiation (versus 4.2% for pure TiO 2 ).With greater doping amounts, the photocatalytic activity did not continue to increase, but instead decreased.Doping with La ions increased catalytic activity, because tombarthite elements can produce electron configuration, polycrystalline type, and thermal stability.Doping with the appropriate amount of a tombarthite element has a positive role in improving the crystal type and photocatalytic properties of nano-TiO 2 .Because the La 3+ radius is 0.106 nm, which is different from that of Ti 4+ (0.068 nm), doping with La ions caused an increase in oxygen vacancy and defects on the surface of the nano-TiO 2 , effectively inhibiting the nano-TiO 2 photo-production of electron-hole pairs, thereby improving the photocatalytic activity.However, too much tombarthite element also may cause a free electron transfer center to become a free electron recombination center and increase the photo-production of electron-hole pairs, thus reducing the photocatalytic activity.The f orbital of tombarthite elements can have a coordination effect with the degradation substrate, and doping with a certain amount of La ions can effectively separate the nano-TiO 2 photo-produced electrons and holes, generating many active groups with strong oxidizing ability involved in the photocatalytic oxidation reduction reaction, thereby improving the photocatalytic activity of the catalyst.However, when the doping amount exceeds a certain concentration, too much tombarthite metal ion deposition on the surface of nano-TiO 2 hinders electron and hole transfer from the surface of the catalyst.Thus, tombarthite metal ions on the surface of the nano-TiO 2 become charge carrier recombination centers, resulting in a decrease in catalytic activity.Fe 3+ /La 3+ codoping on the photocatalytic activity of nano-TiO 2 under UV illumination, and Figure 9(a) shows the effect of Fe 3+ /La 3+ codoping on the photocatalytic activity of nano-TiO 2 under visible light illumination.According to the results shown in these figures, the catalytic activity of codoped nano-TiO 2 is higher than that of catalyst doped with either Fe 3+ or La 3+ .The 0.01% Fe 3+ and 0.6% La 3+ codoped nano-TiO 2 possessed the highest photocatalytic activity.After 3 h of UV irradiation, the decolorization rate of methyl orange for 0.01% Fe 3+ and 0.6% La 3+ codoped nano-TiO 2 was 99.8%.After 5 h of visible light irradiation, the decolorization rate of methyl orange for 0.01% Fe 3+ and 0.6% La 3+ codoped nano-TiO 2 was 40.7%.Both of these rates are greatly improved over those achieved by pure TiO 2 .Doping with transition metal Fe 3+ ions alone did not hinder the modification of tombarthite ions, but worked together with tombarthite La 3+ ions to further improve the activity of the photocatalyst.The experimental results show that there are optimum doping amounts for both Fe 3+ and La 3+ .A high concentration of doping ions can reduce the photocatalytic activity.Under the conditions of high concentrations, neither Fe 3+ nor La 3+ can effectively penetrate the crystal lattice of nano-TiO 2 , and therefore, these ions gather on the surface of crystals.An excessive of doping ions can catch large numbers of electrons and holes, reduce the quantum efficiency, and reduce the activity of catalysts.For low doping concentration, an increase in the doping ion concentration can improve the optical carrier separation effect.Therefore, because the thickness of the space between electrons and the surface of nano-TiO 2 decreases with an increasing amount of doping tombarthite element, when the optimum concentration of doping metal is reached, the distance between the electrons and the surface is equal to the penetration depth of incident light into the solid and photoproduction of electrons and holes is achieved by optimal light irradiation, benefiting the photocatalytic reaction.The combined effects of Fe 3+ and La 3+ upon codoping of nano-TiO 2 photocatalyst promoted the optimum separation of photoproduced electrons and holes and thus improved the photocatalytic activity of the photocatalyst.

Kinetics of the Photocatalytic Activity of Codoped
Nano-TiO 2 .For a heterogeneous photocatalytic system, such as the nano-TiO 2 photocatalytic system, the reaction rate of photocatalytic oxidation can be described by the Langmuir-Hinshelwood dynamics equation as follows [28]: where  is the concentration of reactant,  is the activity constant, and  is the adsorption equilibrium constant of the reaction.Integration of (3) gives When the concentration  is small, (4) can be transformed into ln  0  =    + , where   is the apparent rate constant and  is a constant.The kinetics for the degradation of methyl orange by the different prepared nano-TiO 2 photocatalysts were investigated in the present study.The relationship between ln( 0 /) ( 0 is the initial concentration and  is the concentration at time ) and photocatalysis time  is shown in Figure 9(b).The fitting of the data for the photocatalytic degradation of methyl orange with a first-order kinetic curve is shown in Table 2.
According to Table 2, the  value for the fitted straight line is far less than 0.01, indicating that ln( 0 /) and  are significantly linearly correlated.As shown in Figure 9, under visible light irradiation, the degradation of methyl orange by different doped nano-TiO 2 catalysts is well described by first-order reaction kinetics.The high correlation coefficients indicate that this model can be used to describe this photodegradation reaction.

Conclusions
In the present study, nano-TiO 2 powder photocatalyst was prepared and modified via a sol-gel method by doping with either Fe 3+ or La 3+ individually or codoping with both Fe 3+ and La 3+ .Codoping of nano-TiO 2 photocatalysts with both Fe 3+ and La 3+ resulted in better catalytic performance than that achieved by doping with either Fe 3+ or La 3+ , as well as better inhibition of nanocrystal growth and better refinement of grain size.Doping with tombarthite ions can effectively inhibit the shift of nano-TiO 2 from anatase to rutile.La 3+ doping changed the nano-TiO 2 surface or lattice electron distribution.The sol-gel method can be used to effectively dope the lattice of nano-TiO 2 with Fe 3+ and La 3+ .Compared with catalyst doped with only Fe 3+ or La 3+ , the light absorption intensity of Fe 3+ /La 3+ codoped nano-TiO 2 photocatalyst was stronger.This is because the absorption band edge redshifted obviously, and the spectral response range was extended into the visible light region, increasing the utilization of visible light.Fe 3+ /La 3+ codoped nano-TiO 2 photocatalyst showed superior photocatalytic performance compared to the single-doped samples.Because nano-TiO 2 codoped with two elements can achieve higher catalytic activity under visible light, this approach increases the potential utility of nano-TiO 2 photocatalyst materials in important environmental purification processes.

Figure 5 (
a) shows UV-Vis absorption spectra of nano-TiO 2 doped with different amounts of Fe 3+ .

Figure 8 :
Figure 8: Effect of Fe/La codoping on the photocatalytic activity of nano-TiO 2 under UV light irradiation.

Figure 9 :
Figure 9: (a) Effect of Fe/La codoping on the photocatalytic activity of nano-TiO 2 under visible light irradiation; (b) relationship between ln( 0 /) and photocatalysis time for the different doped nano-TiO 2 catalysts.

Table 2 :
Results of first-order kinetic fitting of the data for methyl orange degradation under visible light irradiation with the different doped nano-TiO 2 catalysts.