Nanotubes with anatase nanoparticulate walls obtained from NH4TiOF3 nanotubes prepared by anodizing Ti

Ildefonso Zamudio Torresa, José de Jesús Pérez Bueno*a, Celeste Yunueth Torres Lópeza, Luis Lartundo Rojasb, Maria Luisa Mendoza Lópezc and Yunny Meas Vonga
aCentro de Investigación y Desarrollo Tecnológico en Electroquímica, Parque Tecnológico Querétaro, Sanfandila, Pedro Escobedo, Querétaro CP 76703, Mexico. E-mail: jperez@ciddeteq.mx
bInstituto Politécnico Nacional, Centro de Nanociencias y Micro y Nanotecnologías, UPALM, Zacatenco, Mexico-D. F. 07738, Mexico
cTecnológico Nacional de México, Instituto Tecnológico de Querétaro, Av. Tecnológico s/n Esq. Mariano Escobedo, Col. Centro, Qro. Mexico, C. P. 76000, Querétaro, Mexico

Received 3rd March 2016 , Accepted 20th April 2016

First published on 21st April 2016


Abstract

In this work, titanium dioxide nanoparticulate nanotubes (NP-NT) in anatase phase from ammonium oxyfluorotitanate nanotubes (NT NH4TiOF3) are shown. The NT were formed from anodized titanium (Ti) in an organic medium. These nanostructures had an internal diameter of 90–120 nm and a nanotube wall thickness of 15–20 nm obtained by anodizing Ti, which resulted in a crystallographic order presented by the NH4TiOF3. After obtaining the NT, they were immersed in deionized water. Then, by using X-ray diffraction, it was possible to establish that the NT evolved from the NH4TiOF3 phase to the anatase phase. Furthermore, by transmission electron microscopy (TEM), it was observed that the nanotubes had an alteration in their morphology that showed their nanoparticulate walls. Also, by this technique, it was also possible to determine the interplanar distances and identify the crystallographic orientation (101). Spectral analysis of photoelectrons emitted by X-ray (XPS) was used to identify the chemical composition and possible mixture of Ti oxidation states. This method also verified the presence of Ti in anatase phase. IR spectroscopy allowed the presence of OH ions to be observed on the surface. During the development of NP-NT in anatase phase during this investigation, no heat treatment was applied.


Introduction

Since the initial reports about obtaining TiO2 nanotubes,1–4 great interest has been aroused in the scientific community for their properties and the potential uses of such structures, among which are the application in: photocatalysis,5–7 sensors,8,9 photoelectrocatalysis,10–12 fotoelectrolisis,13 and photovoltaic,14,15 as well as the application in bone regeneration medicine.16–18 TiO2 nanotubes have been obtained by various methods, which include: deposits on nanoporous alumina templates,19–21 sol–gel,22,23 growth without templates,24 sonochemical,25 hydrothermal,26–28 ionic liquids,29 TiO2 electrodeposits and anodized Ti.1–4

Anodization of Ti is one of the techniques that provides more control over the growth of TiO2 nanotubes. In the literature, different electrolytes have been reported for anodizing Ti, and according to the type of electrolyte, this technique has been classified in four generations.

The first generation is characterized by using an aqueous electrolyte. Typically, amounts of HNO3, H2SO4, H2Cr2O7, CH3COOH or H3PO4 are used in combination with a source of F, which can be NaF, NH4F or HF. With these types of electrolytes, sizes up to 500 microns can be achieved. However, these it has not been found to be useful for practical applications.

The second generation of electrolytes used for producing nanotubes involves pH control. To achieve this, NaOH has been mixed with sulfuric acid, sodium bisulfate or citric acid, and then KF is added to the electrolyte. The voltage applied to this electrolyte is in the range 10–25 V. At more acidic pH, it is possible to obtain long nanotubes of about 6.05 μm ± 0.4, whereas at pH < 1, the length is about 0.28 ± 0.02 μm.

The third generation of TiO2 nanotubes is prepared by anodization using a non-aqueous polar organic, usually viscous, such as: formamide, dimethyl sulfoxide, ethylene glycol or diethylene glycol electrolyte, with which it is possible to achieve lengths of nanotubes from 100 microns to 1000 microns.

The fourth generation prepared with fluoride electrolyte and an oxalic, formic, sulfuric acid or ammonium chloride is added. These nanotubes containing 20% carbon incorporate up to 5% chlorine, suggesting that the role of chlorine in the formation of nanotubes is catalytic, and usually the anodizing times vary from 6 h to 12 h with a potential from 10 V to 20 V.

According to Paulose et al.,30 the key to successfully achieving longer nanotubes lengths is that the water content be at a low percentage. With organic electrolytes, oxygen donation is more difficult compared to water, resulting in a reduced tendency for rust formation, and in turn, the reduced water content allows thinner layers or barriers of low quality, which may be longer through ionic transport.

In previous studies, it has been established that the formation of a compact TiO2 layer is necessary for the formation of nanotubes (stage I). In stage II, the fluoride reacts with the TiO2, causing a complex formation [TiF6],2 which leaves the layer causing the formation of nanopores, which in turn propitiate an increase in current.

In this research, various reactions are proposed to describe first, the formation of NH4TiOF3 nanotubes by means of anodizing Ti, and after those, the formation of TiO2 nanotubes with nanoparticulate walls, which were in anatase crystalline form about 4 nm in size. The method used in this work transforms the metallic titanium into a nanotube structure constituted of H4TiOF3. Then, by moving the nanotube surface into only pure water as a medium, a slow oxidation process occurs and the nanotubes become nanoparticulated at room temperature.

Experimental

The Ti surfaces were industrial grade (97.5% Ti, 2.42% C, 0.08% Sn). The preparation of the Ti plates started by polishing them to remove the rust. Then, they were subjected to ultrasonic washing and dried.

The anodization of Ti was carried out in an organic medium consisting of ethylene glycol 98% v/v; fluoride F 1700 ppm; oxygen O2 2.5 ppm. The oxygen concentration was controlled by continuous water dripping, obtaining measurements in the range 2.3–1.9 ppm. The potential was 60 V applied for 2 h, reached by using steps with increments of 6 V per minute. Ti plates were used as both, anode and cathode.

The measurements of fluorine and oxygen were carry out using Thermo Scientific Orion™ probes, 9609BNWP and 083005MD, respectively.

Unlike most methods for obtaining the anatase phase of NH4TiOF3 nanotubes by anodizing, in this work, it was obtained by immersion in deionized water for 96 hours.

X-ray diffraction analysis was performed by means of a Bruker D8 Advance diffractometer. X-ray diffraction (XRD) patterns were collected over 2 h between the 2θ values of 10 and 80° using a CuKα1 radiation with 1.5405 Å. The Rietveld analysis was carried out using the software MAUD v. 2.55.

The samples were analysed by Scanning Electron Microscopy (JEOL, JSM 7800F at 10 kV of acceleration voltage with secondary electron detector).

Transmission Electron Microscopic studies (JEOL 2100), inverse Fast Fourier Transformation (FFT), and selected area electron diffraction (SAED) pattern were carried out at 120 kV. The sample was prepared by scratching the nanotube layer into ethanol, which was already placed on the carbon coated copper grid.

Raman spectra were measured with an optical spectrometer confocal High Resolution Micro-Raman HR800 Olympus model BX41, at room temperature and pressure, equipment with a microscope Olympus BX41, using a detector CCD, with grid 1800 l mm−1 and excitation source láser of solid state with wavelength of 784.29 nm.

FTIR spectra were recorded with an FTIR module IR2 equipped with an Indium Gallium Arsenide (InGaAs) detector, coupled to a Horiba JobinYvonLabRam HR800 spectrometer. The spectra were recorded in the region of 4000–400 cm−1 with a spectral resolution of 4 cm−1 and 32 scans per measurement, using an ATR contact objective.

XPS analyzes were conducted using a Thermo Fisher Scientific K-Alpha X-ray photoelectron spectrometer with a monochromatized Al Kα X-ray source (1487 eV). O1s peak position at 531.0 eV was used as an internal standard, instead of C1s, to detect and compensate the charge shift of the core level peaks. The preceding is because C was not the main component of the surfaces. Both N1s and F1s core level spectra were fitted using a Gaussian–Lorentzian mix function and Shirley type background subtraction. Throughout all measurements, the basic pressure in the analysis chamber was 10−9 mbar. Survey and high resolution core level spectra were collected at 160 and 60 eV pass energy analyzer, respectively. An X-ray beam, with 400 μm in spot size, was employed to analyze three different regions located onto the sample surfaces.

Results and discussion

Fig. 1 shows the profile of current density vs. applied voltage obtained during anodizing Ti in ethylene glycol for 120 min. The enlarged area on the graphic shows the applied gradient with increments by steps of 6 V per minute. The abrupt increase in the current density was mainly due to the increasing voltage. After the potential of 60 V had been reached, a decrease in the current could be observed. This was due to the oxidation of Ti, which formed a thin titanium oxide film. Then, the plot shows a gradual increase in the current density attributed to the formation of NH4TiOF3 nanotubes.
image file: c6ra05738a-f1.tif
Fig. 1 I and V curves used for obtaining anodized titanium. The insert figure shows an amplification of the ramp used.

The crystalline phase present in the nanotubes was recognized by X-ray diffraction. The nanotubes were initially amorphous after anodizing Ti. Then, the structure underwent a crystallization process as it was progressively oxidized.

In Fig. 2a-i, the pattern of the crystalline phase of the nanotubes formed by anodizing untreated Ti is shown. This phase corresponds to ammonium oxotrifluorotitanate (NH4TiOF3), as is indicated with the JCPS 52-1674. The presence of the Ti phase corresponds to the Ti substrate used for the formation of the nanotubes (JCPS 65-3362). In Fig. 2a-ii, the X-ray diffraction pattern for nanotubes after being immersed in deionized water for about three days is shown. The identified phase corresponds to the anatase phase, and these data were indexed with PDF card #21-272, and confirmed the anatase phase. Also, in the same Fig. 2a-ii, it is possible to observe peaks which correspond to Al2O3. The presence of this compound was due to the sandblasting treatment applied to the Ti surface.


image file: c6ra05738a-f2.tif
Fig. 2 (a-i) Diffractogram of untreated NT. The labeling corresponds to: NH4TiOF3 (▼), and to Ti (●). (a-ii) Diffractogram of NP-NT. The labeling corresponds to: anatase (A). (b) Rietveld profile refinement of NP-NT depicting the observed (line), calculated (dots), and difference (bottom) profiles of XRD data. The identification corresponds to: anatase, corundum, and Ti.

Rietveld's fitting for the pattern shown in Fig. 2a-i, is shown in Fig. 2b. High-intensity peaks of the titanium substrate can be observed. Moreover, in the range 20–38° 2θ peaks attributable to the nanotubes with nanoparticulate anatase walls were present. Rietveld's refinement results indicated a crystallite size of 6 nm, with lattice parameters corresponding to: a = 3.808, b = 4.0, c = 9.535; α = β = γ = 90° cell volume 145.237, and space group I41/amd.

The formation of the nanotubes is limited by the electrochemical oxidation of Ti and chemical dissolution of TiO2. The anodizing medium was composed of 2% in water, and an imposed potential caused its electrolysis, breaking the molecules as presented in reaction (1). With the imposed potential and the presence of oxygen, an oxidation of the metal occurred at the surface as presented in reaction (2). The F were concentrated around the anode under the influence of the electric field. They reacted with the titanium oxide layer causing the formation of titanium complexes [TiOF4]2− (3), which in turn leads the chemical etching to form NH4TiOF3 nanotubes (4). Thus, a self-organized porous layer is obtained. The tube growth will stop when, in the solution, the oxidation or the dissolution is absent.

 
2H2O → O2 + 4H + 4e (1)
 
Ti + O2 → TiO2 (2)
 
TiO2 + 4F + 2H+ → [TiOF4]2− + H2O (3)
 
[TiOF4]2− + NH4+ → NH4TiOF3 + F (4)

Through scanning electron microscopy (SEM), Fig. 3a–e shows these nanostructures formed of nanotubes on surfaces of Ti. The uneven surface in Fig. 3a resembled the characteristics of those surfaces pre-treated by sandblasting before anodizing, which differentiate them from other previous works that start the anodizing process by using polished Ti surfaces. The sandblasting treatment was applied to achieve a nanostructured layer with stronger attachment and to obtain a larger surface area. The titanium roughness was about 40 μm. The nanotubes vary their direction in sector areas according to the original rough titanium surface in an anemone-like conformation. This characteristic was attributed to the growth of the nanotubes in a direction normal to the surface.


image file: c6ra05738a-f3.tif
Fig. 3 (a) SEM image of TiO2 untreated nanotubes showing irregularities caused by sandblasting. (b) Amplification showing the inner diameter (110 nm) and the wall size (10 nm). (c) shows a TEM image of TiO2 untreated nanotubes depicting inner diameter (110 nm) and wall thickness (10 nm). (d) Shows a TEM image of NP-NT with the wall thickness (116 nm). The (e) shows a HRTEM image indicating the family of planes (101) corresponding to anatase with d = 0.35 nm; the selected-area electron diffraction (SAED) pattern of the NP-NT is shown in the top insert, the middle insert is its inverse FFT, and the bottom insert shows the profile of the interplanar spacing, taken from the inverse FFT.

There were incrustations of alumina grits heterogeneously distributed on the titanium surface as a residue from the pretreatment process. The inner diameters of the nanotubes were about 90–120 nm and with walls 10–15 nm in thickness as shown in Fig. 3b.

Fig. 3c shows a TEM image of the nanotubes as prepared after anodizing titanium in an organic medium, corresponding to NH4TiOF3 compound, and before undergoing further oxidization with sizes within the range described above.

Fig. 3d shows the structures that underwent a slow oxidization process in water. Anatase nanoparticles grew and emerged from the nanotubes walls causing a distortion of the structure and leaving fuzzy nanotubes or clusters. Their crystalline orientation is depicted in Fig. 3e, where the family of planes (101) was identified and labeled having a distance of 0.35 nm. The nanotubes resulted hard to detach from the substrate that resemble the Ti substrate with a whiteness tonality, while the NP-NT resulted easy to detach and displayed a white tonality.

In the Fig. 4a-i, the Raman spectrum corresponding to untreated NT is shown. Eight vibrational modes were found. This spectrum shows the vibrational mode at 144 cm−1 corresponding to anatase TiO2 active mode. The modes at 310 cm−1, 363 cm−1, and 475 cm−1 are attributed to the Ti–O influenced by the NH4+. The bands at 206 cm−1 and 705 cm−1 are assigned to the NH4+ translational mode, and 2ν6 of NH4+, respectively.31 The vibrational mode at 870 cm−1 is attributed to the narrowing of the Ti–O–F internal vibrations in NH4TiOF3.32


image file: c6ra05738a-f4.tif
Fig. 4 (a-i) Raman spectra of untreated NT (—) and (a-ii) the NP-NT (•••), their vibrational modes were indicated. (b-i) Infrared spectra of NP-NT (•••) and (b-ii) the untreated NT (—), their vibrational modes were indicated.

In Fig. 4a-ii, the Raman spectrum for NP-NT is presented. According to literature, anatase shows vibrational modes at 144 cm−1, 196 cm−1 and 639 cm−1, which are assigned to the Eg vibration modes, due to symmetric stretching vibration of O–Ti–O.28

The band at 397 cm−1 is the B1g mode and the band at 515 cm−1 is a doublet of A1g and B1g modes caused by symmetric bending vibration of O–Ti–O.33 The A1g peak corresponds to anti-symmetric bending vibration of O–Ti–O in TiO2. The band at 144 cm−1 represents the mode O–Ti–O, which is very sensitive to atomic arrangement, and may be displaced when an oxygen substitution occurs.

However, Swamy et al.34 established that there is a correlation between crystal size of TiO2 and Raman spectrum, and shows that both, the peak position and the full-width at half maximum (FWHM) of the band at 144 cm−1 changes when the TiO2 crystallite size is greater than 34 nm. In this work, the vibrational modes were found at 154 cm−1, 395 cm−1, 510 cm−1, and 625 cm−1. These results are very close to Inoue et al.,35 which corresponds to anatase phase. These positions are attributable to phonon confinement as a result of a crystalline size smaller than 8 nm.

For the IR spectra presented in the Fig. 4b-i, the peaks at 520 cm−1, 790 cm−1, and 870 cm−1 are attributed to Ti–F, Ti–O, and Ti–O–F stretching modes, respectively. The peak at 790 cm−1 is attributed to a combination of Ti–F and Ti–O bands. The Ti–O–F stretching vibration comes from the NH4TiOF3. As in the IR spectra for NP-NT, the band at 1425 cm−1 is attributed to the NH4+ bending mode, which has a first overtone at 2880 cm−1. The strong F and N related bands indicate the high concentration of F and N contained in the NH4TiOF3. The bands at 1622 cm−1 and 3200 cm−1 are attributed to the H–O–H deformation and the O–H stretching modes, respectively. These bands are assigned to the absorbed water molecules.31,36,37

In Fig. 4b-ii, the IR spectrum related to NP-NT is shown. The stretching and bending vibrational peaks of OH functional groups were presented at 3000–3600 cm−1. The peak at 1636 cm−1 and the peak centered at 1060 cm−1 confirmed the presence of hydroxyl species. The broad signal in the range of 400–900 cm−1 corresponds to TiO2. These results are comparable with some values reported.22,38,39

From both FTIR and Raman studies, it is concluded that the entire structure of the NH4TiOF3 is constructed with TiO2 and NH4+. The crystal structure could be zigzag chains of corner connected TiF6 or TiO2 octahedrals with ammonium ions in between.31,37

To establish in more detail the oxidation states and the composition of the chemical species formed in the samples, analysis by decomposition modeling of the high-resolution XPS scans for the Ti2p, O1s, F1s and N1s were performed. In Fig. 5a, the survey XPS spectrum corresponding to a sample of NP-NT is shown. The atomic percentages are provided in the same figure, which indicates that the surface has a considerable quantity of F. The Al identified is the consequence of the sandblasting pretreatment on the Ti plates, which used Al2O3 grits that were 4 mm in size.


image file: c6ra05738a-f5.tif
Fig. 5 (a) General XPS spectrum for a sample of anodized Ti immersed in deionized water (NP-NT). A table of elemental composition (atomic%) is presented. (b) Corresponds to spectra of NP-NT: (b-i) N1s, (b-ii) Ti2p, (b-iii) O2s, and (b-iv) F1s.

Fig. 5b-i shows the high-resolution XPS spectrum for the 1s core level N. The peak centered at 402.5 ± 0.2 eV can be deconvoluted into three signals: 400.3 ± 0.2 eV, 402.5 ± 0.2 eV, and 404.2 ± 0.2 eV. The first contribution is identified as NH4+ species adsorbed on the surface and around the nanotubes.40 The second and third peaks are related to NH3 and N–Ti–O, respectively. However, the last contribution is not associated to Ti–N linkages as substitution nitrogen, but to interstitial nitrogen. The presence of NH4+ and NH3 chemisorbed species is justified since the fluoride source in the process is rich in NH4+, and in this work, no sample was submitted to a heat treatment.

In Fig. 5b-ii, it is possible to identify the positions for peaks of Ti 2p1/2 and Ti 2p3/2, which are at 464.5 and 458.6 ± 0.2 eV, respectively. The double separation between the 2p1/2 and 2p3/2 peaks, at 5.9 eV, is characteristic of TiO2 and is indicative of the presence of Ti4+.37 These two peaks in turn were resolved to 457.1, 458.6, 459.8 and 471.5 ± 0.2 eV. The peaks at 457.1 and 463.3 ± 0.2 eV correspond to the presence of Ti3+.39 The peak located at 458.6 ± 0.2 eV was correlated to Ti anatase.40 The peak at 459.8 ± 0.2 eV could be associated with the presence of Ti–N, which was disregarded and is attributed to N in the interstices, with the peak at 471.5 ± 0.2 eV being the satellite signal.

Fig. 5b-iii shows the high resolution spectrum of core level O1s, which was fitted with three peaks at 529.8 eV, 531.1 eV, and 532.4 ± 0.2 eV. The former was assigned to O1s associated to anatase TiO2. The second peak was identified as N–Ti–O, which was attributed to nitrogen in the interstices. Whereas, the last signal corresponds to adsorbed OH.38,41

In Fig. 5b-iv, the high resolution spectrum for F in a NP-NT sample is shown. The deconvolution data for F1s spectrum contains contributions located at 686.6 and 685.35 ± 0.2 eV. The first value is attributed to F ions that possibly were physically adsorbed at the surface of TiO2.39,40 The contribution observed at 685.3 eV corresponds to Ti link F, in the NH4TiOF3. Table 1 shows the XPS peak positions, their area, FWHM, % Gaussian–Lorentzian, atomic%, and the references related to these emissions. The rows are grouped according to the F, O, Ti, and N, respectively. These values allow location in the spectra and relate more precisely the interaction among the elements conforming the NP-NT.

Table 1 Show the XPS peak positions, their area, FWHM, % Gaussian–Lorentzian, and weight%, according to the F, O, Ti, and N, core level of NP-NT
Name Peak BE Height CPS Height ratio Area CPS (eV) Area ratio FWHM fit param. (eV) L/G mix (%) product
N1s
N1s (1) N–Ti–O 398.1 493.6 0.1 902.33 0.1 1.75 35
N1s (2) N-doped TiO2 400.27 4710.74 1 8847.03 1 1.8 27.25
[thin space (1/6-em)]
Ti2p
Ti2p3 (1) Ti3+ 457.13 1808.89 0.06 2733.01 0.06 1.45 30
Ti2p1 (1′) Ti3+ 463.35 578.84 0.02 874.56 0.02 1.45 30
Ti2p3 (2) anatase 458.58 31[thin space (1/6-em)]160.68 1 45[thin space (1/6-em)]127.22 1 1.39 30
Ti2p1 (2′) anatase 464.38 10[thin space (1/6-em)]675.21 0.34 23[thin space (1/6-em)]359.19 0.52 2.1 30
Ti2p3 (3) Ti–N 459.85 10[thin space (1/6-em)]323.41 0.33 24[thin space (1/6-em)]740.78 0.55 2.3 30
Ti2p1 (3′) Ti–N 465.85 3017.82 0.1 7232.43 0.16 2.3 30
Ti2p4 satellites 471.55 1525.32 0.05 4264.62 0.09 2.71 30
[thin space (1/6-em)]
O1s
O2s (1) O anatase 529[thin space (1/6-em)]832 1355 1.3 30
O2s (2) O–Ti–N 531[thin space (1/6-em)]341 2004 2 30
O2s (3) OH surface 533[thin space (1/6-em)]077 2393 2.4  
[thin space (1/6-em)]
F1s
F1s (1) Ti–F 685.23 28[thin space (1/6-em)]436.76 1 50[thin space (1/6-em)]474.35 1 1.7 30
F1s (2) F (ads) 686.65 9240.34 0.32 26[thin space (1/6-em)]790.59 0.53 2.78 30


The reactions (5) and (6) are proposed for understanding the process of the transformation from NH4TiOF3 nanotubes to TiO2 NP-NT. The H2O dilutes the NH4TiOF3 nanotubes, in TiOF3 and NH4+ ions (5), the formation of NP-NT in anatase phase is reached by the continuous reaction with water, at the end of this process, a decrease in pH occurs, and the formation of HF takes place (6), fluorine an ammonium ions are adsorbed in the nanotubes walls.

 
NH4TiOF3 + H2O → TiOF3 + NH4+ (5)
 
TiOF3 + H2O → TiO2 + 2HF + F (6)

Conclusions

In summary, by anodizing Ti in organic media controlling its oxygen content, it was possible to obtain amorphous NH4TiOF3 nanotubes. The nanotubes inner diameters were about 90–120 nm with walls 10–15 nm in thickness. Subsequently, they evolved into TiO2 nanotubes having nanoparticulate walls that caused distortion of the structure leaving fuzzy nanotubes or clusters. The walls formed by these nanoparticles possessed the anatase crystalline structure and were about 6 nm in particle size. The method for obtaining these nanoparticulated walls was accomplished by immersing the TiO2 nanotubes in deionized water, which provided a medium of slowly oxidizing the NH4TiOF3. The XPS analysis was conducted to propose the presence of NH4+ and NH3 chemisorbed species, which was related to the fluoride source that was rich in NH4+. In obtaining the anatase nanoparticles no sample was submitted to a heat treatment.

Acknowledgements

The authors gratefully acknowledge the financial support from the Mexican Council for Science and Technology. Also, the first author acknowledges CONACyT for his graduate fellowship. Thanks to the Center of Nanoscience and Micro and Nanotechnologies, in obtaining data, specially to Luis Alberto Moreno (Raman, IR), Hugo Martinez Gutierrez and Hector Francisco León Mendoza (SEM), Nicolas Cayetano Castro and Raul Borja Urby (TEM). Thanks to Curtiss Palin for his valuable comments about improving this written work.

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