Well-dispersed titanium dioxide and silver nanoparticles on external and internal surfaces of asymmetric alumina hollow fibers for enhanced chromium (VI) photoreductions

Heterogenous photocatalysis is a suitable alternative for wastewater treatment. The supporting of the solid catalyst in a porous material is suggested to facilitate catalyst recovery and reuse. Here we propose for the first time the evaluation of supporting silver (Ag)-decorated titanium dioxide (TiO2) catalysts on internal and external surfaces of alumina hollow fibers with asymmetric pore size distribution. The produced catalysts were considered for Cr(VI) photoreductions. The ultrasound-assisted process potentialized the distribution of Ag nanoparticles on the TiO2 surface. The loading of Ag nanoparticles at concentrations greater than 5 wt% was necessary to improve the TiO2 activity for Cr(VI) photoreduction. The loading of Ag nanoparticles at 30 wt% improved the Cr(VI) photoreduction of the single TiO2 catalyst from 40.49 ± 0.98 to 55.00 ± 0.83% after 180 min of reaction. Suspended and supported Ag-decorated TiO2 catalysts achieved total Cr(VI) photoreduction after 21 h of reaction. The adjusted reaction rate constant with the externally supported Ag-TiO2 catalyst was 3.57 × 10−3 ± 0.18 × 10−3 min−1. Similar reaction rate constants were achieved with suspended and internally supported catalysts (approximately 2.70 × 10−3 min−1). After 10 sequential reuses, all catalysts presented similar Cr(VI) photoreductions of approximately 66%. Nevertheless, the use of the externally supported catalyst is suggested for Cr(VI) photoreductions due to its superior catalyst activity at least in the first reuse cycles.


Introduction
Chromium (Cr) is a heavy metal that is used in some important industrial processes, such as textile, wood processing, tanning, dyeing, pigment manufacturing, printing, and electroplating. The generated wastewater may contain excess concentrations of chromium that must be treated before the proper discharge. The chromium oxidation states + 3 (Cr((III))) and + 6 (Cr((VI))) are primarily found in wastewaters, and the presence of Cr(VI) represents a great concern due to its high toxicity even at low concentrations. Heterogeneous photocatalysis is suggested as a suitable treatment for Cr(VI) reduction to the less toxic and less soluble Cr(III) (Ding et al. 2023). Different nanomaterials and nanocomposites have been evaluated for photocatalysis processes and also in heavy metal detection applications. Batool et al. (2021) presented an important review of bismuth-based heterojunction nanocomposites for photocatalysis and heavy metal detection applications, which are Responsible Editor: George Z. Kyzas cost-effective, reliable, reusable, and efficient. Askari et al. (2020) proposed the use of graphene quantum dots as fluorescence materials to detect environmental and physiological contaminants. Farhan et al. (2022) presented a comprehensive review of the current aspects of applying multifunctional graphene-based nanocomposites and nanohybrids as photocatalytic materials to remove emerging contaminants from aqueous environments.
Titanium dioxide (TiO 2 ) is commonly suggested as a photocatalyst for Cr(VI) reductions due to its non-toxicity, chemical stability, availability, and low cost (Al-Mamun et al. 2019;Gao et al. 2020). However, the high TiO 2 energy band gap (3.2 eV) imposes a limitation on the use of sunlight as an energy source in photocatalytic processes with TiO 2 as a catalyst (Schneider et al. 2014). Also, the electron-hole charge (e − /h +) recombination should be considered, since it reduces the reactive of electron/hole pairs into interfacial charge-transfer reactions and, consequently, influences the TiO 2 photocatalytic efficiency (Novack et al. 2021). Therefore, noble metals, such as silver (Ag), gold (Au), palladium (Pd), and platinum (Pt), are suggested as electron traps, which stabilize the interfacial charge transfers and decrease the chances of e − /h + recombination of TiO 2 particles. TiO 2 particles decorated with Ag nanoparticles (AgNPs) have greater visible light activity than bare TiO 2 particles mainly due to the surface plasmon band of Ag (Seery et al. 2007). Tang et al. (2022) showed that Ag-decorated and SnO 2 -coupled TiO 2 catalysts presented greater tetracycline hydrochloride photodegradation than bare TiO 2 . According to Narkbuakaew et al. (2022), the g-C 3 N 4 /Ag-TiO 2 photocatalyst presented superior photocatalytic activity for both anionic and cationic dye degradations.
Some procedures are reported in the literature for the synthesis of AgNP-decorated TiO 2 particles, such as electrostatic self-assembly, photo-reduction of Ag salts, and preparation of Ag colloid-TiO 2 dispersions (Stucchi et al. 2018). Ultrasound-assisted processes are suggested to potentialize the distribution of AgNPs on the TiO 2 surface since the collapse of the ultrasound bubbles improves the nucleation rate in a solid/liquid dispersion. Also, the ultrasound waves potentiate the formation of nano-sized particles (Liu et al. 2017). Ye et al. (2015) applied the ultrasound-assisted process to successfully promote the growth of AgNPs on core-shell composites. Stucchi et al. (2018) showed that ultrasound-prepared AgNP-TiO 2 catalysts presented greater acetone photodegradation than the catalysts prepared in the absence of ultrasound.
The catalyst immobilization in a porous solid substrate is presented as a suitable alternative to facilitate catalyst recovery and reuse. Also, the dispersion of the catalyst on a substrate facilitates the assessment of the reactant molecules at the catalyst reaction sites (Lee et al. 2021). Ceramic hollow fibers with asymmetric pore size distributions present potential characteristics to be used as a substrate for particle depositions, since ceramic material presents great mechanical and chemical resistances, the hollow fiber geometry confers great reactor volumes per area, and the pore size distribution enables particle depositions inside the well-designed microvoids and on the outer sponge-like layer (Kingsbury and Li 2009). In our previous works, palladium (Silva et al. 2020), graphite (Terra et al. 2018), and graphene oxide (Ribeiro et al. 2022) were successfully deposited on the outer surface of ceramic hollow fibers, and the composite membranes were used for gas permeation. Also, different oxide catalysts were deposited inside the microvoids of alumina hollow fibers. and the composite systems were evaluated for Cr(VI) (Costa et al. 2019) and methylene blue (Sousa et al. 2022) photodegradation. However, the evaluation of the proper assembling of catalysts in asymmetric hollow fibers was not yet systematically studied. There is a possible trade-off between supporting the catalyst particles on the external and internal surfaces of the hollow fibers. The supporting of the catalyst on the external surface may potentialize the availability of the catalyst active sides to the light exposition, while the supporting of the catalyst inside the hollow fiber microvoids may potentialize the reuse of the supported catalyst. To the best of the authors knowledge, the evaluation of these both configurations was not yet presented in the literature.
Thus, the main objective of this research was to evaluate the efficiency of ultrasound-prepared AgNP-decorated TiO 2 catalysts with different loadings of AgNPs for Cr(VI) photodegradation. Also, the AgNP-TiO 2 particles were deposited on alumina hollow fibers from both the lumen and shell sides. Then, a tailored configuration for the hollow fiber AgNP-decorated TiO 2 catalysts will be presented. Experimental results were adjusted to kinetic and adsorption models to explain Cr(VI) photodegradation mechanisms. Finally, the reuse of free and supported catalysts will be presented. The main innovations of our research are: (1) the proposal of an ultrasound-assisted method with water as the solvent for the synthesis of AgNPs with its simultaneous immobilization on TiO 2 particles; (2) the application of the ultrasound-assisted synthesized AgNP-TiO 2 catalysts for Cr(VI) photoreduction; (3) deposition of the AgNP-TiO 2 catalysts on alumina hollow fibers from the lumen and shell sides and comparison of the composite systems for Cr(VI) photoreduction; and (4) reuse of the free and supported synthesized AgNP-TiO 2 catalysts for Cr(VI) photoreduction.

Sonochemical synthesis of AgNP-TiO 2 photocatalysts
The decoration of micro-sized TiO 2 with Ag nanoparticles was based on the procedures reported by Stucchi et al. (2018). A precursor solution was prepared by mixing 0.02 g of PVP (stabilizing polymer), 2 g of TiO 2 , and different amounts of AgNO 3 in 100 mL of distilled water. Table 1 presents the added amounts of AgNO 3 to obtain samples with Ag percentages varying from 5 to 50 wt% to the amount of TiO 2 .
The precursor solution was magnetically stirred in an ice bath for 10 min followed by the addition of a 0.1 M NaBH 4 aqueous solution by dropping for approximately 2 min. Afterward, an Erlenmeyer of 250 mL containing 115 mL of the mixed solution was placed in the middle of an ultrasound bath (power of 300 W, frequency of 40 kHz, bath volume of 9.5 L, Ultronique model Q9.5/40A, Brazil) for 2 h. Then, the dispersion was centrifuged at 5000 rpm for 10 min, and the bottom solid phase was washed with distilled water. Centrifugation and washing steps were repeated 8 times. The separated solid particles were then dried at 100 °C for 24 h and calcinated at 400 °C for 2 h.
Morphological analyses of the produced AgNP-TiO 2 particles were performed by Transmission Electron Microscopy (TEM, HR, HITACHI Model HT7700). The AgNP-TiO 2 particles were also characterized concerning their crystallinity in an X-ray diffractometer (XRD, Shimadzu, XRD-6000) with an X-ray tube containing a copper anode (Cu-Kα wavelength, λ = 1.54056 Å), at a scan rate of 2° min −1 , 2θ ranging from 10 to 80° with a step of 0.02°, the voltage at 40 kV, and current at 30 mA. The diffraction peaks were compared to the ICDD Powder Diffraction File (PDF) database. Additionally, the crystallite size of the prepared AgNP-TiO 2 particles was calculated by the Scherrer formula (Eq. 1).
where D is the average crystallite size, K is a dimensionless shape factor with a value of 0.9, λ is the X-ray wavelength (CuKα = 0.15406 nm), and β and θ are the full width at half maximum and the diffraction angle of the highest intensity peak, respectively.
Finally, the diffuse reflectance spectra were carried out in an Avantes AvaSpec-ULS2048CL-EVO spectrometer equipped with an integrating sphere. Spectra were collected within the 250-700 nm range, and BaSO 4 was employed as a 100% reflectance standard.

Supporting of Ag-decorated TiO 2 catalysts on external and internal surfaces of asymmetric alumina hollow fibers
Alumina hollow fibers were produced by the phase inversion process followed by a single sintering step (Terra et al. 2018). The mass ratio of 58% of alumina, 36.1% of solvent (DMSO), 0.4% of Arlacel P135, and 5.5% of polymer (PES) was used to prepare the ceramic suspension. The extrusion was performed using a spinneret of two concentrical orifices. The bore fluid, which is responsible for the maintenance of the internal lumen of the fiber, is extruded through the internal orifice of 1.2 mm in diameter. The ceramic suspension is simultaneously extruded through the external orifice of 3 mm in diameter. As proposed by Terra et al. (2018), pure solvent (DMSO) was used as internal bore fluid to increase the number of micro-voids in the produced hollow fiber. The flow rates of internal bore fluid and ceramic suspension were both fixed at 15 mL min −1 and controlled during the extrusion by using two individual pumps (Harvard Apparatus, model XHF). The fibers were directly discharged in the external coagulation bath containing tap water. The fiber precursors were then sintered at 1350 °C in a tubular furnace (Carbolite, model TZF 15) following a specified temperature ramp: from room temperature to 300 °C at 1 °C/min, from 300 to 600 °C at 2 °C/min, holding at 600 °C for 1 h, from 600 to 1350 °C at 5 °C/min, holding at 1350 °C for 5 h, then reducing to the ambient temperature at 5 °C/min. The AgNP30-TiO 2 particles were deposited in the prepared alumina hollow fibers from an AgNP-TiO 2 dispersion at a concentration of 0.2 mg/mL. The AgNP30-TiO 2 dispersion was previously sonicated for 30 min. Individual fibers of 3.5 cm in length were considered for depositions. Before depositions, one of the ends of each fiber was sealed with PTFE tape. The AgNP30-TiO 2 particles were deposited on the hollow fibers from the lumen and shell sides, by means of internal and external depositions, respectively. For internal depositions, 50 mL of AgNP30-TiO 2 dispersion was manually injected into the lumen side of the fiber with a syringe, as proposed by Costa et al. (2019). The vacuumassisted dip-coating methodology presented by Ribeiro et al. (2022) was considered for the deposition of the AgNP30-TiO 2 particles on the external surface of alumina hollow fibers. For external depositions, the fiber was placed inside a graduated cylinder containing 50 mL of the AgNP30-TiO 2 dispersion. Then, the open end of the fiber was connected to a vacuum pump at 300 mmHg for 5 min. Finally, for both internal and external AgNP30-TiO 2 depositions, the fibers were dried at 80 °C for 12 h. The loading of AgNP30-TiO 2 in the fiber substrate was obtained by measuring the mass of the dried fibers before and after AgNP30-TiO 2 depositions.
The morphology of the produced hollow fibers was characterized using a scanning electron microscope (SEM, Carl Zeiss, model EVO MA10, Carl Zeiss). The qualitative elemental composition of the produced fibers was analyzed by energy dispersive spectroscopy (EDS, Oxford, model 51-ADD0048).

Photocatalytic tests for Cr(VI) reductions
Firstly, the photocatalytic experiments were carried out with suspended catalysts at a concentration of 1 g/L in a Cr(VI) solution at 10 mg/L, as suggested in the literature (Costa et al. 2019). All prepared catalysts with different amounts of Ag nanoparticles were considered in the first tests with suspended catalysts. Additional experiments were carried out by varying the Cr(VI) initial concentration from 5 to 20 mg/L with the AgNP30-TiO 2 catalyst at 1 g/L. Individual photocatalytic tests were performed for a total reaction time of 180 min.
Then, additional photocatalytic tests were carried out with suspended and supported AgNP30-TiO 2 catalysts for a prolonged reaction time (1440 min) for catalyst and initial Cr(VI) concentration fixed at 1 g/L and 10 mg/L, respectively. For the test with the supported catalyst, a total of 20 hollow fibers were assembled in a styrofoam holder and immersed in 100 mL of Cr(VI) solution at 10 mg/L. This amount of 20 hollow fibers was considered to contain 100 mg of AgNP30-TiO 2 particles, by means of a catalyst concentration of 1 g/L. The active extension of the hollow fibers was in total contact with the Cr(VI) solution.
For all photocatalytic tests, the pH of the liquid medium was controlled at 2 by adding small volumes of 1 N H 2 SO 4 or 1 N NaOH solutions. For each experiment, the solution was mixed under magnetic stirring at 120 rpm in the darkness for 30 min to reach the adsorption-desorption equilibrium. After this time, the glass reactor (100 mL working volume) was placed 10 cm from the tungsten halogen lamp (100 W, 220 V, FLC, Brazil). Aliquots of 1 mL were withdrawn from the reactor at specific time intervals for Cr(VI) concentration analyses. The total reaction volume decreased by up to 13% after the aliquot was withdrawn. Cr(VI) concentrations were determined according to the diphenylcarbazide method (Sule and Ingle 1996). Before Cr(VI) concentration analyses, samples were filtered through a 0.22-μm PTFE syringe filter.
Experimental data of Cr(VI) reductions were adjusted to the pseudo-first-order reaction model (Eq. 2), as indicated in the literature (Antonopoulou et al. 2017). According to the literature (Trejo-Valdez et al. 2019), heterogeneous photocatalysis consists of two main steps: fast adsorption of reactants on the photocatalyst surface and a slow reaction of the analyte with a photo-generated radical species. The first step related to the adsorption of the Cr 2 O 7 −2 on the catalyst surface can be analyzed in terms of the Langmuir-Hinshelwood model, where the obtained apparent rate constants (k app ) were adjusted to the initial Cr(VI) concentrations according to Eq. 3.
where C 0 is the initial concentration of Cr(VI) (mg/L), C is the concentration of Cr(VI) at the time t (mg/L), t is the reaction time (min), and k app is the apparent rate constant (min −1 ).
where K LH is the adsorption equilibrium constant (L/mg) and k r is the reaction rate constant (mg/L min).
The reuse of the free and supported catalysts was evaluated in 10 sequential batch experiments of 12 h each. Fresh Cr(VI) solutions were used in each batch experiment. The supported catalysts were reused without any cleaning or other recovery procedures. The recovery of the free catalysts from the liquid medium was carried out by centrifugation at 4000 rpm for 10 min. Then, the supernatant was discharged, and the recovery powder was reused in the sequential photocatalyst test. After each photocatalytic cycle, the supported catalysts were washed with distilled water, dried at 50 °C for 12 h, and weighed to account for the detachment of the catalyst from the support. (2)

Characteristics of the AgNP-TiO 2 particles
TEM images were considered to verify the morphology, particle size, and distribution of Ag nanoparticles on the TiO 2 surface (Fig. 1). The TiO 2 presented an agglomeration of rhombohedral nanocrystalline particles (Shawky et al. 2022), with sizes varying from approximately 1 to 0.3 µm (Fig. 1 a). The ultrasound-assisted process enabled the decoration of single Ag nanoparticles on the surface of the micro-sized TiO 2 particles (Fig. 1 b). The ultrasound acoustic cavitation enabled the formation of bubbles which were imploded at the liquid-solid interface and generated transient hot spots which have enhanced the distribution of active sites for Ag deposition on the TiO 2 surface. The attached Ag nanoparticles presented sizes of approximately 30 nm (Fig. 2 b).   (ICDD 04-0783), respectively, which confirmed the presence of metallic Ag nanoparticles (Pu et al. 2018). The other peaks were assigned to the TiO 2 anatase phase (ICDD 071-1166). According to Eq. 1, the average crystallite diameters were 40.1 nm for the nanocrystalline TiO 2 and 29.4 nm for the Ag nanoparticles. Chakhtouna et al. (2021) reported similar values of average crystallite diameters for synthesized Ag/TiO 2 catalysts. Finally, the XRD and TEM analyses revealed that Ag nanoparticles were formed and successfully loaded on the TiO 2 surface.
Optical characterization of the samples was carried out by diffuse reflectance spectroscopy (Fig. 3). For the pristine TiO 2 , a typical spectrum was observed with a broadband gap absorption in the 250-420 nm range, which agrees well with the reported band gap energy of 3.2 eV (Santos et al. 2015). Following the decoration, the TiO 2 particles with Ag nanoparticles become visibly brownish. In the diffuse reflectance spectrum, a broad absorption in the visible range appears, which agrees well with the expected spectral feature for the oxide modified with Ag nanoparticles. It is also expected that the surface of the nanoparticles is partially oxidized since Ag 2 O has a band gap of 1.3 eV (Tjeng et al. 1990). Also, a broad visible light absorption is expected leading to improved light-harvesting efficiency in relation to bare TiO 2 . The close contact between the Ag/Ag 2 O particles and TiO 2 leads then to the formation of heterojunctions, which should be beneficial to the charge separation efficiency and the photocatalytic activity.

Kinetics of Cr(VI) photoreduction with suspended Ag-decorated TiO 2 catalysts at different Ag loadings
Figure 4 a presents the Cr(VI) photoreduction profile during the photocatalytic tests at a catalyst concentration of 1 g/L and an initial Cr(VI) concentration of 10 mg/L. Single and Ag-decorated TiO 2 particles were used as catalysts. The loading of Ag nanoparticles varied from 5 to 50 wt%. The adjustment of experimental data to the pseudo-first-order kinetic model is presented in Fig. 4 b. Table 2 presents the percentages of Cr(VI) reduction after 180 min of reaction and the adjusted apparent rate constant (k app ).
The loading of Ag nanoparticles at 5 wt% did not cause a significant improvement in Cr(VI) photoreductions if compared to the single TiO 2 catalyst. However, Cr(VI) photoreductions were significantly improved for the loading of Ag nanoparticles at mass ratios greater than 10 wt%. The plasmonic resonance of Ag nanoparticles increased the catalyst light absorption capacity and consequently improved the Cr(VI) photoreductions (Xin et al. 2005). Moreover, the applied ultrasound-assisted process enabled the distribution of Ag nanoparticles on the TiO 2 surface, and, thus, the electron sink of Ag nanoparticles was favored (Stucchi et al. 2018). Cr(VI) photoreductions were statistically equivalent for Ag loadings at 30, 40, and 50 wt%. Rosario and Pereira (2014) observed that high Ag concentrations metalize the TiO 2 surface instead of doping the semiconductor particles.
Thus, the loading of Ag nanoparticles at 30 wt% is suggested to promote the Cr(VI) photoreduction with the Ag-decorated TiO 2 catalyst.
Experimental data of Cr(VI) photoreduction were quite well adjusted to the rate expression of a pseudo-first-order reaction (Fig. 4 b), with R 2 values greater than 0.95. As presented in Table 2, the apparent rate constant (k app value) for single TiO 2 is lower than Ag-decorated TiO 2 particles, which confirms the increase of photocatalytic activities and efficiencies of the doped particles. Similar values of apparent rate constant are reported in the literature for Cr(IV) photoreductions (Abdel Moniem et al. 2015). Zhang et al. (2019) reported a rate constant value of 5.05 × 10 −3 min −1 for Cr(VI) reduction with Cu-doped TiO 2 as a photocatalyst. Figure 5 illustrates the effect of initial Cr(VI) concentrations on the efficiency of the AgNP30-TiO 2 catalyst at 1 g/L for Cr(VI) photoreductions. The photocatalytic reductions of Cr(VI) decreased from 87.83 ± 1.83% to 43.57 ± 0.19% if increasing the initial Cr(VI) concentration from 5 to 20 mg/L at a reaction time of 180 min (Fig. 5 a). This behavior was expected since the dosage of AgNP30-TiO 2 was fixed, and, therefore, the catalytic sites were limited. Akbarzadeh et al. (2021) indicated that black TiO 2 nanocomposite doped with Bi-V reduced 94% of Cr(VI) from an aqueous solution at an initial Cr(VI) concentration of 1 mg/L within 20-min irradiation time and catalyst dose of 1 g/L. The adjustment  of experimental data to the kinetic model of pseudo-firstorder is presented in Fig. 5 b. As presented in Table 3, the apparent reaction rate constant (k app ) significantly decreased from 0.01292 ± 0.00049 to 0.00315 ± 0.00009 min −1 with    increasing Cr(VI) concentration from 5 to 20 mg/L. Naimi-Joubani et al. (2015) also observed a significant decrease in the apparent reaction rate constant with increasing Cr(VI) concentration during the photocatalytic process with ZnO/ TiO 2 composite as the catalyst. The observed apparent rate constants (k app values) for each initial Cr(VI) concentration were then adjusted to the Langmuir-Hinshelwood model. The linear adjustment of the apparent rate constants as a function of initial Cr(VI) concentrations was used to calculate values of k r and K LH as 0.061 mg/L min and 4.734 L/mg, respectively. These values are typical of the Langmuir-Hinshelwood model for heterogeneous photocatalysis (Trejo-Valdez et al. 2019).

Characteristics of the supported catalyst
Due to its pronounced photocatalytic activity for Cr(VI) reduction, the AgNP30-TiO 2 catalyst was chosen to be impregnated in the hollow fiber substrate. The produced fibers presented inner and outer diameters of 1.79 ± 0.02 and 2.25 ± 0.01 mm, respectively. Figure 6 a presents the morphology of the produced asymmetric alumina hollow fibers. The fibers presented an asymmetric pore size distribution with well-organized microvoids throughout the fiber crosssection, as observed in Fig. 6 a. The microvoids were formed due to the viscous fingering phenomenon and/or the interfacial instabilities described by the Rayleigh-Taylor theory (Lee et al. 2015;Bessa et al. 2022). Pure solvent was used as internal bore fluid, and, therefore, the microvoids were formed from the fiber outer surface since the fiber nascent was in direct contact with the water coagulation bath. The microvoids extended from the outer to the inner surface of the fiber and remained open in the fiber lumen side, which is favorable for particle impregnation. The fiber outer surface was dense since a very thin outer sponge-like layer was formed on the fiber outer surface, which is favorable for the deposition of a dense layer on the fiber shell side. Figure 6 b, c presents the morphology of the deposited AgNP30-TiO 2 particles on the external and internal sides of the substrate, respectively. The external and internal layers of AgNP30-TiO 2 particles presented thicknesses of 32.91 ± 5.45 and 40.18 ± 4.85 µm, respectively. These thicknesses are statistically equivalent at p < 0.05, which means the external and internal depositions resulted in similar amounts of the deposited particles. Also, similar mass increments of 2.0094 ± 0.6077 and 2.0168 ± 0.1836 mg per cm 2 of fiber surface area were measured after internal and external depositions, confirming that the amounts of deposited particles were similar for both external and internal depositions.
EDS analyses (Fig. 7) confirmed that the alumina hollow fiber is composed of aluminum and oxygen, which are related to the ceramic material (alumina, Al 2 O 3 ). Silver and titanium were observed throughout the fiber cross-section after the impregnation of AgNP30-TiO 2 particles from the fiber lumen side, with a considerable concentration of AgNP30-TiO 2 particles in the internal side of the fiber and inside the microvoids (Fig. 7 a). After AgNP30-TiO 2 impregnation from the fiber shell side (Fig. 7 b), silver and titanium were mainly observed on the fiber external surface, although some particles were also observed throughout the fiber cross-section. Prasetya et al. (2017) showed the proper deposition of Rh/CeO 2 catalysts inside the microchannels of asymmetric alumina hollow fibers. García-García and Li (2013) also deposited a catalyst (CuO/CeO 2 ) in the fingerlike region of alumina hollow fibers. Sousa et al. (2022) deposited ZnO particles on the external surface of alumina hollow fibers, and the composite system was used for methylene blue photodegradation. According to an EDS line scan composition profile analysis through the fiber cross-section (Fig. 8), the thickness of the AgNP30-TiO 2 layer is approximately 30 µm after external deposition, in agreement with the value measured in the SEM image (Fig. 6 b). Figure 9 presents the kinetic curves for Cr(VI) photoreduction during the photocatalytic tests at a catalyst concentration of 1 g/L and initial Cr(VI) concentration of 10 mg/L with the AgNP30-TiO 2 catalyst supported on external and internal sides of alumina hollow fibers (shell and lumen sides, respectively). The Cr(VI) photoreduction with suspended AgNP30-TiO 2 is also presented for comparison.

Kinetics of Cr(VI) photoreduction with the supported AgNP30-TiO 2 catalyst
Total Cr(VI) reductions were achieved with suspended and supported AgNP30-TiO 2 catalysts after 18 h (1080 min) of reaction. According to results reported in our previous work (Costa et al. 2019), free TiO 2 was able to reduce 89% of Cr(VI) after 24 h of reaction at a catalyst concentration of 1 g/L and initial Cr(VI) concentration of 10 mg/L Thus, the addition of Ag nanoparticles caused significant improvement on Cr(VI) photoreduction. Cr(VI) reductions were similar to suspended and internally supported AgNP30-TiO 2 catalysts. The supporting of AgNP-TiO 2 particles on the fiber lumen side caused the fulfillment of the fiber microvoids by the catalyst, and this distribution did not cause substantial changes in the catalyst activity for Cr(VI) reductions. However, the greatest Cr(VI) reduction was achieved with the externally supported AgNP30-TiO 2 catalyst at reaction times of 360 min. Thus, the dispersion of the catalyst on the support outer surface reduced the agglomeration of the nanostructured catalyst particles and provided higher active catalyst surface areas if compared to the bulk dispersed and internally deposited catalysts. Table 4 presents the adjusted apparent rate constant values (k app ) according to the pseudo-first-order kinetic 1 3 Fig. 6 Cross-section SEM images of alumina hollow fibers: (a) pristine, (b) after external deposition of AgNP30-TiO 2 particles, and (c) after internal deposition of AgNP30-TiO 2 particles model for Cr(VI) photoreductions with the suspended and supported AgNP30-TiO 2 catalysts. The rate constant values were similar with suspended and internally supported AgNP30-TiO 2 catalysts. The reaction with the externally supported AgNP30-TiO 2 catalyst presented the highest value of k app , which means the dispersion of the catalyst particles on the support external surface was favorable to accelerate the Cr(VI) photoreductions.

Reuse of suspended and supported AgNP30-TiO 2 catalysts
The reuse of a catalyst in a heterogenous catalytic system is an important issue to be considered. Figure 10 shows the reusability of the proposed catalysts for Cr(VI) photoreduction after 12 h of reaction at each cycle.
All catalysts presented some activity decrease in sequential reuses, which is related to the deposition of generated Cr(OH) 3 on the catalyst surface after photocatalytic reactions and/or by the saturation of photocatalyst surface by the Cr(III) ions photo deposited during the reduction reaction (Aggarwal et al. 2022). The Cr(VI) photoreductions were reduced by approximately 1.2 times after 10 sequential reuses of suspended and internally supported catalysts. After 10 sequential reuses, Cr(VI) photoreductions were reduced by approximately 1.4 times with the externally supported catalyst. Thus, the decrease in the activity of the externally supported catalyst was more pronounced than that of suspended and internally supported catalysts in sequential reuses. Actually, some detachment of the externally supported catalyst may have occurred during the sequential reactions. As presented in Fig. 10, the decrease in the activity of the externally supported catalyst was more accentuated in the first 4 sequential reuses. Then, the catalysts presented similar Cr(VI) photoreduction from the 5 th reuse. However, the reuse of the supported catalysts is simplified since any pretreatment is required, while the suspended catalysts should be separated from the liquid medium by some liquid-solid separation process. The deposition of the AgNP-TiO 2 catalyst on the fiber shell side is suggested since the externally deposited catalyst presented superior Cr(VI) photoreductions at least in the first reuse reactions.

Conclusion
The ultrasound-assisted technique enabled to produce a composite catalyst formed by TiO 2 and Ag nanoparticles in a single and simplified process. The decoration of micro-sized TiO 2 with Ag nanoparticles was confirmed by TEM and XRD analyses. The increment in the diffuse reflectance spectra according to Ag loadings also confirmed the deposition of Ag nanoparticles on the TiO 2 surface. Ag nanoparticles at concentrations greater than  Table 4 Linear fitting parameters to the pseudo-first-order kinetic model for Cr(VI) photoreductions with suspended and supported AgNP30-TiO 2 catalysts Statistically equivalent results at p < 0.05 for the same letters Catalyst 10 3 k app (min −1 ) R 2 Suspended AgNP30-TiO 2 2.70 b ± 0.14 0.9675 Supported AgNP30-TiO 2 (internal side) 2.71 b ± 0.14 0.9690 Supported AgNP30-TiO 2 (external side) 3.57 a ± 0.18 0.9707 1 3 5 wt% are necessary to increase the efficiency of the single TiO 2 catalyst. Asymmetric alumina hollow fibers were successfully used as substrates to impregnate the catalytic particles on the external and internal sides. Cr(VI) photoreductions were greater with the externally supported AgNP-TiO 2 than with suspended and internally supported AgNP-TiO 2 catalysts. Suspended and supported AgNP-TiO 2 catalysts presented similar reusability, but the recovery of the supported catalyst from the liquid medium was facilitated. Further developments should be carried out to investigate the application of other noble metals (gold, palladium, platinum, and others) to form a composite TiO 2 photocatalyst with superior activity.