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Bioactive TiO2 Fibers Prepared by Solution Blow Spinning: A Promising Approach for Microbial Control

Abstract

PEO/TiP fibers were obtained using the Solution Blow Spinning (SBS) apparatus and heat treated to produce TiO2 fibers. The morphological and structural characteristics were assessed using SEM and X-ray diffraction. The fibers, with a thickness of 12 μm, showed a change in crystalline structure with heat treatment. At temperatures as low as 800 °C, only the anatase phase was identified, while at 900 °C, both anatase and rutile phases coexisted. The addition of TiP to the polymer matrix reduced the initial breakdown temperature, and the DSC curves showed exothermic peaks due to the amorphous phase transition to TiO2/anatase. The fibers' photocatalytic capacity was tested, revealing that TiO2-fibers in the anatase phase achieved 97% degradation of Rhodamine-B dye in 40 minutes. The study found that the biocide efficacy of TiO2-fibers depends on their heat treatment. Fibers with anatase/rutile or pure rutile phases did not show significant efficiency. However, fibers treated at 600°C with pure anatase phase were more effective in eliminating E. coli and total coliforms. Finally, we can state that the TiO2 fibers obtained in this work using the SBS technique can be used to produce filters to purify water contaminated by pathogens dangerous to human health or even to purify the air.

Keywords:
TiO2 fibers; solution blow spinning; photocatalytic property; PEO/TiP


1. Introduction

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Electrospinning is a well-established technique for polymeric production of fibers from melt polymers or polymer solutions2525 Samadi M, Moshfegh AZ. Recent developments of electrospinning-based photocatalysts in degradation of organic pollutants: principles and strategies. ACS Omega. 2022;7(50):45867-81.,3030 Sigmund W, Yuh J, Park H, Maneeratana V, Pyrgiotakis G, Daga A, et al. Processing and structure relationships in electrospinning of ceramic fiber systems. J Am Ceram Soc. 2006;89(2):395-407.

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The amount of "free" charge that can be induced in a polymer solution during electrospinning is represented by the dielectric constant of the solvent. Low dielectric constant polymer-solvent solutions limit the initiation of the whipping instability and thinning of the polymer jet3333 Subbiah T, Bhat GS, Tock RW, Parameswaran S, Ramkumar SS. Electrospinning of nanofibers. J Appl Polym Sci. 2005;96(2):557-69.,3434 Horner CB, Low K, Nam J. Electrospun scaffolds for cartilage regeneration. In: Liu H, editor. Nanocomposites for musculoskeletal tissue regeneration. Amsterdam: Elsevier; 2016. p. 213-40.. Because of these constraints, the SBS technique has recently been highlighted in producing polymeric micro/nanfibers3535 Medeiros ES, Glenn GM, Klamczynski AP, Orts WJ, Mattoso LHC. Solution blow spinning: a new method to produce micro- and nanofibers from polymer solutions. J Appl Polym Sci. 2009;113(4):2322-30.

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Compared with electrospinning, the SBS process does not depend on the dielectric constant; fibers can be deposited onto any type of substrate or collector, and the fiber production rate is many times higher, thus having better commercial production potential3535 Medeiros ES, Glenn GM, Klamczynski AP, Orts WJ, Mattoso LHC. Solution blow spinning: a new method to produce micro- and nanofibers from polymer solutions. J Appl Polym Sci. 2009;113(4):2322-30.. As a result, this study aimed to create TiO2 photocatalytic microfibers by thermally treating polyethylene oxide/isopropoxide (PEO/TiP) fibers generated by the SBS apparatus. The influence of thermal treatment on the morphology and crystalline structure of TiO2 microfibers was examined first, followed by an assessment of the photocatalytic activity of microfibers as function of the degradation of the Rhodamine-B (RhB) dye under UV light. The efficiency of TiO2 fibers in the death of bacteria such as E. coli and total coliforms was also evaluated. The results of this study can provide valuable information on the use of TiO2 fibers in various applications, such as water treatment contaminated with pathogens harmful to human health and air purification by pathogens harmful to human health and air purification.

2. Experimental Procedure

2.1. Materials

All chemicals used in this work were purchased from Sigma-Aldrich and used as received: polyethylene oxide powder (PEO) (Average Mw = 5,000,000) titanium (IV) isopropoxide (TiP) (95.0%), RhB dye (95.0%), chloroform (99.5%), and absolute ethanol ( 95.0%).

2.2. Extraction of pure titanium dioxide fibers

The precursor solution was prepared by adding 0.2 g of PEO to a mixture of 3.0 mL of absolute ethyl alcohol and 5.0 mL of chloroform. The mixture was stirred for 40 minutes at room temperature (25 °C). Then, 2.0 mL of TiP was added to the PEO solution which remained stirred for 40 minutes. The final solution was placed in disposable syringes connected to an 18G spinal needle and attached to the injection system (Figure 1). The most optimal conditions for forming of the microfiber were as follows: injection rate of 0.3 L min−1, work distance of 35 cm, and collector speed of 60 rpm. No gas was used to draw the solution to the collector. The (PEO/TiP) fibrous composites were thermally treated at 600, 700, 800, 900, and 1000 °C to remove the polymer component to yield TiO2 fibers.

Figure 1
Experimental apparatus used by the SBS.

2.3. Characterization

The crystallinity and phase of the produced TiO2 fibers were investigated using a Shimadzu X-ray diffractometer (model XRD-6000), Cu Kα (1.54056 Å). The Scherrer equation and the X-ray diffraction pattern were used to calculate the average crystallite size. A scanning electron microscope (SEM, Zeiss EVO LS15) with a voltage range of 5.00 kV to 20.00 kV was used to investigate the morphological structure. Using the image analysis tool "Image J 1.45," the average diameter of the fibers was estimated. Ten milligrams of the sample were used for the thermogravimetric analysis, which was carried out using an SDT model Q 600 from TA instruments. The samples were heated between 25 and 800 °C at 10 °C min-1 in a nitrogen environment with a flow rate of 100 mL min-1. The Varian Cary 50 Scan equipment captured UV-vis spectra to examine the peak decrease in maximum dye absorption.

2.4. Photocatalytic principles and activity evaluation

The band gap, which forms the foundation for heterogeneous photocatalysis, is the area between the semiconductor material's valence (VB) and conduction (CB) bands. Semiconductor activation may occur depending on the energy of the photons from artificial or natural light. According to Equation 1, an electron is promoted from VB to CB by absorption of a photon with energy larger than or equal to the band gap, causing a vacancy (h+) to form in the VB. The positive potential of these vacancies might range from (+2.0 to +3.5 eV) depending on the semiconductor4242 Zhang X, Wang DK, Lopez DRS, Diniz da Costa JC. Fabrication of nanostructured TiO 2 hollow fiber photocatalytic membrane and application for wastewater treatment. Chem Eng J. 2014;236:314-22.. Figure 2 depicts a diagram showing how UV light activates TiO2 microfibers so that they can interact with contaminants such as RhB.

Figure 2
Photocatalytic activity of TiO2 fibers in the presence of UV light in the RhB dye degradation process.

In the photocatalysis process, contaminants can be degraded when water molecules adsorbed on the surface of the semiconductor generate OH radicals (Equations 2 and 3)4343 Hoffmann MR, Martin ST, Choi W, Bahnemann DW. Environmental applications of semiconductor photocatalysis. Chem Rev. 1995;95(1):69-96.,4444 Fujishima A, Rao TN, Tryk DA. Titanium dioxide photocatalysis. J Photochem Photobiol Photochem Rev. 2000;1(1):1-21.. In addition to the OH radicals, the degradation can also occur through oxygen derivatives that are formed when electrons are captured in the system (Equation 4)4444 Fujishima A, Rao TN, Tryk DA. Titanium dioxide photocatalysis. J Photochem Photobiol Photochem Rev. 2000;1(1):1-21..

TiO 2 h ν TiO 2 e CB + h VB + (1)
h + + H 2 O adsorption HO + H + (2)
h + + OH adsorption HO (3)
e + O 2 O 2 (4)

In the development of this work, the photocatalytic activity of samples was evaluated in a photocatalytic reactor equipped with a UV mercury lamp (250 W) and a magnetic stirrer. For this purpose, 80 mg of TiO2 fibers were added to 100 mL of RhB aqueous solution (10 mg/L). The mixture was stirred for 15 minutes at room temperature (25°C) in the absence of light. To start the photocatalysis process, the UV light was turned on, and every 10 minutes, 3 mL aliquot of the mixture was removed and then centrifuged at 6,000 RPM for 5 minutes to separate the microfibers from the solution. After this process, the solution was analyzed by spectra UV-Vis, obtaining its absorption band and possible intensity reduction again.

The photocatalytic degradation efficiencies of samples were determined using the Equation 5

Degradation % = C 0 C C 0 × 100 (5)

where C0 is the concentration of RhB after 15 minutes of agitation without UV exposure, and C is the RhB concentration after UV irradiation for a specific time.

2.5. Procedure for analyzing water contamination and the biocidal efficacy of TiO2 fibers

Water samples were collected from a semi-artesian well contaminated with E. coli and total coliforms. The aim was to evaluate whether TiO2 fibers could eliminate these bacteria. The water samples were filtered through a sterile nitrocellulose membrane with a diameter of 47 mm and a porous size of 1.45 μm to analyze the biological contaminants. This filter is designed to retain and encourage the growth of both bacteria types, E. coli (blue dots) and total coliforms (red dots) (see Figure 3a). To compare the effectiveness of TiO2 fibers, an equivalent amount of fibers, 0,01 g, was applied to the central region of the contaminated membranes (see Figure 3b). All contaminated membranes were then exposed to a 9 W ultraviolet lamp positioned 30 cm away for a brief 2-second irradiation period. After exposure, the membranes were incubated at 36 °C for 28 hours to allow any bacterial growth. Finally, the bacterial colony formation procedure was used to evaluate qualitatively both the treated and untreated membranes, revealing the impact of the TiO2 fibers.

Figure 3
(a) Nitrocellulose membrane contaminated with both E. Coli (blue dots) and total coliforms (red dots) bacteria’s and, (b) contaminated membrane with the presence of TiO2 fibers.

3. Results and Discussion

3.1. TiO2 fibers morphology characterization

PEO/TiO2 fibers were produced using a blow spinning apparatus. The precise combination of injection rate, collector rotation, and working distance made producing precursor fibers without carrier gas possible. These parameters are injection rate of 53 μL, collector rotation of 60 rpm, and working distance of 35 cm. The injected PEO/TiO2 solution presented the shape of a continuous thread that was manually taken from the tip of the nozzle to the collector, and then the rotating collector promoted the process of stretching the polymeric solution.

Figure 4 shows a SEM image of PEO/TiO2 fibers and TiO2 fibers resulting from the calcination of PEO/TIP at 600 °C. Fiber diameters were measured by analyzing SEM images and using ImageJ software. The distribution histograms and the calculated average diameters are shown inset in the figures. The diameter of the precursor fibers (Figure 4a) is larger than that of the calcined fibers (Figure 4b). This occurs due to the decomposition of the PEO polymer matrix. Heat treatment simultaneously removes organic components while promoting the growth of TiO2 crystals due to oxidation of the Ti precursor.

Figure 4
SEM images of PEO/TiO2 precursor fiber (a) and (b) after heat treatment at 600 °C.

A similar decrease in fiber diameter was also observed by Tan et al.4545 Tan NPB, Cabatingan LK, Lim KJA. Synthesis of TiO2 Nanofiber by Solution Blow Spinning (SBS) Method. Key Eng Mater. 2020;858:122-8., who prepared TiO2 fibers using the SBS technique with Polyvinylpyrrolidone (PVP)/TiP. However, unlike the results shown in Figure 4, the fibers obtained after heat treatment were brittle and had reduced length compared to untreated fibers.

Figure 5 demonstrates the impact of varying temperatures on TiO2 fibers during the heat treatment. Despite temperature changes, the fibers maintained their original form.

Figure 5
SEM images of TiO2 fiber after heat treatment for 4h: (a) 600°C; (b) 700°C; (c) 800°C; (d) 900°C, and (e) 1000°C.

The production method allowed the development of some hollow structures, as shown in Figures 4b and 5d. It is evident from a comparison of Figures 4 and 5 that the adherence of fibers during the sintering process may cause this morphological shape. The presence of these hollow structures presents significant advantages, as it significantly increases the accessible surface area of the system, making it ideal for photocatalytic applications.

Fibers processed with SBS showed an average diameter of 11 to 13 μm after heat treatment. This draws attention to a crucial difference between electrospinning and SBS. Electrospinning best produces nanofiber architectures, while SBS generally results in fibers with substantially larger diameters. Daristotle et al.4646 Daristotle JL, Behrens AM, Sandler AD, Kofinas P. A review of the fundamental principles and applications of solution blow spinning. ACS Appl Mater Interfaces. 2016;8(51):34951-63. who investigated the morphological and mechanical characteristics of fibers made with SBS, support this observation.

3.2. Structural analysis

The X-ray diffraction (XRD) pattern of TiO2 fibers is depicted in Figure 6. The process of heat treatment has a significant effect on the formation of crystallographic phases. The peaks of the anatase phase are observed in the thermally treated fibers at 600, 700, and 800°C (main peak is at 2θ = 25.3°). In contrast, the rutile phase peaks are identified in the fibers treated at 900 and 1000 °C (main peak is at 2θ = 27.3°). These findings are consistent with the results reported in the literature that demonstrate using heat treatment temperatures to produce the TiO2 phase4747 Bessergenev VG, Mateus MC, do Rego AMB, Hantusch M, Burkel E. An improvement of photocatalytic activity of TiO2 Degussa P25 powder. Appl Catal A Gen. 2015;500:40-50.,4848 Kralchevska R, Milanova M, Tsvetkov M, Dimitrov D, Todorovsky D. Influence of gamma-irradiation on the photocatalytic activity of Degussa P25 TiO2. J Mater Sci. 2012;47(12):4936-45..

Figure 6
TiO2 fibers XRD heat treated at different temperatures for 4 h.

To completely transform the TiO2 fibers from the anatase phase into rutile, heat treatment at 1000 °C was necessary in this study. Usually, anatase permanently transforms into rutile when exposed to temperatures above 600 °C in an atmosphere of air. However, the transition temperature from the anatase phase to the rutile phase can vary from 400-1200 °C depending on the specific TiO2 synthesis technique4949 Hanaor DAH, Sorrell CC. Review of the anatase to rutile phase transformation. J Mater Sci. 2011;46(4):855-74.,5050 Wang CC, Ying JY. Sol−gel synthesis and hydrothermal processing of anatase and rutile titania nanocrystals. Chem Mater. 1999;11(11):3113-20.. It is essential to evaluate the transition kinetics of these phases. Factors that should be considered include the shape and size of particles, atmosphere, surface area, sample volume, heating rate, sample container type, contaminants, and measurement technique4949 Hanaor DAH, Sorrell CC. Review of the anatase to rutile phase transformation. J Mater Sci. 2011;46(4):855-74..

The coexistence of anatase and rutile phases is observed in fibers treated at 900 °C. The fraction of anatase and rutile phases found in TiO2 fibers was calculated using Equation 6. The rutile and anatase phases present percentages of 64.36% and 35.64%, respectively. Table 1 presents the samples' average size of the TiO2 crystallite calculated by the Scherrer equation and the percentages of anatase and rutile phases5151 Li W, Ni C, Lin H, Huang CP, Shah SI. Size dependence of thermal stability of TiO2 nanoparticles. J Appl Phys. 2004;96(11):6663-8.,5252 Choudhury B, Choudhury A. Local structure modification and phase transformation of TiO2 nanoparticles initiated by oxygen defects, grain size, and annealing temperature. Int Nano Lett. 2013;3(1):55..

w R = I R 0,884 I A + I R , (6)

where WR is the percentage of the rutile phase present in the sample, and IR and IA represent the intensities of the diffraction peaks characteristic of the rutile and anatase phases.

Table 1
Percentage of anatase and rutile phases of TiO2 fibers submitted to different heat treatments.

3.3. Thermal characterization

The thermogravimetric analysis (TGA) technique was utilized to gather information about the thermal stability and breakdown of the polymeric matrix of the PEO and the impact of TiP on the degradation process of the polymeric matrix. The TGA curves for pure PEO and PEO/TiP fibers are displayed in Figure 7a. A single event of mass loss was observed in the polymeric matrix (PEO), which started at around 327 °C, and the intensity decreased at approximately 405 °C, decomposing about 92% of the sample. After this event, the process continued steadily until it reached the end temperature of 800 °C. The stability of the sample is mainly due to the test being conducted in an inert atmosphere (nitrogen flow)5353 Bizarria MTM, d’Ávila MA, Mei LHI. Non-woven nanofiber chitosan/peo membranes obtained by electrospinning. Braz J Chem Eng. 2014;31(1):57-68..

Figure 7
(a) TGA and (b) DSC curves for PEO and PEO/TiP fibers.

The main byproducts of PEO mass loss are methyl alcohol, ethyl alcohol, alkene, formaldehyde, non-cyclic ethers, ethylene oxide, water, acetic aldehyde, CO2, and CO5454 Aydogdu A, Sumnu G, Sahin S. A novel electrospun hydroxypropyl methylcellulose/polyethylene oxide blend nanofibers: morphology and physicochemical properties. Carbohydr Polym. 2018;181:234-46.,5555 Pielichowski K, Flejtuch K. Non-oxidative thermal degradation of poly(ethylene oxide): kinetic and thermoanalytical study. J Anal Appl Pyrolysis. 2005;73(1):131-8.. In the case of the PEO/TiP composite, the integration of the precursor resulted in a decrease in the initial temperature of the polymer matrix breakdown process. There are two distinct events observed in this composite between the temperature range of 24 °C to 116 °C, with a mass loss of approximately 8%, which is attributed to ethanol and water evaporation5656 Kim BS, Lee J. Macroporous PVDF/TiO2 membranes with three-dimensionally interconnected pore structures produced by directional melt crystallization. Chem Eng J. 2016;301:158-65.. The second event occurs between the temperature range of 197 °C to 327 °C, which is attributed to TIP decomposition and PEO degradation.

Figure 7b shows the DSC curves of the PEO matrix and PEO/TiP composite. The melting temperature of the polymer matrix (PEO) corresponds to an endothermic peak at 73 °C, while the decomposition of PEO5454 Aydogdu A, Sumnu G, Sahin S. A novel electrospun hydroxypropyl methylcellulose/polyethylene oxide blend nanofibers: morphology and physicochemical properties. Carbohydr Polym. 2018;181:234-46. produces an endothermic peak at 380 °C. The PEO/TiP composite DSC curve shows an endothermic peak between 24 °C and 116 °C. This weight loss is due to the evaporation of water and organic solvents5757 Hieu NT, Baik SJ, Chung OH, Park JS. Fabrication and characterization of electrospun carbon nanotubes/titanium dioxide nanofibers used in anodes of dye-sensitized solar cells. Synth Met. 2014;193:125-31.. The exothermic peaks at 305 °C and 498 °C are due to the phase transition from amorphous to anatase TiO25858 Yuliarto B, Septina W, Fuadi K, Fanani F, Muliani L, Nugraha. Synthesis of nanoporous TiO 2 and its potential applicability for dye-sensitized solar cell using antocyanine black rice. Adv Mater Sci Eng. 2010;2010:1-6..

3.4. Photocatalytic performance

Figure 8 shows first-order photodegradation and kinetic graphs for TiO2 fibers exposed to UV light (a-b). Table 2 presents the values of the degradation rate constant k (min-1) for each sample. As shown in Figure 8a, after 40 minutes of reaction, the degradation of the RhB dye was 100%, 83%, 83%, 60%, and 18% for fibers heat treated at 600, 700, 800, 900, and 1000 °C, respectively. The anatase phase was the only phase present in fibers heat-treated between 600 °C and 800 °C; however, it was observed that the photocatalytic activity decreased when fibers were treated at temperatures above 600 °C. The observed decrease in photocatalytic activity is attributed to a reduction in the surface area of crystallites caused by an increase in microfiber treatment temperature. Larger average crystallite sizes correspond to a smaller surface area, resulting in a diminished number of active sites available for photocatalytic reactions (Table 1)5959 Zhang J, Yan S, Fu L, Wang F, Yuan M, Luo G, et al. Photocatalytic degradation of rhodamine B on anatase, rutile, and brookite TiO2. Chin J Catal. 2011;32(6-8):983-91.

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Figure 8
(a) Photodegradation of RhB by TiO2 fibers and (b) First order kinetic model for photodegradation of RhB by TiO2 fibers.
Table 2
RhB degradation constant by TiO2 fibers.

It was found that for samples heat-treated at 900 °C and 1000 °C, the increase in rutile phase reduced the photocatalytic efficiency (Fig. 8a-b). The XRD patterns of TiO2 fibers (Table 1) show increased rutile phase formation after heat treatment at higher temperatures, confirming this observation. The anatase phase generally has more significant photocatalytic activity than the pure rutile phase6363 Luttrell T, Halpegamage S, Tao J, Kramer A, Sutter E, Batzill M. Why is anatase a better photocatalyst than rutile? Model studies on epitaxial TiO2 films. Sci Rep. 2014;4(1):4043.. It is believed that the anatase phase has improved characteristics due to a decreased rate of electron-hole recombination and a stronger adsorption affinity for organic molecules6464 Su R, Bechstein R, Sø L, Vang RT, Sillassen M, Esbjörnsson B, et al. How the anatase-to-rutile ratio influences the photoreactivity of TiO 2. J Phys Chem C. 2011;115(49):24287-92.. However, combining different phases has been found to increase the efficiency of photocatalysis. Although some samples heated to 900 °C showed the coexistence of phases, it cannot be assumed that a heterojunction occurred in the photocatalyst, which is a fundamental factor for increased photocatalysis. Therefore, evaluating the photocatalytic activity based solely on phase composition is misleading.

3.5. Antimicrobial activity of PVDF/TiO2 fibers

The process of photocatalytic inactivation of bacteria through TiO2 fibers obtained at different treatment temperatures is illustrated in Figure 9. When contaminated water comes into contact with TiO2 fibers on the surface of the membrane, ultraviolet light generates electron-hole pairs and radicals free (•OH ). The •OH radical is a potent toxin capable of killing bacteria. The formation of the O2 radical can also cause an attack, but the •OH radical is the most reactive because it can oxidize many types of organic compounds, including microbial cells. A thymine dimer forms in the bacterial DNA chromosome when the •OH radical comes into contact with the bacterial cell wall. This dimer forms knots between thymine and the DNA base, obstructing double helix formation and interrupting normal DNA replication. As a result, the cell's blocked growth eventually leads to its death. After two seconds of exposure to UV light, the TiO2 fibers positioned in the central region of the nitrocellulose membranes significantly reduced the number of bacteria, E. coli and total coliforms, as demonstrated in Figure 9. According to the experiment, the membrane containing TiO2 fibers in the anatase phase subjected to heat treatment at 600 °C proved to be the most effective in eliminating bacteria. The experiment results confirmed that the bactericidal efficiency of TiO2 fibers decreases as the heat treatment temperature increases. This decrease in efficiency is due to the increase in the rutile phase, which is less effective in eliminating bacteria. It is worth mentioning that, as shown in Figure 9, the incidence time of the ultraviolet rays used in the development of the work is insufficient to kill bacteria in places without a photocatalyst. Therefore, the presence of TiO2 fibers activated by UV radiation is responsible for the bactericidal effect.

Figure 9
Sterilization efficiency results obtained for TiO2 fibers thermally treated at different temperatures (600, 700, 800, 900 and 1000 °C) and exposed to UV radiation for 2 seconds.

4. Conclusion

In conclusion, this study demonstrates a successful method for producing PEO/Tip precursor fibers using the SBS technique without the need for pressurized gas. The best result was obtained with the sample calcined at 600 °C, which presented an anatase phase with a smaller crystallite size. With this sample, 97% of the RhB dye (aqueous solution) was eliminated after 40 minutes of exposure to UV light. According to the study involving the bactericidal activity of TiO2 fibers, the membrane containing TiO2 fibers in the anatase phase and treated at 600 °C was also considered the most effective for killing bacteria such as E. coli and coliforms. However, the bactericidal efficiency and photocatalytic efficiency of TiO2 fibers decreased as the heat treatment temperature increased due to the increase in the less effective rutile phase. The results obtained in this work indicate that TiO2 fibers produced with SBS technology have antibacterial properties, making them potential candidates for water purification applications contaminated with pathogens dangerous to human health.

5. Acknowledgments

The authors express their gratitude to São Paulo Research Foundation (FAPESP) for their financial support.

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Publication Dates

  • Publication in this collection
    02 Sept 2024
  • Date of issue
    2024

History

  • Received
    22 May 2024
  • Reviewed
    26 July 2024
  • Accepted
    01 Aug 2024
ABM, ABC, ABPol UFSCar - Dep. de Engenharia de Materiais, Rod. Washington Luiz, km 235, 13565-905 - São Carlos - SP- Brasil. Tel (55 16) 3351-9487 - São Carlos - SP - Brazil
E-mail: pessan@ufscar.br