Application of the response surface methodology for the evaluation of Staphylococcus aureus inhibition with Ag/TiO2 nanoparticles

The present work shows the implementation of the response surface methodology, fed by an experimental central composite design (CCD) to find the conditions that allow maximizing the inhibition of the microorganism Staphylococcus aureus with nanoparticles of TiO2 silanized with 3-aminopropyltriethoxysilane (APTES) and doped with Ag. In addition, poly(lactic) acid composites were prepared with these Ag/TiO2 nanoparticles with the aim to confer their antimicrobial effect. The independent variables considered were pH, AgNO3/TiO2 ratio (% w/w), and TiO2 nanoparticles concentration (g/250 mL), and as the variable of response, the length of the diameter of the halo or zone of inhibition presented by the microorganism (mm). Statistical analysis found that maximization of S. aureus inhibition occurs at intermediate levels with a value of 10 for pH and 5 g of TiO2 solids, while for the concentration of AgNO3 high levels are required, greater than 10% w/w. Likewise, the statistical significance was determined using the Student's t test and the p value; it was found that the significant effect corresponds to the concentration of AgNO3, so a second experimental CCD design equiradial with two factors was considered, estimating AgNO3 concentration and TiO2 amount, the pH at constant 10 value. The second experimental design indicated that maximization in S. aureus inhibition occurs at an AgNO3 concentration between 20 and 25% w/w with high amounts of TiO2 solids (7–8 g), with a resulting zone of inhibition between 26 and 28 mm. The quadratic model obtained, which represents the relationship between the lengths of the zone of inhibition with the variables considered, shows an adjustment of experimental data with a coefficient of determination (R2) of 0.82.


Introduction
In recent years, the overuse of synthetic polymers has generated one of the significant environmental problems; consequently, research in the development of materials using natural polymers has responded to a global need, seeking an ecological alternative to reduce environmental impact, whose properties being biodegradable and antimicrobial contribute to mitigating the amount of waste and environmental pollution [1][2][3][4]. Furthermore, with the growing consumer demand and concerns about the environment and limited natural resources, renewable resources to produce edible or biodegradable packaging materials that maintain product quality and safety while reducing waste are widely explored. Consequently, a variety of renewable polymers such as polysaccharides (starch and chitosan), proteins, lipids, and their compounds, as well as polylactic acid (PLA) and polydimethylsiloxane (PDMS) are being developed.
The biocide properties of metal nanoparticles (MNPs) have generated significant interest for their application as new antimicrobial agents [5,6]. Nanogold has presented an excellent antibacterial efficacy toward different pathogenic bacterial species (Gram-positive and Gram-negative) [7,8]. The antimicrobial activity of Ag nanoparticles was investigated against yeast, Escherichia coli, and Staphylococcus aureus, making them applicable to various medical devices and antimicrobial control systems [9,10]. Ag-Au bimetallic nanocomposite is another strategy to study the antipathogenic effect [11,12]. Carbon quantum dots (CQDs) and ZnO/CQDs Ncs have recently been investigated and considered in the family of carbon nanostructures that exhibited excellent antimicrobial potency against Bacillus cereus, E. coli, S. Aureus, S. Typhi, and Candida albicans [13][14][15].
Titanium dioxide (TiO 2 ) is a mineral that finds naturally in three crystalline phases: anatase and rutile (both tetragonal) and brookite (rhombohedral) [4]; it is not toxic and is applied in environmental treatments such as air and water purification, disinfection, and sterilization of water due to its properties and chemical stability [16,17]. It is one of the most studied semiconductors and is an innocuous material with high resistance to photo corrosion. It is stable in aqueous solutions. It is not expensive, abounds in nature, and has good photocatalytic activity under ultraviolet irradiation [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Different routes can synthesize TiO 2 ; these include flame synthesis, chemical vapor deposition, precipitation, and the alkoxide sol-gel method [12]. In recent years, interest in TiO 2 -based nanomaterials has been steadily growing because of their unique physicochemical properties. They are used for photocatalysis, solar energy engineering, air and water purification of organic pollutants, removal of heavy metal ions, detoxification of solutions, antibacterial agents, and medical devices and medicine since it is compatible with human tissues [22,[31][32][33][34]. TiO 2 has been used for the inhibition of microorganisms, especially Grampositive ones such as S. aureus. However, there are limitations with the practical use of TiO 2 , since this material is only photoactive under ultraviolet irradiation (λ < 380 nm), which restricts the use of TiO 2 as an active catalyst for the light since most of the sunlight consists of invisible light and infrared radiation, and only about 5% of UV light [25,31]. Various methods have been used to improve its absorption of visible light; these techniques include surface modification through sensitization of organic or semiconductor materials, modification of the band space creating oxygen vacancies or oxygen sub-valence through the doping with some nonmetals (like nitrogen) or metals (like silver) [20,31]. Modification of TiO 2 with transition metals (including silver, platinum, ruthenium, and palladium) has been reported to decrease the recombination process by forming structures and new interfaces that improve photocatalytic efficiency [17,18,27]. An attractive solution is creating nanosystems with an Ag-TiO 2 structure [33], not only because TiO 2 is a material with desirable properties but also because Ag shows some unique chemical and biological detection activities compared to other noble metals.
Compared to other metal ions, silver-deposited TiO 2 has a broad spectrum of antibacterial activity and is safe due to its non-toxic nature [35], and has also received special attention for its low cost of synthesis and high availability [36]. Therefore, the antibacterial activity applications of silver and TiO 2 generate great interest since they can be applied in the manufacturing of coated sanitary products, medical devices, surfaces for food preparation, air conditioning filters, among others. In addition, the deposition of Ag promotes the transformation of anatase to rutile, which is attributed to the increase in the specific surface area that causes the improvement in the photocatalytic activity and improves the separation of the electron-hole pair [30]. Furthermore, Ag nanoparticles photo catalytically deposited on individual rutile TiO 2 crystals exhibit multicolor photo-chromism and dissolution in different sizes, and Ag deposition causes multicolor spectral changes [37]. Therefore, the study of Ag-TiO 2 modified has a significant practical value [38].
Silver (Ag) is the most studied biocide agent, and numerous information is available regarding its antimicrobial activity mechanism [9,10,39], which is much higher than other metals [32]. It is active against Gram-negative bacteria (Escherichia coli and Pseudomona aeruginosa) and Gram-positive bacteria (Staphylococcus aureus and some species of the Streptococcus family) [21,26,27]. There are also reports on the antimicrobial activity of Ag nanoparticles obtained specifically against Pseudomonas aeruginosa, Microbacterium foliorum, Bacillus subtilis, and Rhodococcus equi [40]. Although there is great controversy about the mechanism of action, these could be summarized in three main points. The first would be explained by the gradual release of Ag ions that inhibit the production of adenosine triphosphate (ATP) and DNA replication, fundamental factors for cell survival. The second mechanism could be attributed to the ability of nanoparticles to generate direct damage to the cell membrane. Then, the third to the generation of reactive oxygen species that generate oxidative stress and subsequent cell death [4]. The production of Ag particles at the nanoscale results in the generation of a high surface area, which is an important property to inhibit bacterial growth [17,18] To prepare metal oxide nanocomposites suitable for antibacterial materials, it is necessary to disperse in organic binders the nanoparticles without aggregation. Nanoparticles tend to agglomerate strongly due to the surface/particle size ratio. At the same time, the use of different coupling agents is recommended for surface modification of the nanoparticles to achieve adequate dispersion of the nanoparticles. A suitable surface modification in the nanoparticles leads to better dispersion and compatibility between them, and the formation of physical and chemical interactions with the polymer matrix guarantees a lasting chemical bond between two incompatible phases. It is crucial to have a homogeneously dispersed metal oxide [41,42].
Polylactic acid (PLA) is a new type of biodegradable material, which is made from renewable plant resources (such as sugar beets, corn, and potato starch) [43,44]. It has high thermal stability, biocompatibility, low cost, and low environmental impact, making it one of the most promising polymers in the twenty-first century [45][46][47]. However, pure PLA films have some disadvantages, such as their null antimicrobial activity and poor mechanical properties. In order to improve the functional properties of PLA films, different investigations have been carried out involving the combination of NPs of TiO 2 and Ag in PLA matrices to increase the effective inhibition of bacterial reproduction and mechanical properties [17,[48][49][50][51][52][53][54][55][56][57]. In addition, researchers have worked to incorporate fillers in PLA matrices to broaden the applications of this polymer, which allows improving the antimicrobial properties [1]. The fillers that have been shown better microbicidal properties are silver, copper, zinc, titanium, and iron oxides [2,3].
There are several works about the synthesis and use of Ag/TiO 2 nanoparticles as antibacterial agents [16,17,19,21,58,59]. However, there are still some limitations related to the adequate deposition of the metal. The suitable dispersion of the nanoparticles is sought to maximize inhibition against S. aureus. Process variables are critical for successfully applying the deposition process of Ag nanoparticles on the silanized TiO 2 with APTES to improve their antibacterial properties, which will be evaluated through the response surface methodology with an experimental central composite design. Finding the optimal conditions for silver deposition based on the highest inhibition is essential to exploit the use and application of nanoparticles. Therefore, what is sought with this work is to maximize the inhibition of S. aureus, considering different variables such as pH, the precursor concentration, AgNO 3 (% w/w), and amount of TiO 2 in solution (g/250 mL). With this, resources would be saved, and the Ag/TiO 2 nanocomposites with outstanding antibacterial properties could be produced. This evaluation will be carried out by implementing a response surface methodology with a central compound type experimental design.
This research aimed to produce and characterize PLA-based high-performance biocomposites with Ag/TiO 2 particles to maximize the inhibition of the microorganism Staphylococcus aureus, using a DCC to obtain the best conditions. The effect of pH, AgNO 3 /TiO 2 ratio (% w/w), and TiO 2 nanoparticles concentration (g/250 mL) in structural and thermal properties and materials behavior against bacterial growth and biofilm development of a strain of E. Aureus was investigated. Once the best values of the variables were found, the nanoparticles obtained by this optimization were immersed in a PLA matrix to evaluate if the resulting polymer will have adequate antimicrobial capacity.

Experimental design
A three-factor central composite design (CCD) was proposed to study the process of Ag nanoparticle deposition in TiO 2 in order to determine the influence of each of these considered factors. The CCD is a fractionated factorial or factorial design with central points, enlarged with a group of axial points that allow estimating the curvature, are used to estimate the first-and second-order terms efficiently and to model a response variable with curvature by adding central and axial points to a previously executed factorial design [60]. The variables evaluated were pH (X 1 ), AgNO 3 /TiO 2 ratio (%w/w) (X 2 ), and TiO 2 nanoparticles concentration (g/250 mL) (X 3 ) having as a response variable, the inhibition zone on the disks (halos measured in mm) of each of the experimental units, in order to demonstrate that there is a significant influence 1 3 of these variables on the inhibition of Staphylococcus aureus. The matrix studied for this CCD is shown in Table 1.

Statistical analysis
MINITAB 2017 Statistical Software (version 17.1; MINITAB Inc., State College, PA, USA) was used for data analysis, prediction models, and construction of surface and contour plots. The accuracy of the polynomial equations was expressed by R 2 (coefficient of determination), and the F-test verified their statistical significance at a 95% confidence level.

Surface modification of TiO 2 nanoparticles with APTES
Incorporating the coupling agent (APTES) superficially on the TiO 2 surface is known as silanization. The best coupling route for the modification of TiO 2 NPs [41] requires 1 mL of APTES and 100 mL of ethanol for every 5 g of TiO 2 to be modified. For incorporating TiO 2 in ethanol, 30 min of stirring was needed using a stirring magnetic grid (Thermo Scientific, Cimarec) with 30 min of sonication at 60 Hz in an ultrasonic bath (Bransonic, model 5510R-MT) until completing a total time of 2.5 h. Subsequently, the APTES was added, and in a 10-min interval, 1 mL of water was added to allow hydrolysis in the reaction. This mixture was left stirring at 400 rpm for 6 more hours. The solution was placed in 50 mL falcon tubes for centrifugation and was washed twice with distilled water and five times with methanol to remove the reaction medium. Each washing was performed at 300 rpm for 10 min with approximately 30 mL of solvent. The silanized sample was dried at 80 °C for 3 h. The dry material was stored in vials for subsequent characterization and use.

Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA)
The FTIR spectra of unmodified silanized TiO 2 NPs were measured using a Fourier Transform Infrared spectrometer (FTIR-ATR Perkin Elmer, Spectrum 100 model).
The analyses included the wavenumber range of 3000-1000 cm −1 with 80 scans or sweeps per spectrum, placing the NPs in granular form for a better reading [50]. The thermogravimetric analysis was carried out on a TGA (TA Instruments Model Q500), performed in a temperature range of 25-600 °C, with a heating ramp of 10 °C per minute in a nitrogen atmosphere with a constant flow of 60 mL per minute. A sample of about 10 mg was placed in platinum baskets [41].

Electron transmission microscopy (TEM)
The size and morphology of the NPs were obtained by transmission electron microscopy (TEM) on a 200 kV microscope (JEOL model JEM 1230). The samples consisted of 0.005 g of each nanocomposite suspended in 2 mL of ethanol and sonicated for 5 min, and a drop of 10 μL was placed on a copper grid [61].

Z Potential
The samples were sonicated and mixed with a Vortex-Genie 2 Scientific Industries vortex shaker to make colloidal solutions [41]. The surface charge (Zeta potential) of the two different TiO 2 nanoparticle systems was characterized by a Delsa Nano C Particle Analyzer Z-Potential meter (A53878), using electrophoretic light scattering (ELS). This equipment has a dual source of 30 mW and a laser diode of 659 nm. The method consisted of suspending the NPs in water at a concentration of 0.01% w/v by scanning pZ at different pH (measured in a Thermo Scientific potentiometer, model Orion Star A211) modified with HCl 0.1 N and NaOH 0.1 N [62].

Nuclear magnetic resonance (NMR)
The NMR spectra ( 29 Si and 13 C) of the NPs were obtained from the Bruker Ascend equipment (400 MHz), which operates at 400 MHz for 29 Si and 100 MHz for 13 C. The parameters established for the 13 C case were a scan number of 16 and a pulse length of 8.5 μs.

Deposition process of TiO 2 with Ag by reduction of AgNO 3
The preparation of metallic silver on the TiO 2 surface was based on the AgNO 3 chemical reduction route proposed by [59]. The amount of TiO 2 (total solids), the pH, and the Ag/ TiO 2 ratio (% w/w) followed the experimental design proposed in "Experimental design" section. The aqueous suspension of TiO 2 NPs was prepared by adding the required amount of it to 250 mL of deionized water followed by sonication for 10 min, heating it to 80 °C with vigorous agitation on a magnetic grid. Once the temperature was reached, the required amount of AgNO 3 was added to the suspension to obtain the desired concentration, maintaining heating and stirring. The required pH of the suspension was adjusted with NaOH 0.5 M, the suspension at 80 °C was mixed for 2 h. The solution was placed in falcon tubes for later centrifugation, performing two washes with distilled water to remove unreacted agents. Each wash was performed at 300 rpm for 10 min with approximately 30 mL of water. The mixture obtained was dried in a convection oven (Lab-Line Instruments, model 3471) at 80 °C for 12 h.

Antibacterial test
The Inhibition test was performed by the disk diffusion method, a modification of the technique described by Bauer, Kirby, Sherris, and Turk; it is described in the following sections [63]. Medium. Mannitol Salt Agar was used. The medium was prepared according to the instructions on the package. Because the temperature of the medium was high at the end of the sterilization time, it was necessary to place it in a water bath until a temperature of approximately 48-50 °C was reached. Finally, the medium was distributed in approximately 25 cm 3 in Petri dishes, previously sterilized. Filter paper disks for nanoparticle impregnation. Filter paper disks were prepared for the different experimental units. First, they were cut out with a commercial hole punch; these disks were each 6 mm in diameter, 6-8 disks were placed in number in Eppendorf tubes of 2 mL capacity (1 tube for each system). Once this was done, the tubes were sterilized in an autoclave at 121 °C for 15 min. Once labeled, approximately 1.5 mL of the nanoparticle solution at 1000 ppm from each system were added to each tube; before this, the tubes remained in a UV light chamber for 15 min. Finally, they were stored at room temperature for 24 h to allow the nanoparticles to soak into the disks.
Inoculum. 4-5 colonies of the microorganism were selected from a pure culture. The colonies were transferred by touching the top of each with a bacteriological loop to a tube containing 3-5 cm 3 of sterile Mueller-Hinton broth. It was incubated at 35 °C for 2 to 8 h until moderate growth occurred. This growth was determined by comparing the pure broth with the one containing microorganisms; a change in turbidity was attributed to the growth of microorganisms. The culture was diluted with sterile broth at 5: 9 until obtaining a turbidity equivalent to a Turbidity standard. To prepare the standard, 0.5 mL of BaCl 2 dihydrate (1.175% w/v) was added to 99.5 mL of H 2 SO 4 0.36 N (1% w/v). It was mixed perfectly and distributed in screw cap tubes in a quantity of 6-8 mL and was hermetically sealed and stored in a dark place at room temperature. To make a comparison with the culture, the standard was vortexed.
Sample seeding. The seeding of the sample was carried out in an extraction hood, previously sterilized with UV light. A sterile cotton swab was immersed into the tube with the suspension of the microorganism in turn, in a 5: 9 dilution (this dilution does not exceed the standard turbidity equivalent to 0.5 on the McFarland scale). Once the swab was inside, it was placed above the level of the contents of the tube and rotated against the tube walls to remove excess inoculum. The inoculum was then evenly seeded on the medium surface of the Petri dish with the swab. This seeding was carried out in four directions, rotating the Petri dish 90 degrees. Thus, it was avoided that the inocula were very concentrated or diluted and that parts of the medium remained uninoculated. Once the boxes of all the systems were inoculated, it was necessary to allow the surface of the seeded medium to dry for 15 min, keeping the Petri dish closed. After a lapse of time, the Eppendorf tubes were labeled with each system (which rested for 24 hours to impregnate the nanoparticles), disks were placed on the surface of the agar with sterile forceps. The disks were slightly pressed on the agar to ensure uniform contact. Each box corresponding to each Eppendorf tube of each system was labeled. A total of 3 disks were placed on the surface of the medium, trying to leave a uniform space between each disk to observe the results of the inhibition halos better. Once the Petri dishes already contained the disks on the surface, they were wrapped with parafilm paper to avoid sudden movements of the medium. Finally, in a drying oven (Lab-Line Instruments, model 3471), all the boxes were incubated at 35 °C for 36 h to allow the microorganism to grow.

Measurement of inhibition halos
To measure the zone of inhibition of each disk, the samples were kept inside the extraction hood on the dark surface, with good lighting and lights reflected on the boxes. Next, electronic photos with 12MP resolution were taken of each of the systems. Finally, these stored photos were analyzed with ImageJ version 1.52a software to obtain the average diameter of the experimental units.

Characterization of TiO 2 particles deposited with Ag
The characterization of TiO 2 particles deposited with Ag was performed within the experimental units that presented the highest and lowest halo/zone inhibition. The samples were analyzed by transmission electron microscopy (TEM) to confirm the superficial modification and the Ag deposition, using a JEOL equipment (model JEM 1230 microscope) with a resolution of 0.4 nm and an acceleration voltage of 100 kV.

Preparation of PLA composites with Ag-deposited TiO 2 nanoparticles
PLA composites at 0.1% w/w were prepared. First, 500 mg of PLA were dissolved in 20 mL of chloroform; once a homogeneous solution was obtained, 0.5 mg of NPs were added and then stirred and sonicated for 30 min at 60 Hz in an ultrasonic bath. Finally, the suspension obtained was placed on a glass container (silica), and the solvent was evaporated at room temperature. This procedure was made for each system of nanoparticles.

Antibacterial analysis of PLA films by drop-test method
PLA composites were tested against S. aureus using the antibacterial drop-test method with some modifications [4]. First, a film of each respective composite was introduced in a different test tube, in duplicate, each containing nutrient broth inoculated with the bacteria. Moreover, a culture of the microorganism was grown without any treatment as a control. Then, the tubes were incubated for 24 h, and the solutions were read with a spectrophotometer. The optical absorptions [A] were recorded, and the inhibition rate (%) was calculated according to the following equation: where [A] i is the optical absorption of control bacteria, and [A] c is the absorption of each composite.

Characterization of the TiO 2 nanoparticles and PLA composites by X-ray diffraction (XRD)
The XRD-measurements for the TiO 2 nanoparticles and PLA composites were used to investigate the crystalline structure of the pristine and Ag-deposited TiO 2 and the influence of these nanoparticles in the crystalline structure of the PLA composites by using a Bruker Model D8 ADVANCE diffractometer with Lynx Eye detector and Copper tube (Wavelength 1.5406A). The scanning of samples (2θ) was performed at 20-80° with a 0.02° increment.

Experimental design and response surface methodology
The application of the experimental CCD design and the response surface methodology allowed the researchers to know the conditions that had a better inhibition of Staphylococcus aureus by using nanoparticles of TiO 2 modified and deposited with Ag as an antibacterial agent. The zone of inhibition, the halos present in the S. aureus plate (mm), obtained by CCD design established are shown in Table 2. The sizes of the halos are in a range of 7.32-11.26 mm.
Polymer Bulletin (2022) 79:6445-6473 The application of the RSM generated the second-order regression polynomial (Eq. 2), which represents an empirical relationship between the response (length of the inhibition halos with Staphylococcus aureus) and the evaluated variables. The statistical significance of each of the coefficients was evaluated by the Student's t test and the p value. Table 3 shows the variables and interactions that have the   highest incidence on the deposition process in Staphylococcus aureus inhibition. In Table 3, a significant variable is found when the p value is less than 0.05, which indicates that the effect is significant with 95% confidence. Therefore, the significant effect corresponds to AgNO3 (× 2) concentration, while the TiO 2 solids in solution and pH are not significant in the process, being pH the least influential. The model shows a good fit with the experimental data, having a coefficient of determination (R 2 ) of 0.86, implying that 86.00% of the variables fit the model and that it only does not explain 14% of the total variation.
The analysis of the response surface, illustrated in Fig. 1, shows the behavior of the different combinations of effects on the size of S. aureus inhibition halos, in which the largest size occurs at intermediate levels, pH of 10 and 5 g of TiO 2 solids in solution. In contrast, for AgNO 3 concentration, high levels are required (10% w/w). The most suitable working ranges were determined from the contour graph (Fig. 2); the results obtained were pH 9-11, a TiO 2 amount between 4 and 6 g, while the range of AgNO 3 concentration covers a region above 11% w/w. From the second-order model (Eq. 2), the canonical model (Eq. 3) was obtained, Based on the results obtained, a second equiradial experimental CCD design was established with two factors (Design 2), considering as independent variables: AgNO 3 concentration concerning TiO 2 (X 1 ) (25, 35, and 45% w/w) and the amount of NPs of TiO 2 in solution (X 2 ) (3, 5 and 7 g/250 mL), and now with constant pH in 10. The response variable remains the same, size of the halo or zone of inhibition of the disks (diameter of halos in mm). Table 4 shows the results obtained from Design 2 of the disk test. The ranges of the S. aureus halo of this second proposed design are between 13.16 and 22.09 mm, and compared to the first experimental design (7.32 to 11.26 mm), it presents an increase of 96.18%, which indicates that there is an enhancement of almost the double in halo size.
Statistical analysis of the results using the Student's t test and calculation of the p value provided the estimated coefficients for the quadratic model. Table 5  variables and interactions present in the deposition process in Staphylococcus aureus inhibition. As a result of Design 2, the p value shows that the TiO 2 solids in solution remain as a nonsignificant variable, while the AgNO 3 concentration is the significant variable in the deposition process due to the p value was found below 0.05. The response function (length of the inhibition halos with Staphylococcus aureus) was represented using an RSM through a second-degree polynomial equation (Eq. 4), where the two independent variables were considered. As a result, the quadratic model shows an acceptable fit of experimental data, with a coefficient of determination (R 2 ) of 0.82, which implies that 82.00% of the experimental data fit the model; therefore, 18% of the total variation was unexplainable.
(4) y = 14.9 − 0.370x 1 + 1.07x 2 + 0.01678x 2 1 + 0.343x 2 2 − 0.1253x 1 x 2 In the response surface graph (Fig. 3), it was observed that the maximization of S. aureus inhibition occurs at a low concentration of AgNO 3 (20-25% w/w) with high amounts of TiO 2 solids. (7-8 g), observing the highest levels of inhibition (26-28 mm) highlights the importance of the addition of TiO 2 solids. In the statistical analysis, the X 1 X 2 interaction was significant; this was observed in the curvature shown by the surface graph. The significance of this interaction indicates that within the experimental domain, synergistic interaction effects commonly attributed to the dispersion of TiO 2 particles were observed when they are dispersed in an aqueous medium in the Ag deposition process.
The most suitable working ranges were determined through the contour graph (Fig. 4), having a value between 21 and 24% w/w for the AgNO 3 concentration, with a TiO 2 quantity ranging from 7.5 to 7.8 g. The results obtained from the second experimental design allowed determining that an AgNO 3 concentration between 20 and 25% w/w with amounts of silanized TiO 2 between 7 and 8 g and pH of 10 achieves an inhibition zone of 28 mm in Staphylococcus aureus. This value has improved 300% regarding the zone of inhibition, reported by [64], who analyzed the antibacterial behavior of an Ag/TiO 2 /PVC composite membrane tested in the same bacterial strain. Likewise, an increase of just over 200% was found in the inhibition of the same microorganism, given that they tested Ag and TiO 2 modified polycaprolactone nanofibers (PCL/TiO 2 -Ag), showing an antibacterial impact of 9.2 mm in the diameter of the zone of inhibition [65]. In other research [36], a 40% increase in the zone of inhibition was obtained compared to unmodified Ag/TiO 2 nanoparticles since they showed a maximum zone of inhibition of 20 mm when working with a similar strain of S. aureus (methicillin-resistant). The most surprising results emerging from the data are that these Ag/TiO 2 showed excellent inhibition against S. aureus since inhibition is better than previous reports. For example, Emam et al. [7] found no antibacterial activity against this Gram-positive bacterium using AuNPs obtained sing starch polymer. While Ahmed et al. [12] obtained nanoparticles using hydroxyethyl cellulose as nanogenerator and surfactant, they reported an inhibition zone of only 16 mm using AgNPs obtained, 15 mm with AuNPs, and 18 mm with Ag-Au bimetallic nano-alloy.

Characterization of TiO 2 nanoparticles
Surface-modified TiO 2 nanoparticles were used in the Ag deposition process and subsequently used in the antibacterial test. The modification of the surface of TiO 2 was carried out with APTES; these particles underwent a series of tests to confirm the presence of silica (present in APTES) on the oxide surface. One of the characterizations performed was the FTIR, which provides information about the functional groups present in the samples to be analyzed. Figure 5 shows the results of the FTIR spectra for unmodified (black line) and modified TiO 2 (red line). It is essential to mention that new bands appeared in the particles modified with APTES; symmetric and asymmetric stretching vibration of the C-H bond was observed in the methylene group at 2960, 2927, and 2858 cm −1 [29,65,66].
The peak spanning between 1630 and 1640 cm −1 is attributed to the stretching vibration of absorbed water and the hydroxyl (OH-) groups present on the surface of the nanoparticles [29,50,65,67]. The small peak at 1641 cm −1 corresponds to Fig. 4 Contour graph of the evaluation of S. aureus, AgNO 3 concentration (% w/w) versus TiO 2 solids (g) the stretching vibration of the (NH)C=O group [65]. Other evidence of the modification with APTES on the nanoparticle surface is the peak at 1560 cm −1 that corresponds to the flexion of the amino-functional group (-NH 2 ) [65,67]. The peak shown between 1420 and 1490 cm −1 corresponds to the elastic band of the C-H organic group bond [29,32,50]. The peak observed at 1378 cm −1 was assigned to the C-N aromatic amine group [68]. The stretch band of the C-O group bonds is also observed at 1259 cm −1 [62] and the carbonyl group at 1300 cm −1 [50]. Finally, the last peaks around 1120, 1130, and 1044 cm −1 are attributed to the Si-O-Si bond, indicating polymeric siloxane as a product of the organosilane precursor [29,50,65,67]. Similarly, peaks at 1045, 1075, and 1130 cm −1 are attributed to Ti-O-C bonds [29,50,65]. The superficial modification of the TiO 2 nanoparticles with the coupling agent (APTES) is confirmed with the above described.
On the other hand, to analyze size and morphology, transmission electron microscopy is a suitable test for this purpose. The images provided by TEM gave further evidence of the superficial modification of the TiO 2 NPs with the coupling agent APTES. Figure 6a shows TiO 2 without modification. These NPs do not have a uniform surface, and it is appreciated how they tend to agglomerate. This behavior is due to the surface/particle size ratio that causes strong agglomerates that limit its suspension stability. Besides, this is attributed to Van der Waals forces, and the attracting effect tends to decrease the dispersion of the nanoparticles, while in Fig. 6b, the micrograph is observed after performing the silanization process. It is possible to observe an organic coating due to the APTES bound to the TiO 2 surface with an average of 2.82 nm thick. All this information confirms the presence of the coupling agent on the TiO 2 surface.
However, it was necessary to verify that the superficial modification of the TiO 2 led to an improvement in the dispersion and colloidal stability, which is necessary to facilitate the interaction in the aqueous medium of these nanoparticles in the deposition process with Ag. The profiles of Z potential as a function of the pH of pure TiO 2 (unmodified) and silanized TiO 2 (modified) are observed in Fig. 7. After surface modification of the NPs, the Zeta potential of the silanized TiO 2 NPs increased considerably due to the amino groups (NH 2 ) that appeared in the outer layer of the surface of the NPs.
The increase in the positive charge generated by the protonation of the amino groups caused an increase in the positive Zeta potential in the acid region [66], increasing the repulsion between the NPs. Likewise, this increase in the Z potential is favorable because it prevents instability (IEP) and agglomeration [41]. The IEP value for the unmodified oxide is approximately at pH 3.5, lower than for modified TiO 2 , at pH 5.6. This shift in IEP is attributed to the alkaline characteristics of NH 2 groups [50] or the easy desorption of hydrogen (H + ) protons found on the NPs surface of silanized TiO 2 . All the aforementioned indicates that the surface behavior of the TiO 2 NPs changed very markedly and that at the same time, the dispersion of the nanoparticles favors the deposition process with Ag since there is a higher surface ratio of TiO 2 nanoparticles dispersed that come into contact and interact with the metal favoring the process and the amount of silver deposited on the surface. Values of Z potential from − 30 to 30 mV indicate instability in the system; values below − 30 and above 30 mV indicate an increase in stability, increasing with higher absolute values of the Z potential [41].
Another essential characteristic sought when developing these types of materials is that they acquire the ability to withstand high temperatures and that there is no degradation thereof, to such a degree that the material is not lost: at the same time, it maintains its characteristics and properties. The TGA analysis corresponding to unmodified TiO 2 is shown in Fig. 8 (black line), in which it is possible to observe that it remains practically stable from 25 to 800 °C, unlike the functionalized system present losses of weight. When analyzing the thermal degradation of the coupling agent APTES on the surface of the TiO 2 (Fig. 8, blue line), it can be distinguished that the modified material has thermal stability at high temperatures, such as the temperatures used in industrial polymer processes, for example, since at approximately 98.5 °C only 0.15% by weight of the material is lost, at 563 °C a total of 0.38% is lost. Finally, until 734 °C, a total of 0.56% of material is lost in weight. This result is incredibly low since little more than 99.4% of the total is conserved; the loss in weight is related to the decomposition of the organic chains of the coating with APTES.
The characterization of the NMR spectrum for 13 C (Fig. 9) shows the existence of 3 peaks in the spectrum that correspond to signals 12.40, 27.84, and 45.76 ppm, they are identified in Fig. 9 as C 1 , C 2, and C 3 , these signals refer to the three carbons of the propyl group (a group that is present in the coupling agent APTES), these signals are approximately the same indicating that the carbons are in the same amount on the surface of the TiO 2 . As already mentioned, the signals belong to carbons. However, the difference between each one is related to the type of group to which it is bond, Carbon 1 is the one that is bond to Silicon, Carbon 2 is linked to two other carbons, and Carbon 3 would be the one that is linked to the amino group (NH 2 ). On the other hand, in Fig. 10, the NMR spectrum for 29 Si denotes signals at − 67.43 and − 59.45 ppm, identified as T 3 and T 2, respectively, attributed to the silica found on the surface of TiO 2 . T 3 is assigned to the bond between silica in the APTES and three oxygens on the TiO 2 surface. In comparison, T 2 silicon refers to silica bonds with only two oxygens on the TiO 2 surface and one remaining oxygen as hydroxyl (OH) group.
Characterization of TiO 2 particles deposited with Ag considering the highest and the lowest result of the response variable of the two-factor experimental CCD design.
The results obtained from implementing the experimental design on the microorganism inhibition allowed the researchers to know the highest and lowest size of the inhibition zone. The results of Table 4 made it possible to determine that the experimental unit 6 presented the maximum size of inhibition (22.09 mm), while sample 1 determined that the halo size (13.16 mm) was not favored under these conditions. Nevertheless, the inhibition of the microorganism exists in all the experimental units of the CDC. Therefore, the characterization was carried out using TEM/EDS to explain the behavior of these two samples. Figure 11 illustrates the TEM micrograph of experimental unit 6 of Table 4. This sample was made up of 49.14% w/w AgNO 3 concentration and 5 g of TiO 2 , that is, the points (+ 1.4142, 0) of the CCD of two-factor, founding the maximum length of  Fig. 12 shows the micrograph of experimental unit 1, which obtained the shortest length of the microorganism's inhibition halo (13.16 mm). This sample was prepared with 25% w/w AgNO 3 concentration and 3 g of TiO 2 , that is, the axial points (− 1, − 1) of the two-factor CCD. Morphologically in both experimental units, TiO 2 nanoparticle with Ag dots on the surface can be seen; the difference is distinguished in the amount of Ag that is superficially distributed on the TiO 2 nanoparticle. This difference is mainly attributed to the AgNO 3 concentration that was used in each sample.   that Ag is distributed on the surface of TiO 2 (same that is confirmed in Figs. 11 and 12), this indicates a correct dispersion of AgNO 3 during the deposition process with the oxide because an ideal chemical interaction was assumed by improving the dispersion of TiO 2 after the silanization process with APTES. The different compositions of the samples are found in Table 6.
The results of the drop-test method carried out to the composites against S. aureus are shown in Fig. 15. The values indicate inhibition activity in the PLA composites prepared with 0.1% TiO 2 nanoparticles deposited with Ag. As observed, better inhibition was obtained for the system with the highest result of the response variable of the two-factor experimental CCD design, M6, with an 18.75% of inhibition rate. Nevertheless, the lowest result, M1, also presented inhibition activity but with less efficiency, only 6.25%. Therefore, with this information, it is possible to report that  it is possible to confer the antimicrobial property from the TiO 2 deposited with Ag to the PLA composites [1]. Last, with this antibacterial test was possible to corroborate the applicability of the experimental CCD design since the best inhibition result for the composite (PLA-M6) aggress with the highest value obtained for the TiO 2 deposited nanoparticles in the disk diffusion method. Compared with the literature, although these results may look lower values than those reported previously, it is important to mention that the filler (Ag/TiO 2 ) in the PLA matrix is exceptionally low. For example, Emam [11] reported a high reduction percentage in S. aureus (96-100); nevertheless, he stated that the antibacterial efficacy was attributed to the bi-action of two nanoparticles: silver and gold; in addition, they worked with a high amount of nanoparticles (0.5 mL/20 mL). At the same time, Ahmed et al. [12] reported great inhibition rates against S. aureus of approximately 60%, but with approximately 0.3% of Au content in silk fabrics. With all this information, it is possible to state that the composites prepared at 0.1% of Ag/TiO 2 in PLA are consistent and even better than previous reports regarding the nanoparticle content.
XRD patterns were used to know the crystalline structure of the TiO 2 particles deposited with Ag. Figure 15a shows by X-ray diffraction (XRD) the results, and it can be observed the characteristic peaks for the structures of anatase and rutile in both samples; these results are due to both phases of titanium dioxide are mixed during their industrial origin [5]. Besides, it is possible to observe the characteristic peaks of the silver nanoparticles at 32.12° (101) and 38.01° (111) [5], while Fig. 15b shows the structures of the PLA nanocomposite films were analyzed to study the effect of nanoparticle content on the crystallinity of the PLA matrix. Both XRD patterns (see Fig. 16) showed an amorphous curve indicating a low degree of crystallinity of PLA and a maximum intensity at approximately 2θ = 17° attributed to the characteristic peaks of PLA [6,6]. On the other hand, the absence of TiO 2 peaks or new diffraction peaks can be seen, which can be attributed to the few numbers of

Conclusions
The superficial modification of the TiO 2 nanoparticles with APTES has a significant influence because they tend to agglomerate due to their high surface area to volume ratio. A correct superficial modification of the TiO 2 nanoparticles was achieved, which was demonstrated with the dispersion of the silanized material favoring colloidal stability; since electrostatic charges increased the repulsion between the nanoparticles present, the measurement of Z Potential gave a value that is outside the range of instability. Likewise, FTIR, TEM, TGA, and NMR measurements confirmed a correct surface modification and an approximate thickness of 2.82 nm of APTES obtained in the silanization process. Current research indicates that the conditions established from the second experimental design in the doping process of TiO 2 with Ag (Concentration of AgNO 3 , Amount of TiO 2, and constant pH) can be applied to make an antibacterial material with a high impact on the inhibition of Staphylococcus aureus. Implementing the first experimental design and the response surface methodology indicated an increase in the AgNO 3 concentration causes an enhanced microorganism inhibition. However, at the same time, the statistical significance evaluated by the Student's t test and the p value showed that the same variable was significant in the process, while pH was the least influential variable. Due to the above, a second experimental design was established, leaving the pH constant at 10. For the inhibition of S. aureus, the AgNO 3 concentration range between 20 and 25% w/w is adequate together with 7 or 8 g of TiO 2 in solution. The length of the S. aureus zone of inhibition can be well represented by the second-order model obtained from the application of the response surface methodology, with a determination coefficient R 2 of 0.82, so the length can be predicted of the inhibition zone with up to 82% precision.