# Optimization of the Antifungal Property in a Composite of Polyurethane and Silver Nanoparticles against the Trichophyton rubrum Fungus

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{3}factorial design with five replicates, which was optimized by the use of multi-objective genetic algorithms. The experimental factors showed a significant effect on the growth inhibition of the fungus, and the optimal levels were determined.

## 1. Introduction

^{3}-factorial design with five replicates, 40 experimental runs were evaluated in accordance with ASTM-G21-15-4 [18]. The fungus Trichophyton rubrum presents a filamentous shape and subtle color, making its quantification via image processing impossible. Hence, it was evaluated qualitatively using observation categories by the standard and subsequently adjusted to an ordinal logistic model. The optimization of the model was made using genetic algorithms due to the presence of logarithmic elements. This technique calculated the optimal parameters of the PUR and AgNPs composite material to obtain the highest growth inhibition of the fungus Trichophyton rubrum.

#### 1.1. Properties of AgNPs against Microorganisms and Fungi

^{−1}. Other studies combining photodynamic therapy with AgNPs [30] and AgNPs-decorated zinc oxide [31] were also demonstrated to be highly effective at inhibiting the growth of fungi from the Trichophyton family.

#### 1.2. The Shape of Nanoparticles and Their Applications on Polyurethanes

#### 1.3. References for Laboratory Testing

## 2. Materials and Methods

#### 2.1. Materials

- 5 g of the 15 nm AgNPs/ethanol dispersion for a concentration of 12.66 mg of AgNPs per 1 kg of polyol. (Small AgNPs size, low concentration)
- 5 g of the 45 nm AgNPs/ethanol dispersion for a concentration of 12.66 mg of AgNPs per 1 kg of polyol. (Large AgNPs size, low concentration)
- 15 g of the 15 nm AgNPs/ethanol dispersion for a concentration of 38 mg of AgNPs per 1 kg of polyol. (Small AgNPs size, high concentration)
- 15 g of the 45 nm AgNPs/ethanol dispersion for a concentration of 38 mg of AgNPs per 1 kg of polyol. (Large AgNPs size, high concentration)

#### 2.2. Definition of Experimental Design

^{3}with five replicates. This experimental design allows the study of the effect of three different factors with two levels each, and it consists of eight different treatments. Using this design, seven effects can be studied: the three main, double, and triple interaction. The objective of the study focuses on analyzing the effects of the following: the AgNPs size (${X}_{1}$), either low-small 15 nm- or high-large 45 nm-; the concentration of nanoparticles (${X}_{2}$), with a low concentration of 5 g of AgNPs/ethanol dispersion and a high-concentration of 10 g of AgNPs/ethanol dispersion; and applying the ultrasonic treatment on the polyol for the AgNPs dispersion (${X}_{3}$), with low −0 s- and high −10 s levels. The experimental matrix is shown in Table 1.

#### 2.3. Sample Preparation

#### 2.4. Ultrasonic Treatment Application

#### 2.5. Obtention of PUR/AgNPs Composite Materials

#### 2.6. Characterization of the PUR/AgNPs Composite Materials

#### 2.7. Culture Medium Preparation

#### 2.8. Activation and Inoculation of the Fungi on the Culture Medium

**Preparation for the mass tests:**Following the disinfection treatments for the PUR pieces and the preparation of the spore suspension, essays were carried out using nutritive salts culture medium added with 50 mg/mL of kanamycin. The PUR pieces were placed in the center of the culture medium, ensuring they did not touch any other agar surface. The 50 µL aliquots of the spore suspension were inoculated, one in the center of the PUR piece, one on the right, and one on the left. The aliquots at the sides of the piece were directly on the culture medium, equidistant, and not in direct contact with the PUR piece nor with the walls of the Petri dish. Each sample of the PUR/AgNPs composite material was conducted in triplicate, with a control for the viability of the cells. The essays were incubated at 26 °C, with a relative humidity of at least 85% for 15 days at least, registering the fungal growth daily. The fungus preparation processes and its visualization with lactophenol cotton blue are illustrated in Figure 5.

#### 2.9. Fungal Incubation

#### 2.10. Fungal Growth Evaluation

#### 2.11. Ordinal Logistic Regression Model

^{th}observation the contribution of the log-likelihood is:

**n**observations:

#### 2.12. Optimization by Genetic Algorithms

## 3. Results

#### 3.1. Analysis of the Main Effects and Interactions

_{1}Size of the AgNPs, X

_{2}Concentration of AgNPs, and X

_{3}Ultrasonic treatment on the samples, on the fungal growth based on a qualitative evaluation. The factors present a similar effect on the fungal growth, obtaining the highest inhibition on their low values. This analysis indicates a more noticeable change in the variable, indicating that the ultrasonic treatment shows a significant effect over the fungal growth inhibition.

#### 3.2. Adjusting the Ordinal Logistic Regression Model

#### 3.3. MOGAs Optimization

#### 3.4. SEM Analysis of the Samples

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Mobeen, H.; Safdar, M.; Fatima, A.; Afzal, S.; Zaman, H.; Mehdi, Z. Emerging Applications of Nanotechnology in Context to Immunology: A Comprehensive Review. Front. Bioeng. Biotechnol.
**2022**, 10, 1024871. [Google Scholar] [CrossRef] - Kim, H.-A.; Lee, B.-T.; Na, S.-Y.; Kim, K.-W.; Ranville, J.F.; Kim, S.-O.; Jo, E.; Eom, I.-C. Characterization of Silver Nanoparticle Aggregates Using Single Particle-Inductively Coupled Plasma-Mass Spectrometry (SpICP-MS). Chemosphere
**2017**, 171, 468–475. [Google Scholar] [CrossRef] [PubMed] - Joudeh, N.; Linke, D. Nanoparticle Classification, Physicochemical Properties, Characterization, and Applications: A Comprehensive Review for Biologists. J. Nanobiotechnology
**2022**, 20, 262. [Google Scholar] [CrossRef] [PubMed] - Sahoo, S.; Hormozi-Nezhad, M.R. Gold and Silver Nanoparticles: Synthesis and Applications; Elsevier: Amsterdam, The Netherlands, 2023; ISBN 9780323994545. [Google Scholar]
- Zhang, X.-F.; Liu, Z.-G.; Shen, W.; Gurunathan, S. Silver Nanoparticles: Synthesis, Characterization, Properties, Applications, and Therapeutic Approaches. Int. J. Mol. Sci.
**2016**, 17, 1534. [Google Scholar] [CrossRef] [PubMed] - Dhaka, A.; Chand Mali, S.; Sharma, S.; Trivedi, R. A Review on Biological Synthesis of Silver Nanoparticles and Their Potential Applications. Results Chem.
**2023**, 6, 101108. [Google Scholar] [CrossRef] - Chanyachailert, P.; Leeyaphan, C.; Bunyaratavej, S. Cutaneous Fungal Infections Caused by Dermatophytes and Non-Dermatophytes: An Updated Comprehensive Review of Epidemiology, Clinical Presentations, and Diagnostic Testing. J. Fungi
**2023**, 9, 669. [Google Scholar] [CrossRef] [PubMed] - Ahirwar, D.; Telang, A.; Purohit, R.; Namdev, A. A Short Review on Polyurethane Polymer Composite. Mater. Today Proc.
**2022**, 62, 3804–3810. [Google Scholar] [CrossRef] - Witkiewicz, W.; Zieliński, A. Properties of the Polyurethane (PU) Light Foams. Adv. Mater. Sci.
**2006**, 6, 35–51. [Google Scholar] - Eugenia, M.M.; Adolfo, T.L.; Rodolfo, E. Characterization of Polyurethane Nanocomposites for Flame Retardant Applications. J. Chem. Chem. Eng.
**2018**, 12, 60–73. [Google Scholar] [CrossRef] - Cui, M.; Chai, Z.; Lu, Y.; Zhu, J.; Chen, J. Developments of Polyurethane in Biomedical Applications: A Review. Resour. Chem. Mater.
**2023**, 2, 262–276. [Google Scholar] [CrossRef] - Wendels, S.; Avérous, L. Biobased Polyurethanes for Biomedical Applications. Bioact. Mater.
**2021**, 6, 1083–1106. [Google Scholar] [CrossRef] [PubMed] - Grzęda, D.; Węgrzyk, G.; Nowak, A.; Idaszek, J.; Szczepkowski, L.; Ryszkowska, J. Cytotoxic Properties of Polyurethane Foams for Biomedical Applications as a Function of Isocyanate Index. Polymers
**2023**, 15, 2754. [Google Scholar] [CrossRef] [PubMed] - Okrasa, M.; Leszczyńska, M.; Sałasińska, K.; Szczepkowski, L.; Kozikowski, P.; Majchrzycka, K.; Ryszkowska, J. Viscoelastic Polyurethane Foams for Use in Seals of Respiratory Protective Devices. Materials
**2021**, 14, 1600. [Google Scholar] [CrossRef] [PubMed] - Sana, S.S.; Haldhar, R.; Parameswaranpillai, J.; Chavali, M.; Kim, S.-C. Silver Nanoparticles-Based Composite for Dye Removal: A Comprehensive Review. Clean. Mater.
**2022**, 6, 100161. [Google Scholar] [CrossRef] - Morena, A.G.; Stefanov, I.; Ivanova, K.; Pérez-Rafael, S.; Sánchez-Soto, M.; Tzanov, T. Antibacterial Polyurethane Foams with Incorporated Lignin-Capped Silver Nanoparticles for Chronic Wound Treatment. Ind. Eng. Chem. Res.
**2020**, 59, 4504–4514. [Google Scholar] [CrossRef] - Xu, C.; Akakuru, O.U.; Ma, X.; Zheng, J.; Zheng, J.; Wu, A. Nanoparticle-Based Wound Dressing: Recent Progress in the Detection and Therapy of Bacterial Infections. Bioconjug. Chem.
**2020**, 31, 1708–1723. [Google Scholar] [CrossRef] - ASTM D ASTM-G21-15-4; Standard Practice for Determining Resistance of Synthetic Polymeric Materials to Fungi. ASTM International: Conshohocken, PA, USA, 2015. Available online: https://www.astm.org/g0021-15r21e01.html (accessed on 5 August 2023).
- Linima, V.K.; Ragunathan, R.; Johney, J. Biogenic Synthesis of RICINUS COMMUNIS Mediated Iron and Silver Nanoparticles and Its Antibacterial and Antifungal Activity. Heliyon
**2023**, 9, e15743. [Google Scholar] [CrossRef] - Gil-Korilis, A.; Cojocaru, M.; Berzosa, M.; Gamazo, C.; Andrade, N.J.; Ciuffi, K.J. Comparison of Antibacterial Activity and Cytotoxicity of Silver Nanoparticles and Silver-Loaded Montmorillonite and Saponite. Appl. Clay Sci.
**2023**, 240, 106968. [Google Scholar] [CrossRef] - Zhao, G.; Stevens, J.S.E. Multiple Parameters for the Comprehensive Evaluation of the Susceptibility of Escherichia Coli to the Silver Ion. Biometals
**1998**, 11, 27–32. [Google Scholar] [CrossRef] - Slawson, R.M.; Trevors, J.T.; Lee, H. Silver Accumulation and Resistance in Pseudomonas Stutzeri. Arch. Microbiol.
**1992**, 158, 398–404. [Google Scholar] [CrossRef] - Vigneshwaran, N.; Ashtaputre, N.M.; Varadarajan, P.V.; Nachane, R.P.; Paralikar, K.M.; Balasubramanya, R.H. Biological Synthesis of Silver Nanoparticles Using the Fungus Aspergillus Flavus. Mater. Lett.
**2007**, 61, 1413–1418. [Google Scholar] [CrossRef] - Skanda, S.; Bharadwaj, P.S.J.; Datta Darshan, V.M.; Sivaramakrishnan, V.; Vijayakumar, B.S. Proficient Mycogenic Synthesis of Silver Nanoparticles by Soil Derived Fungus Aspergillus Melleus SSS-10 with Cytotoxic and Antibacterial Potency. J. Microbiol. Methods
**2022**, 199, 106517. [Google Scholar] [CrossRef] - Gajbhiye, M.; Kesharwani, J.; Ingle, A.; Gade, A.; Rai, M. Fungus-Mediated Synthesis of Silver Nanoparticles and Their Activity against Pathogenic Fungi in Combination with Fluconazole. Nanomedicine
**2009**, 5, 382–386. [Google Scholar] [CrossRef] - Mansoor, S.; Zahoor, I.; Baba, T.R.; Padder, S.A.; Bhat, Z.A.; Koul, A.M.; Jiang, L. Fabrication of Silver Nanoparticles against Fungal Pathogens. Front. Nanotechnol.
**2021**, 3, 679358. [Google Scholar] [CrossRef] - Robles-Martínez, M.; González, J.F.C.; Pérez-Vázquez, F.J.; Montejano-Carrizales, J.M.; Pérez, E.; Patiño-Herrera, R. Antimycotic Activity Potentiation of Allium Sativum Extract and Silver Nanoparticles against Trichophyton Rubrum. Chem. Biodivers.
**2019**, 16, e1800525. [Google Scholar] [CrossRef] [PubMed] - Mohsen, L.Y.; Fadhil Alsaffar, M.; Ahmed Lilo, R.; Khalil Al-Shamari, A. Silver Nanoparticles That Synthesis by Using Trichophyton Rubrum and Evaluate Antifungal Activity. Arch. Razi Inst.
**2022**, 77, 2145–2149. [Google Scholar] - da Silva, C.A.; Ribeiro, B.M.; Trotta, C.D.V.; Perina, F.C.; Martins, R.; Abessa, D.M.d.S.; Barbieri, E.; Simões, M.F.; Ottoni, C.A. Effects of Mycogenic Silver Nanoparticles on Organisms of Different Trophic Levels. Chemosphere
**2022**, 308, 136540. [Google Scholar] [CrossRef] - Wijesiri, N.; Yu, Z.; Tang, H.; Zhang, P. Antifungal Photodynamic Inactivation against Dermatophyte Trichophyton Rubrum Using Nanoparticle-Based Hybrid Photosensitizers. Photodiagnosis Photodyn. Ther.
**2018**, 23, 202–208. [Google Scholar] [CrossRef] - Patiño-Herrera, R.; Catarino-Centeno, R.; Robles-Martínez, M.; Zarate, M.G.M.; Flores-Arriaga, J.C.; Pérez, E. Antimycotic Activity of Zinc Oxide Decorated with Silver Nanoparticles against Trichophyton Mentagrophytes. Powder Technol.
**2018**, 327, 381–391. [Google Scholar] [CrossRef] - Helmlinger, J.; Sengstock, C.; Groß-Heitfeld, C.; Mayer, C.; Schildhauer, T.A.; Köller, M.; Epple, M. Silver Nanoparticles with Different Size and Shape: Equal Cytotoxicity, but Different Antibacterial Effects. RSC Adv.
**2016**, 6, 18490–18501. [Google Scholar] [CrossRef] - Sadeghi, B.; Garmaroudi, F.S.; Hashemi, M.; Nezhad, H.R.; Nasrollahi, A.; Ardalan, S.; Ardalan, S. Comparison of the Anti-Bacterial Activity on the Nanosilver Shapes: Nanoparticles, Nanorods and Nanoplates. Adv. Powder Technol.
**2012**, 23, 22–26. [Google Scholar] [CrossRef] - Pal, S.; Tak, Y.K.; Song, J.M. Does the Antibacterial Activity of Silver Nanoparticles Depend on the Shape of the Nanoparticle? A Study of the Gram-Negative Bacterium Escherichia coli. Appl. Environ. Microbiol.
**2007**, 73, 1712–1720. [Google Scholar] [CrossRef] [PubMed] - Kim, T.-H.; Kim, M.; Park, H.-S.; Shin, U.S.; Gong, M.-S.; Kim, H.-W. Size-Dependent Cellular Toxicity of Silver Nanoparticles. J. Biomed. Mater. Res. A
**2012**, 100A, 1033–1043. [Google Scholar] [CrossRef] - Díaz-Puertas, R.; Rodríguez-Cañas, E.; Bello-Perez, M.; Fernández-Oliver, M.; Mallavia, R.; Falco, A. Viricidal Activity of Thermoplastic Polyurethane Materials with Silver Nanoparticles. Nanomaterials
**2023**, 13, 1467. [Google Scholar] [CrossRef] [PubMed] - Bechtold, M.; Valério, A.; de Souza, A.A.U.; de Oliveira, D.; Franco, C.V.; Serafim, R.; Souza, S.M.A.G.U. Synthesis and Application of Silver Nanoparticles as Biocidal Agent in Polyurethane Coating. J. Coatings Technol. Res.
**2020**, 17, 613–620. [Google Scholar] [CrossRef] - Savelyev, Y.; Gonchar, A.; Movchan, B.; Gornostay, A.; Vozianov, S.; Rudenko, A.; Rozhnova, R.; Travinskaya, T. Antibacterial Polyurethane Materials with Silver and Copper Nanoparticles. Mater. Today Proc.
**2017**, 4, 87–94. [Google Scholar] [CrossRef] - El-Rahman, N.R.A.; Bekhit, M.; Fekry, M. Fabrication and Evaluation of Polyurethane Cationic Surfactants, and Their Potential on Silver Nanoparticles Stability, Surface Activity, and Biological Activity. Egypt. J. Pet.
**2022**, 31, 23–31. [Google Scholar] [CrossRef] - Wijnhoven, S.W.P.; Peijnenburg, W.J.G.M.; Herberts, C.A.; Hagens, W.I.; Oomen, A.G.; Heugens, E.H.W.; Roszek, B.; Bisschops, J.; Gosens, I.; Van De Meent, D.; et al. Nano-Silver—A Review of Available Data and Knowledge Gaps in Human and Environmental Risk Assessment. Nanotoxicology
**2009**, 3, 109–138. [Google Scholar] [CrossRef] - Monje, A.E.; Reséndiz, J.R.H. Synthesis of Urethane Base Composite Materials with Metallic Nanoparticles. MRS Proc.
**2013**, 1547, 141–147. [Google Scholar] [CrossRef] - McCullagh, P.; Nelder, J.A. Generalized Linear Models; Chapman and Hall: London, UK, 1983; pp. 1–19. [Google Scholar]
- Dobson Annette, J. Normal Linear Models. In An Intruction to Generalized Linear models; Chatfield, C., Zidek, J., Eds.; Chapman and Hall: Vancouver, BC, Canada, 2001; pp. 179–196. [Google Scholar]
- Bae, E.; Lee, B.-C.; Kim, Y.; Choi, K.; Yi, J. Effect of Agglomeration of Silver Nanoparticle on Nanotoxicity Depression. Korean J. Chem. Eng.
**2013**, 30, 364–368. [Google Scholar] [CrossRef]

**Figure 2.**Sample preparation: (

**a**) pre-heating polyol and isocyanate on a laboratory heating plate, (

**b**) polyol weighing, (

**c**) isocyanate weighing, and (

**d**) catalyst weighing in a syringe.

**Figure 3.**Homogenization process of the samples using ultrasound. Note: Hielscher is the brand of ultrasound equipment.

**Figure 5.**(

**a**) Preparation of the culture medium and fungal activation, (

**b**) inoculation of the fungus on the culture medium, and (

**c**,

**d**) visualization of the fungus T. rubrum using lactophenol cotton blue dye.

**Figure 6.**Examples of the observed fungal growth are (

**a**) traces of growth below 10% (1), (

**b**) light growth from 10 to 30% (2), (

**c**) medium growth from 30 to 60% (3), and (

**d**) heavy growth from 60% to complete coverage (4).

**Figure 7.**Graph showing the main effects on the average fungal growth on variables X

_{1}size of the AgNPs, X

_{2}concentration of AgNPs, and X

_{3}ultrasonic treatment on polyol. The blue dots represent the average effects of each of the control factors on the average fungal growth of the fungus when changing from low and high levels, respectively.

**Figure 8.**Graph of the interactions for the average fungal growth among the variables X

_{1}size of the AgNPs, X

_{2}concentration of AgNPs, and X

_{3}ultrasonic treatment on polyol.

**Figure 9.**Pareto Front for the set of solutions between objective 1 and objective 2 for the multi-objective optimization problem. The blue points represent the feasible solutions for the optimization problem and are intersections between the vectors (the blue lines) generated in the process according to the optimization problem.

**Figure 10.**SEM micrographs of the samples with 15 nm AgNPs, (

**a**) without ultrasound, (

**b**) with ultrasound, and samples with 45 nm AgNPs, (

**c**) without ultrasound, and (

**d**) with ultrasound.

Treatment | ${\mathbf{X}}_{1}$ | ${\mathbf{X}}_{2}$ | ${\mathbf{X}}_{3}$ | ${\mathbf{Y}}_{1}$ | ${\mathbf{Y}}_{2}$ | ${\mathbf{Y}}_{3}$ | ${\mathbf{Y}}_{4}$ | ${\mathbf{Y}}_{5}$ |
---|---|---|---|---|---|---|---|---|

1 | 15 nm | 5 g | 0 s | ${Y}_{11}$ | ${Y}_{12}$ | ${Y}_{13}$ | ${Y}_{14}$ | ${Y}_{15}$ |

2 | 45 nm | 5 g | 0 s | ${Y}_{21}$ | ${Y}_{22}$ | ${Y}_{23}$ | ${Y}_{24}$ | ${Y}_{25}$ |

3 | 15 nm | 10 g | 0 s | ${Y}_{31}$ | ${Y}_{32}$ | ${Y}_{33}$ | ${Y}_{34}$ | ${Y}_{35}$ |

4 | 45 nm | 10 g | 0 s | ${Y}_{41}$ | ${Y}_{42}$ | ${Y}_{43}$ | ${Y}_{44}$ | ${Y}_{45}$ |

5 | 15 nm | 5 g | 10 s | ${Y}_{51}$ | ${Y}_{52}$ | ${Y}_{53}$ | ${Y}_{54}$ | ${Y}_{55}$ |

6 | 45 nm | 5 g | 10 s | ${Y}_{61}$ | ${Y}_{62}$ | ${Y}_{63}$ | ${Y}_{64}$ | ${Y}_{65}$ |

7 | 15 nm | 10 g | 10 s | ${Y}_{71}$ | ${Y}_{72}$ | ${Y}_{73}$ | ${Y}_{74}$ | ${Y}_{75}$ |

8 | 45 nm | 10 g | 10 s | ${Y}_{81}$ | ${Y}_{82}$ | ${Y}_{83}$ | ${Y}_{84}$ | ${Y}_{85}$ |

**Table 2.**Rating according to the observed growth of the fungus on specimens. Adapted with oermission from [18] Copyrighted by ASTM International, 2013.

Observed Growth on Specimens | Rating |
---|---|

None | 0 |

Traces of growth (less than 10%) | 1 |

Light growth (10 to 30%) | 2 |

Medium growth (30 to 60%) | 3 |

Heavy growth (60% to complete coverage) | 4 |

Treatment | ${\mathbf{X}}_{1}$ | ${\mathbf{X}}_{2}$ | ${\mathbf{X}}_{3}$ | ${\mathbf{Y}}_{1}$ | ${\mathbf{Y}}_{2}$ | ${\mathbf{Y}}_{3}$ | ${\mathbf{Y}}_{4}$ | ${\mathbf{Y}}_{5}$ |
---|---|---|---|---|---|---|---|---|

1 | 15 nm | 5 g | 0 s | 2 | 1 | 1 | 1 | 2 |

2 | 45 nm | 5 g | 0 s | 2 | 2 | 2 | 3 | 1 |

3 | 15 nm | 10 g | 0 s | 4 | 2 | 2 | 2 | 1 |

4 | 45 nm | 10 g | 0 s | 1 | 1 | 1 | 2 | 2 |

5 | 15 nm | 5 g | 10 s | 2 | 2 | 1 | 3 | 2 |

6 | 45 nm | 5 g | 10 s | 4 | 2 | 1 | 1 | 3 |

7 | 15 nm | 10 g | 10 s | 1 | 1 | 3 | 2 | 3 |

8 | 45 nm | 10 g | 10 s | 3 | 2 | 3 | 2 | 2 |

Parameter | Value |
---|---|

Number of variables | 3 |

Population size | 50 |

Limits | [−1, −1, −1]; [1, 1, 1] |

Selection function | Uniform stochastic |

Initial value | [−10, 10] |

Elite counting | 0.05 × initial population |

Crossover fraction | 0.8 |

Mutation function | Dependent on restrictions |

Migration direction | Forward |

Generations | 100 × Number of variables |

Stagnant generations | 50 |

Tolerance of the function | 1 × 10^{−6} |

Predictor | Coef | SE Coef | Z | p |
---|---|---|---|---|

α1 | −0.844483 | 0.368023 | −2.29 | 0.022 |

α2 | 1.41937 | 0.403828 | 3.51 | 0.000 |

α3 | 3.20650 | 0.748000 | 4.29 | 0.000 |

X_{1} | −0.115466 | 0.304130 | −0.38 | 0.704 |

X_{2} | −0.103887 | 0.304001 | −0.34 | 0.733 |

X_{3} | −0.503327 | 0.310272 | −1.62 | 0.105 |

X_{1} ×X_{2} | 0.328445 | 0.305680 | 1.07 | 0.283 |

X_{1} × X_{3} | −0.159936 | 0.304776 | −0.52 | 0.600 |

X_{2} × X_{3} | −0.0594171 | 0.303632 | −0.20 | 0.845 |

X_{1} × X_{2} × X_{3} | −0.517629 | 0.310828 | −1.67 | 0.096 |

Pareto Front Solution | ${\mathbf{X}}_{1}$ | ${\mathbf{X}}_{2}$ | ${\mathbf{X}}_{3}$ | $\mathbf{F}\left({\mathbf{Y}}_{1}\left(\mathbf{X}\right)\right)$ | $\mathbf{F}\left({\mathbf{Y}}_{2}\left(\mathbf{X}\right)\right)$ | $\mathbf{F}({\mathbf{Y}}_{3}\left(\mathbf{X}\right))$ |
---|---|---|---|---|---|---|

28 | 0.98357 | 0.98818 | −0.66040 | 0.03183 | 0.20663 | 0.06601 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mares Castro, A.; Estrada Monje, A.; Saldívar Campos, A.I.; Zaragoza Estrada, A.
Optimization of the Antifungal Property in a Composite of Polyurethane and Silver Nanoparticles against the *Trichophyton rubrum* Fungus. *Appl. Sci.* **2023**, *13*, 12028.
https://doi.org/10.3390/app132112028

**AMA Style**

Mares Castro A, Estrada Monje A, Saldívar Campos AI, Zaragoza Estrada A.
Optimization of the Antifungal Property in a Composite of Polyurethane and Silver Nanoparticles against the *Trichophyton rubrum* Fungus. *Applied Sciences*. 2023; 13(21):12028.
https://doi.org/10.3390/app132112028

**Chicago/Turabian Style**

Mares Castro, Armando, Anayansi Estrada Monje, Alejandra Imelda Saldívar Campos, and Anayansi Zaragoza Estrada.
2023. "Optimization of the Antifungal Property in a Composite of Polyurethane and Silver Nanoparticles against the *Trichophyton rubrum* Fungus" *Applied Sciences* 13, no. 21: 12028.
https://doi.org/10.3390/app132112028