Submitted:
25 January 2026
Posted:
27 January 2026
Read the latest preprint version here
Abstract

Keywords:
1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Dyeing Procedures
2.2.1. Conventional Dyeing Methodology
2.2.2. Microwave-Assisted Dyeing Methodology
2.3. Analytical Procedures
2.3.2. Colorimetric Measurement
3. Results and Discussions
3.1. Conventional Dyeing
3.1.1. Effect of PH
3.1.2. Effect of Time andTemperature
3.1.3. Effect of Dye Concentration According to Different Temperatures
- At lower concentrations (0.1%), K/S values remain relatively low even at high temperatures, indicating limited availability of dye molecules.
- At higher concentrations (0.75% and 1,5%), K/S increases sharply up to 80–90 °C, after which the rate of increase diminishes. This behavior suggests site saturation within the fiber, where additional dye molecules contribute less effectively to color strength.
3.2. Microwave Dyeing
3.2.1. Effect of PH
- Accelerated Diffusion: Microwave heating provides rapid, volumetric heating, which can significantly increase the molecular mobility of the dye and the segmental motion of the polymer chains. This effectively lowers the energy barrier for the internal diffusion of the dye into the fiber matrix, accelerating the overall dyeing rate and allowing for a higher equilibrium dye uptake in a shorter time [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45].
- Synergistic Effect: The microwave energy acts synergistically with the optimal chemical conditions (pH: 3- 6). While the acidic condition provides the necessary thermodynamic driving force (electrostatic attraction), the microwave energy provides acceleration (enhanced diffusion), resulting in the superior color strength observed[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45].
3.2.2. Effect of Time and Temperature
3.2.3. Effect of Dye Concentration According to Different Times
- Faster dye diffusion
- Improved fiber swelling
- Increased accessibility of internal binding sites
3.3. Fastness Properties
| Dyeing Method |
Washing Fastness [ISO105C06 B1S] |
Acidic Persp. [ISO 105 E04] |
Alkaline Persp. [ISO 105 E04] |
Water Fastness [ISO 105 E01] |
Dry/Wet Rubbing Fastness [ISO105X12] |
|---|---|---|---|---|---|
| Conventional | 3/4 | 4 | 3/4 | 4 | 4/5 - 4 |
| Microwave | 3/4 | 4 | 3/4 | 4 | 4/5 - 4 |
3.4. Role of Microwave Irradiation
- Rapid and uniform heating of the dye bath and substrate
- Dipole rotation and ionic conduction effects
- Reduced thermal gradients within the fiber matrix
- Fast color development
- High color strength at short processing times
- Efficient utilization of higher dye concentrations
4. Conclusions
Acknowledgments
References
- Böcek, Nevin (2001), Investigation of Fiber and Temperature Interaction in Dyeing of Synthetic Fibers, [Master’s thesis, Sakarya University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/.
- Haggag, K.; El-Molla, M.M.; Ahmed, K.A. Dyeing of Nylon 66 Fabrics Using Disperse Dyes by Microwave Irradiation Technology. International Research Journal of Pure & Applied Chemistry 2015, 8(2), 103–111. [Google Scholar] [CrossRef]
- Atav, R.; Soysal, S.; Haji, Aminoddin. Environmentally Friendly Coloration of Polyamide Fabrics with the Use of Natural Dyes: A Study Including Results of Industrial Scale Applications. Fibers and Polymers 2024, 25, 2223–2232. [Google Scholar] [CrossRef]
- Ghaheh, F.S.; Razbin, M.; Tehrani, M.; Vayghan, L.Z.A.; Sadrjahani, M. Modeling and optimization of dyeing process of polyamide 6 and woolen fabrics with plum-tree leaves using artificial intelligence. Scientific Reports 2024, 14, 15067. [Google Scholar] [CrossRef] [PubMed]
- Lara, L.; Cabral, I.; Cunha, J. Ecological Approaches to Textile Dyeing: A Review. Sustainability 2022, 14, 8353. [Google Scholar] [CrossRef]
- Atav, R.; Soysal, S.; Hajı, A. Environmentally friendly coloration of polyamide fabrics with the use of natural dyes: A study including results of industrial scale applications. Fibers and Polymers 2024, 25, 2223–2232. [Google Scholar] [CrossRef]
- Ghazal, H.A. Microwave irradiation as a new novel dyeing of polyamide 6 fabrics by reactive dyes. Egypt. J. Chem. 2020, 63(no.6), 2125–2132. [Google Scholar] [CrossRef]
- Nikodijevic, M.; Vuckovic, N.; Dordevic, D. Possibilities of Dyeing of Polyamide Fabric with Substantive Dye. The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM) 2020, Volume 11, 131–135. [Google Scholar]
- Eren, S.; Özyurt, İ. Waterless Dyeing of Polyamide 6.6. Polymers 2024, 16, 1472. [Google Scholar] [CrossRef]
- Irfan, M.; Gao, A. Nylon dyeing with reactive dyes by intermittent exposure to microwave irradiations to improve leveling. Pigment&Resin Technology 2025, 54/5, 674–681. [Google Scholar] [CrossRef]
- Shahmoradi Ghaheh, F.; Razbin, M.; Tehrani, M.; Zolfipour Aghdam Vayghan, L.; Sadrjahani, M. Modeling and optimization of dyeing process of polyamide 6 and woolen fabrics with plum-tree leaves using artificial intelligence. Sci. Rep. 2024, 14, 15067. [Google Scholar] [CrossRef]
- Özcan, Y. Textile Fiber and Dyeing Technique; 1978. [Google Scholar]
- Trotman, E.R. Dyeing and Chemical Technology of Textile Fibres; 1970. [Google Scholar]
- Reda, E.M.; Othman, H.A.; Ghazal, H.; Hassabo, A.G. Kinetic and isothermal study of dye absorption using pre-treated natural fabrics using polyamine compounds. Sci. Rep. 2025, 15, 3794. [Google Scholar] [CrossRef] [PubMed]
- Adeel, S.; Razzaq, A.; Kiran, S.; Ahmad, T.; Hassan, A.; Rehman, H. A Comparative Study on Sustainable Dyeing of Silk and Wool with Acid Red 138 Dye. J. Nat. Fibers 2022, 19, 8181–8190. [Google Scholar] [CrossRef]
- Zhang, R.; Liu, J.; Wang, J.; Wang, J.; Meng, J. A novel process of dyeing wool with acid dyes under microwave irradiation. Journal of Applied Polymer Science 2009, 113(5), 2798–2803. [Google Scholar] [CrossRef]
- Dülek, Y.; Yıldıran, İ.; Sevinç, B.; Mert, E.; Yılmaz, B.; Kut, D. A Comparative Study on Microwave Assisted Dyeing Properties of Conventional and Recycled Polyester Fabrics. Eurasia Proc. Sci. Technol. Eng. Math. 2023, 23, 300–306. [Google Scholar] [CrossRef]
- Khalil, E.; Sarkar, J.; Rahman, M.M.; Shamsuzzaman, M.; Das, D. Advanced Technology in Textile Dyeing. In Advanced Technology in Textiles: Fibre to Apparel; Rahman, M.M., Mashud, M., Rahman, M.M., Eds.; Springer: Singapore, 2023; pp. 97–138. [Google Scholar] [CrossRef]
- Amesimeku, J.; Fan, L.; Jakpa, W.; Wang, C. Dyeing properties of meta-aramid fabric dyed with basic dye using ultrasonic–microwave irradiation. Journal of Cleaner Production 2021, 278, 123987. [Google Scholar] [CrossRef]
- Fiandra, E.F.; Starck, M.; Findlay, E.K.; Binks, J.; Si, G.; Chilton, R.; Sivik, M.R.; Thompson, R.L.; Wilson, M.R.; Mahon, C.S. Polyesters incorporating biobased monomers for soil-release treatment of synthetic textile surfaces. Green Chem. 2025, 27, 14290–14300. [Google Scholar] [CrossRef]
- Xue, Q.; Zhu, J.; Meng, W.; Zhang, K. Effect of MXene Nanosheet Dispersed Phases on the Fabrication of Polyamide Nanofiltration Membranes. ACS Appl. Eng. Mater. 2023, 1, 679–689. [Google Scholar] [CrossRef]
- Alegbe, E.O.; Uthman, T.O. A review of history, properties, classification, applications and challenges of natural and synthetic dyes. Heliyon 2024, 10, e33646. [Google Scholar] [CrossRef] [PubMed]
- Usluoğlu, A.; Teker, M. Investigation of Dyeing Kinetics of Cotton Fiber with C.I. Reactive Yellow 138:1 Dyestuff in Microwave Environment. Journal of the Institute of Science of Yüzüncü Yıl University 2024, 29, 119. [Google Scholar] [CrossRef]
- Yiğit, E.A.; Teker, M. Disperse Dyeability of Polypropylene Fibers via Microwave and Ultrasonic Energy - Polymer and Polymer Composites. 2011, 19, 711. [Google Scholar] [CrossRef]
- Haggag, K.; El-Molla, M.M.; Mahmoued, Z.M. Dyeing of Cotton Fabric using Reactive Dyes by Microwave Irradiation Technique. Indian Journal of Fibre & Textile Research 2014, 9, 406–410. [Google Scholar] [CrossRef]
- Rahman, M.M.; Ahmed, M.; Jalil, M.A.; Mondal, M.I.H. The effect of microwave preheating on the dyeing of wool fabric with a reactive dye. Journal of Applied Polymer Science 2008, 108(1), 314–318. [Google Scholar] [CrossRef]
- Kim, S.S.; Leem, S.G.; Ghim, H.D.; Kim, J.H.; Lyoo, W.S. Microwave heat dyeing of polyester fabric. Fibers and Polymers 2003, 4(4), 204–209. [Google Scholar] [CrossRef]
- Kocak, D.; Akalin, M.; Merdan, N.; Yilmaz Sahinbaskan, B. Effect of Microwave Energy on Disperse Dyeability of Polypropylene Fibres. Marmara Journal of Pure and Applied Sciences 2015, Special Issue-1, 27–31. [Google Scholar]
- Haggag, K.; Hanna, H.L.; Youssef, B.M.; El-Shimy, N.S. Dyeing polyester with microwave heating using disperse dyestuffs. Journal of the Society of Dyers and Colourists 1995, 111(5), 170–173. [Google Scholar] [CrossRef]
- Büyükakıncı, Y.B.; Karada, R.; Guzel, E.T. Organic cotton fabric dyed with dyer’s oak and barberry dye by microwave irradiation and conventional methods. Industria Textila 2021, Vol No, 72, 30–38. [Google Scholar] [CrossRef]
- Gouda, M.; Haggag, K.M.; Boraie, W.E.; Aljaafari, A.; Al-Faiyz, Y. Synthesis and Characterization of Inorganic Pigment Nanoparticles for Textile Coloration Using Microwave Techniques. AATCC Journal of ResearchVolume 2016, Volume 3(Issue 3), 1–8. [Google Scholar] [CrossRef]
- Kale, M.J.; Bhat, N.V. Effect of microwave pretreatment on the dyeing behaviour of polyester fabric, Society of Dyers and Colourists. Color. Technol. 127, 365–371. [CrossRef]
- Popescu, V.; Astanei, D.G.; Burlica, R.; Popescu, A.; Munteanu, C.; Ciolacu, F.; Ursache, M.; Ciobanu, L.; Cocean, A. Sustainable and cleaner microwave-assisted dyeing process for obtaining eco-friendly and fluorescent acrylic knitted fabrics. Journal of Cleaner Production 2019, 232, 451–461. [Google Scholar] [CrossRef]
- Keglevich, G. The Application of Microwaves in the Esterification of P-Acids. Current Microwave Chemistry 2022, 9, 62–64. [Google Scholar] [CrossRef]
- Ghaffar, A.; Adeel, S.; Habib, N.; Jalal, F.; Ul-Haq, A.; Munir, B.; Ahmad, A.; Jahangeer, M.; Jamil, Q. Effects of Microwave Radiation on Cotton Dyeing with Reactive Blue 21 Dye, Pol. J. Environ. Stud. 2019, 28(No. 3), 1687–1691. [Google Scholar] [CrossRef]
- Al-Etaibi, A.M.; El-Apasery, M.A. Microwave-Assisted Synthesis of Azo Disperse Dyes for Dyeing Polyester Fabrics: Our Contributions over the Past Decade. Polymers 2022, 14, 1703. [Google Scholar] [CrossRef] [PubMed]
- Elshemy, N.S.; Haggag, K. New Trend in Textile Coloration Using Microwave Irradiation. J. Text. Color. Polym. Sci. 2019, Vol. 16(No.1), pp 33–48. [Google Scholar] [CrossRef]
- Öner, E.; Büyükakıncı, Y; Sökmen, N. Microwave-assisted dyeing of poly(butylene terephthalate) fabrics with disperse dyes. Coloration Technology 2013, 129(2), 125–130. [Google Scholar] [CrossRef]
- Büyükakıncı, Y; Sökmen, N.; Öner, E. Microwave assisted exhaust dyeing of polypropylene. Paper presented at the 4th Centrel European Conference, Liberec, Czech Republic, 7-9 September 2005. [Google Scholar]
- Haggag, K. Fixation of pad-dyeing on cotton using microwave heating. Am Dyestuff Rep 1990, 26–30. [Google Scholar]
- Lill, J. R. Microwave-Assisted Proteomics. 2009. [Google Scholar] [PubMed]
- Hayes, B. L. Microwave Synthesis. 2002. [Google Scholar]
- Can, M. C. Microwave Heating as a Tool for Sustainable Chemistry; 2010. [Google Scholar]
- Miklavc, A. Chem. Phys.Chem 2001, 552. [CrossRef]
- Binner, J.G.P.; Hassine, N. A.; Cross, T. E. J. Mater. Sci. 1995, 30, 5389.56. [CrossRef]
- Garbacia, S.; Desai, B.; Lavaster, O.; Kappe, C. O. J. Org. Chem. 2003, 68, 9136. [CrossRef]
- Stadler, A.; Kappe, C. O. J. Chem. Soc., Perkin Trans. 2 2000, 2, 1363. [CrossRef]
- Hoz; Diaz-Ortiz, A.; Moreno, A. Chem. Soc. Rev. 2005, 34, 164. [CrossRef]
- Mortimer, M.; Taylor, P. Chemical Kinetics and Mechanism; 2002. [Google Scholar]
- House, J.E. Principles of Chemical Kinetics; 2007. [Google Scholar]
- Balluffi, R.B.; Allen, S.M.; Carter, W.C. Kinetics of Materials; 2005. [Google Scholar]
- Barrante, J.R. Applied Mathematics for Physical Chemistry; 1998. [Google Scholar]
- Yiğit Atabek, E. (2009). Investigation of Dyeability of Polypropylene Fiber [Doctoral thesis, Sakarya University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/.
- Doyuran, A. (2010). Dyeing of Synthetic Fibers in Microwave Environment [Master’s thesis, Sakarya University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/.
- Xiaolei, Z.; Jinwei, M.; Yanxiu, W.; Tianjie, N.; Deshuai, S.; Long, F.; Xiaodong, Z. Investigation on dyeing mechanism of modified cotton fiber. Royal Society of Chemistry 2022, Volume 12(Issue 49), Pages 31596–31607. [Google Scholar] [CrossRef]
- Vassileva, V.; Zheleva, Z.; Valcheva, E. The Kinetic Model of Dye Fixation on Cotton Fibers. Journal of University of Chemical Technology and Metallurgy 2008, 43(3), 323–326. [Google Scholar]
- Teker, M.; Imamoglu, M.; Bocek, N. Adsorption of Some Textile Dyes on Activated Carbon Prepared From Rice Hulls - Fresenıus Environmental Bulletin - Vol.18 - pp.709 - ISSN: 1018-4619 - English - Article - 2009 - WOS:000266898500009. [CrossRef]
- Ujhelyiova, A.; Bolhova, E.; Oravkinova, J.; Tin, R.; Marcin, A. Kinetics of dyeing process of blend polypropylene/polyester fibres with disperse dye. Dyes and Pigments 2007, 72, 212–216. [Google Scholar] [CrossRef]
- Georgiadou, K.L.; Tsatsaroni, E.G.; Eleftheriadis, I.C.; Kehayoglou, A.H. Disperse dyeing of polyester fibers: Kinetic and equilibrium study. J. Appl. Polym. Sci. 2002, 85, 123–128. [Google Scholar] [CrossRef]
- Fattahi, F.S. Investigation on the Kinetic Feature of CI Acid Blue 106 Dyeing on Woolen Material. Nanochem. Res. 2024, 9, 280–290. [Google Scholar] [CrossRef]
- Roy, M.N.; Hossain, M.T.; Hasan, M.Z.; Islam, K.; Rokonuzzaman, M.; Islam, M.A.; Khandaker, S.; Bashar, M.M. Adsorption, Kinetics and Thermodynamics of Reactive Dyes on Chitosan Treated Cotton Fabric. Textile & Leather Review 2023, 6, 211–232. [Google Scholar] [CrossRef]
- Lis, M.J.; Bezerra, F.M.; Meng, X.; Qian, H.; Immich, A.P.S. Kinetics of Dyeing in Continuous Circulation with Direct Dyes:Tencel Case. World Journal of Textile Engineering and Technology 2019, 5, 97–104. [Google Scholar] [CrossRef]
- Elshemy, N.S.; Elshakankery, M.H.; Shahien, S.M.; Haggag El-Sayed, K.H. Kinetic Investigations on Dyeing of Different Polyester Fabrics Using Microwave Irradiation, Egypt. J. Chem. The 8th. t. Conf. Text. Res. Div., Nat. Res. Centre, Cairo 2017, 79–88. [Google Scholar] [CrossRef]
- Ujhelyiova, A.; Bolhova, E.; Oravkinova, J.; Tiňo, R.; Marcinčin, A. Kinetics of dyeing process of blend polypropylene/polyester fibres with disperse dye. Dyes and Pigments 2007, vol. 72(2), 212–216. [Google Scholar] [CrossRef]
- Alşan, H.G. (2019), Investigation of Dyeing Kinetics of Cotton Fiber with Disperse Dyestuff in Microwave Environment [Master’s thesis, Sakarya University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/.











| PH (in) | KS (Color Strength) |
|---|---|
| 3 | 24,4815 |
| 3,5 | 21,0672 |
| 4 | 18,2372 |
| 4,5 | 15,9914 |
| 5,5 | 13,6445 |
| 6 | 12,8571 |
| K/S (Color Strength) | 50 °C | 60 °C | 70 °C | 80 °C | 95 °C |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 |
| 5 | 2,151 | 3,745 | 6,980 | 9,000 | 11,820 |
| 10 | 3,671 | 5,764 | 9,527 | 11,270 | 13,228 |
| 15 | 4,802 | 7,026 | 10,846 | 12,276 | 13,750 |
| 20 | 5,675 | 7,889 | 11,653 | 12,867 | 14,063 |
| 25 | 6,371 | 8,518 | 12,208 | 13,235 | 14,247 |
| 30 | 6,938 | 8,995 | 12,629 | 13,520 | 14,371 |
| Concentration (g./100 ml) | 50 °C | 60 °C | 70 °C | 80 °C | 95 °C |
|---|---|---|---|---|---|
| 0 | 0,01000 | 0,01000 | 0,01000 | 0,01000 | 0,01000 |
| 5 | 0,00824 | 0,00706 | 0,00535 | 0,00400 | 0,00212 |
| 10 | 0,00700 | 0,00548 | 0,00365 | 0,00249 | 0,00118 |
| 15 | 0,00608 | 0,00449 | 0,00277 | 0,00182 | 0,00083 |
| 20 | 0,00537 | 0,00381 | 0,00223 | 0,00142 | 0,00062 |
| 25 | 0,00480 | 0,00332 | 0,00186 | 0,00118 | 0,00050 |
| 30 | 0,00434 | 0,00294 | 0,00158 | 0,00099 | 0,00042 |
| Dye Concentration | Temperature | |||||
|---|---|---|---|---|---|---|
| 50 °C | 60 °C | 70 °C | 80 °C | 90 °C | 95 °C | |
| 0,10% | 0,4150 | 0,7507 | 0,8659 | 0,9112 | 1,7994 | 1,9654 |
| 0,25% | 2,3466 | 2,8823 | 3,5761 | 4,8436 | 5,1342 | 5,4248 |
| 0,50% | 2,6333 | 3,5349 | 4,3872 | 6,5147 | 6,9551 | 7,1561 |
| 0,75% | 2,9199 | 4,1874 | 5,1982 | 8,1848 | 8,7760 | 8,8873 |
| 1,00% | 3,2066 | 4,8399 | 6,0092 | 9,5722 | 11,0113 | 11,2309 |
| 1,50% | 3,7799 | 6,1449 | 7,6311 | 12,3470 | 15,4817 | 15,9181 |
| PH | KS |
|---|---|
| 3 | 25,0513 |
| 3,5 | 20,1982 |
| 4 | 18,2071 |
| 4,5 | 16,1967 |
| 5,75 | 13,3032 |
| 6,5 | 12,6054 |
| K/S (Color Strength) | 50 °C | 60 °C | 70 °C | 80 °C | 95 °C |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1,399 | 3,085 | 2,892 | 8,308 | 11,530 |
| 2 | 2,559 | 4,330 | 5,134 | 9,710 | 12,418 |
| 3 | 3,521 | 5,280 | 6,870 | 10,637 | 12,968 |
| 4 | 4,319 | 6,077 | 8,216 | 11,347 | 13,374 |
| 5 | 4,981 | 6,778 | 9,259 | 11,931 | 13,697 |
| 6 | 5,530 | 7,411 | 10,068 | 12,431 | 13,967 |
| 7 | 5,985 | 7,991 | 10,694 | 12,869 | 14,199 |
| 8 | 6,363 | 8,530 | 11,179 | 13,262 | 14,403 |
| 9 | 6,676 | 9,036 | 11,555 | 13,618 | 14,586 |
| 10 | 6,936 | 9,514 | 11,847 | 13,944 | 14,751 |
| Concentration (g./100 ml) | 50 °C | 60 °C | 70 °C | 80 °C | 95 °C |
|---|---|---|---|---|---|
| 0 | 0,01000 | 0,01000 | 0,01000 | 0,01000 | 0,01000 |
| 1 | 0,00904 | 0,00787 | 0,00813 | 0,00481 | 0,00256 |
| 2 | 0,00824 | 0,00701 | 0,00669 | 0,00393 | 0,00199 |
| 3 | 0,00757 | 0,00636 | 0,00557 | 0,00335 | 0,00163 |
| 4 | 0,00702 | 0,00581 | 0,00470 | 0,00291 | 0,00137 |
| 5 | 0,00656 | 0,00533 | 0,00403 | 0,00254 | 0,00116 |
| 6 | 0,00619 | 0,00489 | 0,00350 | 0,00223 | 0,00099 |
| 7 | 0,00587 | 0,00449 | 0,00310 | 0,00196 | 0,00084 |
| 8 | 0,00561 | 0,00412 | 0,00279 | 0,00171 | 0,00071 |
| 9 | 0,00540 | 0,00377 | 0,00255 | 0,00149 | 0,00059 |
| 10 | 0,00522 | 0,00344 | 0,00236 | 0,00128 | 0,00048 |
| Dye Concentration (mg/100 ml) % |
0 minute | 0,5 minute | 1,5 minute | 2 minute | 2,5 minute | 3 minute | 3,5 minute | 4 minute | 4,5 minute |
|---|---|---|---|---|---|---|---|---|---|
| 0,10% | 0,0000 | 0,1578 | 0,1757 | 0,1936 | 0,4658 | 0,4733 | 0,4810 | 0,8172 | 1,0040 |
| 0,25% | 0,0000 | 0,2241 | 0,4348 | 0,7972 | 1,1874 | 1,3161 | 1,7015 | 2,1245 | 2,7051 |
| 0,50% | 0,0000 | 0,3771 | 0,7977 | 1,1424 | 1,8702 | 2,2534 | 2,7197 | 3,4885 | 3,7910 |
| 0,75% | 0,0000 | 0,4855 | 1,1910 | 1,6459 | 2,2296 | 2,9205 | 3,7077 | 4,5910 | 5,5706 |
| 1,00% | 0,0000 | 0,6010 | 1,1376 | 1,7582 | 2,4080 | 3,0728 | 3,9831 | 5,4080 | 6,1228 |
| 1,50% | 0,0000 | 0,8315 | 1,7471 | 1,9827 | 2,7649 | 3,3774 | 4,5340 | 7,0420 | 7,2272 |
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. |
© 2026 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 (http://creativecommons.org/licenses/by/4.0/).