本研究探討聚對苯二甲酸乙二醇酯/奈米銀纖維 (PET/Ag NF) 薄膜在 X 波段頻譜 (8.2 - 12.4 GHz) 的電磁干擾 (EMI) 屏蔽效能 (SE)。使用掃描電子顯微鏡 (SEM) 分析 PET/Ag NF 樣品的結構特性，並使用向量網路分析儀 (VNA) 量測其 SE 效能，透過相對應的散射參數確定總屏蔽效能。實驗結果顯示，PET/Ag NF 薄膜展現出顯著的 SE 效能，超越許多傳統的遮蔽材料。然而，實驗結果與模擬結果之間存在一些差異，這可能是由於高度無序的纖維和連接路徑不足，影響了薄膜的整體電導性。

為了解決這些差異，我們整合了蒙地卡羅方法與有限元素方法 (FEM)，以進一步研究 PET/Ag NF 薄膜的電導率。蒙地卡羅方法說明了導電率如何隨著導線密度變化，並強調結點在形成導電通路中的重要性。研究結果顯示，增加導線密度可創造更多的導電路徑，進而增強導電性，這與滲透理論相符。這項全面的分析對於影響 PET/Ag NF 薄膜效能的因素，提供了寶貴的見解，並可引導高效能 EMI 屏蔽材料的優化。

This study investigates the electromagnetic interference (EMI) shielding effectiveness (SE) of polyethylene terephthalate/silver nanofiber (PET/Ag NF) thin films across the X-band frequency spectrum (8.2 - 12.4 GHz). The structural characteristics of the PET/Ag NF samples were analyzed using scanning electron microscopy (SEM), and their SE performance was measured using a vector network analyzer (VNA) to determine the total shielding effectiveness through the corresponding scattering parameters. Experimental results reveal that PET/Ag NF thin films exhibit remarkable SE, surpassing many conventional shielding materials. However, some discrepancies between experimental and simulation results were observed, likely due to the highly disordered fibers and insufficient connective paths affecting the films' overall electrical conductivity.

To address these discrepancies, a Monte Carlo approach was integrated with the finite element method (FEM) to further investigate the electrical conductivity of the PET/Ag NF films. The Monte Carlo simulations illustrated how conductivity varies with wire density and highlighted the importance of junctions in forming conductive pathways. The findings demonstrated that increased wire density enhances conductivity by creating more conductive paths, aligning with percolation theory. This comprehensive analysis provides valuable insights into the factors influencing the performance of PET/Ag NF thin films, guiding the optimization of high-performance EMI shielding materials.

[1] B. Deutschmann, G. Winkler, and P. Kastner. "Impact of electromagnetic interference on the functional safety of smart power devices for automotive applications." Elektrotech. Inftech., 135:352–359, 2018.

[2] P. Mathur and S. Raman. "Electromagnetic interference (EMI): Measurement and reduction techniques." J. Electron. Mater., 49:2975–2998, 2020.

[3] Engin G. Kıvrak, Kadir Kemal Yurt, Adem Ali Kaplan, Ihsan Alkan, and Gamze Altun. "Effects of electromagnetic fields exposure on the antioxidant defense system." Journal of Microscopy and Ultrastructure, 5(4):167–176, 2017.

[4] Onur Elmas. "Effects of electromagnetic field exposure on the heart: a systematic review." Toxicol Ind Health, 32(1):76–82, Jan 2016. Epub 2013 Sep 10.

[5] D.J. Helfritch. "16 - Electromagnetic interference shielding by cold spray particle deposition." In Victor K. Champagne, editor, The Cold Spray Materials Deposition Process, Woodhead Publishing Series in Metals and Surface Engineering, pages 315–326. Woodhead Publishing, 2007.

[6] Mailadil Sebastian, R. Ubic, and Heli Jantunen. "Microwave Materials and Applications Volume I II John Wiley Sons in press Editors M. T. Sebastian, R. Ubic, and H. Jantunen." 01 2017.

[7] D.D.L. Chung. "Electromagnetic interference shielding effectiveness of carbon materials." Carbon, 39(2):279–285, 2001.

[8] D.D.L. Chung. "Materials for electromagnetic interference shielding." J. of Materi Eng and Perform., 9:350–354, 2000.

[9] Bouzid Gaoui, Abdelkader Hadjadj, and Mohamed Kious. "Enhancement of the shielding effectiveness of multilayer materials by gradient thickness in the stacked layers." J. Mater. Sci: Mater. Electron., 28:11292–11299, 2017.

[10] Fan Wu, Aming Xie, Mengxiao Sun, Yuan Wang, and Mingyang Wang. "Reduced graphene oxide (RGO) modified spongelike polypyrrole (PPY) aerogel for excellent electromagnetic absorption." J. Mater. Chem. A, 3:14358–14369, 2015.

[11] Cristian Morari, Ionut Balan, Jana Pintea, Chitanu Elena, and Iulian Iordache. "Electrical conductivity and electromagnetic shielding effectiveness of silicone rubber filled with ferrite and graphite powders." Progress In Electromagnetics Research M, 21:93–104, 01 2011.

[12] Hye Ji Im, Jae Young Oh, Seongwoo Ryu, and Soon Hyung Hong. "The design and fabrication of a multilayered graded GNP/NI/PMMA nanocomposite for enhanced EMI shielding behavior." RSC Adv., 9:11289–11295, 2019.

[13] Mingjun Hu, Jiefeng Gao, Yucheng Dong, Kai Li, Guangcun Shan, Shiliu Yang, and Robert Kwok-Yiu Li. "Flexible transparent PES/silver nanowires/PET sandwich-structured film for high-efficiency electromagnetic interference shielding." Langmuir, 28(18):7101–7106, 2012. PMID: 22533864.

[14] Mohammed H. Al-Saleh and Uttandaraman Sundararaj. "Electromagnetic interference shielding mechanisms of CNT/polymer composites." Carbon, 47(7):1738–1746, 2009.

[15] Kenneth L. Kaiser. "Electromagnetic compatibility handbook." CRC press, 2004.

[16] Y. K. Hong, C. Y. Lee, C. K. Jeong, D. E. Lee, K. Kim, and J. Joo. "Method and apparatus to measure electromagnetic interference shielding efficiency and its shielding characteristics in broadband frequency ranges." Review of Scientific Instruments, 74(2):1098–1102, 02 2003.

[17] S. A. Schelkunoff. "Electromagnetic Waves." D. Van Nostrand, Princeton, NJ, 1943.

[18] Richard B. Schulz, V.C. Plantz, and D.R. Brush. "Shielding theory and practice." IEEE Transactions on Electromagnetic Compatibility, 30(3):187–201, 1988.

[19] Mengyue Peng and Faxiang Qin. "Clarification of basic concepts for electromagnetic interference shielding effectiveness." Journal of Applied Physics, 130(22), 2021.

[20] Ranvijai Ram, Dipak Khastgir, and Mostafizur Rahaman. "Electromagnetic interference shielding effectiveness and skin depth of poly (vinylidene fluoride)/particulate nano-carbon filler composites: prediction of electrical conductivity and percolation threshold." Polymer International, 68(6):1194–1203, 2019.

[21] Shuying Yang, Karen Lozano, Azalia Lomeli, Heinrich D. Foltz, and Robert Jones. "Electromagnetic interference shielding effectiveness of carbon nanofiber/LCP composites." Composites Part A: Applied Science and Manufacturing, 36(5):691–697, 2005.

[22] Biao Zhao, Mahdi Hamidinejad, Shuai Wang, Pengwei Bai, Renchao Che, Rui Zhang, and Chul B. Park. "Advances in electromagnetic shielding properties of composite foams." J. Mater. Chem. A, 9:8896–8949, 2021.

[23] Payam Vosoughi, Peter Taylor, and Halil Ceylan. "Impacts of internal curing on the performance of concrete materials in the laboratory and the field." 11 2017.

[24] Mark Fox. "Optical properties of solids," 2002.

[25] Deborah Chung. "Applied materials science: Applications of engineering materials in structural, electronics, thermal, and other industries / D.D.L. Chung." 06 2001.

[26] Ján Kruželák, Andrea Kvasničáková, Klaudia Hložeková, and Ivan Hudec. "Progress in polymers and polymer composites used as efficient materials for EMI shielding." Nanoscale Adv., 3:123–172, 2021.

[27] Junpyo Hong, Jisung Kwon, Dohyun Im, Jeonggil Ko, Chae Yun Nam, Hyeong Gyu Yang, Sun Ho Shin, Soon Man Hong, Seung Sang Hwang, Ho Gyu Yoon, and Albert S. Lee. "Best practices for correlating electrical conductivity with broadband EMI shielding in binary filler-based conducting polymer composites." Chemical Engineering Journal, 455:140528, 2023.

[28] Jimei Xue, Xiaowei Yin, Fang Ye, Litong Zhang, and Laifei Cheng. "Theoretical prediction and experimental verification on EMI shielding effectiveness of dielectric composites using complex permittivity." Ceramics International, 43(18):16736–16743, 2017.

[29] Yuan Liu, Jianming Zhang, Heng Gao, Yan Wang, Qingxian Liu, Siya Huang, Chuan Fei Guo, and Zhifeng Ren. "Capillary-force-induced cold welding in silver-nanowire-based flexible transparent electrodes." Nano Letters, 17(2):1090–1096, 2017. PMID: 28094950.

[30] Philip L. Marston. "James Clerk Maxwell: Life and science." Journal of Quantitative Spectroscopy and Radiative Transfer, 178:50–65, 2016. Electromagnetic and light scattering by nonspherical particles XV: Celebrating 150 years of Maxwell’s electromagnetics.

[31] Vadim Markel. "Introduction to the Maxwell Garnett approximation: tutorial." Journal of the Optical Society of America A: Optics, Image Science, and Vision, 33(7):1244–1256, 2016. hal-01282105v2.

[32] D. A. G. Bruggeman. "Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen." Annalen der Physik, 416(8):665–679, 1935.

[33] H. Chang and C. Liao. "A parallel derivation to the Maxwell-Garnett formula for the magnetic permeability of mixed materials." World Journal of Condensed Matter Physics, 1(2):55–58, 2011.

[34] Craig F. Bohren and Donald R. Huffman. "Absorption and scattering of light by small particles." John Wiley & Sons, 2008.

[35] Ari H. Sihvola. "Electromagnetic mixing formulas and applications." Number 47. IET, 1999.

[36] Tuck C. Choy. "Effective medium theory: principles and applications," volume 165. Oxford University Press, 2015.

[37] P. Chylek, V. Srivastava, and R. G. Pinnick. "Effect of nonsphericity on the extinction of radiation by dielectric grains." Phys. Rev. B, 16:1740–1744, 08 1977.

[38] A. Lakhtakia and R. Messier. "Particle shape and size effects on the infrared spectra of pyroxene and olivine powders." 1994.

[39] J. Clerc, G. Giraud, J. Laugier, and J. Luck. "The electrical conductivity of binary disordered systems, percolation clusters, fractals, and related models." Advances in Physics, 39:191–309, 1990.

[40] K. K. Bardhan and M. K. Sen. "Percolation and dielectric properties of particulate composites." In R. Hackam, editor, Polymer Engineering and Science, volume 26, pages 1145–1152. Hanser Publishers, 1986.

[41] Huiming Hu, K. S. K. Sastry, and K. V. Shenoy. "Electromagnetic theory for mixed materials." Journal of Applied Physics, 70(7):3673–3683, 1991.

[42] M. Sahimi. "Application of percolation theory." Taylor & Francis, 1994.

[43] D. A. G. Bruggeman. "Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. II. Dielectricitätskonstanten von Mehrstoffsystemen." Annalen der Physik, 24(7):636–679, 1935.

[44] Claudio Balocco, Nicola Missaglia, and Vittorio Ferrero. "Theory and applications of electromagnetic waves." CRC Press, 2019.

[45] M. T. Sebastian, R. Ubic, and H. Jantunen. "Microwave materials and their applications." 2017.

[46] J. S. Zhao, M. T. Sebastian, and A. U. Rehman. "Advances in microwave materials." 2019.

[47] J. S. Zhao and M. T. Sebastian. "Microwave dielectric materials." 2021.

[48] J. S. Zhao and R. Ubic. "High-frequency dielectric materials." 2023.

[49] K. F. Li, S. H. Yao, and Y. X. Zhang. "Dielectric properties of materials." 2018.

[50] L. A. Dobrzański and Z. Brytan. "Metallic materials for electromagnetic applications." 2018.

[51] J. Liu, M.-Y. Yu, Z.-Z. Yu, and V. Nicolosi. "Design and advanced manufacturing of electromagnetic interference shielding materials." Materials Today, 66:245–272, 2023.

[52] M. Ahmadi Bonakdar and D. Rodrigue. "Electrospinning: Processes, structures, and materials." Macromol, 4:58–103, 2024.

[53] Monika Knitter, Ewa Markiewicz, and J. Jurga. "Dielectric properties of polyethylene terephthalate/polyphenylene sulfide/barium titanate nanocomposite for application in electronic industry." Polymer Engineering and Science - POLYM ENG SCI, 50, 08 2010.

[54] Jemilat Yusuf et al. "Electromagnetic wave absorption of coconut fiber-derived porous activated carbon." Boletín de la Sociedad Española de Cerámica y Vidrio, 61, 03 2021.

[55] Jiahui () Zhang et al. "2D simulation of the electromagnetic wave across the non-uniform reentry plasma sheath with COMSOL." AIP Advances, 9(5):055316, 05 2019.

[56] Nawfal Jebbor, Seddik Bri, and My Cherif ElBoubakraoui. "Effective complex permittivity determination and microwave absorption properties of a granular dielectric composite material." Procedia Computer Science, 151:1022–1027, 2019.

[57] Lei Sun et al. "A simplified design of broadband metamaterial absorber covering x- and ku- band." Materials Research Express, 6(12):125805, Jan 2020.

[58] A. Bregman, E. Michielssen, and A. Taub. "Comparison of experimental and modeled emi shielding properties of periodic porous xgnp/pla composites." Polymers, 11:1233, 2019.

[59] Dagang Wu et al. "Numerical modeling of periodic composite media for electromagnetic shielding application." Pages 1–5, 08 2007.

[60] H. G. Manning et al. "The electro-optical performance of silver nanowire networks." Sci Rep, 9:11550, 2019.

[61] V. Srivastava, and R. G. Pinnick. "Effect of nonsphericity on the extinction of radiation by dielectric grains." Phys. Rev. B, 16:1740–1744, 08 1977.

[62] A. Lakhtakia and R. Messier. "Particle shape and size effects on the infrared spectra of pyroxene and olivine powders." 1994.

[63] J. Clerc, G. Giraud, J. Laugier, and J. Luck. "The electrical conductivity of binary disordered systems, percolation clusters, fractals, and related models." Advances in Physics, 39:191–309, 1990.

[64] K. K. Bardhan and M. K. Sen. "Percolation and dielectric properties of particulate composites." In R. Hackam, editor, Polymer Engineering and Science, volume 26, pages 1145–1152. Hanser Publishers, 1986.

[65] Huiming Hu, K. S. K. Sastry, and K. V. Shenoy. "Electromagnetic theory for mixed materials." Journal of Applied Physics, 70(7):3673–3683, 1991.

[66] M. Sahimi. "Application of percolation theory." Taylor & Francis, 1994.

[67] D. A. G. Bruggeman. "Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. II. Dielectricitätskonstanten von Mehrstoffsystemen." Annalen der Physik, 24(7):636–679, 1935.