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Modeling and Optimum Design of Carbon Nanotube/Polyvinyl Alcohol Hybrid Nanofibers as Electromagnetic Interference Shielding Material

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Abstract

This study intends to optimize the electromagnetic interference (EMI) shielding effectiveness of multi-walled carbon nanotubes/polyvinyl alcohol (MWCNTs/PVA) composite nanofibers based on multiple nonlinear neuro-regression analysis. The effect of MWCNTs content, thickness, and frequency on the shielding properties of MWCNTs/PVA nanofibers has been investigated in the analysis. The parameters were determined from a literature study focused on the designing and production of MWCNTs/PVA nanofibers as an EMI shielding composite material. Within the scope of the present study, 12 unique candidate models for each response were generated to test the accuracy of the predictions. Determination coefficients and boundedness of models have been checked to acquire the most realistic ones. Nelder-Mead, Simulated Annealing, Differential Evolution, and Random Search algorithms were used to attain the optimum parameters for shielding effectiveness of the composite nanofiber structure by maximizing the absorption while maintaining the minimum reflection. The present paper demonstrates that the proposed methodology can significantly contribute to the experimental studies regarding the materials design by predicting the process reliably.

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Change history

  • 28 August 2022

    Dashes used in Tables 3 and 4 to indicate where values for items are not available were positioned inconsistently in the article as originally published.

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Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Correspondence to Fethullah Güneş.

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Appendices

Appendices

$$L1=5.67714\text{\hspace{0.05em}}+0.985714 \mathrm{C}+0.0571429 \mathrm{T}-0.376\mathrm{ F}$$
$$LR1=(8733.82\text{\hspace{0.05em}}+4216.07 \mathrm{C}-747.909 \mathrm{T}-255.528 \mathrm{F})/(1838.33+91.8026 C-60.0513\mathrm{ T}+138.879\mathrm{ F})$$
$$SON1=-18.7+2.375 \mathrm{C}+0.044 {\mathrm{C}}^{2}-6.25 \mathrm{T}+0.035 \mathrm{CT}-0.55{ \mathrm{T}}^{2}+5.1625 \mathrm{F}-0.1625 \mathrm{CF}+0.6875 \mathrm{TF}-0.3 {\mathrm{F}}^{2}$$
$$SONR1=(1.42021\text{\hspace{0.05em}}+1.70473 \mathrm{C}-3.53146 {\mathrm{C}}^{2}+2.38323 \mathrm{T}+3.01722 \mathrm{CT}-0.959317 {\mathrm{T}}^{2}+10.5435 \mathrm{F}+11.0735 \mathrm{CF}-1.57249 \mathrm{TF}+0.809123 {\mathrm{F}}^{2})/(0.911375\text{\hspace{0.05em}}+1.80765 \mathrm{C}-0.328493 {\mathrm{C}}^{2}+6.08667 \mathrm{T}-0.978142 \mathrm{CT}+12.2058 {\mathrm{T}}^{2}-2.83091 \mathrm{F}-0.0645586 \mathrm{CF}-3.82249 \mathrm{TF}+1.47206 {\mathrm{F}}^{2})$$
$$FOEN1=12.5173\text{\hspace{0.05em}}+0.000295002{e}^{\mathrm{C}}-0.024376{e}^{\mathrm{T}}-2.46849{e}^{0.1 \mathrm{F}}$$
$$FOENR1=(56604.2\text{\hspace{0.05em}}+268.888{e}^{\mathrm{C}}-3741.58{e}^{\mathrm{T}}-5151.23{e}^{0.1 \mathrm{F}})/(20172.5+24.535{e}^{\mathrm{C}}-2986.3{e}^{\mathrm{T}}+2154.52{e}^{0.1 \mathrm{F}})$$
$$SOEN1=9.60886\text{\hspace{0.05em}}+2.75724\times {10}^{-43}{e}^{{\mathrm{C}}^{2}}-0.000238572{e}^{{\mathrm{T}}^{2}}-1.30538{e}^{0.01 {\mathrm{F}}^{2}}$$
$$SOENR1=(5751.91\text{\hspace{0.05em}}+6.31642\times {10}^{-8}{e}^{{\mathrm{C}}^{2}}-36.9434{e}^{{\mathrm{T}}^{2}}-492.749{e}^{0.01 {\mathrm{F}}^{2}})/(2227.06\text{\hspace{0.05em}}+5.70331\times {10}^{-9}{e}^{{\mathrm{C}}^{2}}-33.478{e}^{{\mathrm{T}}^{2}}+58.072{e}^{0.01 {\mathrm{F}}^{2}})$$
$$FOTN1=5.79848\text{\hspace{0.05em}}-3.58828\mathrm{cosC}-1.21003\mathrm{cosT}-0.354125\mathrm{cosF}-0.902239\mathrm{sinC}+1.16372\mathrm{sinT}+0.605955\mathrm{sinF}$$
$$FOTNR1=(2.69515\times {10}^{9}-3.26134\times {10}^{9}\mathrm{cosC}-1.13894\times {10}^{9}\mathrm{cosT}-1.88696\times {10}^{9}\mathrm{cosF}+1.04398\times {10}^{10}\mathrm{sinC}+2.46406\times {10}^{9}\mathrm{sinT}-1.2433\times {10}^{9}\mathrm{sinF})/(5.73497\times {10}^{8}-4.41022\times {10}^{8}\mathrm{cosC}-1.43056\times {10}^{7}\mathrm{cosT}-3.43503\times {10}^{8}\mathrm{cosF}+1.40166\times {10}^{9}\mathrm{sinC}+2.46122\times {10}^{7}\mathrm{sinT}-2.2902\times {10}^{8}\mathrm{sinF})$$
$$SOTN1=0.988537\text{\hspace{0.05em}}-0.925283\mathrm{cosC}+0.764787{\mathrm{cosC}}^{2}-1.10509\mathrm{cosT}+0.217622\mathrm{cosCcosT}+1.88784{\mathrm{cosT}}^{2}-0.363865\mathrm{cosF}-2.91817\mathrm{cosCcosF}+1.12418\mathrm{cosTcosF}+1.17485{\mathrm{cosF}}^{2}-0.523438\mathrm{sinC}+5.06588\mathrm{cosCsinC}+0.612446\mathrm{cosTsinC}-0.999012\mathrm{cosFsinC}+1.68156{\mathrm{sinC}}^{2}+0.991706\mathrm{sinT}-0.28306\mathrm{cosCsinT}-0.940057\mathrm{cosTsinT}-0.538808\mathrm{cosFsinT}-0.15157\mathrm{sinCsinT}+1.03832{\mathrm{sinT}}^{2}-0.0691596\mathrm{sinF}-0.536733\mathrm{cosCsinF}-1.13287\mathrm{cosTsinF}+0.213817\mathrm{cosFsinF}-0.47639\mathrm{sinCsinF}-0.909082\mathrm{sinTsinF}+1.84798{\mathrm{sinF}}^{2}$$
$$SOTNR1=(0.70963\text{\hspace{0.05em}}+5.56039\mathrm{cosC}+0.853226{\mathrm{cosC}}^{2}+3.44637\mathrm{cosT}+0.985258\mathrm{cosCcosT}+1.07597{\mathrm{cosT}}^{2}+4.13462\mathrm{cosF}-0.937413\mathrm{cosCcosF}+1.2201\mathrm{cosTcosF}+0.924086{\mathrm{cosF}}^{2}-0.271485\mathrm{sinC}+3.92877\mathrm{cosCsinC}+2.79851\mathrm{cosTsinC}+4.40545\mathrm{cosFsinC}+0.856403{\mathrm{sinC}}^{2}+0.520532\mathrm{sinT}+5.11474\mathrm{cosCsinT}+3.60244\mathrm{cosTsinT}+3.5689\mathrm{cosFsinT}+0.0234713\mathrm{sinCsinT}+0.633661{\mathrm{sinT}}^{2}+4.18159\mathrm{sinF}+1.40315\mathrm{cosCsinF}+1.66159\mathrm{cosTsinF}+0.711122\mathrm{cosFsinF}+2.7262\mathrm{sinCsinF}+4.2338\mathrm{sinTsinF}+0.785544{\mathrm{sinF}}^{2})/(0.626113\text{\hspace{0.05em}}+2.25758\mathrm{cosC}+0.65177{\mathrm{cosC}}^{2}+1.47855\mathrm{cosT}+0.892797\mathrm{cosCcosT}+0.948732{\mathrm{cosT}}^{2}+2.43714\mathrm{cosF}+1.47921\mathrm{cosCcosF}+1.65465\mathrm{cosTcosF}+0.9564{\mathrm{cosF}}^{2}+1.58684\mathrm{sinC}+2.45307\mathrm{cosCsinC}+2.21448\mathrm{cosTsinC}+2.72766\mathrm{cosFsinC}+0.974343{\mathrm{sinC}}^{2}+0.540738\mathrm{sinT}+2.09094\mathrm{cosCsinT}+1.73445\mathrm{cosTsinT}+2.22512\mathrm{cosFsinT}+1.61132\mathrm{sinCsinT}+0.677381{\mathrm{sinT}}^{2}+1.58368\mathrm{sinF}+0.623785\mathrm{cosCsinF}+1.55036\mathrm{cosTsinF}+1.96654\mathrm{cosFsinF}+2.09904\mathrm{sinCsinF}+1.81129\mathrm{sinTsinF}+0.669713{\mathrm{sinF}}^{2})$$
$$L2=-12.5871+3.30629 \mathrm{C}+2.32286 \mathrm{T}+0.818 \mathrm{F}$$
$$LR2=(931.323\text{\hspace{0.05em}}+2468.74 \mathrm{C}-146.956 \mathrm{T}+214.237\mathrm{ F })/(1891.11\text{\hspace{0.05em}}-44.8854 \mathrm{C}-133.037 \mathrm{T}-35.2433 \mathrm{F })$$
$$SON2=61.975\text{\hspace{0.05em}}-1.07 \mathrm{C}+0.256{ \mathrm{C}}^{2}+11. \mathrm{T}+0.63 \mathrm{CT}-5.175 {\mathrm{T}}^{2}-14.5375 \mathrm{F}+0.065 \mathrm{CF}+0.8375 \mathrm{TF}+0.6875 {\mathrm{F}}^{2}$$
$$SONR2=(1.72091\text{\hspace{0.05em}}+0.670344 \mathrm{C}+1.40386 {\mathrm{C}}^{2}+4.76729 \mathrm{T}+1.06465 \mathrm{CT}+1.39519 {\mathrm{T}}^{2}+14.9915 \mathrm{F}+9.88924 \mathrm{CF}+18.3084 \mathrm{TF}-2.30269 {\mathrm{F}}^{2})/(1.41906\text{\hspace{0.05em}}-0.0540599 \mathrm{C}+0.50117 {\mathrm{C}}^{2}+6.50062 \mathrm{T}-7.19837 \mathrm{CT}+9.83774 {\mathrm{T}}^{2}+10.5969 \mathrm{F}+0.300149 \mathrm{CF}+2.06562 \mathrm{TF}-0.958922 {\mathrm{F}}^{2})$$
$$FOEN2=12.7575\text{\hspace{0.05em}}+0.00116824{e}^{\mathrm{C}}+0.18389{e}^{\mathrm{T}}-1.24261{e}^{0.1\mathrm{F}}$$
$$FOENR2=(66213.\text{\hspace{0.05em}}+45.6959{e}^{\mathrm{C}}-1165.09{e}^{\mathrm{T}}-17525.6{e}^{0.1\mathrm{F}})/(11298.7\text{\hspace{0.05em}}+1.40117{e}^{\mathrm{C}}-552.105{e}^{\mathrm{T}}-2242.02{e}^{0.1\mathrm{F}})$$
$$SOEN2=14.6895\text{\hspace{0.05em}}+1.00888\times {10}^{-42}{e}^{{\mathrm{C}}^{2}}-0.000127278{e}^{{\mathrm{T}}^{2}}-1.1671{e}^{0.01{\mathrm{F}}^{2}}$$
$$SOENR2=(11628.9\text{\hspace{0.05em}}-2.13922\times {10}^{-7}{e}^{{\mathrm{C}}^{2}}-460.482{e}^{{\mathrm{T}}^{2}}+1551.73{e}^{0.01{\mathrm{F}}^{2}})/(5644.38-6.31971\times {10}^{-9}{e}^{{\mathrm{C}}^{2}}-148.739{e}^{{\mathrm{T}}^{2}}+429.47{e}^{0.01{\mathrm{F}}^{2}})$$
$$FOTN2=20.5379\text{\hspace{0.05em}}-12.9023\mathrm{cosC}-2.56492\mathrm{cosT}+2.5408\mathrm{cosF}-2.8903\mathrm{sinC}-4.72337\mathrm{sinT}+0.533284\mathrm{sinF}$$
$$FOTNR2=(3.26814\times {10}^{8}-9.31945\times {10}^{7}\mathrm{cosC}-1.23075\times {10}^{8}\mathrm{cosT}-2.14784\times {10}^{8}\mathrm{cosF}+1.14073\times {10}^{8}\mathrm{sinC}+3.33212\times {10}^{8}\mathrm{sinT}-2.94874\times {10}^{8}\mathrm{sinF})/(3.32586\times {10}^{7}+2.03463\times {10}^{7}\mathrm{cosC}-1.05852\times {10}^{7}\mathrm{cosT}-1.16048\times {10}^{7}\mathrm{cosF}+2.79338\times {10}^{7}\mathrm{sinC}+3.03578\times {10}^{7}\mathrm{sinT}-1.08731\times {10}^{7}\mathrm{sinF})$$
$$SOTN2=2.41935\text{\hspace{0.05em}}-3.92793\mathrm{cosC}+1.87749{\mathrm{cosC}}^{2}-3.76205\mathrm{cosT}+3.7161\mathrm{cosCcosT}+5.94415{\mathrm{cosT}}^{2}+0.507258\mathrm{cosF}-9.74948\mathrm{cosCcosF}+0.449479\mathrm{cosTcosF}+3.94041{\mathrm{cosF}}^{2}-1.6124\mathrm{sinC}+16.5823\mathrm{cosCsinC}+4.10487\mathrm{cosTsinC}-3.68588\mathrm{cosFsinC}+4.1102{\mathrm{sinC}}^{2}+1.88611\mathrm{sinT}-0.986432\mathrm{cosCsinT}-2.50857\mathrm{cosTsinT}-0.464768\mathrm{cosFsinT}-0.0134405\mathrm{sinCsinT}+1.83679{\mathrm{sinT}}^{2}-1.4338\mathrm{sinF}-0.623703\mathrm{cosCsinF}-2.05229\mathrm{cosTsinF}-1.42561\mathrm{cosFsinF}-0.587844\mathrm{sinCsinF}-2.83885\mathrm{sinTsinF}+3.1105{\mathrm{sinF}}^{2}$$
$$SOTNR2=(1.7508\text{\hspace{0.05em}}+3.57435\mathrm{cosC}+1.49058{\mathrm{cosC}}^{2}+1.53758\mathrm{cosT}+2.26216\mathrm{cosCcosT}+1.40472{\mathrm{cosT}}^{2}+4.61609\mathrm{cosF}+2.15707\mathrm{cosCcosF}+1.20078\mathrm{cosTcosF}+0.866748{\mathrm{cosF}}^{2}+0.336386\mathrm{sinC}+2.66175\mathrm{cosCsinC}+2.73075\mathrm{cosTsinC}+0.781586\mathrm{cosFsinC}+1.26022{\mathrm{sinC}}^{2}+3.75292\mathrm{sinT}+3.50828\mathrm{cosCsinT}+2.3912\mathrm{cosTsinT}+4.07459\mathrm{cosFsinT}+0.79925\mathrm{sinCsinT}+1.34608{\mathrm{sinT}}^{2}+1.39011\mathrm{sinF}+1.21331\mathrm{cosCsinF}+2.40965\mathrm{cosTsinF}+0.270881\mathrm{cosFsinF}+3.45108\mathrm{sinCsinF}+1.16659\mathrm{sinTsinF}+1.88406{\mathrm{sinF}}^{2})/(0.628867\text{\hspace{0.05em}}+1.33957\mathrm{cosC}+0.66188{\mathrm{cosC}}^{2}+1.1813\mathrm{cosT}+0.993407\mathrm{cosCcosT}+0.900039{\mathrm{cosT}}^{2}+2.03647\mathrm{cosF}+2.43844\mathrm{cosCcosF}+1.68663\mathrm{cosTcosF}+0.845424{\mathrm{cosF}}^{2}+1.81012\mathrm{sinC}+1.71216\mathrm{cosCsinC}+2.12488\mathrm{cosTsinC}+2.2849\mathrm{cosFsinC}+0.966987{\mathrm{sinC}}^{2}+0.719204\mathrm{sinT}+1.15791\mathrm{cosCsinT}+1.34053\mathrm{cosTsinT}+2.03231\mathrm{cosFsinT}+1.73545\mathrm{sinCsinT}+0.728828{\mathrm{sinT}}^{2}+1.19715\mathrm{sinF}+0.837123\mathrm{cosCsinF}+1.69519\mathrm{cosTsinF}+2.18946\mathrm{cosFsinF}+2.23638\mathrm{sinCsinF}+1.32412\mathrm{sinTsinF}+0.783444{\mathrm{sinF}}^{2})$$

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Aydın, K.B., Aydin, L. & Güneş, F. Modeling and Optimum Design of Carbon Nanotube/Polyvinyl Alcohol Hybrid Nanofibers as Electromagnetic Interference Shielding Material. Integr Mater Manuf Innov 11, 391–406 (2022). https://doi.org/10.1007/s40192-022-00270-7

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Keywords

  • Carbon nanotube
  • Electromagnetic interference shielding
  • Polyvinyl alcohol
  • Neuro-regression modeling
  • Stochastic optimization