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Modeling the dielectric behavior of polymer nanocomposites considering interphase properties and nanoparticle geometry

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Abstract

Controlling the dielectric properties is desirable for monitoring the efficiency of materials, which are newly applicable in electronic devices. In this work, the simple and well-known Rother-Lichtenecker equation has been modified to predict the real part of the dielectric permittivity of polymer nanocomposites. In the proposed model, the real part of dielectric permittivity is a function of interphase properties (thickness, volume fraction, and dielectric permittivity) and nanoparticle characteristics (shape, size, and volume fraction). The model results agree well with the experimental data for polymer nanocomposites containing different spherical, cylindrical, and plate-like nanoparticles. In addition, the predicted interphase properties cope very well with the experimental observations of interfacial interactions from valid literature. The high interphase properties and the small size of the nanoparticles are desired requirements of a nanocomposite with high dielectric permittivity. However, the dielectric permittivity of the nanoparticles barely affects that of the nanocomposite. The proposed model can accurately estimate the interphase properties of any available polymer nanocomposite considering the dielectric permittivity measurements.

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References

  1. Muduli SP, Parida S, Nayak S, Rout SK (2020) Effect of Graphene Oxide loading on ferroelectric and dielectric properties of hot pressed poly(vinylidene fluoride) matrix composite film. Polym Compos 41:2855–2865. https://doi.org/10.1002/pc.25581

    Article  CAS  Google Scholar 

  2. Nisha P, Suresh S, Jayamoorthy K, Dhanalekshmi KI, Ravichandran C (2021) Synthesis, spectral, thermal studies and dielectric behavior of functionalized TiO2-loaded diglycidyl epoxy nanocomposite film. Polym Bull 78:5255–5274. https://doi.org/10.1007/s00289-020-03362-6

    Article  CAS  Google Scholar 

  3. Mannsfeld SCB, Tee BC-K, Stoltenberg RM, Chen CVH-H, Barman S, Muir BVO, Sokolov AN, Reese C, Bao Z (2010) Highly sensitive flexible pressure sensors with microstructured rubber dielectric layers. Nat Mater 9:859–864. https://doi.org/10.1038/nmat2834

    Article  CAS  PubMed  Google Scholar 

  4. Chung J, Chung S-H, Lin Z-H, Jin Y, Hong J, Lee S (2021) Dielectric liquid-based self-operating switch triboelectric nanogenerator for current amplification via regulating air breakdown. Nano Energy 88:106292–106302. https://doi.org/10.1016/j.nanoen.2021.106292

    Article  CAS  Google Scholar 

  5. Singh N (2021) Polypyrrole-based emerging and futuristic hybrid nanocomposites. Polym Bull. https://doi.org/10.1007/s00289-021-03840-5

    Article  Google Scholar 

  6. Ghosh T, Sharma SK, Pradhan D (2020) Giant dielectric constant and superior photovoltaic property of the mechanochemically synthesized stable CH3NH3PbBr 3 in a hole transporter-free solar cell. ACS Sustain Chem Eng 8:1445–1454. https://doi.org/10.1021/acssuschemeng.9b05678

    Article  CAS  Google Scholar 

  7. Kim J-Y, Kim H, Kim T, Yu S, Suk JW, Jeong T, Song S, Bae MJ, Han I, Jung D, Park SH (2013) A chlorinated barium titanate-filled polymer composite with a high dielectric constant and its application to electroluminescent devices. J Mater Chem C 1:5078–5083. https://doi.org/10.1039/C3TC30767K

    Article  CAS  Google Scholar 

  8. Fan FR, Tang W, Wang ZL (2016) Flexible nanogenerators for energy harvesting and self-powered electronics. Adv Mater 28:4283–4305. https://doi.org/10.1002/adma.201504299

    Article  CAS  PubMed  Google Scholar 

  9. Wang X, Sun F, Yin G, Wang Y, Liu B, Dong M (2018) Tactile-sensing based on flexible PVDF nanofibers via electrospinning: a review. Sensors 18:330–346. https://doi.org/10.3390/s18020330

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Zhang X, Ma Y, Zhao C, Yang W (2014) High dielectric constant and low dielectric loss hybrid nanocomposites fabricated with ferroelectric polymer matrix and BaTiO3 nanofibers modified with perfluoroalkylsilane. Appl Surf Sci 305:531–538. https://doi.org/10.1016/j.apsusc.2014.03.131

    Article  CAS  Google Scholar 

  11. Cauda V, Canavese G, Stassi S (2015) Nanostructured piezoelectric polymers. J Appl Polym Sci 132:41667–41681. https://doi.org/10.1002/app.41667

    Article  CAS  Google Scholar 

  12. Cho S, Lee JS, Jang J (2015) Poly(vinylidene fluoride)/NH2-treated graphene nanodot/reduced graphene oxide nanocomposites with enhanced dielectric performance for ultrahigh energy density capacitor. ACS Appl Mater Interfaces 7:9668–9681. https://doi.org/10.1021/acsami.5b01430

    Article  CAS  PubMed  Google Scholar 

  13. Yuan D, Chen M, Xu Y, Huang L, Ma J, Peng Q, Cai X (2020) High-performance PA1/TPU films with enhanced dielectric constant and low loss tangent. J Appl Polym Sci 137:48469–78479. https://doi.org/10.1002/app.48469

    Article  CAS  Google Scholar 

  14. Zare Y, Rhee KY, Park S-J (2017) Modeling of tensile strength in polymer particulate nanocomposites based on material and interphase properties. J Appl Polym Sci 134:44869–44785. https://doi.org/10.1002/app.44869

    Article  CAS  Google Scholar 

  15. Zare Y (2016) Development of Halpin-Tsai model for polymer nanocomposites assuming interphase properties and nanofiller size. Polym Test 51:69–73. https://doi.org/10.1016/j.polymertesting.2016.02.010

    Article  CAS  Google Scholar 

  16. Zhu J-M, Zare Y, Rhee KY (2018) Analysis of the roles of interphase, waviness and agglomeration of CNT in the electrical conductivity and tensile modulus of polymer/CNT nanocomposites by theoretical approaches. Colloids Surfaces A Physicochem Eng Asp 539:29–36. https://doi.org/10.1016/j.colsurfa.2017.12.001

    Article  CAS  Google Scholar 

  17. Nikfar N, Esfandiar M, Shahnazari MR (2017) The reinforcing and characteristics of interphase as the polymer chains adsorbed on the nanoparticles in polymer nanocomposites. Colloid Polym Sci 1:1–10. https://doi.org/10.1007/s00396-017-4164-z

    Article  CAS  Google Scholar 

  18. Srivastava A, Kumar D (2017) A continuum model to study interphase effects on elastic properties of CNT/GS-nanocomposite. Mater Res Exp 4:25036–25053. https://doi.org/10.1088/2053-1591/aa5dd2

    Article  CAS  Google Scholar 

  19. Chen W-S, Hsieh M-Y (2017) Dielectric constant calculation based on mixture equations of binary composites at microwave frequency. Ceram Int 43:343–350. https://doi.org/10.1016/j.ceramint.2017.05.320

    Article  CAS  Google Scholar 

  20. Choudhury A (2010) Dielectric and piezoelectric properties of polyetherimide/BaTiO3 nanocomposites. Mater Chem Phys 121:280–285. https://doi.org/10.1016/j.matchemphys.2010.01.035

    Article  CAS  Google Scholar 

  21. Ahmad Z, Prasad A, Prasad K (2009) A comparative approach to predicting effective dielectric, piezoelectric and elastic properties of PZT/PVDF composites. Phys B Condens Matter 404:3637–3644. https://doi.org/10.1016/j.physb.2009.06.009

    Article  CAS  Google Scholar 

  22. Menon SS, Krishna R, Wilson L, Sambhudevan S, Shankar B, Mayeen A, Kalarikkal N (2018) Magnetic and dielectric properties of nickel-ferrite-embedded natural rubber composites. Polym Bull 75:5217–5234. https://doi.org/10.1007/s00289-018-2323-0

    Article  CAS  Google Scholar 

  23. Ezzat M, Sabiha NA, Izzularab M (2014) Accurate model for computing dielectric constant of dielectric nanocomposites. Appl Nanosci 4:331–338. https://doi.org/10.1007/s13204-013-0201-5

    Article  CAS  Google Scholar 

  24. Lee YJ, Kim JH, Ham S, Ju B-K, Choi WK (2018) Modeling large permittivity of poly(vinylidenefluoride-co-trifluoroethylene) and nanospring single-walled carbon nanotube-polyvinylpyrrolidone nanocomposites. AIP Adv 8:85113–85120. https://doi.org/10.1063/1.5036573

    Article  CAS  Google Scholar 

  25. Vo HT, Shi FG (2002) Towards model-based engineering of optoelectronic packaging materials: dielectric constant modeling. Microelectronics J 33:409–415. https://doi.org/10.1016/S0026-2692(02)00010-1

    Article  CAS  Google Scholar 

  26. Murugaraj P, Mainwaring D, Mora-Huertas N (2005) Dielectric enhancement in polymer-nanoparticle composites through interphase polarizability. J Appl Phys 98:54304–54310. https://doi.org/10.1063/1.2034654

    Article  CAS  Google Scholar 

  27. Todd MG, Shi FG (2005) Complex permittivity of composite systems: a comprehensive interphase approach. IEEE Trans Dielectr Electr Insul 12:601–611. https://doi.org/10.1109/TDEI.2005.1453466

    Article  Google Scholar 

  28. Liu X, Wu Y, Wang X, Li R, Zhang Z (2011) Effect of interphase on effective permittivity of composites. J Phys D Appl Phys 44:115402. https://doi.org/10.1088/0022-3727/44/11/115402

    Article  CAS  Google Scholar 

  29. Daily CS, Sun W, Kessler MR, Tan X, Bowler N (2014) Modeling the interphase of a polymer-based nanodielectric. IEEE Trans Dielectr Electr Insul 21:488–496. https://doi.org/10.1109/TDEI.2013.004181

    Article  CAS  Google Scholar 

  30. Drozdov AD, deClaville CJ (2020) Modeling dielectric permittivity of polymer composites at microwave frequencies. Mater Res Bull 126:110818–110833. https://doi.org/10.1016/j.materresbull.2020.110818

    Article  CAS  Google Scholar 

  31. Shen L, Li J (2005) Homogenization of a fibre/sphere with an inhomogeneous interphase for the effective elastic moduli of composites. Proc R Soc A Math Phys Eng Sci 461:1475–1504. https://doi.org/10.1098/rspa.2005.1447

    Article  CAS  Google Scholar 

  32. Boutaleb S, Zaïri F, Mesbah A, Naït-Abdelaziz M, Gloaguen JM, Boukharouba T, Lefebvre JM (2009) Micromechanics-based modelling of stiffness and yield stress for silica/polymer nanocomposites. Int J Solids Struct 46:1716–1726. https://doi.org/10.1016/j.ijsolstr.2008.12.011

    Article  CAS  Google Scholar 

  33. Saber-Samandari S, Afaghi-Khatibi A (2006) The effect of interphase on the elastic modulus of polymer based nanocomposites. Key Eng Mater 312:199–204. https://doi.org/10.4028/www.scientific.net/KEM.312.199

    Article  CAS  Google Scholar 

  34. Saber-Samandari S, Afaghi-Khatibi A (2007) Evaluation of elastic modulus of polymer matrix nanocomposites. Polym Compos 28:405–411. https://doi.org/10.1002/pc.20322

    Article  CAS  Google Scholar 

  35. Montazeri A, Naghdabadi R (2010) Investigation of the interphase effects on the mechanical behavior of carbon nanotube polymer composites by multiscale modeling. J Appl Polym Sci 117:361–367. https://doi.org/10.1002/app

    Article  CAS  Google Scholar 

  36. Heydari-meybodi M, Saber-samandari S, Sadighi M (2016) 3D multiscale modeling to predict the elastic modulus of polymer/nanoclay composites considering realistic interphase property. Compos Interfaces 6440:1–21. https://doi.org/10.1080/09276440.2016.1166742

    Article  CAS  Google Scholar 

  37. Huang X, Jiang P, Kim C, Liu F, Yin Y (2009) Influence of aspect ratio of carbon nanotubes on crystalline phases and dielectric properties of poly(vinylidene fluoride). Eur Polym J 45:377–386. https://doi.org/10.1016/j.eurpolymj.2008.11.018

    Article  CAS  Google Scholar 

  38. Baji A, Mai Y-W, Abtahi M, Wong S-C, Liu Y, Li Q (2013) Microstructure development in electrospun carbon nanotube reinforced polyvinylidene fluoride fibers and its influence on tensile strength and dielectric permittivity. Compos Sci Technol 88:1–8. https://doi.org/10.1016/j.compscitech.2013.08.021

    Article  CAS  Google Scholar 

  39. Liu S, Xue S, Zhang W, Zhai J (2014) Enhanced dielectric and energy storage density induced by surface-modified BaTiO3 nanofibers in poly(vinylidene fluoride) nanocomposites. Ceram Int 40:15633–15640. https://doi.org/10.1016/j.ceramint.2014.07.083

    Article  CAS  Google Scholar 

  40. Feng Y, Li WL, Hou YF, Yu Y, Cao WP, Zhang TD, Fei WD (2015) Enhanced dielectric properties of PVDF-HFP/BaTiO3-nanowire composites induced by interfacial polarization and wire-shape. J Mater Chem C 3:1250–1260. https://doi.org/10.1039/C4TC02183E

    Article  CAS  Google Scholar 

  41. Devi PI, Ramachandran K (2011) Dielectric studies on hybridised PVDF–ZnO nanocomposites. J Exp Nanosci 6:281–293. https://doi.org/10.1080/17458080.2010.497947

    Article  CAS  Google Scholar 

  42. Fan B, Liu Y, He D, Bai J (2016) Influences of graphene nanoplatelet aspect ratio and thermal treatment on dielectric performances of poly(methyl methacrylate) composites. High Volt 1:146–150. https://doi.org/10.1049/hve.2016.0053

    Article  Google Scholar 

  43. Pan Z, Yao L, Zhai J, Shen B, Wang H (2017) Significantly improved dielectric properties and energy density of polymer nanocomposites via small loaded of BaTiO3 nanotubes. Compos Sci Technol 147:30–38. https://doi.org/10.1016/j.compscitech.2017.05.004

    Article  CAS  Google Scholar 

  44. Sharafkhani S, Kokabi M (2020) Ultrathin-shell PVDF/CNT nanocomposite aligned hollow fibers as a sensor/actuator single element. Compos Sci Technol 200:108425–108435. https://doi.org/10.1016/j.compscitech.2020.108425

    Article  CAS  Google Scholar 

  45. Abbasizadeh S, Keshtkar AR, Mousavian MA (2013) Preparation of a novel electrospun polyvinyl alcohol/titanium oxide nanofiber adsorbent modified with mercapto groups for uranium(VI) and thorium(IV) removal from aqueous solution. Chem Eng J 220:161–171. https://doi.org/10.1016/j.cej.2013.01.029

    Article  CAS  Google Scholar 

  46. Sun H, Liu X, Yan H, Feng Z, Yu B, Ning N, Tian M, Zhang L (2019) The role of dipole structure and their interaction on the electromechanical and actuation performance of homogeneous silicone dielectric elastomers. Polymer 165:1–10. https://doi.org/10.1016/j.polymer.2019.01.017

    Article  CAS  Google Scholar 

  47. Sharafkhani S, Kokabi M (2021) High performance flexible actuator: PVDF nanofibers incorporated with axially aligned carbon nanotubes. Compos Part B Eng 222:109060–109068. https://doi.org/10.1016/j.compositesb.2021.109060

    Article  CAS  Google Scholar 

  48. Chen Q, Sun Y, Qin L, Wang Q-M (2013) Piezoelectric fiber-composite-based cantilever sensor for electric-field-induced strain measurement in soft electroactive polymer. IEEE Trans Ultrasonics, Ferroelectrics, and Frequency Control 60:2142–2153. https://doi.org/10.1109/TUFFC.2013.2805

    Article  PubMed  Google Scholar 

  49. Wu Y, Lin X, Shen X, Sun X, Liu X, Wang Z, Kim J-K (2015) Exceptional dielectric properties of chlorine-doped graphene oxide/poly (vinylidene fluoride) nanocomposites. Carbon N Y 89:102–112. https://doi.org/10.1016/j.carbon.2015.02.074

    Article  CAS  Google Scholar 

  50. Wang D, Zhou T, Zha J-W, Zhao J, Shi C-Y, Dang Z-M (2013) Functionalized graphene–BaTiO3/ferroelectric polymer nanodielectric composites with high permittivity, low dielectric loss, and low percolation threshold. J Mater Chem A 1:6162–6168. https://doi.org/10.1039/C3TA10460E

    Article  CAS  Google Scholar 

  51. Zare Y (2015) Effects of interphase on tensile strength of polymer/CNT nanocomposites by Kelly-Tyson theory. Mech Mater 85:1–6. https://doi.org/10.1016/j.mechmat.2015.02.002

    Article  Google Scholar 

  52. Zare Y, Rhee KY (2017) Dependence of Z Parameter for tensile strength of multi-layered interphase in polymer nanocomposites to material and interphase properties. Nanoscale Res Lett 12:42–49. https://doi.org/10.1186/s11671-017-1830-5

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

The authors wish to thank Tarbiat Modares University and the Iran Nanotechnology Initiative Council (INIC) for their supports.

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Correspondence to Mehrdad Kokabi.

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Sharafkhani, S., Kokabi, M. Modeling the dielectric behavior of polymer nanocomposites considering interphase properties and nanoparticle geometry. Polym. Bull. 80, 6349–6362 (2023). https://doi.org/10.1007/s00289-022-04364-2

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