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Fundamentals of the Models and Spectroscopic Techniques

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Percolation, Scaling, and Relaxation in Polymer Dielectrics

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Abstract

This chapter deals with the fundamental concepts of connectivity and the working of polymer composites along with the important theoretical models, which are used to describe the percolation and scaling behavior of polymer-conductor composites (PCC) and also the non-percolative systems.

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References

  1. Stroud D (1998) The effective medium approximations: some recent developments. Superlattices Microstruct 23:567–573

    Article  Google Scholar 

  2. Bruggeman DAG (1935) Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen. Ann Phys 416:636–664

    Article  Google Scholar 

  3. Sahimi M (2003) Heterogeneous materials I: linear transport and optical properties. Springer, New York

    Google Scholar 

  4. Torquato S (2002) Random heterogeneous materials: microstructure and macroscopic properties. Springer, New York

    Book  Google Scholar 

  5. Priou A (1992) Dielectric properties of heterogeneous materials. In: Progress in electromagnetics research. Elsevier, New York

    Google Scholar 

  6. Opper M, Saad D (2001) Advanced mean field methods: theory and practice. MIT Press, Massachussets

    Book  Google Scholar 

  7. Yamada T, Ueda T, Kitayana T (1982) Piezoelectricity of a high content lead zirconate titanate/polymer composite. J Appl Phys 53:4328–4332

    Article  CAS  Google Scholar 

  8. Tinga WR, Voss WAG, Blossy DF (1973) Generalized approach to multiphase dielectric mixture theory. J Appl Phys 44:3897–3902

    Article  Google Scholar 

  9. Brosseau C (2002) Generalized effective medium theory and dielectric relaxation in particle-filled polymeric resins. J Appl Phys 91:3197–3204

    Article  CAS  Google Scholar 

  10. Calame JP (2008) Dielectric permittivity simulation of random irregularly shaped particle composites and approximation using modified dielectric mixing laws. J Appl Phys 104:114108–114111

    Article  Google Scholar 

  11. Stauffer D, Aharony A (1992) Introduction to percolation theory. Taylor and Francis, London

    Google Scholar 

  12. Sahimi M (1994) Applications of percolation theory. Taylor and Francis, London

    Google Scholar 

  13. Panda M, Srinivas V, Thakur AK (2015) Non-universal scaling behavior of polymer-metal composites across the percolation threshold. Res Phys 5:136–141

    Google Scholar 

  14. Newnham RE, Skinner DP, Cross LE (1978) Connectivity and piezoelectric-pyroelectric composites. Mater Res Bull 13:525–536

    Article  CAS  Google Scholar 

  15. Ryu J, Priya S, Uchino K, Kim HE (2002) Magnetoelectric effect in composites of magnetostrictive and piezoelectric materials. J Electroceramics 8:107–119

    Article  CAS  Google Scholar 

  16. Maxwell JCG (1904) Colours in metal glasses and metal films. Philos Trans R Soc London Sect A 3:385–420

    Google Scholar 

  17. Landauer R (1952) The electrical resistance of binary metallic mixtures. J Appl Phys 23:779–784

    Article  CAS  Google Scholar 

  18. Bergman DJ, Imry Y (1977) Critical behavior of the complex dielectric constant near the percolation threshold of a heterogenous material. Phys Rev Lett 39:1222–1225

    Article  Google Scholar 

  19. Grannan DM, Garland JC, Tanner DB (1981) Critical behavior of the dielectric constant of a random composite near the percolation threshold. Phys Rev Lett 46:375–378

    Article  CAS  Google Scholar 

  20. Wilkinson D, Langer JS, Sen PN (1983) Enhancement of the dielectric constant near a percolation threshold. Phys Rev B 28:1081–1087

    Article  Google Scholar 

  21. Song Y, Noh TW, Lee SI, Gaines JR (1986) Experimental study of the three-dimensional ac conductivity and dielectric constant of conductor-insulator composite near the percolation threshold. Phys Rev B 33:904–908

    Article  CAS  Google Scholar 

  22. Lee SI, Song Y, Noh TW, Chen XD, Gaines JR (1986) Experimental observation of non-universal behavior of the conductivity exponent for three-dimensional continuum percolation systems. Phys Rev B 34:6719–6724

    Article  CAS  Google Scholar 

  23. Gefen Y, Aharony A, Alexander S (1983) Anomalous diffusion on percolating clusters. Phys Rev Lett 50:77–80

    Article  Google Scholar 

  24. Gefen Y, Aharony A, Mandelbrot BB, Kirkpatrick S (1981) Solvable fractal family, and its possible relation to the backbone at percolation. Phys Rev Lett 47:1771–1774

    Article  Google Scholar 

  25. Knite M, Teteris V, Aulika I, Kabelka H, Fuith A (2004) Alternating-current properties of elastomer-carbon nanocomposites. Adv Eng Mater 6:746–749

    Article  Google Scholar 

  26. Laibowitz RB, Gefen Y (1984) Dynamic scaling near the percolation threshold in thin au films. Phys Rev Lett 53:380–383

    Article  CAS  Google Scholar 

  27. Efros AL, Shklovskii BI (1976) Critical behaviour of conductivity and dielectric constant near the metal-non-metal transition threshold. Phys Status Solidi (b) 76:475–485

    Article  CAS  Google Scholar 

  28. Balberg I (2002) A comprehensive picture of the electrical phenomena in carbon black-polymer composites. Carbon 40:139–143

    Article  CAS  Google Scholar 

  29. Balberg I, Bozowski S (1982) Percolation in a composite of random stick-like conducting particles. Solid State Commun 44:551–554

    Article  CAS  Google Scholar 

  30. Halperin BI, Feng S, Sen PN (1985) Difference between lattice and continuum percolation transport exponents. Phys Rev Lett 54:2391–2394

    Article  CAS  Google Scholar 

  31. Feng S, Halperin BI, Sen PN (1987) Transport properties of continuum systems near the percolation threshold. Phys Rev B 35:197–214

    Article  CAS  Google Scholar 

  32. Rubin Z, Sunshine SA, Heaney MB, Bloom I, Balberg I (1999) Critical behavior of the electrical transport properties in a tunneling-percolation system. Phys Rev B 59:12196–12199

    Article  CAS  Google Scholar 

  33. Bug ALR, Grest GS, Cohen MH, Webman I (1987) Ac response near the percolation threshold: transfer-matrix results in two and three dimensions. Phys Rev B 36:3675–3682

    Article  CAS  Google Scholar 

  34. Balberg I (1987) Tunnelling and non-universal conductivity in composite materials. Phys Rev Lett 59:1305–1308

    Article  CAS  Google Scholar 

  35. Debye P (1945) Polar molecules. Dover, New York

    Google Scholar 

  36. Cole KS, Cole RH (1941) Dispersion and absorption in dielectrics I. Alternating current characteristics. J Chem Phys 9:341–351

    Article  CAS  Google Scholar 

  37. Davidson DW, Cole RH (1951) Dielectric relaxation in glycerol, propylene glycol, and n propanol. J Chem Phys 19:1484–1490

    Article  CAS  Google Scholar 

  38. Havriliak S, Havriliak SJ (1997) Dielectric and mechanical relaxation in materials: analysis, interpretation, and application to polymers. Hanser Publishers, Munich

    Google Scholar 

  39. Jonscher AK (1983) Dielectric relaxation in solids. Chelsea Dielectrics press, London

    Google Scholar 

  40. Macdonald JR (1987) Impedance spectroscopy: emphasizing solid materials and systems. Wiley, New York

    Google Scholar 

  41. Hsu CS, Mansfeld F (2001) Concerning the conversion of the constant phase element parameter Y0 into a capacitance. Corrosion 57:747–748

    Article  CAS  Google Scholar 

  42. Moynihan CT, Boesch LP, Laberge NL (1973) Decay function for the electric field relaxation in vitreous ionic conductors. Phys Chem Glasses 14:122–125

    CAS  Google Scholar 

  43. Williams G, Watts DC (1970) Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function. Trans Faraday Soc 66:80–85

    Article  CAS  Google Scholar 

  44. Dyre JC, Schroder TB (2000) Universality of ac conduction in disordered solids. Rev Mod Phys 72:873–892

    Article  Google Scholar 

  45. Gerhardt R (1994) Impedance and dielectric spectroscopy revisited: distinguishing localized relaxation from long-range conductivity. J Phys Chem Solids 55:1491–1506

    Article  CAS  Google Scholar 

  46. Sinclair DC, West AR (1989) Impedance and modulus spectroscopy of semiconducting BaTiO3 showing positive temperature coefficient of resistance. J Appl Phys 66:3850–3856

    Article  CAS  Google Scholar 

  47. Almond DP, Duncan GK, West AR (1983) The determination of hop** rates and carrier concentrations in ionic conductors by a new analysis of ac conductivity. Solid State Ionics 8:159–164

    Article  CAS  Google Scholar 

  48. Stephen MJ (1981) Magnetic susceptibility of percolating clusters. Phys Lett A 87:67–68

    Article  Google Scholar 

  49. Kalinin YE, Sitnikov AV, Skryabina NE, Spivak LV, Artem AA, Shadrin A (2004) Barkhausen effect and percolation threshold in metal-dielectric nanocomposites. J Mag Magn Mater 272–276:E893

    Article  Google Scholar 

  50. Guo Z, Park S, Hahn HT, Wei S, Moldovan M, Karki AB, Young DP (2007) Magnetic and electromagnetic evaluation of the magnetic nanoparticle filled polyurethane nanocomposites. J Appl Phys 101(09M):511

    Google Scholar 

  51. Shekhar S, Sajitha EP, Prasad V, Subramanyam SV (2008) High coercivity below percolation threshold in polymer nanocomposite. J Appl Phys 104:0839101–0839104

    Article  Google Scholar 

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Authors and Affiliations

  1. Multifunctional Polymer Nanocomposites Laboratory, Department of Physics, Dr. Harisingh Gour Vishwavidyalaya (A Central University), Sagar, Madhya Pradesh, India

    Maheswar Panda

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  1. Maheswar Panda
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Correspondence to Maheswar Panda .

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Panda, M. (2023). Fundamentals of the Models and Spectroscopic Techniques. In: Percolation, Scaling, and Relaxation in Polymer Dielectrics. Springer, Cham. https://doi.org/10.1007/978-3-031-27941-6_2

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