Broadband Dielectric Spectroscopy on Polymer Blends

Reference work entry

Abstract

In this chapter broadband dielectric spectroscopy (BDS) is employed to polymeric blend systems. In its modern form BDS can cover an extraordinary broad frequency range from 10−4 to 1012 Hz. Therefore, molecular and collective dipolar fluctuations, charge transport, and polarization effects at inner phase boundaries can be investigated in detail including its temperature dependence. In the first part of the chapter, the theoretical basics of dielectric spectroscopy are briefly introduced covering both static and dynamic aspects. This section is followed by short description of the various experimental techniques to cover this broad frequency range. To provide the knowledge to understand the dielectric behavior of polymeric blend systems, the dielectric features of amorphous homopolymers are discussed in some detail. This concerns an introduction of the most important relaxation processes observed for these polymers (localized fluctuations, segmental dynamics related to the dynamic glass transition, chain relaxation), a brief introduction to the conductivity of disordered systems as well as polarization effects at phase boundaries. Theoretical models for each process are shortly discussed. In the last paragraph the dielectric behavior of polymer blends is reviewed where special attention is paid to binary systems for the sake of simplicity. In detail the dielectric behavior of binary miscible blends is described. The two most important experimental facts like the broadening of the dielectric relaxation spectra and the dynamic heterogeneity of the segmental dynamics are addressed in depth. Appropriate theoretical approaches like the temperature-driven concentration fluctuation model and the self-concentration idea are introduced.

Keywords

Dipole Moment Polymer Blend Relaxation Function Thermally Stimulate Current Complex Dielectric Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

List of Important Symbols and Abbreviations

aT

Shift factor

C

Concentration

C1, C2

Parameters of the WLF equation

D

Dielectric displacement

E

Electric field strength

EA, ΔE

Activation energy, barrier heights

f

Frequency

fi

Relaxation rate at maximal loss, i = β, α, n

f∞i

Preexponential factor, i = β, α, n

Φi

Volume fraction

ϕi

Weight fraction

g, gintra

Dipolar correlation coefficients

ΔGM

Free energy of mixing

Γ*

Reflection coefficient

I, J

Current, Current density

kB

Boltzmann constant, kB = 1.380662 10−23 J K−1; kB = R/NA

M, MW

Molecular weight, weight average

NA

Avogadro number (NA = 6.022 1023 mol−1)

R

Gas constant R = 8.314 kJ mol−1

SC

Configurational entropy

ΔSM

Mixing entropy

σ*, σ′, σ′

Complex conductivity, real and imaginary part

T

Temperature

T0

Vogel temperature, ideal glass transition temperature

Tg

Glass transition temperature

tan δ

Dielectric loss tangent

β, γ

Shape parameter of the HN function

ε0

Permittivity of vacuum (ε0 = 8.854 10−12 As V−1 m−1)

ε*, ε′, ε′

Complex dielectric function, real and imaginary part

Δεi

Dielectric relaxation strength, i = β, α, n,

ζ

Monomeric friction coefficient

ξ

Correlation length

κ

Flory/Huggins interaction parameter

μ

Dipole moment

ω

Angular frequency (ω = 2*π*f)

τ

Relaxation time

τHN

Relaxation time of the HN function

τe

Time constant for conduction

PEO

Poly(ethylene oxide)

PI

Cis-1,4-Polyisorene

PMMA

Poly(methyl methacrylate)

PPG

Poly(propylene glycol)

PS

Polystyrene

PVAC

Poly(vinyl acetate)

PVME

Poly(vinyl methylether)

PoClS

Poly(o-chlorostyrene)

PVC

Poly(vinyl chloride)

U

Voltage, different meanings

ZS*(ω); ZR*(ω)

Sample impedance; Reference impedance

<…>

Correlation function; Averaged quantities

References

  1. A. Abou Elfadl, R. Kahlau, A. Herrmann, V.N. Novikov, E.A. Rössler, Macromolecules 43, 3340 (2010)Google Scholar
  2. K. Adachi, T. Kotaka, Prog. Polym. Sci. 18, 585 (1993)Google Scholar
  3. K. Adachi, T. Wada, T. Kawamoto, T. Kotaka, Macromolecules 28, 3588 (1995)Google Scholar
  4. G. Adam, J.H. Gibbs, J. Chem. Phys. 43, 139 (1965)Google Scholar
  5. Agilent Technologies, Agilent PN 4291–1: New technologies for wide impedance range measurements to 1.8 GHz (2000)Google Scholar
  6. A. Alegria, D. Gomez, J. Colmenero, Macromolecules 35, 2030 (2002)Google Scholar
  7. A. Alegría, O. Mitxelena, J. Colmenero, Macromolecules 39, 2691 (2006)Google Scholar
  8. P.S. Alexandrovich, F.E. Karasz, W.J. MacKnight, J. Macromol. Sci. Phys. B. 7, 501 (1980)Google Scholar
  9. F. Alvarez, A. Alegria, J. Colmenero, Macromolecules 30, 597 (1997)Google Scholar
  10. P.W. Anderson, Science 267, 1615 (1995)Google Scholar
  11. S.R. Angeli, J. Runt, J. Contemp. Top. Polym. Sci. 6, 289 (1989)Google Scholar
  12. S.R. Angeli, J. Runt, ACS Polym. Preprints 31, 286 (1990)Google Scholar
  13. C.A. Angell, Science 267, 1924 (1995)Google Scholar
  14. A. Arbe, A. Alegria, J. Colmenero, S. Hoffmann, L. Willner, D. Richter, Macromolecules 32, 7572 (1999)Google Scholar
  15. S. Arrese-Igor, O. Mitxelena, A. Arbe, A. Alegría, J. Colmenero, B. Frick, Phys. Rev. E. 78, 021801 (2008)Google Scholar
  16. G. Banhegyi, Colloid Polym. Sci. 264, 1030 (1986)Google Scholar
  17. G. Banhegyi, Polym. Plast. Technol. Eng. 30, 183 (1991)Google Scholar
  18. J.L. Barton, Verres Refract 20, 328 (1966)Google Scholar
  19. M. Beiner, H. Huth, Nat. Mater. 2, 595 (2003)Google Scholar
  20. M. Beiner, G. Fytas, G. Meier, S.K. Kumar, Phys. Rev. Lett. 81, 594 (1998a)Google Scholar
  21. M. Beiner, S. Kahle, E. Hempel, K. Schröter, E.J. Donth, Macromolecules 31, 2460 (1998b)Google Scholar
  22. L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, D. El Masri, D. L’Hôte, F. Ladieu, M. Pierno, Science 310, 1797 (2005)Google Scholar
  23. K. Binder, Adv. Polym. Sci. 112, 181 (1994)Google Scholar
  24. H. Block, Adv. Polym. Sci. 33, 94 (1979)Google Scholar
  25. A.R. Blythe, Electrical Properties of Polymers (Cambridge University Press, Cambridge, 1979)Google Scholar
  26. A. Boersema, J. van Turnhout, M. Wübbenhorst, Macromolecules 31, 7453 (1998)Google Scholar
  27. R. Böhmer, M. Maglione, P. Lunkenheimer, A. Loidl, J. Appl. Phys. 65, 901 (1989)Google Scholar
  28. C.J.F. Böttcher, in Theory of Electric Polarization. Dielectrics in Static Fields, vol. I (Elsevier, Amsterdam/Oxford/New York, 1973)Google Scholar
  29. M.J. Brekner, H.A. Schneider, H.J. Cantow, Polymer 29, 78 (1988)Google Scholar
  30. J.F. Bristow, D.S. Kalika, Polymer 38, 287 (1997)Google Scholar
  31. M. Brodeck, F. Alvarez, A. Moreno, J. Colmenero, D. Richter, Macromolecules 43, 3036 (2010)Google Scholar
  32. W. Brostow, R. Chiu, I.M. Kalogeras, A. Vassilikou-Dova, Mater. Lett. 62, 3152 (2008)Google Scholar
  33. C. Bucci, R. Fieschi, G. Guidgi, Phys. Rev. 148, 816 (1966)Google Scholar
  34. D.E. Buerger, R.H. Boyd, Macromolecules 22, 2649 (1989)Google Scholar
  35. D. Cangialosi, G.A. Schwartz, A. Alegria, J. Colmenero, J. Chem. Phys. 123, 144908 (2005)Google Scholar
  36. D. Cangialosi, A. Alegria, J. Colmenero, Macromolecules 39, 7149 (2006)Google Scholar
  37. D. Cangialosi, A. Alegria, J. Colmenero, Phys. Rev. E. 76, 011514 (2007)Google Scholar
  38. P. Cebe, P. Huo, Thermochim. Acta. 238, 229 (1994)Google Scholar
  39. I. Cendoya, A. Alegria, J.M. Alberti, J. Colmenero, H. Grimm, D. Richter, B. Frick, Macromolecules 32, 4065 (1999)Google Scholar
  40. F.V. Chávez, K. Saalwächter, Phys. Rev. Lett. 104, 198305 (2010)Google Scholar
  41. G.-C. Chung, J.A. Kornfield, S.D. Smith, Macromolecules 27, 5729 (1994a)Google Scholar
  42. G.-C. Chung, J.A. Kornfield, S.D. Smith, Macromolecules 27, 964 (1994b)Google Scholar
  43. R. Clausius, Die mechanische Wärmelehre, vol. II (Vieweg und Sohn, Braunschweig, 1879)Google Scholar
  44. J. Coburn, R.H. Boyd, Macromolecules 19, 2238 (1986)Google Scholar
  45. K.S. Cole, R.H. Cole, J. Chem. Phys. 9, 341 (1941)Google Scholar
  46. R.E. Collin, Foundations for Microwave Engineering, 2nd edn. (McGraw-Hill, New York, 1966)Google Scholar
  47. J. Colmenero, Macromolecules 46, 5363 (2013)Google Scholar
  48. J. Colmenero, A. Arbe, Soft Matter 3, 1474 (2007)Google Scholar
  49. J. Colmenero, A. Arbe, A. Alegria, Phys. A. 201, 447 (1993)Google Scholar
  50. S. Corezzi, E. Campani, A.P. Rolla, S. Capaccioli, D. Fioretto, J. Chem. 111, 9343 (1999)Google Scholar
  51. C. Dalle-Ferrier, C. Thibierge, C. Alba-Simionesco, L. Berthier, G. Biroli, J.-P. Bouchaud, F. Ladieu, D. L’Hôte, G. Tarjus, Phys. Rev. E. 76, 041510 (2007)Google Scholar
  52. D.W. Davidson, R.H. Cole, J. Chem. Phys. 18, 1417 (1950)Google Scholar
  53. D.W. Davidson, R.H. Cole, J. Chem. Phys. 19, 1484 (1951)Google Scholar
  54. P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca New York, 1979)Google Scholar
  55. P. Debye, Polar Molecules, Chemical Catalog, reprinted by (Dover, New York, 1929)Google Scholar
  56. P. Debye, F. Bueche, J. Chem. Phys. 7, 589 (1951)Google Scholar
  57. R. Diaz-Calleja, Macromolecules 33, 8924 (2000)Google Scholar
  58. M.C.S. Dionisio, J.J.M. Ramos, A.C. Fernandes, J. Appl. Polym. Sci. 60, 903 (1996)Google Scholar
  59. M. Dionissio, A.C. Fernandes, J.F. Mano, N. Correia, R.C. Sousa, Macromolecules 33, 1002 (2000)Google Scholar
  60. M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)Google Scholar
  61. E.J. Donth, J. Non-Cryst. Solids. 53, 325 (1982)Google Scholar
  62. E.J. Donth, Relaxation and Thermodynamics in Polymers, Glass Transition (Akademie Verlag, Berlin, 1992)Google Scholar
  63. E.J. Donth, The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials (Springer, Berlin, 2001)Google Scholar
  64. E.J. Donth, E. Hempel, C. Schick, J. Phys. Cond. Mat. 12, L281 (2001a)Google Scholar
  65. E.J. Donth, H. Huth, M. Beiner, J. Phys. Cond. Mat. 13, L451 (2001b)Google Scholar
  66. J.C. Dyre, J. Appl. Phys. 64, 2456 (1988)Google Scholar
  67. J.C. Dyre, T.B. Schroder, Rev. Mod. Phys. 72, 873 (2000)Google Scholar
  68. H. Eklind, F.H.J. Maurer, P.A.M. Steeman, Polymer 38, 1047 (1997)Google Scholar
  69. J.D. Ferry, Viscoelastic Properties of Polymers, 3rd edn. (Wiley, New York, 1980)Google Scholar
  70. E.W. Fischer, G.P. Hellmann, H.W. Spiess, F.J. Horth, U. Ecarius, B. Wehrle, Macromol. Chem. Macromol. Chem. Phys. S12, 189 (1985)Google Scholar
  71. J.P. Flory, Statistical Mechanics of Chain Molecules (Hanser Verlag, München, 1989)Google Scholar
  72. G. Floudas, Effect of pressure on the dielectric spectra of polymeric systems (Chapter 8), in Broadband Dielectric Spectroscopy, ed. by F. Kremer, A. Schönhals (Springer, Berlin, 2003)Google Scholar
  73. G. Floudas, M. Paluch, A. Grzybowski, K.L. Ngai, Pressure Effects on Polymer Blends in Molecular Dynamics of Glass-forming Systems (Springer, Berlin, 2011)Google Scholar
  74. H. Fröhlich, Theory of Dielectric (Oxford University Press, London, 1958)Google Scholar
  75. G.S. Fulcher, J. Am. Ceram. Soc. 8, 339 (1925)Google Scholar
  76. R.M. Fuoss, J.G. Kirkwood, J. Am. Chem. Soc. 63, 385 (1941)Google Scholar
  77. G. Schaumburg Dielectric Newsletter of Novocontrol, issue March (1994)Google Scholar
  78. G. Schaumburg Dielectric Newsletter of Novocontrol, issue May (1999)Google Scholar
  79. C. Gainaru, R. Böhmer, Macromolecules 42, 7616 (2009)Google Scholar
  80. P. Gallo, Phys. Chem. Chem. Phys. 2, 1607 (2000)Google Scholar
  81. F. Garwe, A. Schönhals, M. Beiner, K. Schröter, E. Donth, Macromolecules 29, 247 (1996)Google Scholar
  82. J.L. Gomes Ribelles, R.J. Diaz Calleja, J. Polym. Sci. Polym. Polym. Phys. Ed. 23, 1297 (1985)Google Scholar
  83. W. Götze, Complex Dynamics of Glass-forming Liquids – A Mode-Coupling Theory (Oxford University Press, Oxford, 2009)Google Scholar
  84. C. Hall, E. Helfand, J. Chem. Phys. 77, 3275 (1982)Google Scholar
  85. L. Hardy, I. Stevenson, G. Boiteux, G. Seytre, A. Schönhals, Polymer 42, 5679 (2001)Google Scholar
  86. S.J. Havriliak, Dielectric and Mechanical Relaxations in Materials (Hanser Publishers, Munich, 1997)Google Scholar
  87. S. Havriliak, S. Negami, J. Polym. Sci. Part C 16, 99 (1966)Google Scholar
  88. S. Havriliak, S. Negami, Polymer 8, 161 (1967)Google Scholar
  89. T. Hayakawa, K. Adachi, Macromolecules 33, 6834 (2000a)Google Scholar
  90. T. Hayakawa, K. Adachi, Macromolecules 33, 6840 (2000b)Google Scholar
  91. D. Hayward, R.A. Pethrick, T. Siriwittayakorn, Macromolecules 25, 1480 (1992)Google Scholar
  92. Y.Y. He, T.R. Lutz, M.D. Ediger, J. Chem. Phys. 119, 9956 (2003)Google Scholar
  93. P. Hedvig, Dielectric Spectroscopy of Polymers (Adam Hilger, Bristol, 1977)Google Scholar
  94. J. Heijboer, in Moelecular Basis of Transition and Relaxation, ed. by D.J. Meier (Gordon and Breach Science Publishers, New York, 1978)Google Scholar
  95. E. Hempel, M. Beiner, T. Renner, E. Donth, Acta. Polym. 47, 525 (1996)Google Scholar
  96. E. Hempel, G. Hempel, A. Hensel, C. Schick, E.J. Donth, J. Phys. Chem. B 104, 2460 (2000)Google Scholar
  97. D. Herrera, J.C. Zamora, A. Bello, M. Grimau, E. Laredo, A.J. Müller, T.P. Lodge, Macromolecules 38, 5109 (2005)Google Scholar
  98. Hewlett Packard Product Note 8510-3 (1985) Measuring the dielectric constant of solids with the HP8510 network analyzerGoogle Scholar
  99. Y. Hirose, O. Urakawa, K. Adachi, Macromolecules 36, 3699 (2003)Google Scholar
  100. S. Hoffman, L. Willner, D. Richter, A. Arbe, J. Colmenero, B. Farago, Phys. Rev. Lett. 85, 772 (2000)Google Scholar
  101. S. Hoffman, D. Richter, A. Arbe, J. Colmenero, B. Farago, Appl. Phys. A. 74, S442 (2002)Google Scholar
  102. A. Hofmann, F. Kremer, E.W. Fischer, Phys. A. 201, 106 (1993)Google Scholar
  103. B.S. Hsiao, B.B. Sauer, J. Polym. Sci. Polym. Phys. Ed. 31, 901 (1993)Google Scholar
  104. S.D. Hudson, D.D. Davis, A.J. Lovinger, Macromolecules 25, 1759 (1992)Google Scholar
  105. P. Huo, P. Cebe, J. Polym. Sci. Phys. Ed. 30, 239 (1992a)Google Scholar
  106. P. Huo, P. Cebe, Macromolecules 25, 902 (1992b)Google Scholar
  107. P. Huo, P. Cebe, Polymer 34, 696 (1993)Google Scholar
  108. G.Q. Jiang, W.H. Wong, E.Y. Raskovida, W.G. Clark, W.A. Hines, J. Sanny, Rev. Sci. Instrum. 64, 1614 (1993)Google Scholar
  109. X. Jin, S. Zhang, J. Runt, Macromolecules 37, 8110 (2004)Google Scholar
  110. G.P. Johari, J. Chem. Phys. 28, 1766 (1973)Google Scholar
  111. G.P. Johari, M.J. Goldstein, J. Chem. Phys. 53, 2372 (1970)Google Scholar
  112. S. Kahle, J. Korus, E. Hempel, R. Unger, S. Höring, K. Schröter, E.J. Donth, Macromolecules 30, 7214 (1997)Google Scholar
  113. D.S. Kalika, R.K. Krishnaswamy, Macromolecules 26, 4252 (1993)Google Scholar
  114. S. Kamath, R.H. Colby, S.K. Kumar, K. Karatasos, G. Floudas, G. Fytas, J.E.L. Roovers, J. Chem. Phys. 111, 6121 (1999)Google Scholar
  115. S. Kamath, R.H. Colby, S.K. Kumar, Macromolecules 36, 8567 (2003a)Google Scholar
  116. S. Kamath, R.H. Colby, S.K. Kumar, Phys. Rev. E. 67, 010801 (R) (2003b)Google Scholar
  117. R. Kant, S.K. Kumar, R.H. Colby, Macromolecules 36, 10087 (2003)Google Scholar
  118. F.E. Karasz (ed.), Dielectric Properties of Polymers (Plenum, New York, 1972)Google Scholar
  119. K. Karatasos, G. Valaachos, D. Vlassopoulos, G. Fytas, G. Meier, A. Du Chesne, J. Chem. Phys. 108, 5997 (1998)Google Scholar
  120. G. Katana, A. Zetsche, F. Kremer, E.W. Fischer, ACS Polym. Preprints 33, 122 (1992)Google Scholar
  121. G. Katana, F. Kremer, E.W. Fischer, R. Plaetscke, Macromolecules 26, 3075 (1993)Google Scholar
  122. G. Katana, E.W. Fischer, T. Hack, V. Abetz, F. Kremer, Macromolecules 28, 2714 (1995)Google Scholar
  123. J.G. Kirkwood, J. Chem. Phys. 58, 911 (1939)Google Scholar
  124. J.G. Kirkwood, Ann. NY Acad. Sci. 40, 315 (1940)Google Scholar
  125. J.G. Kirkwood, Trans. Faraday Soc. 42A, 7 (1946)Google Scholar
  126. S. Koizumi, J. Polym. Sci. Polym. Phys. Ed. 42, 3148 (2004)Google Scholar
  127. F. Kremer, A. Schönhals, Broadband Dielectric Spectroscopy (Springer, Berlin, 2003)Google Scholar
  128. F. Kremer, A. Schönhals, Broadband dielectric measurement techniques (Chapter 2), in Broadband Dielectric Spectroscopy, ed. by F. Kremer, A. Schönhals (Springer, Berlin, 2003b), pp. 35–58Google Scholar
  129. F. Kremer, A. Hofmann, E.W. Fischer, ACS-Polym. Preprints 33, 96 (1992)Google Scholar
  130. E. Krygier, G. Lin, J. Mendes, G. Mukandela, D. Azar, A.A. Jones, J.A. Pathak, R.H. Colby, S. Kumar, G. Floudas, R. Krishnamoorti, R. Faust, Macromolecules 38, 7721 (2005)Google Scholar
  131. U. Kubon, R. Schilling, J.H. Wendorf, Colloid Polym. Sci. 266, 123 (1988)Google Scholar
  132. A.S. Kulik, H.W. Beckham, K. Schmidt-Rohr, D. Radloff, U. Pawelzik, C. Boeffel, H.W. Spiess, Macromolecules 27, 4746 (1994)Google Scholar
  133. S.K. Kumar, Macromolecules 33, 5285 (2000)Google Scholar
  134. S.K. Kumar, R.H. Colby, S.H. Anastasiadis, G. Fytas, J. Chem. Phys. 105, 3777 (1996)Google Scholar
  135. L.K.H. van Beek Dielectric behavior of heterogeneous systems, in Progress in Dielectrics, vol. 7, ed. by J.B. Birks (Heywood, 1967), pp. 69–114Google Scholar
  136. L.D. Landau, E.M. Lifschitz, Statistical Physics. Textbook of Theoretical Physics, vol. V (Akademie-Verlag, Berlin, 1979)Google Scholar
  137. C. Larvergne, C. Lacabanne, IEEE Elec. Insul. Mag. 9, 5 (1993)Google Scholar
  138. E. Leroy, A. Alegria, J. Colmenero, Macromolecules 35, 5587 (2002)Google Scholar
  139. E. Leroy, A. Alegria, J. Colmenero, Macromolecules 36, 7280 (2003)Google Scholar
  140. H.S. Li, W. Kim, Polymer 38, 2657 (1997)Google Scholar
  141. A.E. Likhtman, T.C.B. McLeish, Macromolecules 35, 6332 (2002)Google Scholar
  142. J.E.M. Lipson, Macrom. Theory Simul. 7, 263 (1998)Google Scholar
  143. J.E.M. Lipson, M. Tambasco, K.A. Willets, J.S. Higgins, Macromolecules 36, 2977 (2003)Google Scholar
  144. C.-Y. Liu, R. Keunings, C.D. Bailly, Phys. Rev. Lett. 97, 246001 (2006)Google Scholar
  145. T.P. Lodge, T.C.B. McLeish, Macromolecules 33, 5278 (2000)Google Scholar
  146. T.P. Lodge, E.R. Wood, J.C. Haley, J. Polym. Sci. Polym. Phys. Ed. 44, 756 (2006)Google Scholar
  147. H.A. Lorentz, Ann. Phys. 9, 641 (1879)Google Scholar
  148. C. Lorthioir, A. Alegria, J. Colmenero, Phys. Rev. E. 86, 031805 (2003)Google Scholar
  149. X. Lu, R.A. Weiss, Macromolecules 25, 3242 (1992)Google Scholar
  150. T.R. Lutz, Y.Y. He, M.D. Ediger, Macromolecules 38, 9826 (2005)Google Scholar
  151. T. Malik, R.E. Prud’homme, Polym. Eng. Sci. 24, 144 (1984)Google Scholar
  152. J. Maranas, Curr. Opin. Colloid Interface Sci. 12, 29 (2007)Google Scholar
  153. P.F. Massotti, Bibl. Univ. Modena 6, 193 (1847)Google Scholar
  154. M. Matsuo, Y. Ishida, K. Yamafuji, M. Takayanagi, F. Irie, Kolloid-Z und Z für Polymere 201, 7 (1965)Google Scholar
  155. J.C. Maxwell, Phil. Trans. 155, 459 (1865)Google Scholar
  156. J.C. Maxwell, Phil. Trans. 158, 643 (1868)Google Scholar
  157. N.G. McCrum, B.E. Read, G. Williams, Anelastic and Dielectric Effects in Polymeric Solids (Wiley, New York, 1967) (reprinted by Dover Publications 1991)Google Scholar
  158. D. Migahed, T. Fahmy, Polymer 35, 1688 (1994)Google Scholar
  159. S.T. Milner, T.C.B. McLeish, Phys. Rev. Lett. 81, 725 (1998)Google Scholar
  160. N. Miura, W. MacKnight, S. Matsuoka, F.E. Karasz, Polymer 40, 6129 (2001)Google Scholar
  161. Y. Miwa, K. Usami, M. Yamamoto, T. Sakaguchi, M. Sakai, S. Shimada, Macromolecules 38, 2355 (2005)Google Scholar
  162. E. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965)Google Scholar
  163. K. Mpoukouvalas, G. Floudas, Macromolecules 41, 1552 (2008)Google Scholar
  164. K. Mpoukouvalas, G. Floudas, S. Zhang, J. Runt, Macromolecules 38, 552 (2005)Google Scholar
  165. T. Nakajima, Annual Report, Conference on Electrical Insulation and Dielectric Phenomena (National Academy of Sciences, Washington, DC, 1971)Google Scholar
  166. H. Namikawa, J. Non-Cryst. Solids 18, 173 (1975)Google Scholar
  167. K.L. Ngai, C.M. Roland, Macromolecules 37, 2817 (2004)Google Scholar
  168. L. Onsager, J. Am. Chem. Soc. 58, 1486 (1938)Google Scholar
  169. J.A. Pathak, R.H. Colby, G. Floudas, R. Jerome, Macromolecules 32, 2353 (1999)Google Scholar
  170. K. Pathmanathan, G.P. Johari, J.P. Faivre, L. Monnerie, J. Polym. Sci. 24, 1587 (1986)Google Scholar
  171. R. Pelster, IEEE Trans. Microw. Theory Tech. 43, 1494 (1995)Google Scholar
  172. B.T. Poh, K. Adachi, T. Kotaka, Macromolecules 29, 6317 (1996)Google Scholar
  173. J. Pugh, T. Ryan, IEE Conf. Dielectric Mater. Meas. Appl. 177, 404 (1979)Google Scholar
  174. M. Rabeony, D.J. Lohse, R.T. Garnert, S.J. Ham, W.W. Graessley, K.B. Migler, Macromolecules 31, 6511 (1998)Google Scholar
  175. G.S. Rellick, J. Runt, J. Polym. Sci. Polym. Phys. Ed. 24, 279 (1986a)Google Scholar
  176. G.S. Rellick, J. Runt, J. Polym. Sci. Polym. Phys. Ed. 24, 313 (1986b)Google Scholar
  177. G.S. Rellick, J. Runt, J. Polym. Sci. Polym. Phys. Ed. 26, 1425 (1988)Google Scholar
  178. E. Riande, R. Diaz-Calleja, Electrical Properties of Polymers (Marcel Dekker, New York, 2004)Google Scholar
  179. E. Riande, E. Saiz, Dipole Moments and Birefringence of Polymers (Prentice Hall, Englewood Cliffs, 1992)Google Scholar
  180. C.M. Roland, K. Ngai, Macromolecules 24, 2261 (1991)Google Scholar
  181. C.M. Roland, K. Ngai, J. Rheol. Acta. 36, 1691 (1992a)Google Scholar
  182. C.M. Roland, K. Ngai, Macromolecules 25, 363 (1992b)Google Scholar
  183. C.M. Roland, S. Hensel-Bielowka, M. Paluch, R. Casalini, Rep. Prog. Phys. 68, 1405 (2005)Google Scholar
  184. C.M. Roland, K.J. MacGrath, R. Cassalini, Macromolecules 39, 3581 (2006)Google Scholar
  185. P.E. Rouse, J. Chem. Phys. 21, 1272 (1953)Google Scholar
  186. W. Ruland, Prog. Colloid Polym. Sci. 57, 192 (1957)Google Scholar
  187. J.P. Runt, Dielectric studies of polymer blends, in Dielectric Spectroscopy of Polymeric Materials, ed. by J.P. Runt, J.J. Fitzgerald (ACS-books, Washington, DC, 1997), pp. 283–302Google Scholar
  188. J.P. Runt, J.J. Fitzgerald (eds.), Dielectric Spectroscopy of Polymeric Materials (American Chemical Society, Washington, DC, 1997)Google Scholar
  189. J. Runt, C.A. Barron, Z.-F. Zhang, S.K. Kumar, Macromolecules 24, 3466 (1991)Google Scholar
  190. T. Sakaguchi, N. Taniguchi, O. Urakawa, K. Adachi, Macromolecules 38, 422 (2005)Google Scholar
  191. S. Salaniwal, R. Kant, R.H. Colby, S.K. Kumar, Macromolecules 35, 9211 (2002)Google Scholar
  192. H. Sasabe, S. Saito, J. Polym. Sci. Part A-2 6, 1401 (1968)Google Scholar
  193. B.B. Sauer, B.S. Hsiao, J. Polym. Sci. Poly. Phys. Ed. 31, 917 (1993)Google Scholar
  194. B.B. Sauer, P. Avakian, G.M. Cohen, Polymer 33, 2666 (1992)Google Scholar
  195. B.B. Sauer, P. Avakian, E.A. Flexman, M. Keating, B.S. Hsiao, R.K. Verma, J. Polym. Sci. Polym. Phys. Ed. 35, 2121 (1997)Google Scholar
  196. B. Schartel, J.H. Wendorff, Polymer 36, 899 (1995)Google Scholar
  197. C. Schick, Calorimetry (Chapter 2.31), in Polymer Science: A Comprehensive Reference, vol. 2, ed. by K. Matyjaszewski, M. Möller (Elsevier, Amsterdam, 2012), pp. 793–823Google Scholar
  198. E. Schlosser, A. Schönhals, Colloid Polym. Sci. 267, 963 (1989)Google Scholar
  199. K. Schneider, A. Schönhals, E.J. Donth, Acta Polym. 32, 471 (1981)Google Scholar
  200. A. Schönhals, Macromolecules 26, 1309 (1993)Google Scholar
  201. A. Schönhals, Europhys. Lett. 56, 815 (2001)Google Scholar
  202. A. Schönhals, Molecular dynamics in Polymeric model systems (Chapter 7), in Broadband Dielectric Spectroscopy, ed. by F. Kremer, A. Schönhals (Springer, Berlin, 2003)Google Scholar
  203. A. Schönhals, F. Kremer, J. Non-cryst. Solids 172–174, 336 (1994)Google Scholar
  204. A. Schönhals, F. Kremer, Analysis of dielectric spectra (Chapter 3), in Broadband Dielectric Spectroscopy, ed. by F. Kremer, A. Schönhals (Springer, Berlin, 2003a), pp. 59–98Google Scholar
  205. A. Schönhals, F. Kremer, Theory of dielectric relaxation (Chapter 1), in Broadband Dielectric Spectroscopy, ed. by F. Kremer, A. Schönhals (Springer, Berlin, 2003c)Google Scholar
  206. A. Schönhals, E. Schlosser, Colloid Polym. Sci. 267, 125 (1989)Google Scholar
  207. A. Schönhals, H. Goering, C. Schick, B. Frick, R. Zorn, J. Non-cryst. Solids 351, 2668 (2005)Google Scholar
  208. A. Schönhals, F. Kremer, Amorphous polymers (Chapter 1.08), in Polymer Science: A Comprehensive Reference, vol. 1, ed. by K. Matyjaszewski, M. Möller (Elsevier, Amsterdam, 2012), pp. 201–226Google Scholar
  209. S. Schrader, A. Schönhals, Prog. Colloid Polym. Sci. 80, 93 (1989)Google Scholar
  210. K. Schröter, R. Unger, S. Reissig, F. Garwe, S. Kahle, M. Beiner, E. Donth, Macromolecules 31, 8966 (1998)Google Scholar
  211. G.A. Schwartz, A. Alegria, J. Colmenero, J. Chem. Phys. 127, 154907 (2007a)Google Scholar
  212. G.A. Schwartz, J. Colmenero, A. Alegria, Macromolecules 40, 3246 (2007b)Google Scholar
  213. K. Se, O. Takayanagi, K. Adachi, Macromolecules 30, 4877 (1997)Google Scholar
  214. A. Serghei, M. Tress, J.R. Sangoro, F. Kremer, Phys. Rev. B 80, 184301 (2009)Google Scholar
  215. T.F. Shatzki, J. Polym. Sci. 57, 496 (1962)Google Scholar
  216. S. Shenogin, R. Kant, R.H. Colby, S.K. Kumar, Macromolecules 40, 5767 (2007)Google Scholar
  217. R.W. Sillars, J. Inst. Elect. Eng. 80, 378 (1937)Google Scholar
  218. G.P. Simon, A. Schönhals, Dielectric relaxation and thermal stimulated currents, in Polymer Characterization Techniques and Their Application to Blends, ed. by G.P. Simon (Oxford University Press, Oxford/New York, 2003), pp. 96–131Google Scholar
  219. J. Skolnik, R. Yaris, Macromolecules 15, 1041 (1982)Google Scholar
  220. L.H. Sperling, Introduction to Physical Polymer Science (Wiley, New York, 1986)Google Scholar
  221. P.A.M. Steeman, F.H.J. Maurer, Colloid Polym. Sci. 268, 315 (1990)Google Scholar
  222. P.A.M. Steeman, F.H.J. Maurer, Colloid Polym. Sci. 270, 1069 (1992)Google Scholar
  223. P.A.M. Steeman, J. van Turnhout, Dielectric properties of inhomogeneous media (Chapter 13), in Broadband Dielectric Spectroscopy, ed. by F. Kremer, A. Schönhals (Springer, Berlin, 2003), pp. 495–522Google Scholar
  224. P.A.M. Steeman, F.H.J. Maurer, J. van Turnhout, Polym. Eng. Sci. 34, 697 (1994)Google Scholar
  225. W.H. Stockmayer, Pure Appl. Chem. 15, 539 (1967)Google Scholar
  226. W.H. Stockmayer, J.J. Burke, Macromolecules 2, 647 (1969)Google Scholar
  227. G.R. Strobl, The Physics of Polymers (Springer, Heidelberg, 1996)Google Scholar
  228. J. Swenson, R. Bergman, S. Longeville, J. Chem. Phys. 115, 1299 (2001)Google Scholar
  229. J.W. Sy, J. Mijovic, Macromolecules 33, 933 (2000)Google Scholar
  230. M. Tambasco, J.E.M. Lipson, J.S. Higgins, Macromolecules 39, 4860 (2006)Google Scholar
  231. G. Tammann, W. Hesse, Z. Anorg. Allg. Chem. 156, 245 (1926)Google Scholar
  232. T. Tetsutani, M. Kakizaki, T. Hideshima, Polym. J. 14, 305 (1982a)Google Scholar
  233. T. Tetsutani, M. Kakizaki, T. Hideshima, Polym. J. 14, 471 (1982b)Google Scholar
  234. G. Teyssedre, S. Mezghani, A. Bernes, C. Lacabanne, in Thermally Stimulated Currents of Polymers in Dielectric Spectroscopy of Polymeric Materials, ed. by J. Runt, J.J. Fitzgerald (ACS, Washington, DC, 1997), pp. 227–258Google Scholar
  235. M. Topic, Z. Veksli, Polymer 34, 2118 (1993)Google Scholar
  236. M. Topic, A. Mogus-Milankovic, Z. Katovic, Polymer 28, 33 (1987)Google Scholar
  237. G. Turky, D. Wolff, A. Schönhals, Macromol. Chem. Phys. 22, 2420 (2012)Google Scholar
  238. M. Tyagi, A. Arbe, J. Colmenero, B. Frick, J.R. Stewart, Macromolecules 39, 3007 (2006)Google Scholar
  239. M. Tyagi, A. Arbe, A. Alegria, J. Colmenero, B. Frick, Macromolecules 40, 4568 (2007)Google Scholar
  240. O. Urakawa, K. Adachi, T. Kotaka, Macromolecules 26, 2036 (1993a)Google Scholar
  241. O. Urakawa, K. Adachi, T. Kotaka, Macromolecules 26, 2042 (1993b)Google Scholar
  242. O. Urakawa, Y. Fuse, H. Hori, Q. Tran-Cong, O. Yano, Polymer 42, 765 (2001)Google Scholar
  243. O. Urakawa, T. Sugihara, K. Adachi, Polym. Appl. (Japan) 51, 10 (2002)Google Scholar
  244. O. Urakawa, T. Ujii, K. Adachi, J. Non-cryst. Solids 352, 5042 (2006)Google Scholar
  245. B. Valeur, J.P. Jarry, F. Geny, J. Monnerie, J. Polym. Sci. Polym, Polym. Phys. Ed. 13, 667 (1975a)Google Scholar
  246. B. Valeur, J. Monnerie, J.P. Jarry, J. Polym. Sci. Polym. Phys. Ed. 13, 675 (1975b)Google Scholar
  247. J. van Turnhout, Thermally Stimulated Discharge of Polymer Electrets (Elevier, Amsterdam, 1975)Google Scholar
  248. J. Vanderschueren, M. Landang, J.M. Heuschen, Macromolecules 13, 973 (1980)Google Scholar
  249. H. Vogel, Phys. Z. 22, 645 (1921)Google Scholar
  250. M.V. Volkenstein, Configurational Statistics of Polymeric Chains (Wiley Interscience, New York, 1963)Google Scholar
  251. R.W. Wagner, Arch. Elektrotech. 2, 371 (1914)Google Scholar
  252. H. Watanabe, M. Yamazaki, H. Yoshida, K. Adachi, T. Kotaka, Macromolecules 24, 5365 (1991)Google Scholar
  253. H. Watanabe, O. Urakawa, H. Yamada, M.-L. Yao, Macromolecules 29, 755 (1996)Google Scholar
  254. R.E. Wetton, W.J. MacKnight, J.R. Fried, F.E. Karasz, Macromolecules 11, 158 (1978)Google Scholar
  255. G. Williams, Adv. Polym. Sci. 33, 60 (1979)Google Scholar
  256. G. Williams, D.A. Edwards, Trans. Faraday Soc. 62, 1329 (1966)Google Scholar
  257. G. Williams, D.C. Watts, Trans. Faraday Soc. 67, 2793 (1971)Google Scholar
  258. G. Williams, in Comprehensive Polymer Science, vol. II, ed. by G. Allen, J.C. Bevington (Pergamon Press, Oxford, 1989)Google Scholar
  259. G. Williams, in Structure and Properties of Polymers, ed. by E.L. Thomas. Materials Science & Technology Series, vol. 12 (Wiley and Sons, Hoboken, New Jersey, 1993), p. 471Google Scholar
  260. B. Wunderlich, Prog. Polym. Sci. 28, 383 (2003)Google Scholar
  261. H. Yin, S. Napolitano, A. Schönhals, Macromolecules 45, 1652 (2012)Google Scholar
  262. M. Zamponi, A. Wischnewski, M. Monkenbusch, L. Willner, D. Richter, A.E. Likhtman, G. Kali, B. Farago, Phys. Rev. Lett. 96, 238302 (2006)Google Scholar
  263. S. Zeeb, S. Höring, F. Garwe, M. Beiner, A. Schönhals, K. Schröter, E. Donth, Polymer 38, 4011 (1997)Google Scholar
  264. A. Zetsche, E.W. Fischer, Acta Polym. 45, 168 (1994)Google Scholar
  265. A. Zetsche, F. Kremer, H. Jung, Polymer 31, 1883 (1990)Google Scholar
  266. S. Zhang, X. Jin, P.C. Painter, J. Runt, Macromolecules 38, 6216 (2005)Google Scholar
  267. R. Zorn, L. Hartmann, B. Frick, D. Richter, Kremer F 307, 547 (2002)Google Scholar

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.BAM Federal Institute for Materials Research and TestingBerlinGermany
  2. 2.BAM Federal Institute for Materials Research and TestingBerlinGermany

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