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A theory of dielectric loss of polar polymers at high dilution in a nonpolar plasticizer is developed. The theory leads to a broad distribution in relaxation times, associated with the internal rotato...
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Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics

J. Chem. Phys. 9, 341 (1941); doi:10.1063/1.1750906

Issue Date: April 1941

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Kenneth S. Cole
Department of Physiology, Columbia University, New York, New York

Robert H. Cole
Research Laboratory of Physics, Harvard University, Cambridge, Massachusetts
The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula

[dformula epsilon[sup *] - epsilon[sub [infinity]] = (epsilon[sub 0] - epsilon[sub [infinity]])/[1 + (i omega tau[sub 0])[sup 1 - alpha]].]

In this equation, epsilon* is the complex dielectric constant, epsilon0 and epsilon[infinity] are the ``static'' and ``infinite frequency'' dielectric constants, omega=2pi times the frequency, and tau0 is a generalized relaxation time. The parameter alpha can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three-element electrical circuit, the mechanism responsible for the dispersion is equivalent to a complex impedance with a phase angle which is independent of the frequency. On this basis, the mechanism of interaction has the striking property that energy is conserved or ``stored'' in addition to being dissipated and that the ratio of the average energy stored to the energy dissipated per cycle is independent of the frequency. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

History: Received February 4, 1941
Permalink: http://link.aip.org/link/?JCPSA6/9/341/1
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REFERENCES (42)
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  1. P. Debye, Polar Molecules (Chemical Catalogue Company, New York, 1929).
  2. Reference 1, p. 94.
  3. This constant tau0 is not the same as the relaxation time as defined by Debye, differing from it by a constant factor which depends on the theory assumed for the static dielectric constant, cf. R. H. Cole, J. Chem. Phys. 6, 385 (1938). The distinction is unimportant for the present discussion.
  4. J. C. Maxwell, Electricity and Magnetism (Oxford Press, London, 1892), Vol. I.
  5. K. W. Wagner, Ann. d. Physik 40, 817 (1913).
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  7. H. B. G. Casimir and F. K. du Pre, Physica 5, 507 (1938).
  8. C. Zener, Phys. Rev. 53, 90 (1938).
  9. “Dispersion and absorption in dielectrics. II. Direct current characteristics,” to be submitted to this journal.
  10. See, for example, K. S. Cole, J. Gen. Physiol. 12, 29 (1928);
    11. 15, 641 (1932).
  11. This procedure is not without uncertainty because of the possibility of atomic polarization giving rise to absorption in the infra-red and a related dispersion of which this extrapolation takes no account. In the absence of definite information on this point, one can do no better than to ignore the difficulty. The error should not, in most cases, be serious.
  12. G. Bäz, Physik. Zeits. 40, 394 (1939).
  13. K. E. Slevogt, Ann. d. Physik 36, 141 (1939).
  14. P. Girard, Trans. Faraday Soc. 30, 763 (1934).
  15. S. O. Morgan, Trans. Electrochem. Soc. 65, 109 (1934).
  16. A. H. White and S. O. Morgan, J. Frank. Inst. 216, 635 (1933).
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  20. C. P. Smyth and C. S. Hitchcock, J. Am. Chem. Soc. 54, 4631 (1932).
  21. E. J. Murphy, Trans. Electrochem. Soc. 65, 309 (1934).
  22. A. H. White, S. S. Biggs, and S. O. Morgan, J. Am. Chem. Soc. 62, 16 (1940).
  23. A. H. White and W. S. Bishop, J. Am. Chem. Soc. 62, 8 (1940).
  24. The sources of the data are: chlorinated diphenyl, reference 16; glycol phthalate resin, W. A. Yager, Physics 7, 434 (1936);
    25. Halowax, reference 15;
    slate, G. E. Bairsto, Proc. Roy. Soc. 96, 363 (1920).
  25. K. S. Cole, J. Gen. Physiol. 12, 29 (1928).
  26. H. A. Kramers, Atti Congr. dei Fisici, Como, 545, 1927. See also reference 6.
  27. H. J. MacLeod, Phys. Rev. 21, 53 (1923).
  28. S. O. Morgan, J. Ind. and Eng. Chem. 30, 273 (1938).
  29. It should be emphasized that this “absorption conductivity” refers only to the conductivity associated with dispersion. It does not include any “direct current” steady-state conductivity as will be discussed in a later paper (reference 6).
  30. W. Dahms, Physik. Zeits. 37, 158 (1936).
    31. See also: M. Wien, Physik. Zeits. 37, 870 (1936).
  31. K. Schmale, Ann. d. Physik 35, 671 (1939).
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  33. L. Hartshorn, N. J. L. Megson, and E. Rushton, Proc. Phys. Soc. 52, 796 (1940).
  34. A. H. Scott, A. T. McPherson, and H. L. Curtis, Bur. Stand. J. Research 11, 173 (1933).
  35. See, however, reference 10.
  36. P. Debye, Physik. Zeits. 36, 100, 193 (1935).
  37. P. Debye and W. Ramm, Ann. d. Physik 28, 28 (1937).
  38. See, for instance, J. H. Van Vleck, J. Chem. Phys. 5, 556 (1937), and reference 3.
  39. J. Perrin, J. de Phys. et Rad. [7] 5, 497 (1934);
    40. A. Budo, Physik. Zeits. 40, 603 (1939).
  40. E. von Schweidler, Ann. d. Physik 24, 711 (1907).
  41. R. Fuoss and J. G. Kirkwood, J. Am. Chem. Soc. 63, 385 (1941).
  42. A. Gemant, Physics 7, 311 (1936).

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