No Access Submitted: 01 August 2009 Accepted: 12 October 2009 Published Online: 13 November 2009
J. Chem. Phys. 131, 184510 (2009); https://doi.org/10.1063/1.3258430
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Dielectric loss spectra of glass forming liquids are analyzed, with emphasis on systems for which a peak due to a secondary relaxation is not immediately obvious. Thus, glass formers are considered for which the high-frequency flank of the α-relaxation peak appears to be dominated by a so-called wing contribution. It is shown that even for such supercooled liquids the shape of the α-peak has to be characterized by two parameters. By performing a series of aging experiments it is demonstrated that the high-frequency flank of the α-relaxation, assumed to follow a power-law behavior, is superimposed by contributions from an excess wing and from a β-relaxation peak. In particular, the excess wing, previously associated with either the α- or the β-relaxation, is identified as a feature that evolves in its own right. It is argued that excess wing and β-relaxation are always present albeit with relative strengths that may vastly differ from glass former to glass former.
  1. 1. G. P. Johari and M. Goldstein, J. Chem. Phys. 53, 2372 (1970). https://doi.org/10.1063/1.1674335, Google ScholarScitation, ISI
  2. 2. K. L. Ngai and M. Paluch, J. Chem. Phys. 120, 857 (2004). https://doi.org/10.1063/1.1630295, Google ScholarScitation, ISI
  3. 3. P. K. Dixon, L. Wu, S. R. Nagel, B. D. Williams, and J. P. Carini, Phys. Rev. Lett. 65, 1108 (1990). https://doi.org/10.1103/PhysRevLett.65.1108, Google ScholarCrossref
  4. 4. A. Hofmann, F. Kremer, E. W. Fischer, and A. Schönhals, in Disorder Effects on Relaxation Processes, edited by R. Richert and A. Blumen (Springer, Berlin, 1994), p. 309. Google ScholarCrossref
  5. 5. H. Z. Cummins, G. Li, Y. H. Hwang, G. Q. Shen, W. M. Du, J. Hernandez, and N. J. Tao, Z. Phys. B: Condens. Matter 103, 501 (1997). https://doi.org/10.1007/s002570050405, Google ScholarCrossref
  6. 6. C. A. Angell, K. L. Ngai, G. B. McKenna, P. F. McMillan, and S. W. Martin, J. Appl. Phys. 88, 3113 (2000). https://doi.org/10.1063/1.1286035, Google ScholarScitation, ISI
  7. 7. K. L. Ngai, J. Non-Cryst. Solids 275, 7 (2000). https://doi.org/10.1016/S0022-3093(00)00238-6, Google ScholarCrossref
  8. 8. W. Götze, J. Phys.: Condens. Matter 11, A1 (1999). https://doi.org/10.1088/0953-8984/11/10A/002, Google ScholarCrossref
  9. 9. T. Blochowicz, A. Brodin, and E. A. Rössler, Adv. Chem. Phys. 133, 127 (2006). Google Scholar
  10. 10. P. Lunkenheimer, A. Pimenov, B. Schiener, R. Böhmer, and A. Loidl, Europhys. Lett. 33, 611 (1996) https://doi.org/10.1209/epl/i1996-00387-4; Google ScholarCrossref
    P. Lunkenheimer, U. Schneider, R. Brand, and A. Loidl, Contemp. Phys. 41, 15 (2000). https://doi.org/10.1080/001075100181259, , Google ScholarCrossref
  11. 11. A. Kudlik, S. Benkhof, T. Blochowicz, C. Tschirwitz, and E. A. Rössler, J. Mol. Struct. 479, 201 (1999). https://doi.org/10.1016/S0022-2860(98)00871-0, Google ScholarCrossref
  12. 12. A. Tölle, Rep. Prog. Phys. 64, 1473 (2001). https://doi.org/10.1088/0034-4885/64/11/203, Google ScholarCrossref
  13. 13. A. Brodin and E. A. Rössler, Eur. Phys. J. B 44, 3 (2005). https://doi.org/10.1140/epjb/e2005-00093-7, Google ScholarCrossref
  14. 14. N. B. Olsen, T. Christensen, and J. C. Dyre, Phys. Rev. Lett. 86, 1271 (2001). https://doi.org/10.1103/PhysRevLett.86.1271, Google ScholarCrossref
  15. 15. W. Kob and H. C. Andersen, Transp. Theory Stat. Phys. 24, 1179 (1995). https://doi.org/10.1080/00411459508203949, Google ScholarCrossref
  16. 16. S. Kämmerer, W. Kob, and R. Schilling, Phys. Rev. E 58, 2131 (1998) https://doi.org/10.1103/PhysRevE.58.2131; Google ScholarCrossref
    S. Kämmerer, W. Kob, and R. Schilling, Phys. Rev. E58, 2141 (1998). https://doi.org/10.1103/PhysRevE.58.2141, , Google ScholarCrossref
  17. 17. W. Götze and L. Sjögren, Rep. Prog. Phys. 55, 241 (1992). https://doi.org/10.1088/0034-4885/55/3/001, Google ScholarCrossref
  18. 18. T. Blochowicz, C. Tschirwitz, S. Benkhof, and E. A. Rössler, J. Chem. Phys. 118, 7544 (2003). https://doi.org/10.1063/1.1563247, Google ScholarScitation, ISI
  19. 19. K. L. Ngai, P. Lunkenheimer, C. León, U. Schneider, R. Brand, and A. Loidl, J. Chem. Phys. 115, 1405 (2001). https://doi.org/10.1063/1.1381054, Google ScholarScitation, ISI
  20. 20. A. I. Nielsen, T. Christensen, B. Jakobsen, K. Niss, N. B. Olsen, R. Richert, and J. C. Dyre, J. Chem. Phys. 130, 154508 (2009) https://doi.org/10.1063/1.3098911; Google ScholarScitation, ISI
    A. I. Nielsen, S. Pawlus, M. Paluch, and J. C. Dyre, Philos. Mag. 88, 4101 (2008). https://doi.org/10.1080/14786430802607093, , Google ScholarCrossref
  21. 21. A. Brodin, C. Gainaru, V. Porokhonskyy, and E. A. Rössler, J. Phys.: Condens. Matter 19, 205104 (2007). https://doi.org/10.1088/0953-8984/19/20/205104, Google ScholarCrossref
  22. 22. S. Hensel-Bielowka and M. Paluch, Phys. Rev. Lett. 89, 025704 (2002). https://doi.org/10.1103/PhysRevLett.89.025704, Google ScholarCrossref
  23. 23. K. L. Ngai, R. Casalini, S. Capaccioli, M. Paluch, and C. M. Roland, J. Phys. Chem. B 109, 17356 (2005). https://doi.org/10.1021/jp053439s, Google ScholarCrossref
  24. 24. U. R. Pedersen, N. P. Bailey, T. B. Schrøder, and J. C. Dyre, Phys. Rev. Lett. 100, 015701 (2008). https://doi.org/10.1103/PhysRevLett.100.015701, Google ScholarCrossref
  25. 25. R. V. Chamberlin, Phys. Rev. B 48, 15638 (1993). https://doi.org/10.1103/PhysRevB.48.15638, Google ScholarCrossref
  26. 26. G. Tarjus, D. Kivelson, and P. Viot, J. Phys.: Condens. Matter 12, 6497 (2000). https://doi.org/10.1088/0953-8984/12/29/321, Google ScholarCrossref
  27. 27. T. Blochowicz, C. Gainaru, P. Medick, C. Tschirwitz, and E. A. Rössler, J. Chem. Phys. 124, 134503 (2006). https://doi.org/10.1063/1.2178316, Google ScholarScitation, ISI
  28. 28. C. Gainaru, A. Brodin, V. N. Novikov, and E. A. Rössler, arXiv:cond-mat/0604597. Google Scholar
  29. 29. R. Böhmer, K. L. Ngai, C. A. Angell, and D. J. Plazek, J. Chem. Phys. 99, 4201 (1993). https://doi.org/10.1063/1.466117, Google ScholarScitation, ISI
  30. 30. K. Niss, C. Dalle-Ferrier, G. Tarjus, and C. Alba-Simionesco, J. Phys.: Condens. Matter 19, 076102 (2007). https://doi.org/10.1088/0953-8984/19/7/076102, Google ScholarCrossref
  31. 31. R. Böhmer, G. Diezemann, B. Geil, G. Hinze, A. Nowaczyk, and M. Winterlich, Phys. Rev. Lett. 97, 135701 (2006). https://doi.org/10.1103/PhysRevLett.97.135701, Google ScholarCrossref
  32. 32. K. Kessairi, S. Capaccioli, D. Prevosto, M. Lucchesi, S. Sharifi, and P. A. Rolla, J. Phys. Chem. B 112, 4470 (2008). https://doi.org/10.1021/jp800764w, Google ScholarCrossref
  33. 33. V. N. Novikov and A. P. Sokolov, Phys. Rev. E 67, 031507 (2003). https://doi.org/10.1103/PhysRevE.67.031507, Google ScholarCrossref
  34. 34. R. Casalini and C. M. Roland, Phys. Rev. Lett. 91, 015702 (2003). https://doi.org/10.1103/PhysRevLett.91.015702, Google ScholarCrossref
  35. 35. U. Schneider, R. Brand, P. Lunkenheimer, and A. Loidl, Phys. Rev. Lett. 84, 5560 (2000). https://doi.org/10.1103/PhysRevLett.84.5560, Google ScholarCrossref
  36. 36. F. Qi, T. El Goresy, R. Böhmer, A. Döß, G. Diezemann, G. Hinze, H. Sillescu, T. Blochowicz, C. Gainaru, E. Rössler, and H. Zimmermann, J. Chem. Phys. 118, 7431 (2003). https://doi.org/10.1063/1.1563599, Google ScholarScitation, ISI
  37. 37. This does not necessarily imply that local (internal) motions are absent. From NMR and calorimetry a CH3 rotation was identified for PC, see F. Qi, R. Böhmer, and H. Sillescu, Phys. Chem. Chem. Phys. 3, 4022 (2001). https://doi.org/10.1039/b102391h, Google ScholarCrossref
  38. 38. A pattern similar to that shown in Fig. 1 is also observed for a series of polyalcohols, see A. Döß, M. Paluch, H. Sillescu, and G. Hinze, Phys. Rev. Lett. 88, 095701 (2002) https://doi.org/10.1103/PhysRevLett.88.095701; Google ScholarCrossref
    A. Döß, M. Paluch, H. Sillescu, and G. Hinze, J. Chem. Phys. 117, 6582 (2002). https://doi.org/10.1063/1.1506147, , Google ScholarScitation
  39. 39. A. Brodin and E. A. Rössler, J. Chem. Phys. 125, 114502 (2006) https://doi.org/10.1063/1.2336782; Google ScholarScitation
    A. Brodin and E. A. Rössler, J. Chem. Phys.126, 244508 (2007). https://doi.org/10.1063/1.2748390, , Google ScholarScitation
  40. 40. M. Ricci, P. Bartolini, and R. Torre, Philos. Mag. B 82, 541 (2002). https://doi.org/10.1080/13642810110084858, Google ScholarCrossref
  41. 41. K. Kessairi, S. Capaccioli, D. Prevosto, M. Lucchesi, and P. A. Rolla, J. Chem. Phys. 127, 174502 (2007). https://doi.org/10.1063/1.2784190, Google ScholarScitation
  42. 42. R. Kahlau et al. (unpublished). Google Scholar
  43. 43. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (National Bureau of Standards, Washington, D.C., 1964), Chap. 26. Google Scholar
  44. 44. C. J. F. Böttcher and P. Bordewijk, Theory of Electric Polarization: Dielectrics in Time-Dependent Fields (Elsevier, Amsterdam, 1978), Vol. 2. Google Scholar
  45. 45. Note that this connection of α-process and EW does not imply that these processes are identical. Recent studies show that while the α-process is isotropic, the excess wing originates from a spatially highly restricted motion, see M. Vogel, C. Tschirwitz, S. Schneider, C. Koplin, P. Medick, and E. Rössler, J. Non-Cryst. Solids 307–310, 326 (2002) https://doi.org/10.1016/S0022-3093(02)01492-8; Google ScholarCrossref
    C. Gainaru, O. Lips, A. Troshagina, R. Kahlau, A. Brodin, F. Fujara, and E. A. Rössler, J. Chem. Phys. 128, 174505 (2008). https://doi.org/10.1063/1.2906122, , Google ScholarScitation, ISI
  46. 46. The Fourier transformation was carried out numerically using a program written by Dr. A. Brodin whom we thank for making this program available to us. Google Scholar
  47. 47. The emergence of the EW at high temperatures is best recognized in optical Kerr effect as well as in light scattering experiments, see Ref. 21 and H. Cang, V. N. Novikov, and M. D. Fayer, J. Chem. Phys. 118, 2800 (2003). https://doi.org/10.1063/1.1536612, Google ScholarScitation, ISI
  48. 48. Note that for polymeric glass formers two parameters are in general required for a description of the main relaxation, albeit there for a different reason, see A. Schönhals, F. Kremer, and E. Schlosser, Phys. Rev. Lett. 67, 999 (1991). https://doi.org/10.1103/PhysRevLett.67.999, Google ScholarCrossref
  49. 49. The conditions (i) through (iii) can be fulfilled with β=0.63 and γ=0.21 for glycerol and with β=0.78 and γ=0.23 for PC. Here the β-parameters are those resulting from previous scaling analyses of glycerol (Ref. 68) and of PC (Ref. 27), respectively. Google Scholar
  50. 50. A recent study on glycerol at ultrahigh pressure also reports more “normal” β time constants below the α-β merging region, see A. A. Pronin, M. V. Kondrin, A. G. Lyapin, V. V. Brazhkin, A. A. Volkov, P. Lunkenheimer, and A. Loidl (unpublished). Google Scholar
  51. 51. For xylitol extended aging led to a resolved β-peak, see R. Wehn, P. Lunkenheimer, and A. Loidl, J. Non-Cryst. Solids 353, 3862 (2007). https://doi.org/10.1016/j.jnoncrysol.2007.03.023, Google ScholarCrossref
  52. 52. It is clear that at the lowest temperatures the high-frequency part of the α-process is irrelevant for determining τβ. Google Scholar
  53. 53. G. P. Johari, Ann. N. Y. Acad. Sci. 279, 117 (1976). https://doi.org/10.1111/j.1749-6632.1976.tb39701.x, Google ScholarCrossref
  54. 54. For MTHF the E/Tg ratio was reported to be 1650/91=18.1, see Ref. 36. Since in that article a different method of analysis was employed the data are not included in Fig. 7. Google Scholar
  55. 55. T. Blochowicz and E. A. Rössler, Phys. Rev. Lett. 92, 225701 (2004). https://doi.org/10.1103/PhysRevLett.92.225701, Google ScholarCrossref
  56. 56. R. Brand, P. Lunkenheimer, U. Schneider, and A. Loidl, Phys. Rev. B 62, 8878 (2000) (and references cited therein). https://doi.org/10.1103/PhysRevB.62.8878, Google ScholarCrossref
  57. 57. See, e.g., T. El Goresy and R. Böhmer, J. Phys.: Condens. Matter 19, 205134 (2007) and references cited therein. https://doi.org/10.1088/0953-8984/19/20/205134, Google ScholarCrossref
  58. 58. K. L. Ngai, Phys. Rev. E 57, 7346 (1998). https://doi.org/10.1103/PhysRevE.57.7346, Google ScholarCrossref
  59. 59. D. Pisignano, S. Capaccioli, R. Casalini, M. Lucchesi, P. A. Rolla, A. Justl, and E. A. Rössler, J. Phys.: Condens. Matter 13, 4405 (2001). https://doi.org/10.1088/0953-8984/13/20/303, Google ScholarCrossref
  60. 60. The same value for the exponent γ was used by U. Buchenau, J. Chem. Phys. 131, 074501 (2009) https://doi.org/10.1063/1.3207140; see also , Google ScholarScitation
    R. Casalini and C. M. Roland, Phys. Rev. B 69, 094202 (2004). https://doi.org/10.1103/PhysRevB.69.094202, , Google ScholarCrossref
  61. 61. The behavior of TPP was rationalized in Ref. 21. Google Scholar
  62. 62. A. Rivera-Calzada, (private communication), see also Fig. 3 in A. Rivera-Calzada, K. Kaminski, C. Léon, and M. Paluch, J. Phys.: Condens. Matter 20, 244107 (2008). https://doi.org/10.1088/0953-8984/20/24/244107, Google ScholarCrossref
  63. 63. C. Gainaru, A. Rivera, S. Putselyk, G. Eska, and E. A. Rössler, Phys. Rev. B 72, 174203 (2005). https://doi.org/10.1103/PhysRevB.72.174203, Google ScholarCrossref
  64. 64. Apart from the data of Refs. 63 and 65 we included data on 3,3,4,4-benzophenonetetracarboxylic dianhydride (2PC) from Ref. 2 and data on DHIQ from this work. Google Scholar
  65. 65. C. Gainaru, Dissertation, Universität Bayreuth, 2007. Google Scholar
  66. 66. The peaks observed for T<0.3Tg in Fig. 8 are due to the relaxation in asymmetric double well potentials, see the discussion in Ref. 63. Google Scholar
  67. 67. A. Kudlik, C. Tschirwitz, T. Blochowicz, S. Benkhof, and E. Rössler, J. Non-Cryst. Solids 235-237, 406 (1998). https://doi.org/10.1016/S0022-3093(98)00510-9, Google ScholarCrossref
  68. 68. S. Adichtchev, T. Blochowicz, C. Gainaru, V. N. Novikov, E. A. Rössler, and C. Tschirwitz, J. Phys.: Condens. Matter 15, S835 (2003). https://doi.org/10.1088/0953-8984/15/11/308, Google ScholarCrossref
  69. 69. C. Gainaru et al. (unpublished). Google Scholar
  70. 70. A. Brodin, R. Bergman, J. Mattsson, and E. A. Rössler, Eur. Phys. J. B 36, 349 (2003). https://doi.org/10.1140/epjb/e2003-00353-6, Google ScholarCrossref
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