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Glass transition cooperativity from broad band heat capacity spectroscopy

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Abstract

Molecular dynamics is often studied by broad band dielectric spectroscopy (BDS) because of the wide dynamic range available and the large number of processes resulting in electrical dipole fluctuations and with that in a dielectrically detectable relaxation process. Calorimetry on the other hand is an effective analytical tool to characterize phase and glass transitions by its signatures in heat capacity. In the linear response scheme, heat capacity is considered as entropy compliance. Consequently, only processes significantly contributing to entropy fluctuations appear in calorimetric curves. The glass relaxation is a prominent example for such a process. Here, we present complex heat capacity at the dynamic glass transition (segmental relaxation) of polystyrene (PS) and poly(methyl methacrylate) (PMMA) in a dynamic range of 11 orders of magnitude, which is comparable to BDS. As one of the results, we determined the characteristic length scale of the corresponding fluctuations. The dynamic glass transition measured by calorimetry is finally compared to the cooling rate dependence of fictive temperature and BDS data. For PS, dielectric and calorimetric data are similar but for PMMA with its very strong secondary relaxation process some peculiarities are observed.

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References

  1. Donth E (2001) Glass transition. Thermal glass transition. Glass temperature. Partial freezing. Springer, Berlin

    Google Scholar 

  2. Hensel A, Schick C (1998) Relation between freezing-in due to linear cooling and the dynamic glass transition temperature by temperature-modulated DSC. J Non Cryst Solids 235–237:510–516

    Article  Google Scholar 

  3. Hodge IM (1994) Enthalpy relaxation and recovery in amorphous materials [Review]. J Non Cryst Solids 169(3):211–266

    Article  CAS  Google Scholar 

  4. Schmelzer JWP (2012) Kinetic criteria of glass formation and the pressure dependence of the glass transition temperature. J Chem Phys 136(7):074512

    Article  Google Scholar 

  5. Huth H, Wang LM, Schick C, Richert R (2007) Comparing calorimetric and dielectric polarization modes in viscous 2-ethyl-1-hexanol. J Chem Phys 126(10):104503

    Article  Google Scholar 

  6. Brás AR, Dionísio M, Huth H, Schick C, Schönhals A (2007) Origin of glassy dynamics in a liquid crystal studied by broadband dielectric and specific heat spectroscopy. Phys Rev E 75:061708

    Article  Google Scholar 

  7. Schick C, Sukhorukov D, Schönhals A (2001) Comparison of the molecular dynamics of a liquid crystalline side group polymer revealed from temperature modulated DSC and dielectric experiments in the glass transition region. Macromol Chem Phys 202(8):1398–1404

    Article  CAS  Google Scholar 

  8. Gutzow IS, Schmelzer JWP (2013) The vitreous state thermodynamics, structure, rheology, and crystallization, 2nd edn. Springer, Heidelberg

    Google Scholar 

  9. Ediger MD, Angell CA, Nagel SR (1996) Supercooled liquids and glasses. J Phys Chem 100(31):13200–13212

    Article  CAS  Google Scholar 

  10. Kremer F, Schönhals A (2002) Broadband dielectric spectroscopy. Springer, Heidelberg

    Google Scholar 

  11. Vogel H (1921) Das Temperaturabhängigkeitsgesetz der Viskosität. Phys Z 22:645–646

    CAS  Google Scholar 

  12. Fulcher GS (1925) Analysis of recent measurements of the viscosity of glasses. J Am Ceram Soc 8:339–355

    Article  CAS  Google Scholar 

  13. Tammann G, Hesse G (1926) Die Abhängigkeit der Viscosität von der Temperatur bei unterkühlten Flüssigkeiten. Z Anorg Allg Chem 156:245–257

    Article  Google Scholar 

  14. Hensel A, Dobbertin J, Schawe JEK, Boller A, Schick C (1996) Temperature modulated calorimetry and dielectric spectroscopy in the glass transition region of polymers. J Therm Anal 46(3–4):935–954

    Article  CAS  Google Scholar 

  15. Donth E (1993) Relaxation and thermodynamics in polymers, glass transition. Akademie Verlag, Berlin

    Google Scholar 

  16. Donth E (1982) The size of cooperatively rearranging regions at the glass transition. J Non Cryst Solids 53(3):325–330

    Article  CAS  Google Scholar 

  17. Schawe JEK (1996) Investigations of the glass transitions of organic and inorganic substances—DSC and temperature-modulated DSC. J Therm Anal 47(2):475–484

    Article  CAS  Google Scholar 

  18. Donth E, Korus J, Hempel E, Beiner M (1997) Comparison of DSC heating rate and HCS frequency at the glass transition. Thermochim Acta 305:239–249

    Article  Google Scholar 

  19. Schmelzer JWP, Tropin TV (2013) Dependence of the width of the glass transition interval on cooling and heating rates. J Chem Phys 138:034507. doi:10.1063/1.4775802

    Article  Google Scholar 

  20. Minakov AA, Schick C (2007) Ultrafast thermal processing and nanocalorimetry at heating and cooling rates up to 1 MK/s. Rev Sci Instr 78(7):073902–073910

    Article  Google Scholar 

  21. Huth H, Minakov AA, Schick C (2006) Differential AC-chip calorimeter for glass transition measurements in ultrathin films. J Polym Sci B Polym Phys 44:2996–3005

    Article  CAS  Google Scholar 

  22. Huth H, Minakov AA, Serghei A, Kremer F, Schick C (2007) Differential AC-chip calorimeter for glass transition measurements in ultra thin polymeric films. Eur Phys J Spec Top 141(1):153–160

    Article  Google Scholar 

  23. Zhou D, Huth H, Gao Y, Xue G, Schick C (2008) Calorimetric glass transition of Poly(2,6-dimethyl-1,5-phenylene oxide) thin films. Macromolecules 41:7662–7666

    Article  CAS  Google Scholar 

  24. Shoifet E, Chua YZ, Huth H, Schick C (2013) High frequency alternating current chip nano calorimeter with laser heating. Rev Sci Instr 84(7):073903–073912. doi:10.1063/1.4812349

    Article  CAS  Google Scholar 

  25. Adam G, Gibbs JH (1965) On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J Chem Phys 43(1):139–146

    Article  CAS  Google Scholar 

  26. Huth H, Beiner M, Weyer S, Merzlyakov M, Schick C, Donth E (2001) Glass transition cooperativity from heat capacity spectroscopy—temperature dependence and experimental uncertainties. Thermochim Acta 377(1–2):113–124

    Article  CAS  Google Scholar 

  27. Huth H, Beiner M, Donth E (2000) Temperature dependence of glass-transition cooperativity from heat-capacity spectroscopy: Two post-Adam-Gibbs variants. Phys Rev B 61(22):15092–15101

    Article  CAS  Google Scholar 

  28. Hempel E, Hempel G, Hensel A, Schick C, Donth E (2000) Characteristic length of dynamic glass transition near T-g for a wide assortment of glass-forming substances. J Phys Chem B 104(11):2460–2466. doi:10.1021/jp991153f

    Article  CAS  Google Scholar 

  29. Saiter A, Delbreilh L, Couderc H, Arabeche K, Schönhals A, Saiter JM (2010) Temperature dependence of the characteristic length scale for glassy dynamics: Combination of dielectric and specific heat spectroscopy. Phys Rev E 81(4):041805

    Article  CAS  Google Scholar 

  30. Hamonic F, Prevosto D, Dargent E, Saiter A (2014) Contribution of chain alignment and crystallization in the evolution of cooperativity in drawn polymers. Polymer (0). doi:10.1016/j.polymer.2014.04.030

  31. Saiter A, Prevosto D, Passaglia E, Couderc H, Delbreilh L, Saiter JM (2013) Cooperativity length scale in nanocomposites: Interfacial and confinement effects. Phys Rev E 88(4):042605

    Article  CAS  Google Scholar 

  32. Stickel F, Fischer EW, Richert R (1995) Dynamics of glass-forming liquids. I. Temperature-derivative analysis of dielectric relaxation data. J Chem Phys 102(15):6251–6257

    Article  CAS  Google Scholar 

  33. Tool AQ (1946) Relation between inelastic deformability and thermal expansion of glass in its annealing range. J Am Ceram Soc 29:240

    Article  CAS  Google Scholar 

  34. Moynihan CT, Easteal AJ, De Bolt MA, Tucker J (1976) Dependence of the fictive temperature of glass on cooling rate. Am Ceram Soc 59:12–16

    Article  CAS  Google Scholar 

  35. Schick C, Lexa D, Leibowitz L (2012) Differential scanning calorimetry and differential thermal analysis. In: Kaufmann EN (ed) Characterization of materials, vol. 1. John Wiley & Sons, New York, pp 483–495. doi:10.1002/0471266965.com030.pub2

    Google Scholar 

  36. Gao S, Koh YP, Simon SL (2013) Calorimetric glass transition of single polystyrene ultrathin films. Macromolecules 46:562–570. doi:10.1021/ma3020036

    Article  CAS  Google Scholar 

  37. Sarge SM, Hemminger W, Gmelin E, Hohne GWH, Cammenga HK, Eysel W (1997) Metrologically based procedures for the temperature, heat and heat flow rate calibration of DSC. J Therm Anal 49:1125–1134

    Article  CAS  Google Scholar 

  38. Kraftmakher Y (2002) Modulation calorimetry and related techniques. Phys Rep 356:1–117

    Article  CAS  Google Scholar 

  39. Birge NO (1986) Specific-heat spectroscopy of glycerol and propylene glycol near the glass transition. Phys Rev B 34(3):1631–1642

    Article  CAS  Google Scholar 

  40. Birge NO, Nagel SR (1985) Specific-heat spectroscopy of the glass transition. Phys Rev Lett 54(25):2674–2677

    Article  CAS  Google Scholar 

  41. Christensen T (1985) The frequency dependence of the specific heat at the glass transition. J Phys (Paris) 46(12):C8-635–C638-637

    Google Scholar 

  42. Jeong YH (1997) Progress in experimental techniques for dynamic calorimetry. Thermochim Acta 305:67–98

    Article  Google Scholar 

  43. Merzlyakov M, Schick C (2001) Step response analysis in DSC—a fast way to generate heat capacity spectra. Thermochim Acta 380(1):5–12

    Article  CAS  Google Scholar 

  44. Merzlyakov M, Schick C (2001) Simultaneous multi-frequency TMDSC measurements. Thermochim Acta 377(1–2):193–204

    Article  CAS  Google Scholar 

  45. Hohne GWH, Merzlyakov M, Schick C (2002) Calibration of magnitude and phase angle of a TMDSC signal Part 1: Basic considerations. Thermochim Acta 391(1–2):51–67

    Article  CAS  Google Scholar 

  46. Merzlyakov M, Hohne GWH, Schick C (2002) Calibration of magnitude and phase angle of a TMDSC signal Part 2: Calibration practice. Thermochim Acta 391(1–2):69–80. doi:10.1016/S0040-6031(02)00164-8

    Article  CAS  Google Scholar 

  47. Sullivan P, Seidel G (1966) An ac temperature technique for measuring heat capacities. Ann Acad Sci Fenn A VI 210:58–62

    Google Scholar 

  48. Kraftmakher Y (2004) Modulation calorimetry, vol XII. Theory and applications. Springer, Berlin

    Book  Google Scholar 

  49. Adamovsky SA, Minakov AA, Schick C (2003) Scanning microcalorimetry at high cooling rate. Thermochim Acta 403(1):55–63

    Article  CAS  Google Scholar 

  50. Zhuravlev E, Schick C (2010) Fast scanning power compensated differential scanning nano-calorimeter: 1. The device. Thermochim Acta 505(1–2):1–13. doi:10.1016/j.tca.2010.03.019

    Article  CAS  Google Scholar 

  51. Minakov AA, Adamovsky SA, Schick C (2005) Non adiabatic thin-film (chip) nanocalorimetry. Thermochim Acta 432(2):177–185

    Article  CAS  Google Scholar 

  52. Christensen T, Olsen NB, Dyre JC (2008) Can the frequency dependent isobaric specific heat be measured by thermal effusion methods? In: AIP Conference Proceedings. pp 139–141

  53. Jakobsen B, Olsen NB, Christensen T (2010) Frequency-dependent specific heat from thermal effusion in spherical geometry. Phys Rev E 81(6):061505

    Article  Google Scholar 

  54. Christensen T, Olsen NB, Dyre JC (2007) Conventional methods fail to measure c[sub p](omega) of glass-forming liquids. Phys Rev E Stat Nonlinear Soft Matter Phys 75(4):041502–041511

    Article  Google Scholar 

  55. Glorieux C, Nelson KA, Hinze G, Fayer MD (2002) Thermal, structural, and orientational relaxation of supercooled salol studied by polarization-dependent impulsive stimulated scattering. J Chem Phys 116(8):3384–3395

    Article  CAS  Google Scholar 

  56. Bentefour EH, Glorieux C, Chirtoc M, Thoen J (2003) Broadband photopyroelectric thermal spectroscopy of a supercooled liquid near the glass transition. J Appl Phys 93(12):9610–9614

    Article  CAS  Google Scholar 

  57. van Herwaarden AW (2005) Overview of calorimeter chips for various applications. Thermochim Acta 432(2):192–201

    Article  Google Scholar 

  58. Merzlyakov M (2003) Integrated circuit thermopile as a new type of temperature modulated calorimeter. Thermochim Acta 403(1):65–81

    Article  CAS  Google Scholar 

  59. Ahrenberg M, Shoifet E, Whitaker KR, Huth H, Ediger MD, Schick C (2012) Differential alternating current chip calorimeter for in situ investigation of vapor-deposited thin films. Rev Sci Instr 83(3):033902–033912

    Article  CAS  Google Scholar 

  60. Minakov A, Morikawa J, Hashimoto T, Huth H, Schick C (2006) Temperature distribution in a thin-film chip utilized for advanced nanocalorimetry. Meas Sci Technol 17:199–207

    Article  CAS  Google Scholar 

  61. Svanidze AV, Huth H, Lushnikov SG, Schick C (2012) Study of phase transition in tetragonal lysozyme crystals by AC-nanocalorimetry. Thermochim Acta 544:33–37. doi:10.1016/j.tca.2012.06.013

    Article  CAS  Google Scholar 

  62. Svanidze AV, Huth H, Lushnikov SG, Seiji K, Schick C (2009) Phase transition in tetragonal hen egg-white lysozyme crystals. Appl Phys Lett 95(26):263702

    Article  Google Scholar 

  63. Ahrenberg M, Chua YZ, Whitaker KR, Huth H, Ediger MD, Schick C (2013) In situ investigation of vapor-deposited glasses of toluene and ethylbenzene via alternating current chip-nanocalorimetry. J Chem Phys 138(2):024501–024511. doi:10.1063/1.4773354

    Article  CAS  Google Scholar 

  64. Weyer S, Hensel A, Schick C (1997) Phase angle correction for TMDSC in the glass-transition region. Thermochim Acta 305:267–275. doi:10.1016/S0040-6031(97)00180-9

    Article  Google Scholar 

  65. Minakov AA, Schick C Dynamics of the temperature distribution in ultra-fast thin-film calorimeter sensors. Thermochim Acta. doi:10.1016/j.tca.2014.05.030

  66. Minakov AA, Roy SB, Bugoslavsky YV, Cohen LF (2005) Thin-film alternating current nanocalorimeter for low temperatures and high magnetic fields. Rev Sci Instrum 76:043906

    Article  Google Scholar 

  67. Weyer S, Hensel A, Korus J, Donth E, Schick C (1997) Broad band heat capacity spectroscopy in the glass-transition region of polystyrene. Thermochim Acta 305:251–255

    Article  Google Scholar 

  68. Hempel E, Beiner M, Renner T, Donth E (1996) Linearity of heat capacity step near the onset of alpha glass transition in poly(n-alkylmethacrylate)s. Acta Polym 47(11–12):525–529

    Article  CAS  Google Scholar 

  69. Hao N, Bohning M, Schonhals A (2007) Dielectric properties of nanocomposites based on polystyrene and polyhedral oligomeric phenethyl-silsesquioxanes. Macromolecules 40:9672–9679

    Article  CAS  Google Scholar 

  70. Beiner M, Garwe F, Schroter K, Donth E (1994) Dynamic shear modulus in the splitting region of poly(alkyl methacrylates). Colloid Polym Sci 272(11):1439–1446

    Article  CAS  Google Scholar 

  71. Bergman R, Alvarez F, Alegria A, Colmenero J (1998) The merging of the dielectric alpha- and beta-relaxations in poly-(methyl methacrylate). J Chem Phys 109(17):7546–7555

    Article  CAS  Google Scholar 

  72. Soreto Teixeira S, Dias CJ, Dionisio M, Costa LC (2013) New method to analyze dielectric relaxation processes: a study on polymethacrylate series. Polym Int. doi:10.1002/pi.4479

    Google Scholar 

  73. Garwe F, Schonhals A, Lockwenz H, Beiner M, Schroter K, Donth E (1996) Influence of cooperative dynamics on local relaxation during the development of the dynamic glass transition in poly(n-alkyl methacrylate)s. Macromolecules 29(1):247–253

    Article  CAS  Google Scholar 

  74. Schröter K, Unger R, Reissig S, Garwe F, Kahle S, Beiner M, Donth E (1998) Dielectric spectroscopy in the râ splitting region of glass transition in poly(ethyl methacrylate) and poly(n-butyl methacrylate): Different evaluation methods and experimental conditions. Macromolecules 31:8966–8972

    Article  Google Scholar 

  75. Beiner M, Kahle S, Hempel E, Schroter K, Donth E (1998) Two calorimetrically distinct parts of the dynamic glass transition. Europhys Lett 44(3):321–327

    Article  CAS  Google Scholar 

  76. Havriliak S, Negami S (1966) A complex plane analysis of alpha-dispersions in some polymer systems. J Polym Sci Part C 14:99–117

    Article  Google Scholar 

  77. Donth E (2003) Can dynamic neutron scattering help to understand a thermodynamic variant of an internal quantum-mechanical experiment in the angstrom range? Eur Phys J E Soft Matter Biol Phys 12(1):11–18. doi:10.1140/epje/i2003-10051-5

    Article  CAS  Google Scholar 

  78. Colmenero J, Arbe A, Alegria A (1994) The dynamics of the alpha- and beta-relaxations in glass-forming polymers studied by quasielastic neutron scattering and dielectric spectroscopy. J Non Cryst Solids 172(1):126–137

    Article  Google Scholar 

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Acknowledgments

We acknowledge F. Kremer, Leipzig, E. Donth, Dresden and A. Schönhals, Berlin for stimulating discussions and financial support from the German Science Foundation (DFG) and the European Union.

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Authors and Affiliations

  1. Institute of Physics, University of Rostock, Wismarsche Str. 43-45, 18051, Rostock, Germany

    Yeong Zen Chua, Gunnar Schulz, Evgeni Shoifet, Heiko Huth, Jürn W. P. Scmelzer & Christoph Schick

  2. Juelich Centre for Neutron Science, 52425, Juelich, Germany

    Reiner Zorn

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  1. Yeong Zen Chua
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Chua, Y.Z., Schulz, G., Shoifet, E. et al. Glass transition cooperativity from broad band heat capacity spectroscopy. Colloid Polym Sci 292, 1893–1904 (2014). https://doi.org/10.1007/s00396-014-3280-2

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