Advertisement

Comparison of three enthalpy relaxation models based on fictive temperature and nonlinear Adam–Gibbs formulation

  • Xuan Wang
  • Kesong Xiao
  • Xiangnong Liu
  • Hao Wu
  • Cai GaoEmail author
Article
  • 11 Downloads

Abstract

The phenomenological models based on fictive temperature and nonlinear Adam–Gibbs formulation have been widely used to describe the enthalpy relaxation kinetics. Although the parameters in Adam–Gibbs formulation are physically explicable, the reasonabilities of the parameters obtained from curve-fitting procedures have not been systematically discussed yet. In this work, differential scanning calorimetry was employed to measure the heat capacities of maltitol in both the amorphous and the crystalline states, and the data were used to generate the model parameters. Results showed that the configurational ground state plays an important role in extracting the model parameters. Selecting the crystal rather than the glass as the ground state seems to be effective to improve the reasonabilities of the fitted parameters. It suggested that even if the fit quality seems sound, the physical reasonability of the best-fit parameters still needs to be treated with caution.

Keywords

Enthalpy relaxation DSC Fictive temperature Adam–Gibbs Maltitol 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51876053).

References

  1. 1.
    Graeser KA, Patterson JE, Zeitler JA, Gordon KC, Rades T. Correlating thermodynamic and kinetic parameters with amorphous stability. Eur J Pharm Sci. 2009;37(3–4):492–8.  https://doi.org/10.1016/j.ejps.2009.04.005.CrossRefPubMedGoogle Scholar
  2. 2.
    Hancock BC, Zografi G. Characteristics and significance of the amorphous state in pharmaceutical systems. J Pharm Sci. 1997;86(1):1–12.  https://doi.org/10.1021/js9601896.CrossRefPubMedGoogle Scholar
  3. 3.
    Díaz-Calderón P, MacNaughtan B, Hill S, Mitchell J, Enrione J. Reduction of enthalpy relaxation in gelatine films by addition of polyols. Int J Biol Macromol. 2018;109:634–8.  https://doi.org/10.1016/j.ijbiomac.2017.12.030.CrossRefPubMedGoogle Scholar
  4. 4.
    Hancock BC, Shamblin SL. Molecular mobility of amorphous pharmaceuticals determined using differential scanning calorimetry. Thermochim Acta. 2001;380(2):95–107.  https://doi.org/10.1016/s0040-6031(01)00663-3.CrossRefGoogle Scholar
  5. 5.
    Hodge IM. Enthalpy relaxation and recovery in amorphous materials. J Noncryst Solids. 1994;169:211–66.CrossRefGoogle Scholar
  6. 6.
    Cowie JMG, Ferguson R. Physical aging studies in polymer blends. 2. Enthalpy relaxation as a function of aging temperature in a poly(vinyl methyl ether)/polystyrene blend. Macromolecules. 1989;22(5):2312–7.  https://doi.org/10.1021/ma00195a054.CrossRefGoogle Scholar
  7. 7.
    Sasaki K, Takatsuka M, Kita R, Shinyashiki N, Yagihara S. Enthalpy and dielectric relaxation of poly(vinyl methyl ether). Macromolecules. 2018;51(15):5806–11.  https://doi.org/10.1021/acs.macromol.8b00780.CrossRefGoogle Scholar
  8. 8.
    Ketkaew J, Fan M, Shattuck MD, O’Hern CS, Schroers J. Structural relaxation kinetics defines embrittlement in metallic glasses. Scr Mater. 2018;149:21–5.  https://doi.org/10.1016/j.scriptamat.2018.01.024.CrossRefGoogle Scholar
  9. 9.
    Mao C, Prasanth Chamarthy S, Byrn SR, Pinal R. A calorimetric method to estimate molecular mobility of amorphous solids at relatively low temperatures. Pharm Res. 2006;23(10):2269–76.  https://doi.org/10.1007/s11095-006-9071-9.CrossRefPubMedGoogle Scholar
  10. 10.
    Shamblin SL, Hancock BC, Dupuis Y, Pikal MJ. Interpretation of relaxation time constants for amorphous pharmaceutical systems. J Pharm Sci. 2000;89(3):417–27.  https://doi.org/10.1002/(sici)1520-6017(200003)89:3%3c417:Aid-jps12%3e3.0.Co;2-v.CrossRefPubMedGoogle Scholar
  11. 11.
    Hodge IM. Structural relaxation. In: Classical relaxation phenomenology. 2019; p. 197–222.CrossRefGoogle Scholar
  12. 12.
    Debolt MA, Easteal AJ, Macedo PB, Moynihan CT. Analysis of structural relaxation in glass using rate heating data. J Am Ceram Soc. 1976;59(1–2):16–21.  https://doi.org/10.1111/j.1151-2916.1976.tb09377.x.CrossRefGoogle Scholar
  13. 13.
    Hodge IM, Berens AR. Effects of annealing and prior history on enthalpy relaxation in glassy polymers. 2. Mathematical modeling. Macromolecules. 1982;15:762–70.  https://doi.org/10.1021/ma00231a016.CrossRefGoogle Scholar
  14. 14.
    Moynihan CT, Easteal AJ, Debolt MA. Dependence of the fictive temperature of glass on cooling rate. J Am Ceram Soc. 1976;59:12–6.  https://doi.org/10.1111/j.1151-2916.1976.tb09376.x.CrossRefGoogle Scholar
  15. 15.
    Svoboda R, Málek J, Liška M. Correlation between the structure and relaxation dynamics of (GeS2) y (Sb2S3) 1 − y glassy matrices. J Noncryst Solids. 2018;479:113–9.  https://doi.org/10.1016/j.jnoncrysol.2017.11.004.CrossRefGoogle Scholar
  16. 16.
    Tanaka Y, Sakamoto N. Analysis of TNM model calculation for enthalpy relaxation based on the fictive temperature model and the configurational entropy model. J Noncryst Solids. 2017;473:26–32.  https://doi.org/10.1016/j.jnoncrysol.2017.07.023.CrossRefGoogle Scholar
  17. 17.
    Svoboda R, Málek J. Enthalpy relaxation kinetics of GeTe4 glass. J Noncryst Solids. 2015;422:51–6.  https://doi.org/10.1016/j.jnoncrysol.2015.05.016.CrossRefGoogle Scholar
  18. 18.
    Gao C, Ma HM. Enthalpy relaxation in d-sorbitol glass. J Therm Anal Calorim. 2015;120(3):1905–12.  https://doi.org/10.1007/s10973-015-4463-x.CrossRefGoogle Scholar
  19. 19.
    Hodge IM. Adam–Gibbs formulation of non-linear enthalpy relaxation. J Noncryst Solids. 1991;131–133:435–41.  https://doi.org/10.1016/0022-3093(91)90336-5.CrossRefGoogle Scholar
  20. 20.
    Mao C, Chamarthy SP, Pinal R. Calorimetric study and modeling of molecular mobility in amorphous organic pharmaceutical compounds using a modified Adam–Gibbs approach. J Phys Chem B. 2007;111(46):13243–52.  https://doi.org/10.1021/jp072577+.CrossRefPubMedGoogle Scholar
  21. 21.
    Hodge IM. Adam–Gibbs formulation of nonlinearity in glassy-state relaxations. Macromolecules. 1986;19(3):936–8.  https://doi.org/10.1021/ma00157a082.CrossRefGoogle Scholar
  22. 22.
    Andreozzi L, Faetti M, Giordano M, Palazzuoli D. Enthalpy recovery in low molecular weight PMMA. J Noncryst Solids. 2003;332(1–3):229–41.  https://doi.org/10.1016/j.jnoncrysol.2003.09.006.CrossRefGoogle Scholar
  23. 23.
    Scherer GW. Use of the Adam–Gibbs equation in the analysis of structural relaxation. J Am Ceram Soc. 1984;67(7):504–11.  https://doi.org/10.1111/j.1151-2916.1984.tb19643.x.CrossRefGoogle Scholar
  24. 24.
    Adam G, Gibbs JH. On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J Chem Phys. 1965;43(1):139–46.  https://doi.org/10.1063/1.1696442.CrossRefGoogle Scholar
  25. 25.
    Hodge IM. Effects of annealing and prior history on enthalpy relaxation in glassy polymers. 6. Adam–Gibbs formulation of nonlinearity. Macromolecules. 1987;20(11):2897–908.  https://doi.org/10.1021/ma00177a044.CrossRefGoogle Scholar
  26. 26.
    Kauzmann W. The nature of the glassy state and the behavior of liquids at low temperatures. Chem Rev. 1948;43(2):219–56.  https://doi.org/10.1021/cr60135a002.CrossRefGoogle Scholar
  27. 27.
    Angell CA. Relaxation in liquids, polymers and plastic crystals—strong/fragile patterns and problems. J Noncryst Solids. 1991;131–133:13–31.  https://doi.org/10.1016/0022-3093(91)90266-9.CrossRefGoogle Scholar
  28. 28.
    Simon SL. Enthalpy recovery of poly(ether imide): experiment and model calculations incorporating thermal gradients. Macromolecules. 1997;30(14):4056–63.  https://doi.org/10.1021/ma9614508.CrossRefGoogle Scholar
  29. 29.
    Andreozzi L, Faetti M, Zulli F, Giordano M. Connecting shear stress relaxation and enthalpy recovery in polymers through a modified TNM approach. Macromolecules. 2004;37(21):8010–6.  https://doi.org/10.1021/ma049334p.CrossRefGoogle Scholar
  30. 30.
    Gao C, Ye B, Jiang B, Liu X-N. Comparative investigation on the enthalpy relaxation of four amorphous pentose isomers. J Therm Anal Calorim. 2013;115(1):37–44.  https://doi.org/10.1007/s10973-013-3217-x.CrossRefGoogle Scholar
  31. 31.
    Shamblin LS, Tang X, Chang L, Hancock BC, Pikal MJ. Characterization of the time scales of molecular motion in pharmaceutically important glasses. J Phys Chem B. 1999;103:4113–21.  https://doi.org/10.1021/jp983964+.CrossRefGoogle Scholar
  32. 32.
    Svoboda R, Málek J. Description of enthalpy relaxation dynamics in terms of TNM model. J Noncryst Solids. 2013;378:186–95.  https://doi.org/10.1016/j.jnoncrysol.2013.07.008.CrossRefGoogle Scholar
  33. 33.
    Hodge IM, Heslin R. Effects of thermal history on enthalpy relaxation in glasses 7. Thermal time constants. J Noncryst Solids. 2010;356(28–30):1479–87.  https://doi.org/10.1016/j.jnoncrysol.2010.04.037.CrossRefGoogle Scholar
  34. 34.
    Mao C, Chamarthy SP, Byrn SR, Pinal R. Theoretical and experimental considerations on the enthalpic relaxation of organic glasses using differential scanning calorimetry. J Phys Chem B. 2010;114(1):269–79.  https://doi.org/10.1021/jp906633k.CrossRefPubMedGoogle Scholar
  35. 35.
    Koh YP, Grassia L, Simon SL. Structural recovery of a single polystyrene thin film using nanocalorimetry to extend the aging time and temperature range. Thermochim Acta. 2015;603:135–41.  https://doi.org/10.1016/j.tca.2014.08.025.CrossRefGoogle Scholar
  36. 36.
    Phalen RN, Cousins K, Usher T, Young M, Zhang R. Revising the formulization of the Narayanaswamy equation using the Adam–Gibbs theory. J Noncryst Solids. 2016;453:59–65.  https://doi.org/10.1016/j.jnoncrysol.2016.09.025.CrossRefGoogle Scholar
  37. 37.
    Bari R, Simon SL. Determination of the nonlinearity and activation energy parameters in the TNM model of structural recovery. J Therm Anal Calorim. 2017;131(1):317–24.  https://doi.org/10.1007/s10973-017-6381-6.CrossRefGoogle Scholar
  38. 38.
    Bustin O, Descamps M. Slow structural relaxations of glass-forming Maltitol by modulated DSC calorimetry. J Chem Phys. 1999;110(22):10982–92.  https://doi.org/10.1063/1.478041.CrossRefGoogle Scholar
  39. 39.
    Chen K, Vyazovkin S. Isoconversional kinetics of glass aging. J Phys Chem B. 2009;113(14):4631–5.  https://doi.org/10.1021/jp811412q.CrossRefPubMedGoogle Scholar
  40. 40.
    Claudy P, Siniti M, El Hajri J. Thermodynamic study of the glass relaxation phenomena: DSC study of annealing of maltitol glass. J Therm Anal Calorim. 2002;68(1):251–64.  https://doi.org/10.1023/a:1014973719280.CrossRefGoogle Scholar
  41. 41.
    Faivre A, Niquet G, Maglione M, Fornazero J, Jal JF, David L. Dynamics of sorbitol and maltitol over a wide time-temperature range. Eur Phys J B. 1999;1999:277–86.  https://doi.org/10.1007/s100510050.CrossRefGoogle Scholar
  42. 42.
    Lebrun N, Van Miltenburg JC, Bustin O, Descamps M. Calorimetric fragility of maltitol. Phase Transit. 2003;76(9–10):841–6.  https://doi.org/10.1080/0141159031000085723.CrossRefGoogle Scholar
  43. 43.
    Vyazovkin S, Dranca I. Comparative relaxation dynamics of glucose and maltitol. Pharm Res. 2006;23(9):2158–64.  https://doi.org/10.1007/s11095-006-9050-1.CrossRefPubMedGoogle Scholar
  44. 44.
    Lebrun N, van Miltenburg JC. Calorimetric study of maltitol: correlation between fragility and thermodynamic properties. J Alloys Compd. 2001;320(2):320–5.  https://doi.org/10.1016/s0925-8388(00)01490-0.CrossRefGoogle Scholar
  45. 45.
    Roos Y. Melting and glass transitions of low molecular weight carbohydrates. Carbohydr Res. 1993;238:39–48.  https://doi.org/10.1016/0008-6215(93)87004-c.CrossRefGoogle Scholar
  46. 46.
    Hancock BC, Christensen K, Shamblin SL. Estimation the critical molecular mobility temperature (Tk) of amorphous pharmaceuticals. Pharm Res. 1998;15(11):1649–51.  https://doi.org/10.1023/a:1011983923386.CrossRefPubMedGoogle Scholar
  47. 47.
    Jiang Q, Zhao M, Xu XY. Kauzmann temperature of alloys obtained by different methods. Philos Mag B. 2006;76(1):1–10.  https://doi.org/10.1080/01418639708241074.CrossRefGoogle Scholar
  48. 48.
    Johari GP. An equilibrium supercooled liquid’s entropy and enthalpy in the Kauzmann and the third law extrapolations, and a proposed experimental resolution. J Chem Phys. 2000;113(2):751–61.  https://doi.org/10.1063/1.481850.CrossRefGoogle Scholar
  49. 49.
    Hodge IM. Adam–Gibbs formulation of enthalpy relaxation near the glass transition. J Res Nat Inst Stand Technol. 1997;102(2):195–205.  https://doi.org/10.6028/jres.102.015.CrossRefGoogle Scholar
  50. 50.
    Angell CA. Entropy and fragility in supercooling liquids. J Res Natl Inst Stand Technol. 1997;102(2):171–85.  https://doi.org/10.6028/jres.102.013.CrossRefPubMedPubMedCentralGoogle Scholar
  51. 51.
    Hancock BC, Shamblin SL, Zografi G. Molecular mobility of amorphous pharmaceutical solids below their glass transition temperatures. Pharm Res. 1995;12(6):799–806.  https://doi.org/10.1023/a:1016292416526.CrossRefPubMedPubMedCentralGoogle Scholar
  52. 52.
    Walters C. Temperature dependency of molecular mobility in preserved seeds. Biophys J. 2004;86(2):1253–8.CrossRefGoogle Scholar
  53. 53.
    Martinez LM, Angell CA. A thermodynamic connection to the fragility of glass-forming liquids. Nature. 2001;410(6829):663–7.  https://doi.org/10.1038/35070517.CrossRefPubMedGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Hefei University of TechnologyHefeiChina

Personalised recommendations