Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Continuum Mechanics and Thermodynamics
Published in: Continuum Mechanics and Thermodynamics 1/2021

19-05-2020 | Original Article

Analysis of the minimal model for the enthalpy relaxation and recovery in glass transition: application to constant-rate differential scanning calorimetry

Authors: Ivan Argatov, Vitaly Kocherbitov

Published in: Continuum Mechanics and Thermodynamics | Issue 1/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The so-called minimal model is formulated for describing the enthalpy relaxation and recovery in glass transition. The model is based on the Arrhenius law for the enthalpy relaxation, which uses two-dimensional parameters, namely the activation energy and the so-called pre-factor (relaxation time at relatively high temperature). A numerically effective exact analytical solution is obtained for the case of constant-rate differential scanning calorimetry. The developed model is analyzed according to the logic of the model itself without introducing additional simplifying assumptions of thermodynamic nature. For typical range of the model parameters, the resulting differential equation contains a large parameter, which offers an opportunity for the application of asymptotic and approximate techniques. A number of simple approximations have been provided for some thermodynamic quantities of interest.
previous article Distance estimations in unknown sea underwater conditions by power LED for robotics swarms
next article Shock structure in extended thermodynamics with second-order maximum entropy principle closure

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Hodge, I.M.: Enthalpy relaxation and recovery in amorphous materials. J. Non-Cryst. Solids 169(3), 211–266 (1994)CrossRefADS
2.
Seibert, H., Scheffer, T., Diebels, S.: Thermomechanical characterisation of cellular rubber. Contin. Mech. Thermodyn. 28(5), 1495–1509 (2016)CrossRefADS
3.
Leistner, C., Hartmann, S., Abliz, D., Ziegmann, G.: Modeling and simulation of the curing process of epoxy resins using finite elements. Contin. Mech. Thermodyn. 32, 327–350 (2020)MathSciNetCrossRefADS
4.
Angell, C.A.: Perspective on the glass transition. J. Phys. Chem. Solids 49(8), 863–871 (1988)CrossRefADS
5.
6.
Gutzow, I., Schmelzer, J.W.P., Petroff, B.: Phenomenological theories of glass transition: classical approaches, new solutions and perspectives. J. Non-Cryst. Solids 354(2–9), 311–324 (2008)CrossRefADS
7.
Bari, R., Simon, S.L.: Determination of the nonlinearity and activation energy parameters in the TNM model of structural recovery. J. Therm. Anal. Calorim. 131(1), 317–324 (2018)CrossRef
8.
Mauro, J.C., Mauro, Y.Z.: On the Prony series representation of stretched exponential relaxation. Physica A Stat. Mech. Appl. 506, 75–87 (2018)MathSciNetCrossRefADS
9.
Flügel, K., Hennig, R., Thommes, M.: Determination of the structural relaxation enthalpy using a mathematical approach. J. Pharmaceut. Sci. 108(11), 3675–3683 (2019)
10.
Lion, A., Yagimli, B.: Differential scanning calorimetry-continuum mechanical considerations with focus to the polymerisation of adhesives. Zeitschrift für Angewandte Mathematik und Mechanik: Appl. Math. Mech. 88(5), 388–402 (2008)CrossRefADS
11.
Ferhoum, R., Aberkane, M., Ouali, M.O.: Distribution of nonliner relaxation (DNLR) approach of the annealing effects in semicristalline polymers: structure-property relation for high-density polyethylene (HDPE). Contin. Mech. Thermodyn. 26(3), 373–385 (2014)MathSciNetCrossRefADS
12.
Jennrich, R., Lion, A., Johlitz, M., Ernst, S., Dilger, K., Stammen, E.: Thermomechanical characterization and modeling of fast-curing polyurethane adhesives. Contin. Mech. Thermodyn. 32(2), 421–432 (2020)MathSciNetCrossRefADS
13.
Kovacs, A.J., Aklonis, J.J., Hutchinson, J.M., Ramos, A.R.: Isobaric volume and enthalpy recovery of glasses. II. A transparent multiparameter theory. J. Polym. Sci. Polym. Phys. Ed. 17(7), 1097–1162 (1979)CrossRefADS
14.
Tool, A.Q.: Relation between inelastic deformability and thermal expansion of glass in its annealing range. J. Am. Ceram. Soc. 29(9), 240–253 (1946)CrossRef
15.
Narayanaswamy, O.S.: A model of structural relaxation in glass. J. Am. Ceram. Soc. 54(10), 491–498 (1971)CrossRef
16.
Moynihan, C.T., Easteal, A.J., DeBolt, M.A., Tucker, J.: Analysis of structural relaxation in glass using rate heating data. J. Am. Ceram. Soc. 59, 12–16 (1976)CrossRef
17.
Fan, M., Zhang, K., Schroers, J., Shattuck, M.D., O’Hern, C.S.: Particle rearrangement and softening contributions to the nonlinear mechanical response of glasses. Phys. Rev. E 96(3), 032602 (2017)CrossRefADS
18.
Kohlrausch, R.: Theorie des elektrischen Rückstandes in der Leidener Flasche. Annalen der Physik 167(2), 179–214 (1854)CrossRefADS
19.
Williams, G., Watts, D.C.: Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function. Trans. Faraday Soc. 66, 80–85 (1970)CrossRef
20.
Moynihan, C.T., Easteal, A.J., Wilder, J., Tucker, J.: Dependence of the glass transition temperature on heating and cooling rate. J. Phys. Chem. 78(26), 2673–2677 (1974)CrossRef
21.
Schmelzer, J.W.P., Tropin, T.V.: Dependence of the width of the glass transition interval on cooling and heating rates. J. Chem. Phys. 138(3), 034507 (2013)CrossRefADS
22.
Gutzow, I., Ilieva, D., Babalievski, F., Yamakov, V.: Thermodynamics and kinetics of the glass transition: A generic geometric approach. J. Chem. Phys. 112(24), 10941–10948 (2000)CrossRefADS
23.
Gutzow, I., Yamakov, V., Ilieva, D., Babalievski, Ph, Pye, L.D.: Generic phenomenological theory of vitrification. Glass Phys. Chem. 27(2), 148–159 (2001)CrossRef
24.
Volkenshtein, M.V., Ptitsyn, O.B.: The relaxation theory of glass transition. Dokl. Phys. 103(5), 795–798 (1955)
25.
Vol’kenshtein, M.V., Ptitsyn, O.B.: Relaxation theory of vitrification. Solution of basic equation and its studying. Russ. J. Appl. Phys. 26(10), 2204–2222 (1956)
26.
Sanditov, D.S., Ojovan, M.I.: Relaxation aspects of the liquid-glass transition. Physics-Uspekhi 62(2), 111 (2019)CrossRefADS
27.
Bragg, W.L., Williams, E.J.: The effect of thermal agitation on atomic arrangement in alloys. Proc. R. Soc. Lond. Ser. A 145(855), 699–730 (1934)CrossRefADS
28.
Wunderlich, B., Bodily, D.M., Kaplan, M.H.: Theory and measurements of the glass-transformation interval of polystyrene. J. Appl. Phys. 35(1), 95–102 (1964)CrossRefADS
29.
Fedoryuk, M.V.: Asymptotics: Integrals and Series (In Russian). Nauka, Moscow (1987)MATH
30.
Tropin, T.V., Schmelzer, J.W., Aksenov, V.L.: Modern aspects of the kinetic theory of glass transition. Physics-Uspekhi 59(1), 42 (2016)CrossRefADS
31.
Sanditov, D.S., Ojovan, M.I.: On relaxation nature of glass transition in amorphous materials. Physica B: Condensed Matter 523, 96–113 (2017)CrossRefADS
32.
Doyle, C.D.: Series approximations to the equation of thermogravimetric data. Nature 207(4994), 290 (1965)CrossRefADS
33.
Flynn, J.H., Wall, L.A.: General treatment of the thermogravimetry of polymers. J. Res. Natl. Bureau Stand. 70(6), 487–523 (1966)CrossRef
34.
Ozawa, T.: Kinetic analysis of derivative curves in thermal analysis. J. Therm. Anal. Calorim. 2(3), 301–324 (1970)CrossRef
Metadata
Title
Analysis of the minimal model for the enthalpy relaxation and recovery in glass transition: application to constant-rate differential scanning calorimetry
Authors
Ivan Argatov
Vitaly Kocherbitov
Publication date
19-05-2020
Publisher
Springer Berlin Heidelberg
Published in
Continuum Mechanics and Thermodynamics / Issue 1/2021
Print ISSN: 0935-1175
Electronic ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-020-00891-3

Other articles of this Issue 1/2021

Continuum Mechanics and Thermodynamics 1/2021 Go to the issue

Original Article

A model system of mixed ionized gas dynamics

Original Article

Elastoplastic buckling of FGM beams in thermal environment

Original Article

Multiscale thermodynamics of charged mixtures

Original Article

Finite deformation analysis of isotropic magnetoactive elastomers

Original Article

Wave propagation in viscoelastic composite materials with long-memory effects

Correction

Correction to: A two-temperature generalized magneto-thermoelastic formulation for a rotating medium with thermal shock under hydrostatic initial stress

Premium Partners

    Image Credits