The impact of the stretching exponent on fragility of glass-forming liquids
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Abstract
The paper compared two factors governing fragility. The first one is thermodynamic, depending on the change in configurational entropy. The second one is kinetic and is determined by the stretching exponent β. Using a simple mathematical development, we show that the kinetic term \(m_{\text{K}} = f( {\beta_{{T_{\text{g}} }} } )\partial \ln \beta \left( T \right)/\partial \ln T|_{{T = T_{\text{g}} }}\) is always smaller than 1, where T g is the glass transition temperature and \(f( {\beta_{{T_{\text{g}} }} } )\) is the given functions of the stretching exponent at T = T g. As a result, the contribution of the kinetic term on the fragility of strong glasses is <6 %. Fragile glasses have a larger value of fragility index m, and for them, the influence of the kinetic term is significantly smaller. In any case, the thermodynamic term plays the main role in fragility and the kinetic one can be neglected.
Keywords
Kinetic fragility Configurational entropy Stretching exponentNotes
Acknowledgements
This work has been carried out with the financial support of the Serbian Ministry of Science and Technological Development, within the projects Nos III 45021 and 172059. Special thanks are due to Dr. Dušan Petković for his useful comments.
References
- 1.Angell CA. Spectroscopy simulation and the medium range order problem in glass. J Non-Cryst Solids. 1985;73:1–17.CrossRefGoogle Scholar
- 2.Angell CA. Relaxation in liquids, polymers and plastic crystals—strong/fragile patterns and problems. J Non-Cryst Solids. 1991;131–133:13–31.CrossRefGoogle Scholar
- 3.Angell CA, Ngai KL, McKenna GB, McMillan PF, Martin SW. Relaxation in glass forming liquids and amorphous solids. J Appl Phys. 2000;88:3113–57.CrossRefGoogle Scholar
- 4.Qin Q, McKenna GB. Correlation between dynamic fragility and glass transition temperature for different classes of glass forming liquids. J Non-Cryst Solids. 2006;352:2977–85.CrossRefGoogle Scholar
- 5.Bohmer R, Ngai KL, Angell CA, Plazek DJ. Nonexponential relaxations in strong and fragile glass formers. J Chem Phys. 1993;99:4201–9.CrossRefGoogle Scholar
- 6.Aniya M. A model for the fragility of the melts. J Therm Anal Calorim. 2002;69:971–8.CrossRefGoogle Scholar
- 7.Ruocco G, Sciortino F, Zamponi F, De Michele C, Scopigno T. Landscapes and fragilities. J Chem Phys. 2004;120:10666–80.CrossRefGoogle Scholar
- 8.Wang LM. Enthalpy relaxation upon glass transition and kinetic fragility of molecular liquids. J Phys Chem B. 2009;113:5168–71.CrossRefGoogle Scholar
- 9.Gupta PK, Mauro JC. Composition dependence of glass transition temperature and fragility. I. A topological model incorporating temperature-dependent constraints. J Chem Phys. 2009;130:094503–10.CrossRefGoogle Scholar
- 10.Smedskjaer MM, Mauro JC, Yue YZ. Ionic diffusion and the topological origin of fragility in silicate glasses. J Chem Phys. 2009;131:244514–22.CrossRefGoogle Scholar
- 11.Hong L, Novikov VN, Sokolov AP. Is there a connection between fragility of glass forming systems and dynamic heterogeneity/cooperativity? J Non-Cryst Solids. 2011;357:351–6.CrossRefGoogle Scholar
- 12.Niss K, Dalle-Ferrer C, Tarjus G, Alba-Simionesco C. On the correlation between fragility and stretching in glassforming liquids. J Phys Condens Matter. 2007;19:076102.CrossRefGoogle Scholar
- 13.Mauro JC, Gupta PK, Loucks RJ. Composition dependence of glass transition temperature and fragility. II. A topological model of alkali borate liquids. J Chem Phys. 2009;130:234503–10.CrossRefGoogle Scholar
- 14.Svoboda R, Málek J. Kinetic fragility of Se-based binary chalcogenide glasses. J Non-Cryst Solids. 2015;419:39–44.CrossRefGoogle Scholar
- 15.Gupta PK, Mauro JC. Two factors governing fragility: stretching exponent and configurational entropy. Phys Rev E. 2008;78:062501–3.CrossRefGoogle Scholar
- 16.Kohlrausch R. Theorie des elektrischen rückstandes in der leidener flasche. Ann Phys Chem. 1854;167:179–214.CrossRefGoogle Scholar
- 17.Williams G, Watts DC. Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function. Trans Faraday Soc. 1970;66:80–5.CrossRefGoogle Scholar
- 18.Sakatsuji W, Konishi T, Miyamoto Y. Effect of thermal history on enthalpy relaxation. J Therm Anal Calorim. 2013;113:1129–34.CrossRefGoogle Scholar
- 19.Dyre JC. Ten themes of viscous liquid dynamics. J Phys Condens Matter. 2007;19:205105–12.CrossRefGoogle Scholar
- 20.Cangialosi D, Alegria A, Colmenero J. On the temperature dependence of the nonexponentiality in glass-forming liquids. J Chem Phys. 2009;130:124902–9.CrossRefGoogle Scholar
- 21.Mauro JC. Through a glass, darkly: dispelling three common misconceptions in glass science. Int J Appl Glass Sci. 2011;2:245–61.CrossRefGoogle Scholar
- 22.Martinez-Garcia JC, Rzoska SJ, Drozd-Rzoska A, Starzonek S, Mauro JC. Fragility and basic process energies in vitrifying systems. Sci Rep. 2015;5:8314–20.CrossRefGoogle Scholar
- 23.Palato S, Metatla N, Soldera A. Temperature behavior of the Kohlrausch exponent for a series of vinylic polymers modelled by an all-atomistic approach. Eur Phys J E. 2011;34:90–5.CrossRefGoogle Scholar
- 24.Hodge IM. Adam–Gibbs formulation of enthalpy relaxation near the glass transition. J Res Natl Inst Stand Technol. 1997;102:195–205.CrossRefGoogle Scholar
- 25.Tool AQ. Relation between inelastic deformability and thermal expansion of glasses in its annealing range. J Am Ceram Soc. 1946;29:240–53.CrossRefGoogle Scholar
- 26.Narayanaswamy OS. A model of structural relaxation in glass. J Am Ceram Soc. 1971;54:491–8.CrossRefGoogle Scholar
- 27.Moynihan CT, Easteal AJ, DeBolt MA, Tucker J. Dependence of the fictive temperature of glass on cooling rate. J Am Ceram Soc. 1976;59:12–6.CrossRefGoogle Scholar
- 28.Scherer GW. Theories of relaxation. J Non-Cryst Solids. 1990;123:75–89.CrossRefGoogle Scholar
- 29.Svoboda R, Málek J, Pustková P. Structural relaxation of polyvinyl acetate (PVAc). Polymer. 2008;49:3176–85.CrossRefGoogle Scholar
- 30.Scherer GW. Use of the Adam–Gibbs equation in the analysis of structural relaxation. J Am Ceram Soc. 1984;67:504–11.CrossRefGoogle Scholar
- 31.Scherer GW. Volume relaxation far from equilibrium. J Am Ceram Soc. 1986;26:374–81.CrossRefGoogle Scholar
- 32.Hodge IM. Adam–Gibbs formulation of nonlinearity in glassy-state relaxations. Macromolecules. 1986;19:936–8.CrossRefGoogle Scholar
- 33.Moynihan CT, Crichton SN, Opalka SM. Linear and non-linear structural relaxation. J Non-Cryst Solids. 1991;131–133:420–34.CrossRefGoogle Scholar
- 34.Svoboda R, Málek J. Enthalpy relaxation kinetics of GeTe4 glass. J Non-Cryst Solids. 2015;422:51–6.CrossRefGoogle Scholar
- 35.Potuzak M, Welch RC, Mauro JC. Topological origin of stretched exponential relaxation in glass. J Chem Phys. 2011;135:214502–8.CrossRefGoogle Scholar
- 36.Wang LM, Richert R. Primary and secondary relaxation time dispersions in fragile supercooled liquids. Phys Rev B. 2007;76:064201–8.CrossRefGoogle Scholar
- 37.Phillips JC. Stretched exponential relaxation in molecular and electronic glasses. Rep Prog Phys. 1996;59:1133–207.CrossRefGoogle Scholar
- 38.Martinez LM, Angell CA. A thermodynamic connection to the fragility of glass-forming liquids. Nature. 2001;410:663–7.CrossRefGoogle Scholar
- 39.Sastry S. The relationship between fragility, configurational entropy and the potential energy landscape of glass-forming liquids. Nature. 2001;409:164–7.CrossRefGoogle Scholar
- 40.Dudowicz J, Freed KF, Douglas JF. Entropy theory of polymer glass-formation: I. Gen Formul J Chem Phys. 2006;124:064901–14.CrossRefGoogle Scholar
- 41.Yue Y. The iso-structural viscosity, configurational entropy and fragility of oxide liquids. J Non-Cryst Solids. 2009;355:737–44.CrossRefGoogle Scholar
- 42.Gupta PK, Mauro JC. The configurational entropy of glass. J Non-Cryst Solids. 2009;355:595–9.CrossRefGoogle Scholar
- 43.Senkov O, Miracle D. Description of the fragile behavior of glass-forming liquids with the use of experimentally accessible parameters. J Non-Cryst Solids. 2009;355:2596–603.CrossRefGoogle Scholar
- 44.Chovanec J, Chromčíková M, Liška M, Shánělová J, Málek J. Thermodynamic model and viscosity of Ge–S glasses. J Therm Anal Calorim. 2014;116:581–8.CrossRefGoogle Scholar