Structural order parameters, the Prigogine–Defay ratio and the behavior of the entropy in vitrification

Schmelzer, Jürn W. P.; Gutzow, I.

doi:10.1016/j.jnoncrysol.2008.12.014

Cited by 28 publications

(48 citation statements)

References 29 publications

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“…17 Among these recent works, Gutzow, Schmelzer, and co-workers have brought new aspects to the field. [18][19][20][21][22][23][24] Using the so-called lattice-hole theory of liquids, and an evolution equation for the order parameter as a function of temperature, they investigated the process of vitrification and structural recovery following defined temperature protocols. 18,19,23,24 Among other points, a new expression for the Prigogine-Defay ratio and a thermodynamic definition of the fictive temperature was provided.…”

Section: Introductionmentioning

confidence: 99%

Affinity and its derivatives in the glass transition process

Garden

Guillou

Richard

et al. 2012

The Journal of Chemical Physics

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The thermodynamic treatment of the glass transition remains an issue of intense debate. When associated with the formalism of non-equilibrium thermodynamics, the lattice-hole theory of liquids can provide new insight in this direction, as has been shown by Schmelzer and Gutzow [J. Chem. Phys. 125, 184511 (2006) (2011)]. Here, we employ a similar approach. We include pressure as an additional variable, in order to account for the freezing-in of structural degrees of freedom upon pressure increase. Second, we demonstrate that important terms concerning first order derivatives of the affinity-driving-force with respect to temperature and pressure have been previously neglected. We show that these are of crucial importance in the approach. Macroscopic non-equilibrium thermodynamics is used to enlighten these contributions in the derivation of C p ,κ T , and α p . The coefficients are calculated as a function of pressure and temperature following different theoretical protocols, revealing classical aspects of vitrification and structural recovery processes. Finally, we demonstrate that a simple minimalist model such as the lattice-hole theory of liquids, when being associated with rigorous use of macroscopic non-equilibrium thermodynamics, is able to account for the primary features of the glass transition phenomenology. Notwithstanding its simplicity and its limits, this approach can be used as a very pedagogical tool to provide a physical understanding on the underlying thermodynamics which governs the glass transition process.

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Section: Introductionmentioning

confidence: 99%

Affinity and its derivatives in the glass transition process

Garden

Guillou

Richard

et al. 2012

The Journal of Chemical Physics

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“…Despite of this rather complicated formulation, its physical foundation is comparable to that which forms the basis of older and more recently published models in which the pressure and the volume are used as mechanical state variables (cf. Schmelzer and Gutzow, 2009;Christensen et al, 2007;Christensen and Dyre, 2008;Jones, 1953a, 1953b;de Donder andvan Rysselberghe, 1936 or Lesikar andMoynihan, 1980). In comparison with pure frequency-domain approaches as developed, for example, in Christensen et al (2007) or Christensen and Dyre (2008) the current model is originally formulated in the time domain and then evaluated for harmonic temperature-or stress-controlled excitations in the frequency domain.…”

Section: Discussionmentioning

confidence: 99%

“…These variables are introduced as phenomenological measures for the configurational order of the material (cf. Schmelzer and Gutzow, 2009;Jones, 1953b or Möller et al, 2006) and are denoted as order parameters. They describe the deviation of the current state of the material from its equilibrium and remain constant, if the pressure or the temperature is changing rapidly.…”

Section: Models To Describe Glass-forming Materials In the Region Of mentioning

confidence: 99%

Representation of the glass-transition in mechanical and thermal properties of glass-forming materials: A three-dimensional theory based on thermodynamics with internal state variables

Lion

Liebl

Kolmeder

et al. 2010

Journal of the Mechanics and Physics of Solids

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“…2,3,9 No proof is given in Ref. 1 and in previous works that suggest neglecting the two affinity derivatives in Eq.…”

Section: ∂V ∂ξmentioning

confidence: 99%

“…Since some of these errors are systematically reproduced in several papers published these last years by the same group, we feel obliged to draw attention to them. [2][3][4] In the seminal papers of Davies and Jones on the irreversible approach to equilibrium in glasses, 5 or on the thermodynamic and kinetic properties of glasses, 6 the notion of structural order parameter ξ was used to describe the nonequilibrium behavior of systems undergoing a glass transition. Particularly, it is nowadays admitted that, since the experimentally determined values of the Prigogine-Defay (PD) ratio at the glass temperature are generally different from unity, then more than one structural order parameter are involved in the thermodynamics of the glass transition.…”

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confidence: 99%