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, Alexander; Liebl, Christoph; Kolmeder, S.; Peters, J.

doi:10.1016/j.jmps.2010.05.010

Cited by 29 publications

(25 citation statements)

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“…16,17 Promising works by Lion and co-workers who developed for few years a more accurate non-equilibrium thermodynamics with internal state variables offer interesting perspectives in this direction. [10][11][12] …”

Section: Discussionmentioning

confidence: 99%

“…3 Non-equilibrium thermodynamics has been used all along the last century by different groups of researchers, and has seen renewed interest in the last few years. [4][5][6][7][8][9][10][11][12][13][14][15] As an example, Bouchbinder equilibrium thermodynamics based on internal variables to investigate one of the most striking aspect of the glass transition, i.e., the Kovacs effect. 16 They provided fits of the numerical simulation curves obtained by Mossa and Sciortino on the Kovacs effect.…”

Section: Introductionmentioning

confidence: 99%

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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: Discussionmentioning

confidence: 99%

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 constitutive theory to be developed is a substantial extension of recently published approaches to model the glass transition of amorphous polymers, cf. [49][50][51][52] and [53].…”

Section: Fundamentalsmentioning

confidence: 99%

A thermodynamic approach to model the caloric properties of semicrystalline polymers

Lion

Johlitz

2015

Continuum Mech. Thermodyn.

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It is well known that the crystallisation and melting behaviour of semicrystalline polymers depends in a pronounced manner on the temperature history. If the polymer is in the liquid state above the melting point, and the temperature is reduced to a level below the glass transition, the final degree of crystallinity, the amount of the rigid amorphous phase and the configurational state of the mobile amorphous phase strongly depend on the cooling rate. If the temperature is increased afterwards, the extents of cold crystallisation and melting are functions of the heating rate. Since crystalline and amorphous phases exhibit different densities, the specific volume depends also on the temperature history. In this article, a thermodynamically based phenomenological approach is developed which allows for the constitutive representation of these phenomena in the time domain. The degree of crystallinity and the configuration of the amorphous phase are represented by two internal state variables whose evolution equations are formulated under consideration of the second law of thermodynamics. The model for the specific Gibbs free energy takes the chemical potentials of the different phases and the mixture entropy into account. For simplification, it is assumed that the amount of the rigid amorphous phase is proportional to the degree of crystallinity. An essential outcome of the model is an equation in closed form for the equilibrium degree of crystallinity in dependence on pressure and temperature. Numerical simulations demonstrate that the process dependences of crystallisation and melting under consideration of the glass transition are represented.

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“…In some cases, it is also possible to work with the Gibbs free energy instead of the Helmholtz, e.g. (Haslach, 2009;Lion et al, 2010;Schapery, 1997). For hyperelastic materials, the Ogden model, e.g.…”

Section: Three-dimensional Constitutive Viscoelastic Model For Isotromentioning

confidence: 99%