Simulation of temperature history-dependent phenomena of glass-forming materials based on thermodynamics with internal state variables

Lion, Alexander; Peters, J.; Kolmeder, S.

doi:10.1016/j.tca.2010.12.017

Cited by 21 publications

(18 citation statements)

References 47 publications

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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%

“…15 Since the affinity is a state function, its total differential is dA = ∂A ∂T p,ξ dT + ∂A ∂P T ,ξ dp + ∂A ∂ξ p,T dξ. (12) Maxwell relations 32 are used to transform the partial derivatives, and the equation above may be expressed in a practical way making explicitly apparent the infinitesimal time evolution…”

Section: B Expression Of the Configurational Parts General Casementioning

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: B Expression Of the Configurational Parts General Casementioning

confidence: 99%

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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“…For the fundamentals of continuum mechanics, the readers are referred, for example, to the textbooks of Altenbach (2015), Haupt (2002), Altenbach and Altenbach (1994) or Malvern (1969) and for details with regard to the constitutive representation of the glass transition with thermoviscoelastic methods to Lion et al (2011) or Lion et al (2014 and the citations therein.…”

Section: Fundamentalsmentioning

confidence: 99%

Constitutive Modelling of the Glass Transition and Related Phenomena: Relaxation of Shear Stress Under Pressure

Lion

Johlitz

Mittermeier

2016

Advanced Structured Materials

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In industrial fabrication processes as well as in many applications of polymer parts, the glass transition plays a significant role. This is due to high mechanical processing speeds, high temperatures or large cooling rates. The mechanical, the thermomechanical and the caloric properties of polymers differ below and above the glass transition which is a thermoviscoelastic phenomenon. It depends on the ratio between the intrinsic time scale of the polymer and that of the thermomechanical loading process. If both scales are comparable, the material is in the glass transition region. Otherwise it is in the equilibrium or in the glassy region. In the industry, there are increasing demands to simulate fabrication processes in order to estimate the resulting behaviour of the polymer parts before they are manufactured. To this end, constitutive models of finite thermoviscoelasticity are needed which can represent the volumetric as well as the isochoric mechanical behaviour of the polymer in combination with the caloric and the thermomechanical properties. In a recent paper of the authors, the concept of a hybrid free energy has been developed. This approach will be applied in the current essay where the pressure-dependent relaxation behaviour under shear deformations is of interest.

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“…Let us remark that this general definition above is valid for arbitrary time-dependent temperature excitations in combination with the associated process-dependent order parameters (see for example the equation (3.37) of the recent reference [27], where the glass transition process is tackled via thermodynamics with internal variables). The order parameter is the thermo-1 Certainly this appellation comes from Landau general theory on phase transitions, where order parameter and degree of order have been defined.…”

Section: The Order Parameter Modelmentioning

confidence: 99%

Non-equilibrium configurational Prigogine–Defay ratio

Garden

Guillou

Richard

et al. 2012

Journal of Non-Equilibrium Thermodynamics

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Classically, the Prigogine-Defay (PD) ratio involves differences in isobaric heat capacity, isothermal compressibility, and isobaric thermal expansion coefficient between a super-cooled liquid and the corresponding glass at the glass transition. However, determining such differences by extrapolation of coefficients that have been measured for super-cooled liquid and glassy state, respectively, poses the problem that it does not exactly take into account the non-equilibrium character of the glass transition. In this paper, we assess this question by taking into account the time dependence of configurational contributions to the three thermodynamic coefficients in the glass transition range upon varying temperature and/or pressure. Macroscopic non-equilibrium thermodynamics is applied to obtain a generalised form of the PD ratio. The classical PD ratio can then be taken as a particular case of this generalisation. Under some assumptions, the configurational PD ratio (CPD ratio) can be expressed in terms of fictive temperature and fictive pressure which, hence, provides another possibility to experimentally verify this formalism.

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Simulation of temperature history-dependent phenomena of glass-forming materials based on thermodynamics with internal state variables

Cited by 21 publications

References 47 publications

Affinity and its derivatives in the glass transition process

Affinity and its derivatives in the glass transition process

Constitutive Modelling of the Glass Transition and Related Phenomena: Relaxation of Shear Stress Under Pressure

Non-equilibrium configurational Prigogine–Defay ratio

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