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Note
1 Reviewers:R. Hand, Department of Materials Science and Engineering, University of Sheffield, Sheffield, UKV. Stolyarova, Saint Petersburg State University, Saint Petersburg, Russian Federation
3.2 Thermodynamics of Glasses
Jean‐Luc Garden and Hervé Guillou
CNRS, Institut Néel and Université de Grenoble Alpes, Grenoble, France
1 Introduction
Thermodynamics states that the properties of a system in equilibrium depend neither on time nor on past history. Glasses clearly violate this postulate. Not only do their properties depend on history but they also vary with time at temperatures at which relaxation toward internal thermodynamic equilibrium does occur, but at a rate slow enough to be observable at the timescale of the experiment performed. To deal with glasses, thermodynamics must thus consider nonequilibrium states and their actual cause, namely the irreversibility of the transition that occurs when relaxation times eventually become much longer than experimental timescales such that the material freezes in as a glass.
Much attention is currently paid to the processes driving the glass transition at a microscopic scale and also to their implications for the macroscopic properties of glasses. Because this topic is extensively discussed in this chapter, we will deal here with a second fundamental issue, namely that of the phenomenological approaches followed to understand the observable macroscopic properties of glasses and, thus, to design new applications. To quote a single example, density gradients in tempered glasses are the key to thermal strengthening, which is achieved irreversibly upon cooling (Chapter 3.12).
In this chapter, the basic concepts of macroscopic nonequilibrium thermodynamics will first be summarized and illustrated with experimental heat capacities for a model system, PolyVinylAcetate [PVAc, (C4H6O2)n]). The basic concepts of equilibrium and nonequilibrium will then be introduced to point out why glasses challenge the laws of thermodynamics. Next, properties of the supercooled liquid state above Tg will be presented and the phenomenology of the glass transition examined in the light of calorimetric data, in particular in terms of configurational properties. The basics of nonequilibrium thermodynamics in the glass transition range will finally be reviewed along with the issue of aging below the glass transition range.
2 Basics of Nonequilibrium Thermodynamics
In thermodynamics one investigates the changes occurring when a system passes from a state A to another state B. At constant chemical composition, the system is in internal equilibrium if its state is defined by only two macroscopic variables such as temperature (T), pressure (P), volume (V), enthalpy (H), internal energy (U), or Gibbs free energy (G). Their values are not only constant but independent of the pathway actually followed between any two states A and B. As stated by the First Law of thermodynamics, between A and B the internal energy varies as:
(1)
where QA → B and WA → B are the heat and work exchanged by the system with its surroundings, respectively. Likewise, the entropy is decomposed into two parts,
(2)
where the first represents the heat exchanged with the surroundings and the second the entropy created within the system itself during the transformation.
If two equilibrium states are connected by a reversible process, then Δi SA → B = 0. If the system undergoes instead an irreversible process through which it falls out of equilibrium, then Δi SA → B > 0 since a spontaneous process is always associated with an entropy increase of the system.
