Affinity and its derivatives in the glass transition process

Abstract

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.

Thermal collapse of SAPO-34 molecular sieve towards a perfect glass

“…They are traditionally formed via a high temperature route, i.e., by freezing-in of a supercooled melt [1,2]. Crystalline zeolites with molecular or nanoscopic porosity, on the other hand, can transform into a low-entropy and low-density amorphous (LDA) phase when exposed to either high pressures or high temperatures [3][4][5].…”

Thermodynamic analysis of the classical lattice-hole model of liquids

“…The requested number of internal variables is classically discussed in relation to the Defay-Prigogine ratio [4], [5], [6], [7], [2], [8], [9]. Without being exhaustive, it is worth mentioning the single structural order parameter approaches of Schmelzer, Gutzow, Tropin and coworkers [10], [11], [12], [13], [14], [15], [8] and the one of Garden, Guillou, Richard and Wondraczek [9], [16]. In the following, these two approaches will be referred to by the acronyms SGT and GGRW respectively.…”

“…As a complementary tool to reference [3], we propose an extended thermodynamic analysis of the same model. When trying to apply it to a real liquid/glass, such as in [16] for the extensively studied orthoterphenyl, this in-depth analysis can bring new insight on the physical signification of the model and the choice of the best parametrization methodology.…”

Comment on “On the theoretical determination of the Prigogine-Defay ratio in glass transition” [J. Chem. Phys. 136, 124502 (2012)]

“…On the contrary, Garden et al 10 demonstrated recently that the two affinity-derivative contributions are of fundamental importance in the phenomenological description of the glass transition (see Figs. 5 and 9 in Ref.…”

“…They are both involved in the thermodynamics describing the temperature and pressure behaviors of the coefficients C p , κ T , and α p and thus in their changes at T g . 10 For non-equilibrium systems (A = 0), it is obvious that the expression (3) above is different from unity. The question now arises whether this departure from unity has something in common with the classical question on measured PD ratios of glasses such as claimed by the authors.…”