Glass transition temperature variation, cross-linking and structure in network glasses: A stochastic approach (original) (raw)
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On the glass transition temperature in covalent glasses
Journal of Non-Crystalline Solids, 1997
We give a simple demonstration of the formula relating the glass transition temperature, T g , to the molar concentration x of a modifier in two types of glasses: binary glasses, whose composition can be denoted by X n Y m +x M p Y q , with X an element of III-rd or IV -th group (e.g. B, or Si, Ge), while M p Y q is an alkali oxide or chalcogenide; next, the network glasses of the type A x B 1−x , e.g. Ge x Se 1−x , Si x T e 1−x , etc. After comparison, this formula gives an exact expression of the parameter β of the modified Gibbs-Di Marzio equation.
The European Physical Journal B, 1998
In this article, we present a universal relationship between the glass transition temperature T g and the local glass structure. The derivation of the simplest expression of this relationship and some comparisons with experimental T g values have already been reported in a recent letter [1]. We give here the analytical expression of the parameter β of the Gibbs-Di Marzio equation and also new experimental probes for the validity of the relationship, especially in low modified binary glasses. The influence of medium range order is presented and the unusual behavior of T g in binary B 2 S 3 and P 2 S 5 systems explained by the presence of modifier-rich clusters (denoted by B − B doublets).
Local structure and glass transition temperature in binary glasses
Journal of Non-Crystalline Solids, 1998
We present in this article a new relationship between the glass transition temperature, g , and the local glass structure, dealing with binary glasses and involving the rate of local coordination. In IV±VI based glasses, the predicted coordination number ratio is 3/4, according to the presence of Q 4 and Q 3 units. Experimental measurements lead to the value of 0.66±0.85. The new relationship is applied to B 2 S 3 and P 2 S 5 based glasses, and the unusual behavior of g is explained by the possibility of modi®er-rich clustering eects. Ó
Quantitative field theory of the glass transition
Proceedings of the National Academy of Sciences, 2012
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations.
Microscopic-phenomenological Model of Glass Transition- I. Foundations of the Model - Partly Revision, 2019
The determination of Tg 0 from the Tg (qT) values measured at a higher rate of temperature change is one of the key tasks of the problems associated with glass transition. There is a wealth of published work on both the theoretical basis and the detailed definition of the measured Tg values. An evaluation of the different measuring methods and definitions cannot be made by the author due to lack of own experiences and is also not the goal of this work. As an important result, however, it can be seen from the literature and it should be stressed that the Tg (qT) values, even at the same cooling or heating rate, can be quite different. Dilatometric and calorimetric measuring methods are common. However, there are obviously experimental difficulties in achieving the Tg (qT) values. With dilatometry problems occur due to the deformability of the melt and with calorimetry mainly the problem of thermal lag in the samples causes difficulties and the calibration of the instruments seem to be a source of uncertainty. From the principle of physical simplicity, dilatometry should actually be preferred, but due to the experimental manageability and the small sample quantities required, DSC measurements have established themselves in practice. But DSC measurements are not handled uniformly and the definition of the Tg value found in literature varies. As is well known, the measured Tg value is not a constant value, but depends on temperature changing rate qT and should usually be marked with a suffix. If the rate of temperature change is equal to or less than the reciprocal value of the structural equilibrium constant τ, no deviation from the equilibrium density or enthalpy of the liquid should be obtained above Tg 0. At Tg 0 , within an interval corresponding to the distribution width of the molecular vibrations, the equilibrium line is turned into the glass state. The measurements can be carried out at equal or different heating or cooling rates and the position of Tg in the glass transition interval can be defined diversely. There should be no question that the relationship between heating rate and structural relaxation constant τ, i.e. the distance to thermal equilibrium, determines the course of and within the transition interval. The tangential inclination of the liquid side of the DSC-transition step should be further on a function of the volume viscosity. The latter is very different for different substances at the same distance to Tg 0 , since it is very likely that the molecular packing density also determines the inclination. Consequently, the physical importance of Tg (qT>0) is thereby restricted. Further on it is very questionable that the rate dependence can be calculated with one and the same equation for measurements with different definition of Tg (qT). In the best case only the parameters of the equation are different, but it is quite likely that the general dependency is distinct. Therefore the determination of Tg 0 from the Tg (qT) data represents a major challenge. Incidentally, the detected time dependence is not limited to Tg only. DSC measurements of crystalline matter show a temporal dependence of the same order for the beginning of crystallization i (Fig. 3b there). As the molecular vibrations are not uniform but distributed around a center value, the glass transition should not take place as singularity but in an interval. This should be valid independently from the preset cooling or heating rate, even for qT→0 (resp. qt min , s. l.).
The Journal of Physical Chemistry B, 2000
Dynamic heterogeneity is an active field of glass-transition research. The length scale of this heterogeneity is called the characteristic length. It can be calculated from complex heat capacity curves in the equilibrium liquid or from dynamic calorimetry curves corrected with regard to nonequilibrium. No molecular parameters or microscopic models are necessary for obtaining the length. We report the characteristic length near glass temperature for about 30 glass formers including small-molecule liquids, polymers, silicate glasses, a metallic glass, a liquid crystal, and a plastic crystal. The lengths are between 1.0 and 3.5 nm with certain cumulations between 1.0 and 2.0 nm and between 2.5 and 3.5 nm. To try a correlation to other properties, we find that at least two should be included, e.g., Angell's fragility and the distance of T g from the crossover temperature,
Theory of the structural glass transition: a pedagogical review
Advances in Physics, 2015
The random first-order transition (RFOT) theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it corresponds with a breaking of the translational symmetry; analogies with freezing transitions in spin systems can also be made. The common aspect of these seemingly distinct phenomena is a spontaneous emergence of the molecular field, a venerable and well-understood concept. In crucial distinction from periodic crystallisation, the free energy landscape of a glassy liquid is vastly degenerate, which gives rise to new length and time scales while rendering the emergence of rigidity gradual. We obviate the standard notion that to be mechanically stable a structure must be essentially unique; instead, we show that bulk degeneracy is perfectly allowed but should not exceed a certain value. The present microscopic description thus explains both crystallisation and the emergence of the landscape regime followed by vitrification in a unified, thermodynamics-rooted fashion. The article contains a self-contained exposition of the basics of the classical density functional theory and liquid theory, which are subsequently used to quantitatively estimate, without using adjustable parameters, the key attributes of glassy liquids, viz., the relaxation barriers, glass transition temperature, and cooperativity size. These results are then used to quantitatively discuss many diverse glassy phenomena, including: the intrinsic connection between the excess liquid entropy and relaxation rates, the non-Arrhenius temperature dependence of α-relaxation, the dynamic heterogeneity, violations of the fluctuation-dissipation theorem, glass ageing and rejuvenation, rheological and mechanical anomalies, super-stable glasses, enhanced crystallisation near the glass transition, the excess heat capacity and phonon scattering at cryogenic temperatures, the Boson peak and plateau in thermal conductivity, and the puzzling midgap electronic states in amorphous chalcogenides.
COMPOSITIONAL TREND OF THE GLASS TRANSITION TEMPERATURE IN AsxSe1-x NETWORK GLASSES
2018
glasses (x = 0 to 0.4) is investigated using differential scanning calorimetry. The variation of Tg with As content and the mean coordination number of aged and rejuvenated samples are discussed in terms of proposed theoretical and empirical models. Critical assessment of the applicability of various models to explain the compositional variations of Tg is presented. Evidence of multiple rigidity transitions in the present network glasses is reported and the influence of the long-term physical aging is discussed.
Statistical Mechanics of the Glass Transition
The statistical mechanics of simple glass forming systems in two dimensions is worked out. The glass disorder is encoded via a Voronoi tesselation, and the statistical mechanics is performed directly in this encoding. The theory provides, without free parameters, an explanation of the glass transition phenomenology, including the identification of two different temperatures, T g and T c , the first associated with jamming and the second associated with crystallization at very low temperatures.