Change in entropy in thermal hysteresis of liquid-glass-liquid transition and consequences of violating the Clausius theorem

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.

Origin of two maxima in specific heat in enthalpy relaxation under thermal history composed of cooling, annealing, and heating

The origin of two maxima in specific heat observed at the higher and the lower temperatures in the glass-transition region in the heating process has been studied for polymethyl methacrylate and polyvinyl chloride using differential scanning calorimetry, and the calculation was done using the phenomenological model equation under a thermal history of the typical annealing experiment composed of cooling, annealing, and heating. The higher maximum is observed above the glass-transition temperature, and it remains almost unchanged independent of annealing time t_{a}, while the lower one is observed above an annealing temperature T_{a} and shifts toward the higher one, increasing its magnitude with t_{a}. The analysis by the phenomenological model equation proposed in order to interpret the memory effect in the glassy state clarifies that under a typical annealing history, two maxima in specific heat essentially appear. The shift of the lower maximum toward higher temperatures from above T_{a} is caused by an increase in the amount of relaxation during annealing with t_{a}. The annealing temperature and the amount of relaxation during annealing play a major role in the determination of the number of maxima in the specific heat.

Structural fluctuations and orientational glass of levoglucosan--High stability against ordering and absence of structural glass

To investigate whether a non-exponential relaxation always indicates 2-4 nm-size regions of dynamic heterogeneity, we studied the kinetic freezing and unfreezing of structural fluctuations involving the rotational modes in orientationally disordered crystal (ODIC) of levoglucosan by calorimetry. The heat capacity, Cp, of levoglucosan measured over the 203 K-463 K range shows that its low-temperature, orientationally ordered crystal (ORC) transforms to ODIC phase on heating, which then melts to a low viscosity liquid. On cooling, the melt transforms to the ODIC which then does not transform to the ORC. Instead, the ODIC supercools. Fluctuations resulting from hindered (random) rotations of levoglucosan molecules confined to the lattice sites and from their conformational changes become progressively slower on cooling and an orientational glass (O-G) forms showing the sigmoid shape decrease in Cp characteristic of structural arrest like that of a glass. On heating the O-G state, rotational fluctuations begin to contribute to Cp at To-g of 247.8 K and there is an overshoot in Cp and thermal hysteresis (characteristic of physical ageing) in the temperature range of 230-260 K. The non-exponential relaxation parameter, β(cal), determined by fitting the Cp data to a non-exponential, nonlinear model for relaxation of a glass is 0.60, which is similar to β(cal) found for polymers, molecular liquids, and metal-alloy melts in which Brownian diffusion occurs. Such β(cal) < 1 are seen to indicate 2-4 nm-size dynamically heterogeneous domains in an ultraviscous liquid near the glass formation, but its value of 0.60 for ODIC levoglucosan, in which Brownian diffusion does not occur, would not indicate such domains. Despite the lack of Brownian diffusion, we discuss these findings in the potential energy landscape paradigm. Levoglucosan melt, which is believed to vitrify and to stabilize a protein's disordered structure, did not supercool even at 200 K/min cooling rate. The findings have consequences for reports on the dielectric relaxation studies that indicated that levoglucosan melt supercools to form a structural glass of Tg of ∼245 K, and for computer simulation of its dynamics. Levoglucosan is the ninth ODIC that forms O-G. It does so more easily than the other eight.

Non-exponential relaxation, fictive temperatures, and dispersive kinetics in the liquid-glass-liquid transition range of acetaminophen, sulfathiazole, and their mixtures

To investigate the effects of added molecular heterogeneity on the hysteretic features of liquid-glass-liquid transition, we studied acetaminophen, sulfathiazole, and three of their mixtures by calorimetry, and determined the T(g) and the fictive temperature, T(f), from changes in the enthalpy and entropy on the cooling and heating paths, as well as the non-exponential parameter, β(cal). We find that, (i) T(f) for cooling is within 1-3 K of T(f) for heating and both are close to T(g), (ii) the closed loop entropy change in the liquid-glass-liquid range is negligibly small, (iii) T(g) and T(f) increase on increasing sulfathiazole in the mixture, (iv) β(cal) first slightly increases when the second component is added and then decreases, and (v) ageing causes deviations from a non-exponential, nonlinear behavior of the glass. In terms of fluctuations in a potential energy landscape, adding a solute heterogeneity would shift the state point to another part of the landscape with a different distribution of barrier heights and a different number of minima accessible to the state point. Part of the change in β(cal) is attributed to hydrogen-bond formation between the two components. Ageing changes the relaxation times distribution, more at short relaxation times than at long relaxation times, and multiplicity of relaxation modes implied by β(cal) < 1 indicates that each mode contributing to the enthalpy has its own T(g) or T(f). β(cal) differs from β(age) determined from isothermal ageing, and the distribution parameter of α-relaxation times would differ from both β(cal) and β(age).