First-principles study of the specific heat of glass at the glass transition with a case study on glycerol

The standard method to determine the transition temperature (T_g) of glasses is the jump in the specific heat,ΔCp. Despite its importance, standard theory for this jump is lacking. The difficulties include lack of proper treatment of the specific heat of liquids, hysteresis, and the timescale issue. The first part of this paper provides a non-empirical method for calculating the specific heat in the glass transition. The method consists of molecular dynamics (MD) simulations based on density-functional theory (DFT) and thermodynamics methods. Calculation of the total energy, which is the heart of DFT, is the most general method for obtaining specific heat for any state of matters. The influence of energy dissipation processes on specific heat is treated by adiabatic MD simulations. The problems of hysteresis and the timescale are alleviated by restricting the scope of calculations to equilibrium states only. The second part of this paper demonstrates the validity and usefulness of the methods by applying to the specific-heat jump of glycerol. By decomposingΔCpinto contributions of the structural, phonon, and thermal expansion energies, an appropriate interpretation for the specific-heat jump has been established: the major contribution toΔCpis the change in the structural energy. From this, a neat energy diagram about the glass transition is obtained. An outcome of this study is verification of the empirical relationship between the fragility and the specific-heat jump. These two quantities scale to the ratiok=Tg/ΔTg, whereΔTgis the width of the transition, through which the two quantities are interrelated.

"Inner clocks" of glass-forming liquids

Providing a physically sound explanation of aging phenomena in non-equilibrium amorphous materialsis a challenging problem in modern statistical thermodynamics. The slow evolution of physical propertiesafter quenches of control parameters is empirically well interpreted via the concept of material time (orinternal clock), based on the Tool-Narayanaswamy-Moynihan (TNM) model. Yet, the fundamental reasonsof its striking success remain unclear. We propose a microscopic rationale behind the material time onthe basis of the linear laws of irreversible thermodynamics and its extension that treats the correspondingkinetic coefficients as state functions of a slowly evolving material state. Our interpretation is based onthe recognition that the same mathematical structure governs both the Tool model and the recently devel-oped non-equilibrium extension of the self-consistent generalized Langevin equation theory (NE-SCGLE),guided by the universal principles of Onsager's theory of irreversible processes. This identification opensthe way for a generalization of the material-time concept to aging systems where several relaxation modeswith very different equilibration processes must be considered, and partially frozen glasses manifest theappearance of partial ergodicity breaking, and hence materials with multiple very distinct inner clocks.

Communication: Glass transition and melting lines of an ionic liquid

The phase diagram of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethanesufonyl)imide, [Pyrr_1,4][NTf₂], was explored by synchroton X-ray diffraction and Raman scattering measurements as a function of temperature and pressure. Glass transition T_g(p) and melting T_m(p) temperatures were obtained from atmospheric pressure up to ca. 2.0 GPa. We found that both the T_g(p) and T_m(p) curves follow essentially the same pressure dependence. The similarity of pressure coefficients, dT_g/dp ≈ dT_m/dp, is explained within the non-equilibrium thermodynamics approach for the glass transition by assuming that one of the Ehrenfest equations is appropriated for T_g(p), whereas T_m(p) follows the Clausius-Clapeyron equation valid for the first-order transitions. The results highlight that ionic liquids are excellent model systems to address fundamental questions related to the glass transition.

Kinetics of Dissolution of an Amorphous Solid

The kinetics of dissolution of an amorphous solid is studied using a simple model of a glass that captures with reasonable accuracy the dynamic heterogeneities associated with the relaxation of an amorphous material at low temperatures. The intrinsic dissolution rate is shown to be proportional to the concentration of surface particles kinetically able to exchange with the solvent, independent of temperature or the thermal history of the glass. The morphology of the dissolving surface is described, and the possibility of using surface etching to image dynamic heterogeneities is explored.

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.

Thermodynamic and structural properties of binary calcium silicate glasses: insights from molecular dynamics

The thermodynamic and structural properties of calcium-modified binary silicate glasses have been computed using molecular dynamics simulations.

Thermodynamic consequences of the kinetic nature of the glass transition

In this paper, we consider the glass transition as a kinetic process and establish one universal equation for the pressure coefficient of the glass transition temperature, dTg/dp, which is a thermodynamic characteristic of this process. Our findings challenge the common previous expectations concerning key characteristics of the transformation from the liquid to the glassy state, because it suggests that without employing an additional condition, met in the glass transition, derivation of the two independent equations for dTg/dp is not possible. Hence, the relation among the thermodynamic coefficients, which could be equivalent to the well-known Prigogine-Defay ratio for the process under consideration, cannot be obtained. Besides, by comparing the predictions of our universal equation for dTg/dp and Ehrenfest equations, we find the aforementioned supplementary restriction, which must be met to use the Prigogine-Defay ratio for the glass transition.

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

Change in the entropy, dS, with change in the temperature T, with or without phase transformation, is determined only if the thermal path is reversible. For an irreversible thermal path, dS > dqirrev/T, an expression known as inequality in the Clausius theorem. In the glass formation range, Cp and enthalpy show a time-dependent hysteresis between the cooling and heating paths and the two Cp paths cross each other. We provide new data on Cp of poly(styrene) and use the previous Cp data [E. Tombari, C. Ferrari, G. Salvetti, and G. P. Johari, Phys. Rev. B 78, 144203 (2008)], both data obtained from measurements performed on cooling from melt to glass and heating from glass to melt at unusually slow rates, and show that violation of the Clausius theorem in such cases has insignificant consequences for determining the entropy of glass. We also report Cp of the samples annealed for different times at different temperatures in which the enthalpy spontaneously decreased. These measurements also show that violation of the Clausius theorem is relatively inconsequential for interpreting the entropy of the glassy state.

On the theoretical determination of the Prigogine-Defay ratio in glass transition

In a recent analysis [J. W. P. Schmelzer and I. Gutzow, J. Chem. Phys. 125, 184511 (2006)] it was shown for the first time that--in contrast to earlier belief arising from the works of Prigogine and Defay [Chemical Thermodynamics (Longman, London, 1954), Chap. 19; The first French edition of this book was published in 1950] and Davies and Jones [Adv. Phys. 2, 370 (1953); and Proc. R. Soc. London, Ser. A 217, 26 (1953)]--a satisfactory theoretical interpretation of the experimentally observed values of the so-called Prigogine-Defay ratio Π, being a combination of jumps of thermodynamic coefficients at glass transition, can be given employing only one structural order parameter. According to this analysis, this ratio has to be, in full agreement with experimental findings, larger than one (Π > 1). Its particular value depends both on the thermodynamic properties of the system under consideration and on cooling and heating rates. Based on above-mentioned analysis, latter dependence on cooling rates has been studied in detail in another own preceding paper [T. V. Tropin, J. W. P. Schmelzer, and C. Schick, J. Non-Cryst. Solids 357, 1303 (2011)]. In the present analysis, an alternative general method of determination of the Prigogine-Defay ratio is outlined, allowing one to determine this ratio having at ones disposal the generalized equation of state of the glass-forming melts under consideration and, in particular, the knowledge of the equilibrium properties of the melts in the glass transformation range. Employing, as an illustration of the method, a particular model for the description of glass-forming melts, theoretical estimates are given for this ratio being, again, in good agreement with experimental data.

Correlated volume-energy fluctuations of phospholipid membranes: a simulation study

This paper reports all-atom computer simulations of five phospholipid membranes (DMPC, DPPC, DMPG, DMPS, and DMPSH) with focus on the thermal equilibrium fluctuations of volume, energy, area, thickness, and chain order. At constant temperature and pressure, volume and energy exhibit strong correlations of their slow fluctuations (defined by averaging over 0.5 ns). These quantities, on the other hand, do not correlate significantly with area, thickness, or chain order. The correlations are mainly reported for the fluid phase, but we also give some results for the ordered (gel) phase of two membranes, showing a similar picture. The cause of the observed strong correlations is identified by splitting volume and energy into contributions from tails, heads, and water, and showing that the slow volume-energy fluctuations derive from van der Waals interactions of the tail region; they are thus analogous to the similar strong correlations recently observed in computer simulations of the Lennard-Jones and other simple van der Waals type liquids (U. R. Pedersen et al., Phys. Rev. Lett. 2008, 100, 015701). The strong correlations reported here confirm one crucial assumption of a recent theory for nerve signal propagation proposed by Heimburg and Jackson (T. Heimburg and A. D. Jackson, Proc. Natl. Acad. Sci. 2005, 102, 9790-9795).

Single-order-parameter description of glass-forming liquids: A one-frequency test

Thermoviscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear dynamic Prigogine-Defay ratio" LambdaTp(omega) with the property that if LambdaTp(omega)=1 at one frequency, then LambdaTp(omega) is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermoviscoelastic linear responses via an order parameter (which may be nonexponential in time). Generalizations to other cases of thermodynamic control parameters than temperature and pressure are also presented.

The Prigogine-Defay ratio revisited

One of the basic characteristics of the glass transition, the Prigogine-Defay ratio, connecting jumps of the thermal expansion coefficient, isothermal compressibility, and isobaric specific heat capacity in vitrification is rederived in the framework of the thermodynamics of irreversible processes employing the order-parameter concept introduced by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)]. In our analysis, glass-forming liquids and glasses are described by only one structural order parameter. However, in contrast to previous approaches to the derivation of this ratio, the process of vitrification is treated not in terms of Simon's simplified model [Z. Anorg. Allg. Chem. 203, 219 (1931)] as a freezing-in process proceeding at some sharp temperature, the glass transition temperature T(g), but in some finite temperature interval accounting appropriately for the nonequilibrium character of vitrifying systems in this temperature range. As the result of the theoretical analysis, we find, in particular, that the Prigogine-Defay ratio generally has to have values larger than 1 for vitrification in cooling processes. Quantitative estimates of the Prigogine-Defay ratio are given utilizing a mean-field lattice-hole model of glass-forming melts. Some further consequences are derived concerning the behavior of thermodynamic coefficients, in particular, of Young's modulus in vitrification. The theoretical results are found to be in good agreement with experimental data.

Freezing-in and production of entropy in vitrification

Following the classical concepts developed by Simon [Z. Anorg. Allg. Chem. 203, 219 (1931)], vitrification in the cooling of glass-forming melts is commonly interpreted as the transformation of a thermodynamically (meta)stable equilibrium system into a frozen-in, thermodynamically nonequilibrium system, the glass. Hereby it is assumed that the transformation takes place at some well-defined sharp temperature, the glass transition temperature Tg. However, a more detailed experimental and theoretical analysis shows that the transition to a glass proceeds in a broader temperature range, where the characteristic times of change of temperature, tauT=-(TT), and relaxation times, tau, of the system to the respective equilibrium states are of similar order of magnitude. In this transition interval, the interplay of relaxation and change of external control parameters determines the value of the structural order parameters. In addition, irreversible processes take place in the transition interval, resulting both in an entropy freezing-in as well as in an irreversible increase of entropy and, as a result, in significant changes of all other thermodynamic parameters of the vitrifying systems. The effect of entropy production on glass transition and on the properties of glasses is analyzed here for the first time. In this analysis, the structural order-parameter concept as developed by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)] and Prigogine and Defay [Chemical Thermodynamics (Longmans, London, 1954)] is employed. In the framework of this approach we obtain general expressions for the thermodynamic properties of vitrifying systems such as heat capacity, enthalpy, entropy, and Gibbs' free energy, and for the entropy production. As one of the general conclusions we show that entropy production has a single maximum upon cooling and two maxima upon heating in the glass transition interval. The theoretical concepts developed allow us to explain in addition to the thermodynamic parameters also specific features of the kinetic parameters of glass-forming melts such as the viscosity. Experimental results are presented which confirm the theoretical conclusions. Further experiments are suggested, allowing one to test several additional predictions of the theory.

Spinodal and ideal glass limits for metastable liquids

A spinodal line provides a high-temperature limit to the stability of a superheated liquid and a line of ideal glass transitions may provide a low-temperature limit for a supercooled liquid. For models in which the thermodynamic properties depend on only one independent external variable the line of ideal glass transition can be viewed as a second-order transition between two equilibrated phases and it meets the spinodal with the same slope at the maximum tension a stretched liquid can sustain. For real materials there are two independent external variables, temperature and pressure; the line of ideal glass transitions cannot be viewed as a second-order phase transition and the two lines need not have the same slope where they meet.