The free-volume model, which has been useful for describing the behavior of the viscosity $\ensuremath{\eta}$ of dense liquids and glasses, is extended to account for their thermodynamic behavior as well. Experimental results for the heat capacity ${C}_{p}$ and the volume $\overline{v}$ show that the system falls out of complete, metastable thermodynamic equilibrium at the glass transition temperature ${T}_{g}$. As a first step in understanding these universal phenomena, a theory of the underlying metastable phase, the amorphous phase, is developed. Recent molecular-dynamic calculations demonstrating the existence of a cellular structure in liquids and the properties of the local free energy of the molecular cells permit us to formulate more precisely and justify in more detail the standard free-volume model. In particular, it is possible to define the free volume and distinguish solid-like and liquidlike cells. This leads to the introduction of percolation theory, which is used to describe the gradual development of the communal entropy of the amorphous phase. We then determine the probability distribution of the cellular volume as a function of the fraction of liquidlike cells, $p$. The equilibrium liquid-glass transition is associated with the increase of $p$ with temperature. This occurs via a phase transition which is most probably first order. The results of our theory give a generalized equation for the viscosity which agrees accurately with experimental results at all temperatures. Results for ${C}_{p}$ and $\overline{v}$ are also obtained. This equilibrium theory can provide the basis for a relaxation theory of the kinetic effects observed around and below ${T}_{g}$. The relationship between the entropy theory and the free-volume model is also clarified.

Liquid-glass transition, a free-volume approach

https://www.umsl.edu/~chickosj/JSCPUBS/dsccal.pdf

Reference materials for calorimetry and differential thermal analysis

The different physical aspects of glass transitions are reviewed and models aiming at their explanation are described. The following three main aspects are distinguished: the degree of stability of supercooled liquids with respect to crystallisation; the variation of physical properties of supercooled liquids in metastable equilibrium above the glass transition; the arrest of structural relaxation at the glass transition. The physical significance of computer simulations of glass transitions in simple liquids and the question of a hidden phase transition underlying an observed glass transition are examined critically. In relation to the stability problem, the geometrical constraints operative in typical disordered structures, such as random sphere packings and random covalent networks, are also discussed. A general survey of glass transition phenomena and concepts is presented in an introductory section.

https://iopscience.iop.org/article/10.1088/0034-4885/49/2/002/pdf

Models of the glass transition

The solid–liquidphase transition temperatures and heats of fusion ΔH f of nonpolar organic solids confined in the pores of controlled pore glasses were measured by differential scanning calorimetry. The pore diameters d were in the range of 40–730 A and the organics studied were cis‐decalin, trans‐decalin, cyclohexane, benzene, chlorobenzene, naphthalene, and heptane. In accordance with previous reports on studies of primarily inorganic materials, the melting point of the pore solidT(d) decreased with decreasing pore diameter. In addition, a large reduction in the bulk enthalpy of fusion ΔH f of the pore solid was measured, which apparently has not been studied in detail by other workers. A linear correlation was found between the melting point depression (ΔT m ) and the reciprocal diameter, as predicted by theories of solidification in a capillary. The calculated values of the solid–liquid interfacial energy σsl were in reasonable agreement with values reported in the literature based on other methods of measurement.

/pdf/the-melting-behavior-of-organic-materials-confined-in-porous-315yrxd5fm.pdf

The melting behavior of organic materials confined in porous solids

We compare dielectric relaxation τ(T) data of several low molecular weight glass-forming liquids with the predictions of the Adam–Gibbs theory using experimental data for the configurational entropy Sc(T). Combination of Adam–Gibbs and Vogel–Fulcher equations yields an expression for Sc(T) which can be compared with experimental data. Good agreement is found for a range of temperatures near Tg<T<TB which depends on the fragility of the liquid and on the presence of a β relaxation. For fragile liquids, TB coincides with a qualitative change in the temperature dependence of the relaxation time scale or viscosity, with the temperature Tβ, where Johari–Goldstein-type β processes tend to merge into the α process, and with other crossover temperatures. For nonfragile liquids, TB/Tg increases, and the deviations from the Adam–Gibbs equation weaken or disappear altogether. The significance of TB, and of the Sc(T) temperature dependence implied by the Vogel–Fulcher theory fitting, are discussed in terms of the lan...

Dynamics of glass-forming liquids. V. On the link between molecular dynamics and configurational entropy

The heat capacity of o‐terphenyl has been measured with an adiabatic calorimeter for the crystal from 2°K to Tm (329.35°K), for the glasses from 2°K to Tg (around 240°K) and for the liquid from Tg to 360°K, on a sample with less than 0.005 mole % impurity. The heat of fusion and the entropy of fusion are 17 191 J mole−1 and 52.20 J°K−1· mole−1, respectively. The residual entropy of the glasses at 0°K is about 15 J°K−1· mole−1. Above 170°K, the heat capacity of the o‐terphenyl crystal is nearly proportional to the temperature to within 1%. Configurational entropy of the supercooled liquid, estimated from the result of this investigation, is used to relate the relaxation properties of glass‐forming liquids according to the theory of Adam and Gibbs. Good agreement is found for both viscosity and NMR correlation frequency data.

S. S. Chang

Papers

Heat Capacity and Thermodynamic Properties of o‐Terphenyl Crystal, Glass, and Liquid