Nature of the Glass Transition and the Glassy State

Abstract

The thermodynamic properties of amorphous phases of linear molecular chains are obtained from statistical mechanics by means of a form of the quasi-lattice theory which allows for chain stiffness and the variation of volume with temperature. A second-order transition is predicted for these systems. This second-order transition has all the qualitative features of the glass transition observed experimentally. It occurs at a temperature which is an increasing function of both chain stiffness and chain length and a decreasing function of free volume. The molecular ``relaxation times'' are shown to increase rapidly as the second-order transition temperature is approached from above. To permit quantitative application of the theory and determine the relationship between the second-order transition and the glass transition observed in ``slow'' experiments these two transitions are tentatively identified. By this means quantitative predictions are made concerning the variations of (1) glass temperature with molecular weight, (2) volume with temperature, (3) volume with molecular weight, (4) volume at the glass temperature with the glass temperature for various molecular weights of the same polymer, (5) specific heat vs temperature, and (6) glass temperature with mole fraction of low-molecular weight solvent, since extensive experimental results are available for these properties. These and other theoretical predictions are found to be in excellent agreement with the experimental results.

An overview of the nonequilibrium behavior of polymer glasses

“…The prediction by the WLF equation that viscosity becomes infinite at T = T -51.6 has also been approached from the thermodynamic viewpoint by Gibbs and DiMarzio [13,14] and Adam and Gibbs [15]. Gibbs and DiMarzio proposed that the dilatometric Tg discussed earlier is simply a kinetic manifestation of a true equilibrium second-order transition.…”

The Relaxation Dynamics of a Supercooled Liquid Confined by Rough Walls

“…Some concentrate on thermodynamic aspects and propose a first or second order phase transition (e.g. free volume theory [2] or entropy models [3,4]), while others, such as mode-coupling theory [5], focus on the microscopic dynamics that shows non-linear feedback effects which are responsible for the slow dynamics.…”

Thermodynamics of the Glassy State

“…In the standard definition [3] the configurational entropy I is the entropy of the glass minus the one of the vibrational modes of the crystal. For polymers it still includes short-distance rearrangements, which is a relatively fast mode.…”

“…It should be kept in mind that, so far, the approaches leaned very much on equilibrium ideas. Well known examples are the 1951 Davies-Jones paper [2], the 1958 GibbsDiMarzio [3] and the 1965 Adam-Gibbs [4] papers, while a 1981 paper by DiMarzio has title "Equilibrium theory of glasses" and a subtitle "An equilibrium theory of glasses is absolutely necessary" [5]. We shall stress that such approaches are not applicable, due to the inherent non-equilibrium character of the glassy state.…”