Glass Transition of Polymers from a Thermodynamic Point of View

The physical properties of materials change dramatically at the glass transition. The glass transition can in principle be considered from the mechanical or from the thermodynamic point of view. In this contribution, we will focus on the thermodynamic point of view. The Generalized Entropy Theory (GET), originally developed by Freed and coworkers [1], relates the glass transition to the entropy density of the considered material. The glass transition temperature is defined with respect to the structure relaxation time, which must exceed 100 seconds. For mixtures, the GET allows the consideration of local fluctuations. The GET enables us to predict the glass transition temperature if the entropy density can be calculated. For this purpose, a thermodynamic equation of state based on statistical mechanics of the molecules can be used. One example is the lattice theory, developed by Sanchez-Lacombe (SL) [2]. This theory requires for every kind of molecule three pure-component parameters which can be adjusted to experimental data related to the pressure-volume temperature behavior in the amorphous state. In the case of mixtures, combining rules must be applied. After the parameterization of the SL, different thermodynamic quantities, including density, entropy as well as phase diagrams, can be calculated. We use the SL within the GET for the calculation of glass transition temperatures of pure polymers and polymer blends. The application of this framework permits the calculation of the glass transition of polymers as a function of molecular weight and pressure. In the case of polymer blends, the glass transition temperature can be predicted as a function of the blend composition. We will discuss this phenomenon for miscible blends (Polyisoprene + Polybutadiene, Polystyrene + Polyphenylenether) and for blends showing demixing behavior (Polystyrene + Poly(vinyl methyl ether)). In the case of copolymers (Poly(styrene co acrylonitrile)), the glass transition can be calculated as a function of the chemical composition. Additionally, the impact of small molecules, for instance softener or humidity, on the glass transition can be studied. The predictions will be compared with experimental data taken from the literature.

References

1. J. Dudowicz, K. F. Freed, and J. F. Douglas, Generalized entropy theory of polymer glass formation, Advances in Chemical Physics, 137:125–222, 2007, https://doi.org/10.1002/9780470238080.ch3.
2. I. C. Sanchez and R. H. Lacombe, Statistical thermodynamics of polymer solutions, Macromolecules, 11(6):1145–1156, 1978, https://doi.org/10.1021/ma60066a017.