The development of reliable approaches for the prediction of the thermodynamic properties of polymer systems is crucial for the rational design of polymer materials and polymer processing in a wide range of polymer applications (for example energy storage, electronics, food, controlled drug delivery systems, medical devises). Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids.
The assumption that the glass transition is basically thermodynamic in nature was used to derive a theoretical framework for the calculation of the glass transition temperature of polymers, copolymers and polymer blends [1,2,3]. The theory is a synthesis of the Lattice Cluster Theory (LCT) of blend thermodynamics, the generalized entropy theory for glass-formation in polymer materials, and the rigorous Kirkwood-Buff theory for concentration fluctuations in binary mixtures [2,3].
In the present contribution this theoretical framework is applied in order to compare the theoretical results with experimental data taken from the literature. However, in our calculations the LCT is replaced by the Sanchez-Lacombe equation of state (SL-EOS) [4], because the pure-component parameters for several different polymers (polystyrene, (PS); poly(vinyl methyl ether), (PVME); poly(methyl methacrylate), (PMMA); poly(###i
/i###-phenylene oxide), (PPO)) as well as for the statistical copolymer consisting of styrene and acrylonitrile (PSAN) are available. Unfortunately, the parameters for polyacrylonitrile (PAN) are not available, because no PVT data can be measured with high accuracy. The reason for this finding is the thermal instability of this polymer. Therefore, the pure-component parameter for PAN were estimated using PS and PSAN data simultaneously.
Using the above mentioned theoretical framework [1] the glass transition temperature of pure polymers was calculated as function of the molecular weight, and compared to experimental data. The analysis shows, that one adjustable parameter per pure polymer is required to match experimental glass transition temperature data. Regarding the molecular weight dependency, the theory predicts correctly that the glass transition temperature tends towards a limiting value for high molecular weight polymers. This concept can also be applied to statistical copolymers (i.e. PSAN), where the glass transition temperature is predicted as function of the chemical composition in excellent agreement with experimental data taken from the literature[5].
This theoretical method can also be applied for polymer blends, where the Kirkwood-Buff formalism serves for the determination of the concentration fluctuation. These calculations were performed for blends made of PS and PVME, where the glass transition temperature was investigated as function of blend composition. The obtained values agree very nicely with experimental data [6].
References
[1] J. Dudowicz, K.F. Freed, J.F. Douglas, Adv. Chem. Physics 137 (2008) 125.
[2] J. Dudowicz, J.F. Douglas, K.F. Freed, J. Chem. Phys. 140 (2014) 244905.
[3] J. Dudowicz, J.F. Douglas, K.F. Freed, J. Chem. Phys. 141 (2014) 234903.
[4] I.C. Sanchez, R.H. Lacombe, Macromolecules 11 (1978) 1145-1156.
[5] J.F. Pei, C.Z. Cai, J.L. Tang, S. Zhao, F.Q. Yuan, J. Macromol. Sci., Part B Physics 51 (2012) 1437-1448.
[6] E. Leroy, A. Alegría, J. Colmenero, Macromolecules 35 (2002) 5587–5590.
