Calculation of Glass Transition Using Sanchez-Lacombe - Eos

Calculation of glass transition using Sanchez-Lacombe - EOS

Margarete Roericht, Kirstin Taufertshöfer, Sabine Enders

Karlsruhe Institute of Technology, Institute of Technical Thermodynamics and Refrigeration Engineering, Engler-Bunte-Ring 21, 76131 Karlsruhe, Germany.

Email: margarete.roericht@kit.edu, kirstin.taufertshoefer@kit.edu; sabine.enders@kit.edu

Key words: Glass transition temperature of polymers and polymer blends, Sanchez-Lacombe Model, generalized entropy theory

Abstract:

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 (T_g) of polymers, copolymers and polymer blends [1,2,3]. The theory is a synthesis of a thermodynamic equation of state suitable for polymers, 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. We apply 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(p-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 T_g 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 T_g data. Regarding the molecular weight dependency, the theory predicts correctly that the T_g tends towards a limiting value for high molecular weight polymers. This concept can also be applied to statistical copolymers (i.e. PSAN), where the T_g 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 T_g was investigated as function of blend composition [6]. Blends made of PS and PPO serve as an additional example, where experimental data are taken from [7]. In both cases, the T_g runs monotonically from the T_g of one pure polymer to the T_g of the other pure polymer. In contrast, the T_g as function of blend composition made of PSAN + PMMA [8] runs through a maximum.

The obtained values agree very nicely with experimental data [6,7,8].

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.

[5] L. Fan, D. Zhao, C. Bian, Y. Wang, G. Liu, Polym. Bull. 67 (2011) 1311.

[6] E. Leroy, A. Alegría, J. Colmenero, Macromolecules 35 (2002) 5587.

[7] W.M. Prest, R.S. Porter, J. Polym. Sci. A-2 10 (1972) 1639.

[8] G. Wen, L. An, J. Appl. Polym. Sci. 90 (2003) 959.