265190 Application of Lattice Cluster Theory to Polymer Phase Behavior

Wednesday, October 31, 2012: 2:05 PM
412 (Convention Center )
Sabine Enders1, Christina Browarzik1, Michael Fischlschweiger1,2 and Dieter Browarzik3, (1)Thermodynamics and Thermal Engineering, TU Berlin, Berlin, Germany, (2)Forschung GmBH, Materials Center Leoben, Leoben, Austria, (3)Physical Chemistry, Martin-Luther University Halle-Wittenberg, Halle, Germany

Application of Lattice Cluster Theory to Polymer Phase Behavior

S. Enders1, C. Browarzik1, M. Fischlschweiger1,2, D. Browarzik3

1Thermodynamics and Thermal Engineering (BH-7-1), TU Berlin, Ernst Reuter Platz 1, 10587 Berlin, Germany,

2 Materials Center Leoben, Forschung GmbH, Roseggerstrasse 12, 8700 Leoben, Austria,

3Institute of Chemistry, Physical Chemistry, Martin-Luther University Halle-Wittenberg, 06099 Halle, Germany

E-mail : Sabine.Enders@tu-berlin.de

Key words: liquid-liquid equilibria, solid-liquid equilibria, lattice cluster theory, linear, branched and hyperbranched polymers

The phase behavior of polymer containing systems, like polymer solutions or polymer blends; depend strongly on the molecular weight and the architecture of the polymer in terms of linear, branched or hyperbranched polymers. In order to model the influence of architecture on the phase behavior the Lattice Cluster Theory (LCT), developed by Freed and coworker[1], can be utilized. This approach takes the architecture of the polymer by the short range correlations directly into account. The theoretical framework provides an analytical expression for the Helmholtz energy, where the architecture is incorporated by the architecture coefficients. These coefficients can be estimate by the united-atom approach using graph theory[2]. Even for linear polymers, the LCT offers several advantages in comparison with the classical Flory-Huggins theory, without the application of additional adjustable parameters.

In this contribution the LCT is applied to the liquid-liquid equilibria (LLE) of hyperbranched polymer solutions in a single solvent or a solvent mixture[3]. The calculated phase diagrams of aqueous solutions of hyperbranched polyesters are compared with own experimental data. In the case of hyperbranched polymers the influence of the polar functional groups has to be considered.

Additionally, the solid-liquid equilibrium (SLE) of linear and branched polymers in a solvent is discussed. These equilibria form the thermodynamic background of temperature rising elution fractionation (TREF) and crystallization analysis fractionation (CHYRSTAF). In order to obtain quantitative information about the distribution of lengths of crystallizable polymer sequences mathematical models relating the crystallization conditions inside the TREF or CRYSTAF columns with the microstructural details of the polymer are needed. The LCT, in its in-compressible version, is applied for the calculation of the activity coefficients in the liquid phase and the melting enthalpy and the melting temperature were taken from DSC-measurements. From experimental studies[4] is known that the branching leads to lower melting temperatures. Exactly, this situation is predicted by the LCT, without any adjustable parameter. The difference between both melting temperatures increases with decreasing polymer concentration. The proposed thermodynamic theory is able to describe the most important experimental findings4, especially the influence of the short-chain branching on the SLE. For this reason, the new approach can be used for the extraction of information of the polymer based on TREF or CHYRSTAF data.

[1] K.F. Freed, J. Dudowicz, Adv. Polym. Sci. 183 (2005) 63-126.

[2] S. Enders, K. Langenbach, P. Schrader, T. Zeiner, Polymers 4 (2012) 72115.

[3] T. Zeiner, S. Enders, Chem. Eng. Sci. 66 (2011) 52445252.

[4] B. Monrabal, P. Del Hierro, Anal. Bioanal. Chem. 399 (2011) 1557-1561.

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See more of this Session: Thermophysical Properties and Phase Behavior IV
See more of this Group/Topical: Engineering Sciences and Fundamentals