(525f) Application of Lattice Cluster Theory to Polymer Phase Behavior

S. Enders¹, C. Browarzik¹,
M. Fischlschweiger^1,2, 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.