Entwicklung einer kontinuierlichen Lattice Cluster Theory

Polymer thermodynamics and its application to phase equilibrium calculations is essential to obtain desired polymer blend properties. However, modeling of polymer-solvent phase equilibria is challenging due to the complex architectural structure and polydispersity of the polymer which influence the thermodynamic properties.
In this work a model approach is presented which combines continuous thermodynamics and the Lattice Cluster Theory (LCT) to incorporate polydispersity into the excess Gibbs free energy of the LCT. Starting point of the theoretical framework is the multicomponent LCT model which allows the consideration of the polymer segments as individual components. Based on this model the contributions of the correction to the entropy, the first order energy and the second order energy, which all define the excess Gibbs free energy, are divided into individual coefficients. In the context of continuous thermodynamics every coefficient is continuously expanded. In doing so a continuous Lattice Cluster Theory (CLCT) is obtained. Based on this developed CLCT model the equations of the cloud curve and the critical point for a binary polymer-solvent liquid-liquid equilibrium (LLE) are formulated.
In order to reflect the influence of the polydispersity on the CLCT model with respect to the LCT with continuous mean field, the LLE of different polymer structures are investigated. It can be shown that the CLCT model produces a shift of the critical point and the cloud curve with respect to the LCT with continuous mean field. Depending on the number of branching points of the polymer and the polydispersity the critical temperature calculated with the CLCT is either much higher or slightly lower than the prediction of the LCT with continuous mean field.
Furthermore, the CLCT model is applied to the LLE of polymer-solvent blends with known molecular architecture and compared to experimental results. Additionally calculations are performed with the classical LCT model and LCT model with continuous mean field to compare their results with the calculations of the CLCT model. The incorporation of polydispersity in the correction of entropy, first order energy and second order energy within the CLCT model shows a significant improvement of the prediction of the LLE phase behavior. The CLCT model is the first model which allows the consideration of polydispersity not only in the mean field but also in the excess Gibbs free energy.