Presence of branches in the molecular structure results in properties different from that of linear molecules and also leads to special industrial value and diverse novel applications. However, a basic knowledge of thermodynamics of branched molecules is lacking. Experimental data for branched molecules are far less abundant compared with linear molecules and are usually questionable under harsh conditions such as high temperature and high pressure. Therefore, the goal of this thesis is to enhance our understanding of the phase behavior and microstructure of branched molecules using statistical mechanics based theories.

A new equation of state based on statistical associating fluid theory (SAFT) is developed and applied to isomeric alkanes. The branching effect is explicitly accounted and the results are in good agreement with experimental data. The density functional theory (DFT) version of SAFT, modified iSAFT, is applied to study conformations of branched polymers of special architecture, such as dendrimer and bottlebrush polymers. Related parameters such as molecule size, solvent quality and temperature that affect the phase behavior of these polymers have been investigated. The theoretical results are qualitatively consistent with experimental observations and are also validated by molecular simulation. In addition, several functional polymers are studied, where we see potential lower critical solution temperature (LCST) behavior of an associating dendrimer and partially hidden conformations of an amphiphilic bottlebrush polymer.

The theories and models developed for branched molecules in this thesis are proved to not only be able to explain and support existent experimental results, but also have strong prediction ability where there is no data at all. These models will provide physical insight and helpful guidance for the design and application of branched molecules.