Statistical mechanics and thermodynamics for typical hyperbranched polymerization systems

Abstract

We summarize statistical thermodynamics of two typical polymerization systems to relate thermodynamic quantities to the properties of hyperbranched polymers(HBPs) such as average degree of polymerization(DP), radius of gyration, and branching density. An attempt is made to obtain the regulation mechanism of structure and properties of HBPs. Starting from the physical viewpoint, the isothermal compressibility has been associated with the weight average DP of polymers that is interpreted as the spatial correlation of monomers due to polymerization. The subchain is employed to derive the mean square radius of gyration and hydrodynamics radius, and a calculation is implemented in terms of the adjacent matrix of an HBP. Furthermore, the scaling behavior of the system is studied to give the generalized scaling law. The average properties of HBPs under the semi-batch mode are also presented by means of the generation function method. In addition, a Monte Carlo simulation method based on the growth generation is proposed, by which the spatial structure of an HBP can be easily analyzed in detail. As an application, the effect of cyclization, nonequal reactivity, and solvent quality on the polymerization is also carried out.