Reaction Dynamics And Statistics For A_aB_b Type Hyperbranched Polymers

This dissertation for M. S. degree is mainly composed of two chapters concerning some theoretical investigations for the hyperbranched polymers(HPs) formed by the AaBb type polycondensation reaction.Firstly, we focused on the relevant problems associated with the ABb typereaction, which is frequently encountered in the synthesis of HPs, and also the mostimportant reaction type. With the help of a differential equation describing theconsumption and creation of n-mer polymers in reaction process, the number fractiondistribution of n-mer is obtained. As an application, the number-, weight- andZ-average molecular weights and mean-square radius of gyration are deduced. Basedon the statistical theory for the polymeric reactions, we derived a relationship betweenthe conversions and Gibbs free energy, changes of entropy and enthalpy, pressure,temperature and concentrations. The dynamics, kinetics and thermodynamics for thisreaction system are studied, it is shown that the conclusions obtained by statistics anddynamics and kinetics agree well with each other, and the two later methods cansimplify the characterizations of some average polymer physical quantities. We thendiscussed the polymer defects in dendritic polymers that lead to the formation of theHPs. A critical generation is derived for the reaction system under consideration.Furthermore, A Monte Carlo simulation is performed to show the changes of somephysical quantities with the conversions increasing.As an extend study, we continue to consider another system named AaBb typewith a≥2, which implies that the gelation would occurs in this system under some proper conditions, and therefore one must care the sol-gel transition and keep the system to be in pregel regime in order to obtain HP in a relative easy manner. Based on these ideas, some equations satisfied by the sol fraction are given by means of the theory of probability. The gelation condition is obtained through these sol-gelpartition equations, and then the molecular size distribution, all average molecular weights and radius of gyration are derived. With the detailed discussions of dynamics, kinetics and thermodynamics of polymerization process, the relationship between some average polymer quantities and conversions and also some physical conditions are undertaken, which is useful to determine the physical and chemical properties of the HPs, and hence some of results given by this dissertation are able to provide a new way of investigating HPs in a deep level.