A Statistical Theory For Self-Condensing Vinyl Polymerization

The method of statistical mechanics is used to investigate some average properties of several types of self-condensing vinyl polymerization systems. The corresponding partition functions of each system are constructed from two different viewpoints, respectively. One is from the configurations of hyperbranched polymers, while the other is associated with functional groups. Then the equilibrium free energy and the law of mass action concerning the polymerization process can be obtained, and they can be jointly used to study the thermodynamic and dynamic properties of the related systems. As a result, the explicit expressions of the number- and weight-average degrees of polymerization, polydispersity index, specific heat, isothermal compressibility, radius of gyration and the numbers of different structural units are presented. The main contents of the dissertation are as follows:Chapter 1. The developments of hyperbranched polymers are summarized. In detail, some relevant experiments about self-condensing vinyl systems of homopolymerization, binary and ternary copolymerization are introduced. Theoretically, the application of some methods to investigate the self-condensing vinyl polymerization systems is outlined, which involve the methods of solving kinetic differential equation, generating function, statistical mechanics and Monte Carlo simulation.Chapter 2. The method of statistical mechanics is used to study several properties of self-condensing vinyl homopolymerization system. Under the framework of mean field theory, two types of partition functions of the system are constructed from viewpoints of functional groups and polymers, and by which the explicit expressions of equilibrium free energy and the law of mass action are obtained. Based on the free energy, the same size distribution function of hyperbranched polymers is derived by two different methods. This implies that the two partition functions are consistent with each other. Furthermore, in terms of the size distribution function, the k-th radius of gyration as well as its scaling behavior near the critical point is studied, and the corresponding scaling law is given. Alternatively, the influence of the solvent effect on the average dimension of hyperbranched polymers is discussed. As an application, the isothermal compressibility is derived on the basis of equation of state, which indicates that the spatial correlation between monomers increases with the increasing of conversion of the double bonds, and reaches the maximum at the critical point. In addition, it is shown that a usual treatment on the polydispersity index would lead it to be infinite, which is not agreement with the true result of 1 at the end of the reaction system. To clarify this fact, we find that the correlation length plays an important role, and then by using asymptotic forms of the size distribution and the second moment, the reasonable result can be carried out. At last, to investigate the structal properties of the hyperbranched polymers, the numbers of different structural units and the fraction of branched-point are calculated.Chapter 3. The thermodynamic properties of a binary self-condensing vinyl polymerization system consisting of monomers and inimers are investigated by the principle of statistical mechanics. In detail, in terms of two types of canonical partition functions constructed from different viewpoints, the equilibrium free energy, the law of mass action and the size distribution of hyperbranched polymers are obtained. As an application, the specific heat, equation of state and isothermal compressibility concerning the polymerization are given as well. To study the dimension of hyperbranched polymers in the system, a recursion formula satisfied by the (k+1)-th and k-th mean square radius of gyration is derived, and then the first, second and third radius of gyration under different solvent conditions are presented. The influences of the fraction of inimers, the conversion of vinyl groups and the solvent effect on the average dimension of hyperbranched polymers are discussed. To study the effect of monomers on the structural properties of the hyperbranched polymers, the numbers of different structural units are calculated. The result shows that the molar ratio of inimers to monomers has significant effect on the branch units.Chapter 4. The self-condensing vinyl polymerization system consisting of inimers and multifunctional core initiators is studied by the principle of statistical mechanics. From viewpoints of functional groups and polymers, two types of canonical partition functions are constructed and further are proved to be consistent with each other. In this way, the explicit expressions of equilibrium free energy and law of mass action concerning the polymerization are obtained, and then the equilibrium size distribution functions of hyperbranched polymers are given. With the help of the size distribution functions, the k-th mean square radii of gyration of hyperbranched polymers with and without a core are derived, respectively. In addition, the numbers of four types of structural units are calculated. In order to investigate the effect of core initiators on the statistical properties of the system, the number and functionality of core initiators have been explicitly taken into account, and the variations of relevant physical quantities against the conversion of vinyl groups under various conditions are presented. It is shown that the presence of core initiator results in a significant influence on average properties of the system, which can be explained from the competition between polymers with and those without a core initiator in their growth process.Chapter 5. A ternary self-condensing vinyl polymerization system consisting of monomers, inimers and core initiators is studied by the principle of statistical mechanics. As a result, two types of canonical partition functions for polymerization are constructed from different viewpoints, and then the explicit expressions of equilibrium size distribution function, the equilibrium free energy and the law of mass action are obtained. In addition, the isothermal compressibility, the specific heat and the numbers of different structural units are calculated. To investigate the average property of the system, the mean square radius of gyration as well as the recursion formula satisfied by the k-th and the (k+1) -th mean square radius of gyration are given, where the solvent quality and excluded volume effect are taken into account.Finally, some limitations of the present method are pointed out, and meanwhile, some possible and desired developments of SCVP systems are stated. It is expected that with our results, the topic in this field can further continue to success.