title: A statistical theory for self-condensing vinyl polymerization.
abstract: The method of statistical mechanics is used to investigate several properties of self-condensing vinyl polymerization system. Under the framework of mean field theory, two types of canonical 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, which is identical with the previous result given by solving the kinetic differential equations. This implies that the two partition functions are consistent with each other. Furthermore, in terms of the size distribution function, the kth radius of gyration as well as its scaling behavior near the critical point are studied, and the corresponding scaling law is given. 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 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.
authors.affiliation: College of Chemistry and Environment Science, Hebei University, Baoding 071002, People's Republic of China.
authors.forename: Zuo-Fei
authors.initials: ZF
authors.lastname: Zhao
authors.forename: Hai-Jun
authors.initials: HJ
authors.lastname: Wang
authors.forename: Xin-Wu
authors.initials: XW
authors.lastname: Ba
mesh_terms: D008956:Models, Chemical; D011145:Polyvinyls / Q000737:chemistry*; D013816:Thermodynamics
chemical_list: D011145:Polyvinyls