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.

No abstract

No abstract

No abstract

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.self-condensing vinyl polymerization, law of mass action, mean square radius of gyration, solvent effect