Statistical and thermodynamic properties of binary self-condensing vinyl polymerization

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

Statistical thermodynamic properties of a new self-condensing vinyl polymerization system

“…Making use of the equation of state in Eq. (26) together with the law of mass action given by Eqs. (15) and (18), the isothermal compressibility  T can be carried out as:…”

“…Recently, the method of statistical mechanics has been applied to study a series of SCVP systems [25][26][27][28], and the equilibrium free energy and law of mass action were given in their explicit expressions. Furthermore, some average physical quantities such as polymeric moments and mean square radius of gyration can be correlated with thermodynamic quantities of the system.…”

“…It should be noted that, throughout the paper, the classical assumptions of ideal polymerization have been adopted, namely, (1) all the double bonds of vinyl group A are of equal reactivities; (2) all the double bonds of vinyl group A react independently; and (3) the intramolecular reaction is excluded throughout the paper. In fact, these approximations had been used in previous studies [15][16][17][18][25][26][27][28].…”

“…To study the related physical and chemical properties of a system with a great number of species, the method of statistical mechanics is often used as a powerful theoretical tool [25][26][27][28]. In this section, two kinds of partition functions would be constructed from different viewpoints, then the equilibrium free energy, law of mass action, and the size distribution function are given in their explicit forms.…”

The radius of gyration for a ternary self-condensing vinyl polymerization system

“…Thus the method of statistical mechanics becomes a powerful tool in the investigation of some average properties of polymers. Recently, we have demonstrated that the statistical mechanical method can be employed to study several SCVP systems [23][24][25]. As a consequence, the SDF, number-, weight-, and z-average molecular weights, polydispersity index, and the degree of branching can be evaluated.…”