Distribution of Cyclic and Linear Macromolecules in the Polymerization of Cyclic Monomers with Simultaneous Backbiting and End biting Reactions

Abstract

Abstract A system is discussed in which two kinds of cyclic macromolecules, without and with the active center located on the ring, are formed from linear ones (and vice versa) by two discrete processes: backbiting and endbiting, respectively. Thus, the probability of cyclization is not a function of the distance between one kind of the reacting groups, as in the Jacobson-Stockmayer (J-S) theory, but there are two sets of groups that can react and lead to cyclization. The proportion of the end- to-end process in the linear ⇄ cyclic macromolecule equilibration decreases with an increase in the average degree of polymerization of the macromolecules, as was assumed, but it differs from the J-S theory. The present treatment gives a quantitative solution of this new system; equations describing the equilibrium distribution of cyclic and linear oligomers are formulated. These equations are solved numerically, and the dependence of the fraction of macrocyclics, the dependence of the number-average degrees of pol...