Kinetics of Ring-Opening Polymerization
There is general similarity between the kinetics of many ring-opening polymerization and those of step-growth polymerizations that are discussed in Chap. 7. Some kinetic expressions in ring-opening polymerizations, on the other hand, resemble ionic chain-growth reactions. There are several forms of the rate law that describe the cationic ring-opening polymerization. For living or polymerizations without termination, one can write
where [M*] is the concentration of the propagating oxonium ions. Such ions could be oxonium, sulfonium, and others. When, however, there is propagation–depropagation equilibrium, it can be expressed as follows:
The rate expression can be written as propagation–depropagation
At condition of equilibrium, if we designate the monomer concentration [M]C, and the polymerization rate is zero, we can write
Kp(M)C= KDP
Hirota and Fukuda [1] described the quantitative dependence of the degree of polymerization on various reaction parameters for an equilibrium polymerization. The equilibrium can be described as
where, I is the initiating species. It is assumed that the equilibrium constants for the initiation and propagation are independent of the size of the propagating species. The concentration of the propagating chains [M*] of size n at equilibrium c then can be written as:
(M)=KI(I)C(M)C(Kp(M)C) n-1
The total concentration of molecules size N can be expressed as follows
The total concentration of monomer segments that are incorporated into the polymer can also be expressed as follows:
This allows us to express the average degree of polymerization that is [W]/[N] as follows:
We can describe the rate of polymerization in terms of -d[M]/dt as
The expression can be integrated to yield:
where [M]0 is the initial monomer concentration
