Kinetics of Reversible ROP

7-2b-5-a Rate of Polymerization. The rate laws that describe conventional cationic ringopening polymerizations take several forms. Some polymerizations can be described by expressions similar to those in alkene polymerizations (Sec. 5-2d). In polymerizations with little or no termination one can use kinetic expressions similar to those of living polymerizations (Secs. 5-2g, 7-2b-3). 

Some cationic ring-opening polymerizations take place without termination and are reversible. Oxirane and oxetane polymerizations are seldom reversible, but polymerizations of larger-sized rings such as tetrahydrofuran are often reversible. The description of reversible ROP is presented below [Afshar-Taromi et al., 1978 Beste and Hall, 1964 Kobayashi et al., 1974 Szwarc, 1979]. It is also applicable to other reversible polymerizations such as those of alkene and carbonyl monomers. The propagation-depropagation equilibrium can be expressed by 

For the case where the concentration of propagating centers changes with time, integration of Eq. 7-44 yields 

The value of kp (= kp) decreases with increasing solvent polarity for mixtures of THF with CCI4 and CH3NO2 [Dreyfuss et al., 1989]. For free ions or their equivalent, loose and 

7-2b-5-C Degree of Polymerization. The quantitative dependence of the degree of polymerization on various reaction parameters has been described [Hirota and Fukuda, 1987 Tobolsky, 1957, 1958 Tobolsky and Eisenberg, 1959, 1960] for an equilibrium polymerization involving initiation 

---