Polimery 1998, No 3, 135
The polymer polydispersity index, DPw/DPn, i.e., the weightaverage over the number-average degree of polymerization (DP), is discussed in relation to the degree of monomer conversion (α) for studying the reversible living polymerization and polymerization involving a bimolecular transfer onto the polymer followed by chain scission. The scission leads to segment al exchange though the concentrations of both active species and growing macromolecules remain unaffected (constant). Even in the ideal irreversible polymerization when the DP of the growing macromolecules follows the Poisson distribution function type, the polydispersity index is related to a and to the initial monomer [M]0 and initiator [I]0 concentrations., viz., DPw/DPn = 1 + α ([M]0/[I]0) /( 1 + α [M]0/[I]0)2; the index may differ much from unity. In the living polymerization with reversible propagation, the DP distribution is described by the Flory-Schulz function (the most probable one) for which DP DPw/DPn = 2 - 1/ DPn. The relationship DPw/DPn.=- ƒ (α) can be evaluated by numerical methods only (e.g., Monte Carlo method, numerical integration). Styrene (S), L,L-lactide (LA) and tetrahydrofuran (THF) polymerizations were used to demonstrate that, the higher the monomer concentration at equilibrium ([M]eq) (cf. Table 1), the shorter the time of transition of the DP distribution from the Poisson to the most probable one. Next, by Monte Carlo calculations, the polymerization involving segmental exchange was show to yield two populations of macromolecules having the same DPn but different DP distributions, viz., the Poisson type and the negative binomial Polya type. A numerical method was developed to evaluate the DPw/DPn = ƒ (α) relationship for the polymerization involving segmental exchange, chich made it possible to evaluate — for the first time — tke kp/ktr(2) ratio (kp and ktr(2) being the propagation rate constant and the bimolecular transfer rate constant, resp.). This ratio was evaluated by comparing the family of DPw/DPn = ƒ (α) curves generated numerically at preset kp/ktr(2) -values, with the experimentally observed DPw/DPn = ƒ (α) relationship obtained from SEC measurements. This method was used to analyze the polymerization of LA, initiated by an Al(O-iPr)3 trimer, for which it was found that kp/ktr(2) = 100 (THF, 80°C). Since kp = 8.4 x 10-3 mol-1·L·s-1 , then ktr(2) = 8.4 x 10-5 mol-1·L·s-1.
Keywords: living polymerization, distribution of polymerization degree, equilibrium monomer concentration, segmental exchange in polymerization, polymerization of L,L-lactide