Non-stationary states in free-radical polymerizations with size-dependent termination. Studies by the group-termination procedure—3. Further consideration of after-and pre-effects and evaluation of absolute coefficients

✍ Scribed by C.H. Bamford

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 486 KB
• Volume: 30
• Category: Article
• ISSN: 0014-3057
• DOI: 10.1016/0014-3057(94)90249-6

✦ Synopsis

Al~traet--In earlier studies of the kinetic quantities in non-stationary stages of non-classical free-radical polymerization a relation between the total pre-and after-effects (AMos, AM~, respectively) and the rate coefficients kp kto was proposed. This arose from the results of numerical computation. Further work shows that the relation is derivable from the basic kinetic equations and is therefore of general validity.

We have been able to formulate a new quantity A which is a function of the ratio of the final and initial rates of initiation (J2, ~'l, respectively) (not the individual values) and is independent of the rate coefficients. It is useful for the evaluation of absolute rate coefficients in non-classical systems and the procedure involved is explained. Values of A are presented in the form of contour lines on a fl vs J2/,~'1 diagram.

A method for calculating A based on empirical relations between radical concentrations and mean radical sizes is outlined.

A special case has been found [fl = 0.25, see equation ( 1)] for which analytical solutions can be obtained. The derived expressions for radical concentrations and AMp~ and AMan are presented.

As in earlier papers in this series concerned with non-stationary states we assume chain transfer to be insignificant.

NOMENCLATURE

= rate of initiation R'= total radical concentration f= number-average radical size ,~'t, J2, RI, R~, rl, f2 are the values of J, R', 7 in the stationary states at the beginning and end, respectively, of a non-stationary phase 0=(J2/Ji) m for pre-effect, (Jl/J2) 1/2 for after-effect M = monomer concentration AM = total pre-effect (AMp~) or total after-effect (AMaa), both counted as positive AMpr c = kpM fo ~ (R'2 -R') dt AMar t = kpM (R" -R2) dt do Z = {r2/(l -/~)}P/{F 1/1(1 -/~)}' +~.