Non-stationary states in free-radical polymerizations with size-dependent termination. Studies by the group-termination procedure—2. Pre-effects and systems with intermittent initiation

Abstract

Calculations on non-classical systems of the type mentioned in the title have been carried out using the treatment described in Part I. As before chain transfer has been neglected. It is shown that the properties of the total pre-effect ΔM pre are analogous to those previously deduced for the after-effect. Thus, for given rates of chain-starting in the initial and final stationary states, the following proportionalities are found: ΔM pre ∝(k p M) (1+β) (1−β) k to (1−β) , ΔM pre ∝k p MR 1p 2· and ΔM pre∝ k p MR 2p 2·. R 1 · and R 2· are the initial and final radical concentrations, β is the geometric mean exponent in the relation between termination coefficient and radical size and other symbols have their conventional meanings. Non-classical polymerizations with intermittent initiation of the “rotating sector” type (light and dark rates of initiation I 2p, I 2a, respectively) have been treated by the same procedure. Plots of the ratio ω/ω s ( ω = mean rate of polymerization and ω s = rate with continuous full rate of initiation) against t l / τ have been constructed ( t l = duration of “light” period, τ = mean life-time of chains ) for β = 0.1, β = 0.139 and β = 0.2. It is shown that, for given β and with I 2 a = 0, ω/ω s is a single-valued function of t l / τ. The resulting curves, although resembling those for classical systems, are displaced from the latter; moreover, members of different families (different β) are not superposable. Systems with intermittent initiation together with a constant background (thermal) initiation and β = 0.1 and β = 0.2 have been investigated similarly. Applications to the evaluation of absolute rate coefficients are discussed.