Diffusion‐controlled reactions in free radical polymerisation

Abstract

The evidence that the rates of radicalradical recombination reactions in solution are diffusion-controlled is assessed and the consequences of diffusion-controlled termination reactions in radical polymerisation examined. The cross-termination rate coefficients for two different radicals should be the s u m of the two mutual-termination rate coefficients of these radicals. The frequently used geometric mean relationship is not relevant to diffusion-controlled reactions. The dependence of the diffusion-controlled kt on the size of the macroradicals and its effect on the rate equation for polymerisation is examined. The nature of the mean value, Et, which is measured experimentally, is discussed.The role of diffusion-control a t high conversion is discussed. It is shown that simple diffusion-control of the propagation reaction is incompatible with the observed diffusivities of small molecules in polymer gels. ZUSAMMENFASSUNG:Der Beweis, dafi die Geschwindigkeiten der Kombiinationsreaktionen von Radikalen in Losung durch die Diffusion beschrankt werden, wird erortert und die Folgen der Diffusionsbeschrankungen bei der Abbruchsreaktion der radikalischen Polymerisation untersucht. Wenn die Reaktionen diffusionsbeschrankt sind, sollte die Abbruchsgeschwindigkeitskonstante zwischen zwei verschiedenen Radikalen (R, + R,) der Summe der zwei Abbruchskonstanten der gleichen Radikale (R, + R, nnd R, + R,) gleichen. Das oftmals verwandte geometrische Mittel ist nicht anwendbar. Die Abhiingigkeit des diffusionsbeschrankten kt von der GroBe der Makroradikale und dessen Auswirkung auf die Polymerisationsgeschwindigkeit werden untersucht. Die mittels Versuchen meBbare mittlere Abbruchskonstante Et wird diskutiert.Die Rolle der Diffusionsbeschrdcung bei hohem Umsatz wird erortert, und es wird gezeigt, daS die einfache D i f f u s i o n s b e s c h r l g der Wachstumsreaktion mit den Diffusionsgeschwindigkeiten kleiner Molekiile in makromolekularen Gelen unvereinbar ist.Molecules in the liquid phase, being closely packed, have much lower mobilities than those in the gas phase. This reduced mobility has two effects. Firstly it increases the time taken for two molecules, initially separated, to encounter one another, and secondly it increases the length of the period for which two molecules, having come together, remain in close proximity. The second of these effects is generally known as the 1) E. RABINOWITCE, Trans. Faraday SOC. 33 (1937) 1225.

Termination in Dilute‐Solution Free‐Radical Polymerization: A Composite Model

“…[34,39] As this statement implies, Equation (18) is not restricted to steady states. Rather, it always holds, but in non-steady states it results in hk t i varying with time.…”

Critically Evaluated Termination Rate Coefficients for Free‐Radical Polymerization, 1. The Current Situation

“…In carrying out an FRP experiment, one will invariably measure the overall rate of termination, which is the sum of the rates of termination for all possible pairs of radical sizes. Thus hk t i, the overall or average rate coefficient for termination, defined such that hk t i replaces k t in whichever of Equation (1a) or Equation (1b) one is using, is related to the more physically meaningful k i; j t values by [29] k…”

Scope for Accessing the Chain Length Dependence of the Termination Rate Coefficient for Disparate Length Radicals in Acrylate Free Radical Polymerization

“…Much work has been carried out to characterize the termination rate coefficient (k t ) and how it depends on the polymerization conditions, e.g., the temperature; pressure; solvent concentration; reaction medium viscosity and the growing radical's size. [14][15][16][17][18][19][20][21][22][23][24][25][26] Previously, the dependence of the termination rate coefficient on the radical's size for equal size radicals, i.e., a, where k i t / i Àa and i represents the average radical size when only one reversible addition fragmentation chain transfer (RAFT) distribution exists, was ascertained utilizing RAFT chemistry. [19,25,27] This method termed the RAFT chain length dependent termination (RAFT-CLD-T) method extracts the termination rate coefficient as a function of chain length (k i t ) from the on-line determination of the polymerization rate as a function of time, R p (t), and hence, allows for access to k t 's chain length dependency, i.e., the scaling exponent a when the chain length dependency follows a power law relationship.…”