Free radical addition steady-state kinetics

The specificity of the reaction mechanism to the chemistry of the initiator, co-initiator and monomer as well as to the termination mechanism means that a totally general kinetic scheme as has been possible for free-radical addition polymerization is inappropriate. However, the general principles of the steady-state approximation to the reactive intermediate may still be applied (with some limitations) to obtain the rate of polymerization and the kinetic chain length for this living polymerization. Using a simplified set of reactions (Allcock and Lampe, 1981) for a system consisting of the initiator, I, and co-initiator, RX, added to the monomer, M, the following elementary reactions and their rates may be... 

In order to simplify the kinetic scheme a steady-state approximation has to be made. It is assumed that under steady-state conditions the net rate of production of radicals is zero. This means that in unit time the number of radicals produced by the initiation process must equal the number destroyed during the termination process. If this were not so and the total number of radicals increased during the reaction, the temperature would rise rapidly and there could even be an explosion since the propagation reactions are normally exothermic. In practice it is found that the steady-state assumption is usually valid for all but the first few seconds of most free radical addition polymerization reactions. 

It is often found that there can be serious deviations from steady-state kinetics during free radical addition polymerization especially towards the end of reactions using pure monomers or concentrated solutions. This can be most readily demonstrated by looking at the simplified equation for the rate of polymerization... 

The key problems in a polymerization CSTR are the determination and characterization of micro- and macromixing, and the possibility of multiple steady states due to the exothermic nature of the reactions. Recent studies of CSTRs for bulk or solution free-radical polymerization indicate the possibility of multiple steady states due to the large heat evolution and difficult heat transfer that are characteristic of the reactors. Furthermore, even in simple solution polymerization (for example, in methyl methacrylate polymerization in ethyl acetate solvent), autocatalytic kinetics can lead to runaway conditions even with perfect temperature control for certain combinations of solvent concentration and reactor residence time. In practice, the heat evolution can be an additional source of autocatalytic behavior. 

The kinetic isotope effect observed on the overall rates of hydrogenolytic demethylation of propylene in the presence of deuterium was successfully interpreted in terms of a free radical chain mechanism. Little differences were inferred to exist between the rates of addition of H or D- to propylene and also between those of unimolecular decomposition of the produced hot n-propyl radicals, and thus the kinetic isotope effect was ascribed mainly to the difference between the steady state concentrations of [H-] in the presence of hydrogen and the concentrations of [D ] + [H ] in the presence of deuterium. In more detail, conversion of rather inactive allyl radical by metathesis with deuterium into an active D is relatively slow. This was concluded to be the main cause of the observed kinetic isotope effect, which agrees well with the calculated... 

The kinetic isotope effect observed on the overall rates, ranging from 2.0 at 700 C to 1.5 at 800 C, was interpreted in terms of a free radical chain mechanism where a unimolecular decomposition of a hot n-propyl radical, produced by addition of H or D to propylene, plays a key role. The difference in the observed overall rates was mainly ascribed to that in steady state Concentrations of H and D which are produced, in part, through the reaction between allyl radical and H2 or D2. No appreciable difference between the decomposition rates of C3H7 and C3H6D was infered by RRKM theory. 

The data are from a free radical polymerization of butyl acrylate (BA) in butyl acetate. When fractional monomer conversion reached 0.4, an extra amount of azobisisobutyro-nitrile (AIBN) initiator was added (initiator boost). Its effect can be immediately seen in the rapid drop of as the quasi-steady state approximation (QSS A) predicts for kinetic chain length (e.g., see Chapters 1 and 5) which is the molecular weight of chains being produced at any instant in a free radical reactions. It is proportional to the concentration of monomer to that of initiator. Hence, the addition of initiator causes the instantaneous chain length, and hence to fall. 

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