Diffusion control in radiation graft polymerization with varying dependence of rate on monomer concentration

Abstract

Abstract The quantitative effect of diffusion control on the rate of radiation‐initiated graft polymerization has been studied theoretically for systems in which the diffusion‐free reaction may show various dependencies of rate on monomer concentration other than the usual first‐order dependence. The study is also very general in that it can be applied to systems involving a variety of different modes of initiation and termination. Whether the grafting process is diffusion‐free or diffusion‐controlled has been analyzed in terms of the interaction of the initiation rate R i , the propagation and termination rate constants k p and k t , the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L , the diffusivity D of the monomer in the polymer, and the diffusion‐free kinetic order of dependence v of the grafting rate on monomer concentration. The dependence of the grafting rate for both the diffusion‐free and diffusion‐controlled reactions on these parameters is expressed both by mathematical experssions and graphically. Diffusion control is shown to occur at a critical value of the parameter A which is proportional to L ( k p R i w / k t z D ) 1/2 M (ε−1)/2 where w , z , and v have different values depending on the specific modes of initiation, propagation and termination in a particular grafting system. The grafting rate is shown to vary with the value of A according to specific mathematical expressions. In comparing diffusion‐free to diffusion‐controlled reaction, it is shown that the former is independent of L and D while the latter is directly dependent on L and inversely on D 1/2 . Further, the change from diffusion‐free to diffusion‐controlled reaction involves a change in the dependence of rate on monomer from v ‐order to [( v − 1)/2]‐order. The nonsteady‐state as well as the steady‐state reaction rates have been analyzed.