Effect of diffusion on rates and molecular weights in graft polymerization

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Abstract
A theoretical analysis has been made of the graft polymerization process in terms of the quantitative interrelationship between the initiation rate Ri, the kp/kt1/ ratio of the monomer, the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L, and the diffusivity D of the monomer in the polymer. It is shown how the values of these parameters in any grafting system interact to lead to diffusion‐controlled graft polymerization. Whether graft polymerization is diffusion‐free or diffusion‐controlled depends on the values of Kp, d, kp/kp1/2, and L as gathered in the parameter A = [(Kp/kt1/2)Ri, D,/1/2] L/2. When the values of the various terms are such that A is less than 0.1 (i.e., D is large while Ri, kp, and L are small), the reaction is diffusion‐free. When A is greater than 3 (i.e., D is small while Ri, kp, and L are large), the reaction is diffusion‐controlled. The derived equations showing the relationship between kinetic and diffusional parameters are theoretically applicable to all grafting systems, i.e., for all monomer‐polymer combinations under all conditions of reaction temperature, radiation intensity and polymer film thickness. The theoretical analysis has been verified for the rate and degree of polymerization for the radiation‐induced graft polymerization of styrene to polyethylene.

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