The effect of diffusion on radiation-initiated graft polymerization has been studied with emphasis on the single- and two-penetrant cases. When the physical properties of the penetrants are similar, the two-penetrant problem can be reduced to the single-penetrant problem by redefining the characteristic parameters of the system. The diffusion-free graft polymerization rate is assumed to be proportional to the
v power of the monomer concentration
C, in which the proportionality constant
a =
kpR/
k, where
kp and
kt are the propagation and termination rate constants, respectively, and
Ri is the initiation rate. The values of
v,
w, and
z depend on the particular reaction system. The results of our earlier work were generalized by allowing a non-Fickian diffusion rate, obtained from an extension of the Fujita free-volume theory, which predicts an essentially exponential dependence on the monomer concentration of the diffusion coefficient,
D =
D0 [exp(δ
C/M)], where
M is the saturation concentration. It was shown that a reaction system is characterized by the three dimensionless parameters
v, δ, and
A = (
L/2)[
aM(v?1)/
D0]
1/2, where
L is the polymer film thickness. Graft polymerization tends to become diffusion controlled as
A increases. Larger values of δ and
v cause a reaction system to behave closer to the diffusion-free regime. The transition from diffusion-free to diffusion-controlled reaction involves changes in the dependence of the reaction rate on film thickness, initiation rate, and monomer concentration. Although the diffusion-free rate is
w order in initiation rate,
v order in monomer, and independent of film thickness, the diffusion-controlled rate is
w/2 order in initiator rate and inverse first-order in film thickness. The dependence of the diffusion-controlled rate on monomer is dependent in a complex manner on the diffusional characteristics of the reaction system.
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