Particle growth Equilibrium monomer concentration

Williams s core-shell theory of particle growth, however, has many unresolved conflicts. Napper [18] pointed out that the diffusion rates of species present within the polymer particle did not support the hypothesis for such large differences in the polymer concentrations between the core and shell. Moreover, Garden [19] showed that the diffusive mean free path of monomer molecules, which was much larger than the radius of the polymer particle, would not favour the core-shell equilibrium theory. Garden, as well as Friis and Hamielec [20], also indicated that Williams experimental results, i.e. a nearly constant polymerization rate, could be attributed to the concurrent decrease in [M]p due to... 

Equation (1) is a growth law for particles of radius R(r,t) in the vicinity of spatial point f and time t k is a rate constant, c is a monomer concentration and c (R) is the R-dependent equilibrium concentration. As shown in Ref. 13, the fact that c decreases with R for supracritical particles implies that the uniform sol is unstable to pattern-forming perturbations. 

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