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Diffusive growth of a polymer layer by in situ polymerization

We consider the growth of a polymer layer on a flat surface in a good solvent by in situ polymerization. This is viewed as a modified form of diffusion-limited aggregation without branching. We predict theoretically the formation of a pseudo-brush with density ϕ(z) ∝ z−2/3 and characteristic height H ∝ t3. These results are found by combining a mean-field treatment of the diffusive growth (marginally valid in three dimensions) with a scaling theory (Flory exponent ν = 3/5) of the growing polymers. We confirm their validity by Monte Carlo simulations.