Kinetics of Anchoring of Polymer Chains on Substrates with Chemically Active Sites

Details Kinetics of Anchoring of Polymer Chains on Substrates with Chemically Active Sites Kinetics of Anchoring of Polymer Chains on Substrates with Chemically Active Sites

1998-07-13

arxiv.org/abs/cond-mat/9807184v1

Phys. Rev. E 58, 6134 (1998)

Physics

Condensed Matter

Soft Condensed Matter

Latex file, 19 pages, one ps figure, to appear in PRE

Scientific paper

10.1103/PhysRevE.58.6134

We consider dynamics of an isolated polymer chain with a chemically active end-bead on a 2D solid substrate containing immobile, randomly placed chemically active sites (traps). For a particular situation when the end-bead can be irreversibly trapped by any of these sites, which results in a complete anchoring of the whole chain, we calculate the time evolution of the probability $P_{ch}(t)$ that the initially non-anchored chain remains mobile until time $t$. We find that for relatively short chains $P_{ch}(t)$ follows at intermediate times a standard-form 2D Smoluchowski-type decay law $ln P_{ch}(t) \sim - t/ln(t)$, which crosses over at very large times to the fluctuation-induced dependence $ln P_{ch}(t) \sim - t^{1/2}$, associated with fluctuations in the spatial distribution of traps. We show next that for long chains the kinetic behavior is quite different; here the intermediate-time decay is of the form $ln P_{ch}(t) \sim - t^{1/2}$, which is the Smoluchowski-type law associated with subdiffusive motion of the end-bead, while the long-time fluctuation-induced decay is described by the dependence $ln P_{ch}(t) \sim - t^{1/4}$, stemming out of the interplay between fluctuations in traps distribution and internal relaxations of the chain.

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