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

Source: [Kinetics of Anchoring of Polymer Chains on Substrates with Chemically Active Sites](<https://www.sota2.com/research/paper/68fa24902c2a3760193a5dd2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:18:10.151Z

Authors: G.Oshanin, S.Nechaev, A.M.Cazabat, M.Moreau(1) \_\_INSTITUTION\_4\_\_ LPTL, Universite de Paris VI, France; (2) IPN, Orsay, France, Landau Institute, Moscow, Russia; (3) LPMC, College de France, Paris, France)

Published: 1998-07-13T15:23:44.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9807184>)

[PDF](<https://arxiv.org/pdf/cond-mat/9807184.pdf>)