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

G. Oshanin 1, S. Nechaev 2, A. M. Cazabat 3, M. Moreau 1

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 58 (1998) 6134-6144

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.

  • 1. Laboratoire de Physique Théorique des Liquides (LPTL),
    CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
  • 2. Division de Physique Théorique, IPN,
    Université Paris XI - Paris Sud
  • 3. Laboratoire de Physique de la Matière Condensée (LPMC),
    CNRS : UMR7125 – Collège de France