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

TL;DR

This paper investigates the dynamics of polymer chain anchoring on a substrate with active sites, revealing different kinetic regimes for short and long chains, characterized by specific decay laws of the anchoring probability over time.

Contribution

It provides a detailed theoretical analysis of the time evolution of polymer anchoring probabilities, highlighting distinct behaviors based on chain length and trap distribution fluctuations.

Findings

Short chains follow a 2D Smoluchowski decay law at intermediate times.

Long chains exhibit subdiffusive end-bead motion with unique decay laws.

Fluctuation effects dominate at very long times, altering decay behavior.

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.