Knot localization in adsorbing polymer rings

TL;DR

This study uses Monte Carlo simulations to analyze how knotted polymer rings adsorb onto surfaces, revealing that knots become localized upon adsorption and that this localization is well described by the flat knot model.

Contribution

It demonstrates that knot localization occurs during adsorption without affecting the transition temperature or critical exponents, and characterizes the localization transition in detail.

Findings

Adsorbed knots are localized.

Knot localization is strong in the adsorbed phase.

The localization behavior aligns with the flat knot model.

Abstract

We study by Monte Carlo simulations a model of knotted polymer ring adsorbing onto an impenetrable, attractive wall. The polymer is described by a self-avoiding polygon (SAP) on the cubic lattice. We find that the adsorption transition temperature, the crossover exponent $\phi$ and the metric exponent $\nu$, are the same as in the model where the topology of the ring is unrestricted. By measuring the average length of the knotted portion of the ring we are able to show that adsorbed knots are localized. This knot localization transition is triggered by the adsorption transition but is accompanied by a less sharp variation of the exponent related to the degree of localization. Indeed, for a whole interval below the adsorption transition, one can not exclude a contiuous variation with temperature of this exponent. Deep into the adsorbed phase we are able to verify that knot localization is strong and well described in terms of the flat knot model.