The dynamics of a reacting polymer attached to a surface

Abstract

Scaling arguments are presented for end-to-wall reaction and end-to-end reactions of grafted chains for non-self-avoiding and self-avoiding chains with and without hydrodynamic interaction. The most realistic minimal model for the experiments of Kim and Lee (J Phys Chem Lett 12:4576, 2021. https://doi.org/10.1021/acs.jpclett.1c00962) is a chain tethered to a plane, the chain having excluded volume and hydrodynamic interaction with end-to-end reactions. From our scaling argument, such a chain obeys a law of mass action where the macroscopic reaction rate is proportional to the microscopic reaction rate multiplied by the probability that the chain ends are close together. More precisely, this means for long chains there is no diffusion controlled limit. In addition, a polymer attached to a plane where the end reacts with the entire plane, end-to-wall reactions, was also investigated. For sufficiently long polymers, this system is always diffusion controlled, even with excluded volume and hydrodynamic interaction. We test the scaling arguments for the simplest case of a non-self-avoiding chains obeying Rouse dynamics. The numerical results agree with the scaling analysis for both end-to-wall and end-to-end reactions of the grafted chain. In particular, our numerical simulations support the end-to-end reaction of a tethered non-self-avoiding is the marginal case in the scaling sense.