Polymer Detachment Kinetics from Adsorbing Surface: Theory, Simulation and Similarity to Infiltration into Porous Medium

TL;DR

This paper develops a theoretical framework and simulations to understand how polymers detach from surfaces under force, revealing universal square-root-of-time kinetics and scaling laws with polymer length.

Contribution

It introduces a nonlinear porous medium equation approach to polymer detachment kinetics and identifies three distinct regimes based on force and adsorption strength.

Findings

Detachment follows a universal square-root-of-time law.

Total detachment time scales quadratically with polymer length.

Theoretical predictions agree with Monte Carlo and Molecular Dynamics simulations.

Abstract

The force-assisted desorption kinetics of a macromolecule from adhesive surface is studied theoretically, using the notion of tensile (Pincus) blobs, as well as by means of Monte-Carlo (MC) and Molecular Dynamics (MD) simulations. We show that the change of detached monomers with time is governed by a differential equation which is equivalent to the nonlinear porous medium equation (PME), employed widely in transport modeling of hydrogeological systems. Depending on the pulling force and the strength of adsorption, three kinetic regimes can be distinguished: (i) "trumpet" (weak adsorption and small pulling force), (ii) "stem-trumpet" (weak adsorption and moderate force), and (iii) "stem" (strong adsorption and large force). Interestingly, in all regimes the number of desorbed beads $M(t)$, and the height of the first monomer (which experiences a pulling force) $R(t)$ above the surface follow an universal square-root-of-time law. Consequently, the total time of detachment $<\tau_d>$, scales with polymer length $N$ as $<\tau_d> \propto N^2$. Our main theoretical conclusions are tested and found in agreement with data from extensive MC- and MD-simulations.