Dynamics of pulled desorption with effects of excluded volume interaction: The p-Laplacian diffusion equation and its exact solution

TL;DR

This paper models the desorption dynamics of a pulled polymer considering excluded volume effects, deriving exact solutions using a p-Laplacian diffusion equation, and reveals a universal quadratic relation between desorption time and monomers desorbed.

Contribution

It introduces an exact analytical framework for polymer desorption dynamics incorporating excluded volume interactions via a p-Laplacian diffusion equation, extending previous models.

Findings

Desorption time scales quadratically with the number of desorbed monomers.

Exact solutions are obtained for different regimes of polymer desorption.

Near critical force, desorption time depends on force as f_c/(f^{2/3}-f_c^{2/3}).

Abstract

We analyze the dynamics of desorption of a polymer molecule which is pulled at one of its ends with force $f$, trying to desorb it. We assume a monomer to desorb when the pulling force on it exceeds a critical value $f_{c}$. We formulate an equation for the average position of the $n^{th}$ monomer, which takes into account excluded volume interaction through the blob-picture of a polymer under external constraints. The approach leads to a diffusion equation with a $p$-Laplacian for the propagation of the stretching along the chain. This has to be solved subject to a moving boundary condition. Interestingly, within this approach, the problem can be solved exactly in the trumpet, stem-flower and stem regimes. In the trumpet regime, we get $\tau=\tau_{0}n_d^{2}$ where $n_d$ is the number of monomers that have desorbed at the time $\tau$. $\tau_{0}$ is known only numerically, but for $f$ close to $f_{c}$, it is found to be $\tau_{0}\sim f_c/(f^{2/3}-f_{c}^{2/3})$. If one used simple Rouse dynamics, this result changes to {\normalsize $\tau\sim f_c n_d^2/(f-f_{c})$.} In the other regimes too, one can find exact solution, and interestingly, in all regimes $\tau \sim n_d^2$.