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

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 $\tau \sim n_d^2$.