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 τ=τ₀n_d², where n_d is the number of monomers that have desorbed at the time τ. τ₀ is known only numerically, but for f close to f_c, it is found to be τ₀~f_c/(f^2/3-f_c^2/3). If one used simple Rouse dynamics, this result would change to τ~f_cn_d²/(f-f_c). In the other regimes too, one can find exact solution, and interestingly, in all regimes τ~n_d².