Dynamics of pulled desorption with effects of excluded-volume interaction: The p-Laplacian diffusion equation and its exact solution
Max Planck Institute for Polymer Research - 10 Ackermannweg, 55128 Mainz, Germany, EU
2 Department of Inorganic and Physical Chemistry, Indian Institute of Science - Bangalore 560012, India
Accepted: 5 July 2011
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 fc. 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=τ0nd2, where nd is the number of monomers that have desorbed at the time τ. τ0 is known only numerically, but for f close to fc, it is found to be τ0∼fc/(f2/3−fc2/3). If one used simple Rouse dynamics, this result would change to τ∼fcnd2/(f−fc). In the other regimes too, one can find exact solution, and interestingly, in all regimes τ∼nd2.
PACS: 82.35.Gh – Polymers on surfaces; adhesion / 62.25.-g – Mechanical properties of nanoscale systems / 82.37.-j – Single molecule kinetics
© EPLA, 2011