Rupture dynamics in model polymer systems

In this paper we explore the rupture dynamics of a model polymer system to capture the microscopic mechanism during relative motion of surfaces at the single polymer level. Our model is similar to the model for friction introduced by Filippov, Klafter, and Urbakh [Filippov et al., Phys. Rev. Lett., 2004, 92, 135503]; but with an important generalization to a flexible transducer (modelled as a bead spring polymer) which is attached to a fixed rigid planar substrate by interconnecting bonds (modelled as harmonic springs), and pulled by a constant force FT. Bonds are allowed to rupture stochastically. The model is simulated, and the results for a certain set of parameters exhibit a sequential rupture mechanism resulting in rupture fronts. A mean field formalism is developed to study these rupture fronts and the possible propagating solutions for the coupled bead and bond dynamics, where the coupling excludes an exact analytical treatment. Numerical solutions to mean field equations are obtained by standard numerical techniques, and they agree well with the simulation results which show sequential rupture. Within a travelling wave formalism based on the Tanh method, we show that the velocity of the rupture front can be obtained in closed form. The derived expression for the rupture front velocity gives good agreement with the stochastic and mean field results, when the rupture is sequential, while propagating solutions for bead and bond dynamics are shown to agree under certain conditions.