Solution of steady state in the model polymer system with rupture and rebinding

In this paper, we study the steady state attained in our model polymer system that attempts to explain the relative motion between soft rubbing surfaces at the single polymer level. We generalize our one-dimensional model [Borah et al , 2016 Soft Matter 12 4406] by including the rebinding of interconnecting bonds between a flexible transducer (bead spring polymer) and a rigid fixed plate. The interconnecting bonds described as harmonic springs rupture and rebind stochastically when a constant force pulls the flexible transducer. We obtain a distinct steady state in stochastic simulations of the model when the bead positions and the bond states (closed or open) are independent of time, analogous to creep states in frictional systems and rupture termination states in earthquakes. The simulation results of the stochastic model for specific parameter sets agree with the numerical solution to the mean-field equations developed for analytical tractability. We develop an analytical solution for the steady state within the homotopy analysis method, which converges and agrees well with the numerical results.