A toy model of polymer stretching

We present an extremely simplified model of multiple-domain polymer stretching in an atomic force microscopy experiment. We portray each module as a binary set of contacts and decompose the system energy into a harmonic term (the cantilever) and long-range interaction terms inside each domain. Exact equilibrium computations and Monte Carlo simulations qualitatively reproduce the experimental sawtooth pattern of force-extension profiles, corresponding (in our model) to first-order phase transitions. We study the influence of the coupling induced by the cantilever and the pulling speed on the relative heights of the force peaks. The results suggest that the increasing height of the critical force for subsequent unfolding events is an out-of-equilibrium effect due to a finite pulling speed. The dependence of the average unfolding force on the pulling speed is shown to reproduce the experimental logarithmic law.