  We present an extremely simplified model of multiple-domains 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 interactions terms inside each domain. Exact
equilibrium computations and Monte Carlo simulations qualitatively reproduce
the experimental saw-tooth 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.
