We formulate the proper statistical mechanics to describe the stretching of a macromolecule under a force provided by the cantilever of an atomic force microscope. In the limit of a soft cantilever the generalized ensemble of the coupled molecule/cantilever system reduces to the Gibbs ensemble for an isolated molecule subject to a constant force in which the extension is fluctuating. For a stiff cantilever we obtain the Helmholtz ensemble for an isolated molecule held at a fixed extension with the force fluctuating. Numerical examples are given for poly (ethylene glycol) chains.

• Received 28 June 2000

DOI:https://doi.org/10.1103/PhysRevE.63.021906