Stretching a macromolecule in an atomic force microscope: Statistical mechanical analysis

We formulate the proper statistical mechanics to describe the stretching of a macromolecule under a force provided by the cantilever of an Atomic Forc e Microscope. In the limit of a soft cantilever, the generalized ensemble o f 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, one obtains the Helmholtz ensemble for an isolated molecule held at a fixed extension with the force fluctuating. Numerical examples and predictions for experiments with cantilevers of dif fering stiffness are given for short and long chains of poly (ethylene glyc ol), based on parameter-free ab initio calculations.