Stretching a Macromolecule in an Atomic Force Microscope: Statistical Mechanical Analysis

Abstract

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, 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 differing stiffness are given for short and long chains of poly (ethylene glycol), based on parameter-free ab initio calculations.

The Study of Molecular Interactions by AFM Force Spectroscopy

“…Strictly, neither the Gibbs ensemble (no force fluctuations) nor the Helmholtz ensemble (no distance fluctuations) is correct, and one has to find a proper statistical analysis of a system with constant spring constant. [124,125] However, it has been found that, in the soft cantilever regime (which applies to the usual experimental conditions), the Gibbs ensemble is a good approximation. Based on this, the well-accepted concept of entropic elasticity manifests itself in an effective restoring force upon stretching (or compressing) a flexible polymer chain by an external force field as a result of a loss in conformational freedom.…”

Elastic Properties of Semi‐Flexible Chains and Networks

“…In derivation of this formula the force f was considered as an independent variable (the isotensional boundary conditions [9,10] ). The formula accurately represents the small and large force regime but has a maximum error of 10% in the intermediate force regime.…”

Breaking bonds in the atomic force microscope: Extracting information

“…In general, the controlled position scenario has finite force fluctuations. 15,16 These become particularly important when the polymer spacer is pulled very fast and equilibrium theories become inapplicable. In such a scenario, one might consider an approach as outlined elsewhere.…”