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Reconstruction of Energy Surfaces from Friction Force Microscopy Measurements with the Jarzynski Equality

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Scanning Probe Microscopy in Nanoscience and Nanotechnology 3

Part of the book series: NanoScience and Technology ((NANO))

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Abstract

Free energy is one of the most fundamental thermodynamic functions, determining relative phase stability and serving as a generating function for other thermodynamic quantities. The calculation of free energies is a challenging enterprise. In equilibrium statistical mechanics, the free energy is related to the canonical partition function. The partition function itself involves integrations over all degrees of freedom in the system and, in most cases, cannot be easily calculated directly. In 1997, Jarzynski proved a remarkable equality that allows computing the equilibrium free-energy difference between two states from the probability distribution of the nonequilibrium work done on the system to switch between the two states. The Jarzynski equality provides a powerful free-energy difference estimator from a set of irreversible experiments. This method is closely related to free-energy perturbation approach, which is also a computational technique for estimating free-energy differences. The ability to map potential profiles and topologies is of major significance to areas as diverse as biological recognition and nanoscale friction. This capability has been demonstrated for frictional studies where a force between the tip of the scanning force microscope and the surface is probed. The surface free-energy corrugation produces a detectable friction forces. Thus, friction force microscopy (FFM) should be able to discriminate between energetically different areas on the probed surface. Here, we apply the Jarzynski equality for the analysis of FFM measurements and thus obtain a variation of the free energy along a surface.

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Author information

Authors and Affiliations

  1. Department of Biological Sciences, Columbia University, New York, NY, USA

    Ronen Berkovich

  2. Orenstein 209, School of Chemistry, Tel-Aviv University, Tel Aviv, Israel

    Joseph Klafter

  3. Orenstein 207, School of Chemistry, Tel-Aviv University, Tel Aviv, Israel

    Michael Urbakh

Authors
  1. Ronen Berkovich
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  2. Joseph Klafter
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  3. Michael Urbakh
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Editor information

Editors and Affiliations

  1. , Nanoprobe Laboratory for Bio- &, Ohio State University, West 19th Avenue 201, Columbus, 43210-1142, Ohio, USA

    Bharat Bhushan

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Berkovich, R., Klafter, J., Urbakh, M. (2012). Reconstruction of Energy Surfaces from Friction Force Microscopy Measurements with the Jarzynski Equality. In: Bhushan, B. (eds) Scanning Probe Microscopy in Nanoscience and Nanotechnology 3. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25414-7_12

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