# Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation

Evstigneev M, Reimann P (2015) *Journal of Physics Condensed Matter* 27(12): 125004.

Download

**No fulltext has been uploaded. References only!**

*Journal Article*|

*Original Article*|

*Published*|

*English*

No fulltext has been uploaded

Abstract

Friction force microscopy and single-molecule force spectroscopy are experimental methods to explore multistable energy landscapes by means of a controlled reduction of the energy barriers between adjacent potential minima. This affects the system's interstate transition rates proportional to e-(Delta E(f)/kBT), with Delta E(f) being the barrier height, k(B)T the thermal energy, and f the elastic force applied. It is often assumed that, at large forces, the barrier height scales as (f(c)-f)(3/2), where f(c) is the critical force, at which the barrier vanishes. We show that, for the elastic forces produced by a pulling device of finite stiffness., this scaling relation is actually incorrect. Rather, the barrier is a double-valued function of force of the form Delta E(f) alpha (kappa/kappa(c) +/- root 1-f/f(0))(3), where f(0) is the maximal force that the system potential can generate, and the characteristic stiffness kappa(c) is not necessarily much larger than.. In particular, for finite kappa, the barrier vanishes at a certain force f(kappa) < f(0), but, in view of the double-valuedness of Delta E(f), the maximal force f(0) can still be reached. We derive the relation between the most probable force at the moment of transition, f(m), and the pulling velocity, v. The usually assumed scaling f(m) alpha (ln v)(2/3) is recovered as the kappa -> 0 limit of our more general result, but becomes increasingly worse as grows. We introduce a new data analysis method that allows one to quantitatively characterize the system potential and evaluate the stiffness of the pulling device, kappa, which is usually not known beforehand. We demonstrate the feasibility of our method by analyzing the results of a numerical experiment based on the standard Prandtl-Tomlinson model of nanoscale friction.

Keywords

Publishing Year

ISSN

PUB-ID

### Cite this

Evstigneev M, Reimann P. Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation.

*Journal of Physics Condensed Matter*. 2015;27(12): 125004.Evstigneev, M., & Reimann, P. (2015). Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation.

*Journal of Physics Condensed Matter*,*27*(12), 125004. doi:10.1088/0953-8984/27/12/125004Evstigneev, M., and Reimann, P. (2015). Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation.

*Journal of Physics Condensed Matter*27:125004.Evstigneev, M., & Reimann, P., 2015. Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation.

*Journal of Physics Condensed Matter*, 27(12): 125004. M. Evstigneev and P. Reimann, “Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation”,

*Journal of Physics Condensed Matter*, vol. 27, 2015, : 125004. Evstigneev, M., Reimann, P.: Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation. Journal of Physics Condensed Matter. 27, : 125004 (2015).

Evstigneev, Mykhaylo, and Reimann, Peter. “Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation”.

*Journal of Physics Condensed Matter*27.12 (2015): 125004.
This data publication is cited in the following publications:

This publication cites the following data publications:

### 1 Citation in Europe PMC

Data provided by Europe PubMed Central.

Driven diffusion against electrostatic or effective energy barrier across α-hemolysin.

Ansalone P, Chinappi M, Rondoni L, Cecconi F.,

PMID: 26493899

Ansalone P, Chinappi M, Rondoni L, Cecconi F.,

*J Chem Phys*143(15), 2015PMID: 26493899

### Export

0 Marked Publications### Web of Science

View record in Web of Science®### Sources

PMID: 25694420

PubMed | Europe PMC