Rheologica Acta

, Volume 56, Issue 1, pp 21–26 | Cite as

Improved approximations for some polymer extension models

  • Rafayel PetrosyanEmail author
Original Contribution


We propose approximations for force-extension dependencies for the freely jointed chain (FJC) and worm-like chain (WLC) models as well as for extension-force dependence for the WLC model. Proposed expressions show less than 1 % relative error in the useful range of the corresponding variables. These results can be applied for fitting force-extension curves obtained in molecular force spectroscopy experiments. Particularly, they can be useful for cases where one has geometries of springs in series and/or in parallel where particular combination of expressions should be used for fitting the data. All approximations have been obtained following the same procedure of determining the asymptotes and then reducing the relative error of that expression by adding an appropriate term obtained from fitting its absolute error.


Force-extension curve Freely jointed chain model Worm-like chain model Inverse Langevin function 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Biosystems Science and EngineeringEidgenössische Technische Hochschule (ETH) ZurichBaselSwitzerland
  2. 2.Department of PhysicsUniversity of AlbertaEdmontonCanada

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