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Beilstein Journal of Nanotechnology logoLink to Beilstein Journal of Nanotechnology
. 2021 Jan 28;12:137–138. doi: 10.3762/bjnano.12.10

Correction: Extracting viscoelastic material parameters using an atomic force microscope and static force spectroscopy

Cameron H Parvini 1, M A S R Saadi 1, Santiago D Solares 1,
Editor: Thomas Schimmel
PMCID: PMC7849245  PMID: 33564608

In the “Useful Viscoelastic Quantities” section of the original publication, it is stated that the storage modulus (E′) and storage compliance (J′) are inverses of one another (Equation 10). Similarly, it is stated that the loss modulus (E″) and loss compliance (J″) are inverses of one another (Equation 11). However, it is the relaxance (Q) and retardance (U) that are inverses of one another in the Laplace domain (not in the time domain), leading to a more complex relationship between the moduli and their respective compliances. Translation between harmonic quantities can be accomplished through the expressions below, where Inline graphic is the absolute modulus and Inline graphic is the absolute compliance [1]:

graphic file with name Beilstein_J_Nanotechnol-12-137-e001.jpg [1]
graphic file with name Beilstein_J_Nanotechnol-12-137-e002.jpg [2]
graphic file with name Beilstein_J_Nanotechnol-12-137-e003.jpg [3]
graphic file with name Beilstein_J_Nanotechnol-12-137-e004.jpg [4]

Absolute modulus and absolute compliance are calculated as:

graphic file with name Beilstein_J_Nanotechnol-12-137-e005.jpg [5]
graphic file with name Beilstein_J_Nanotechnol-12-137-e006.jpg [6]

The leftmost term in Equation 10 and Equation 11 in the original manuscript is thus incorrect and needs to be removed, leaving the following corrected expressions:

Equation 10:

graphic file with name Beilstein_J_Nanotechnol-12-137-i003.jpg

Equation 11:

graphic file with name Beilstein_J_Nanotechnol-12-137-i004.jpg

References

  • 1.Tschoegl N W. The Phenomenological Theory of Linear Viscoelastic Behavior. Berlin Heidelberg, Germany: Springer; 1989. [DOI] [Google Scholar]

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