Extracting viscoelastic material parameters using an atomic force microscope and static force spectroscopy - Parvini, Cameron H.; Saadi, M. A. S. R.; Solares, Santiago D. (Beilstein Journal of Nanotechnology, 2020)
Atomic force microscopy (AFM) techniques have provided and continue to provide increasingly important insights into surface morphology, mechanics, and other critical material characteristics at the nanoscale. One attractive implementation involves extracting meaningful material properties, which demands physically accurate models specifically designed for AFM experimentation and simulation. The AFM community has pursued the precise quantification and extraction of rate-dependent material properties, in particular, for a significant period of time, attempting to describe the standard viscoelastic response of materials. AFM static force spectroscopy (SFS) is one approach commonly used in pursuit of this goal. It is capable of acquiring rich temporal insight into the behavior of a sample. During AFM-SFS experiments the cantilever base approaches samples with a nearly constant velocity, which is manipulated to investigate different timescales of the mechanical response. This manuscript seeks to build upon our previous work and presents an approach to extracting useful linear viscoelastic information from AFM-SFS experiments. In addition, the basis for selecting and restricting the model parameters for fitting is discussed from the perspective of applying this technique on a practical level. This work begins with a guided discussion that develops a fit function from fundamental laws, continues with conditioning a raw SFS experimental dataset, and concludes with the fit and prediction of viscoelastic response parameters such as storage modulus, loss modulus, loss angle, and compliance. These steps constitute a complete guide to leveraging AFM-SFS data to estimate key material parameters, with a series of detailed insights into both the methodology and supporting analytical choices.
Keywords: atomic force microscopy (AFM); creep; force mapping; indentation; Kelvin–Voigt; static force spectroscopy (SFS); viscoelasticity

(untitled) - Dittmer, J. J.; Lazzaroni, R.; Leclère, P.; Moretti, P.; Granström, M.; Petritsch, K.; Marseglia, E. A.; Friend, R. H.; Brédas, J. L.; Rost, H.; Holmes, A. B. (Sol. Energy Mater. Sol. Cells, 2000)

(untitled) - Mayol, L.; Quaglia, F.; Borzacchiello, A.; Ambrosio, L.; La Rotonda, M. I. (Eur. J. Pharm. Biopharm., 2008)

(untitled) - Lekka, M.; Laidler, P. (Nat. Nanotechnol., 2009)

(untitled) - Eslami, B.; López-Guerra, E. A.; Diaz, A. J.; Solares, S. D. (Nanotechnology, 2015)

(untitled) - Lekka, M. (Bionanosci., 2016)

(untitled) - Guerrero, C. R.; Garcia, P. D.; Garcia, R. (ACS Nano, 2019)

(untitled) - Attard, P. (J. Phys.: Condens. Matter, 2007)

Analytical Developments for the Measurement of Viscoelastic Properties with the Atomic Force Microscope - López Guerra, E. A. (The George Washington University, 2018)

(untitled) - Proksch, R.; Kocun, M.; Hurley, D.; Viani, M.; Labuda, A.; Meinhold, W.; Bemis, J. (J. Appl. Phys., 2016)

(untitled) - Efremov, Y. M.; Wang, W.-H.; Hardy, S. D.; Geahlen, R. L.; Raman, A. (Sci. Rep., 2017)

(untitled) - Garcia, P. D.; Garcia, R. (Nanoscale, 2018)

(untitled) - Benaglia, S.; Amo, C. A.; Garcia, R. (Nanoscale, 2019)

The phenomenological theory of linear viscoelastic behavior: an introduction - Tschoegl, N. W. (Springer Science & Business Media, 2012)

Polymer Engineering Science and Viscoelasticity - Brinson, H. F.; Brinson, L. C. (Springer US, 2008)

(untitled) - López-Guerra, E. A.; Solares, S. D. (Beilstein J. Nanotechnol., 2014)

(untitled) - Chen, W.-q. (J. Zhejiang Univ., Sci., A, 2014)

(untitled) - López-Guerra, E. A.; Eslami, B.; Solares, S. D. (J. Polym. Sci., Part B: Polym. Phys., 2017)

(untitled) - Lee, E. H.; Radok, J. R. M. (J. Appl. Mech., 1960)

(untitled) - Graham, G. A. C. (Q. Appl. Math., 1968)

(untitled) - Ting, T. C. T. (J. Appl. Mech., 1966)

(untitled) - Hunter, S. C. (J. Appl. Mech., 1961)

Solid mechanics lecture notes - Kelly, P.

(untitled) - Schwarzl, F. R. (Rheol. Acta, 1971)

(untitled) - López-Guerra, E. A.; Solares, S. D. (Beilstein J. Nanotechnol., 2017)

(untitled) - Liu, C.; Matseevich, T.; Askadskii, A.; Popova, M.; Serenko, O.; Zhang, X. (AIP Conf. Proc., 2017)

Characterization of Viscoelastic Properties of a Material Used for an Additive Manufacturing Method - Iqbal, S. (University of North Texas, 2013)

(untitled) - Levenberg, K. (Q. Appl. Math., 1944)

ICM99: Proceedings of the Fourth International Congress on Industrial and Applied Mathematics - Yuan, Y.-x. (A review of trust region algorithms for optimization, 2000)

(untitled) - Hutter, J. L.; Bechhoefer, J. (Rev. Sci. Instrum., 1993)

Film Properties of Plastics and Elastomers - McKeen, L. W. (8 - Polyamides (Nylons), 2012)