TY - JOUR A1 - Uluutku, Berkin A1 - López-Guerra, Enrique A. A1 - Solares, Santiago D. T1 - A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques JF - Beilstein Journal of Nanotechnology PY - 2021/// VL - 12 SP - 1063 EP - 1077 SN - 2190-4286 DO - 10.3762/bjnano.12.79 PB - Beilstein-Institut JA - Beilstein J. Nanotechnol. UR - https://doi.org/10.3762/bjnano.12.79 KW - atomic force microscopy KW - force spectroscopy KW - material properties KW - viscoelasticity N2 - Viscoelastic characterization of materials at the micro- and the nanoscale is commonly performed with the aid of force–distance relationships acquired using atomic force microscopy (AFM). The general strategy for existing methods is to fit the observed material behavior to specific viscoelastic models, such as generalized viscoelastic models or power-law rheology models, among others. Here we propose a new method to invert and obtain the viscoelastic properties of a material through the use of the Z-transform, without using a model. We present the rheological viscoelastic relations in their classical derivation and their z-domain correspondence. We illustrate the proposed technique on a model experiment involving a traditional ramp-shaped force–distance AFM curve, demonstrating good agreement between the viscoelastic characteristics extracted from the simulated experiment and the theoretical expectations. We also provide a path for calculating standard viscoelastic responses from the extracted material characteristics. The new technique based on the Z-transform is complementary to previous model-based viscoelastic analyses and can be advantageous with respect to Fourier techniques due to its generality. Additionally, it can handle the unbounded inputs traditionally used to acquire force–distance relationships in AFM, such as ramp functions, in which the cantilever position is displaced linearly with time for a finite period of time. ER - TY - JOUR AU - Binnig, G. AU - Quate, C. F. AU - Gerber, C. JF - Phys. Rev. Lett. PY - 1986/// VL - 56 SP - 930 EP - 933 DO - 10.1103/physrevlett.56.930 ER - TY - JOUR AU - García, R. AU - Pérez, R. JF - Surf. Sci. Rep. PY - 2002/// VL - 47 SP - 197 EP - 301 DO - 10.1016/s0167-5729(02)00077-8 ER - TY - JOUR AU - Garcia, R. AU - Herruzo, E. T. JF - Nat. Nanotechnol. PY - 2012/// VL - 7 SP - 217 EP - 226 DO - 10.1038/nnano.2012.38 ER - TY - JOUR AU - Herruzo, E. T. AU - Perrino, A. P. AU - Garcia, R. JF - Nat. Commun. PY - 2014/// VL - 5 SP - 3126 DO - 10.1038/ncomms4126 ER - TY - JOUR AU - Amo, C. A. AU - Perrino, A. P. AU - Payam, A. F. AU - Garcia, R. JF - ACS Nano PY - 2017/// VL - 11 SP - 8650 EP - 8659 DO - 10.1021/acsnano.7b04381 ER - TY - JOUR AU - Rico, F. AU - Roca-Cusachs, P. AU - Gavara, N. AU - Farré, R. AU - Rotger, M. AU - Navajas, D. JF - Phys. Rev. E PY - 2005/// VL - 72 SP - 021914 DO - 10.1103/physreve.72.021914 ER - TY - JOUR AU - López-Guerra, E. A. AU - Banfi, F. AU - Solares, S. D. AU - Ferrini, G. JF - Sci. Rep. PY - 2018/// VL - 8 SP - 7534 DO - 10.1038/s41598-018-25828-4 ER - TY - JOUR AU - López-Guerra, E. A. AU - Somnath, S. AU - Solares, S. D. AU - Jesse, S. AU - Ferrini, G. JF - Sci. Rep. PY - 2019/// VL - 9 SP - 12721 DO - 10.1038/s41598-019-49104-1 ER - TY - JOUR AU - Radmacher, M. AU - Tillmann, R. W. AU - Gaub, H. E. JF - Biophys. J. PY - 1993/// VL - 64 SP - 735 EP - 742 DO - 10.1016/s0006-3495(93)81433-4 ER - TY - JOUR AU - Yuya, P. A. AU - Hurley, D. C. AU - Turner, J. A. JF - J. Appl. Phys. PY - 2008/// VL - 104 IS - 7 SP - 074916 DO - 10.1063/1.2996259 ER - TY - JOUR AU - Attard, P. JF - J. Phys.: Condens. Matter PY - 2007/// VL - 19 SP - 473201 DO - 10.1088/0953-8984/19/47/473201 ER - TY - BOOK AU - Ferry, J. D. T1 - Viscoelastic Properties of Polymers PY - 1980/// PB - John Wiley & Sons ER - TY - BOOK AU - Tschoegl, N. W. T1 - The Phenomenological Theory of Linear Viscoelastic Behavior PY - 1989/// DO - 10.1007/978-3-642-73602-5 PB - Springer CY - Berlin, Heidelberg ER - TY - JOUR AU - Lee, E. H. AU - Radok, J. R. M. JF - J. Appl. Mech. PY - 1960/// VL - 27 SP - 438 EP - 444 DO - 10.1115/1.3644020 ER - TY - JOUR AU - Graham, G. A. C. JF - Int. J. Eng. Sci. PY - 1965/// VL - 3 SP - 27 EP - 46 DO - 10.1016/0020-7225(65)90018-2 ER - TY - JOUR AU - Ting, T. C. T. JF - J. Appl. Mech. PY - 1966/// VL - 33 SP - 845 EP - 854 DO - 10.1115/1.3625192 ER - TY - JOUR AU - de Sousa, J. S. AU - Santos, J. A. C. AU - Barros, E. B. AU - Alencar, L. M. R. AU - Cruz, W. T. AU - Ramos, M. V. AU - Mendes Filho, J. JF - J. Appl. Phys. PY - 2017/// VL - 121 SP - 034901 DO - 10.1063/1.4974043 ER - TY - JOUR AU - Efremov, Y. M. AU - Wang, W.-H. AU - Hardy, S. D. AU - Geahlen, R. L. AU - Raman, A. JF - Sci. Rep. PY - 2017/// VL - 7 SP - 1541 DO - 10.1038/s41598-017-01784-3 ER - TY - JOUR AU - López-Guerra, E. A. AU - Shen, H. AU - Solares, S. D. AU - Shuai, D. JF - Nanoscale PY - 2019/// VL - 11 SP - 8918 EP - 8929 DO - 10.1039/c8nr10287b ER - TY - JOUR AU - López-Guerra, E. A. AU - Eslami, B. AU - Solares, S. D. JF - J. Polym. Sci., Part B: Polym. Phys. PY - 2017/// VL - 55 IS - 10 SP - 804 EP - 813 DO - 10.1002/polb.24327 ER - TY - JOUR AU - Garcia, P. D. AU - Guerrero, C. R. AU - Garcia, R. JF - Nanoscale PY - 2017/// VL - 9 SP - 12051 EP - 12059 DO - 10.1039/c7nr03419a ER - TY - JOUR AU - Garcia, P. D. AU - Guerrero, C. R. AU - Garcia, R. JF - Nanoscale PY - 2020/// VL - 12 SP - 9133 EP - 9143 DO - 10.1039/c9nr10316c ER - TY - JOUR AU - Rajabifar, B. AU - Jadhav, J. M. AU - Kiracofe, D. AU - Meyers, G. F. AU - Raman, A. JF - Macromolecules PY - 2018/// VL - 51 SP - 9649 EP - 9661 DO - 10.1021/acs.macromol.8b01485 ER - TY - JOUR AU - Chyasnavichyus, M. AU - Young, S. L. AU - Tsukruk, V. V. JF - Langmuir PY - 2014/// VL - 30 SP - 10566 EP - 10582 DO - 10.1021/la404925h ER - TY - JOUR AU - Parvini, C. H. AU - Saadi, M. A. S. R. AU - Solares, S. D. JF - Beilstein J. Nanotechnol. PY - 2020/// VL - 11 SP - 922 EP - 937 DO - 10.3762/bjnano.11.77 ER - TY - JOUR AU - Forstenhäusler, M. AU - López-Guerra, E. A. AU - Solares, S. D. JF - Facta Univ., Ser.: Mech. Eng. PY - 2021/// VL - 19 SP - 133 EP - 153 DO - 10.22190/fume200920009f ER - TY - JOUR AU - Garcia, R. JF - Chem. Soc. Rev. PY - 2020/// VL - 49 SP - 5850 EP - 5884 DO - 10.1039/d0cs00318b ER - TY - BOOK AU - Oppenheim, A. V. AU - Willsky, A. S. AU - Nawab, S. H. T1 - Signals & Systems PY - 1997/// PB - Prentice Hall CY - Upper Saddle River, NJ, USA ER - TY - JOUR AU - Evans, R. M. L. AU - Tassieri, M. AU - Auhl, D. AU - Waigh, T. A. JF - Phys. Rev. E PY - 2009/// VL - 80 SP - 012501 DO - 10.1103/physreve.80.012501 ER - TY - JOUR AU - Aspden, R. M. JF - J. Phys. D: Appl. Phys. PY - 1991/// VL - 24 SP - 803 EP - 808 DO - 10.1088/0022-3727/24/6/002 ER - TY - JOUR AU - Holly, E. E. AU - Venkataraman, S. K. AU - Chambon, F. AU - Henning Winter, H. JF - J. Non-Newtonian Fluid Mech. PY - 1988/// VL - 27 SP - 17 EP - 26 DO - 10.1016/0377-0257(88)80002-8 ER - TY - BOOK AU - Gardner, M. F. AU - Barnes, J. L. T1 - Transients in Linear Systems Studied by the Laplace Transformation PY - 1956/// PB - John Wiley & Sons ER - TY - BOOK AU - Stroud, K. A. AU - Booth, D. J. T1 - Advanced Engineering Mathematics PY - 2011/// PB - Palgrave Macmillan ER - TY - JOUR AU - Cooley, J. W. AU - Tukey, J. W. JF - Math. Comput. PY - 1965/// VL - 19 SP - 297 DO - 10.1090/s0025-5718-1965-0178586-1 ER - TY - BOOK AU - Oppenheim, A. V. AU - Schafer, R. W. T1 - Digital Signal Processing PY - 1974/// PB - Pretince-Hall CY - Englewood Cliffe, NJ, USA ER - TY - BOOK AU - McClellan, J. H. AU - Schafer, R. W. AU - Yoder, M. A. T1 - Signal Processing First PY - 2003/// PB - Pearson\Prentice Hall CY - Upper Saddle River, NJ, USA ER - TY - BOOK AU - Smith, S. W. T1 - The Scientist & Engineer’s Guide to Digital Signal Processing PY - 1997/// PB - California Technical Publishing CY - San Diego, CA, USA ER - TY - JOUR AU - Schapery, R. A. AU - Park, S. W. JF - Int. J. Solids Struct. PY - 1999/// VL - 36 SP - 1677 EP - 1699 DO - 10.1016/s0020-7683(98)00060-2 ER - TY - JOUR AU - Park, S. W. AU - Schapery, R. A. JF - Int. J. Solids Struct. PY - 1999/// VL - 36 SP - 1653 EP - 1675 DO - 10.1016/s0020-7683(98)00055-9 ER - TY - JOUR AU - Mead, D. W. JF - J. Rheol. PY - 1994/// VL - 38 SP - 1769 EP - 1795 DO - 10.1122/1.550526 ER - TY - THES AU - López Guerra, E. A. T1 - Analytical Developments for the Measurement of Viscoelastic Properties with the Atomic Force Microscope PY - 2018/// PB - The George Washington University CY - Washington, D.C., USA ER - TY - JOUR AU - Sorvari, J. AU - Malinen, M. JF - Int. J. Solids Struct. PY - 2007/// VL - 44 SP - 1291 EP - 1303 DO - 10.1016/j.ijsolstr.2006.06.029 ER - TY - BOOK AU - Kusse, B. R. AU - Westwig, E. A. T1 - Mathematical Physics PY - 2006/// DO - 10.1002/9783527618132 PB - Wiley-VCH CY - Weinheim, Germany ER -