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

Abstract

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.

Nanomechanical mapping of soft materials with the atomic force microscope: methods, theory and applications

“…The deduction of viscoelastic parameters from a FDC demands significant theoretical and modelization efforts. 49,[93][94][95][96][126][127][128][129][130][131][132][133][134][135] Typical viscoelastic parameters measured in nanoscale rheology are loss and storage moduli, viscosity coefficient or loss tangent. In addition, a nanoscale rheology experiment might involve some changes in the experimental FV set-up.…”

“…The overall result of this activity is poised to have an impact in mechanobiology. 49,52,67,[92][93][94][95][126][127][128][129][130][131][132][133][134][135] 7 Nanomechanical maps obtained from force-distance curves: on-resonance methods Force-distance curves are not directly measured in amplitude modulation AFM because the observables are averages over a period. Therefore, the observables (static deflection, amplitude and phase shift) are determined as a function of an average distance instead of the instantaneous tip-sample distance.…”

A New Method for Obtaining Model-Free Viscoelastic Material Properties from Atomic Force Microscopy Experiments Using Discrete Integral Transform Techniques

“…Atomic force microscopy (AFM) is a prominent technique for investigating material properties at the micro-and nanoscale [1][2][3], within which a wide variety of instruments, probes and analysis techniques have been developed to attempt meaningful material property extraction [4][5][6][7][8][9][10][11]. With regards to viscoelasticity, efforts that incorporate classical viscoelastic theory [12][13][14][15][16] rely on forcedistance curves [17][18][19][20][21][22][23][24][25][26], which describe the dependence of the probe-sample interaction force with respect to the probe-surface distance for a particular location on the sample [27]. Force-distance analysis provides direct information on the force and indentation history with respect to time, which makes it appropriate for viscoelastic material property inversion.…”

Guidelines to Simulate Linear Viscoelastic Materials With an Arbitrary Number of Characteristic Times in the Context of Atomic Force Miscroscopy

“…Unfortunately, due to mathematical complexity, the viscoelastic nature of such materials is often overlooked or oversimplified in scientific studies. Recent investigations [16][17][18][19][20][21][22][23][24][25][26] have explored more rigorous approaches to take into consideration the intricacies of real viscoelastic behaviors by combining the classical theory of viscoelasticity [1,2,[27][28][29] with modern characterization techniques, such as atomic force microscopy (AFM) [10,[30][31][32][33][34][35][36][37][38][39]. These efforts are especially important to close the gap between the thorough and rigorous mechanical modeling approach of early theories and the interests of scientists that deal with modern techniques.…”