SummaryWe examine different approaches to model viscoelasticity within atomic force microscopy (AFM) simulation. Our study ranges from very simple linear spring–dashpot models to more sophisticated nonlinear systems that are able to reproduce fundamental properties of viscoelastic surfaces, including creep, stress relaxation and the presence of multiple relaxation times. Some of the models examined have been previously used in AFM simulation, but their applicability to different situations has not yet been examined in detail. The behavior of each model is analyzed here in terms of force–distance curves, dissipated energy and any inherent unphysical artifacts. We focus in this paper on single-eigenmode tip–sample impacts, but the models and results can also be useful in the context of multifrequency AFM, in which the tip trajectories are very complex and there is a wider range of sample deformation frequencies (descriptions of tip–sample model behaviors in the context of multifrequency AFM require detailed studies and are beyond the scope of this work).

We explore the physics of an atomic force microscopy (AFM) cantilever tip interacting with a generalized viscoelastic sample containing an arbitrary number of characteristic times, when the cantilever's base is driven with constant velocity toward the sample. This mode of operation, often called static force spectroscopy (SFS), can be harnessed to thoroughly analyze time-dependent viscoelastic information frequently overlooked in experiments. We generalize the solution of previous authors who have studied the standard linear solid model, and offer a solution applicable to any linear viscoelastic model. This generalization is crucial for the prediction of the model's response over wide ranges of time-scale. As a demonstration, successful predictions of harmonic functions (e.g., loss tangent) over a wide frequency range are obtained through analysis of simulated SFS results. In addition, we show that analysis through the generalized solution and previous expressions is no longer valid when the force does not grow linearly in time, so we also deliver an alternate route for extracting the viscoelastic information, which does not rely on the force linearity assumption. Despite the large amount of theoretical content (included for theoretical rigor's sake), the practical user can also benefit from the new procedures offered and the corresponding explanations.

Biofilms are a cluster of bacteria embedded in extracellular polymeric substances (EPS) that contain a complex composition of polysaccharides, proteins, and extracellular DNA (eDNA). Desirable mechanical properties of the biofilms are critical for their survival, propagation, and dispersal, and the response of mechanical properties to different treatment conditions also sheds light on biofilm control and eradication in vivo and on engineering surfaces. However, it is challenging yet important to interrogate mechanical behaviors of biofilms with a high spatial resolution because biofilms are very heterogeneous. Moreover, biofilms are viscoelastic, and their time-dependent mechanical behavior is difficult to capture. Herein, we developed a powerful technique that combines the high spatial resolution of the atomic force microscope (AFM) with a rigorous history-dependent viscoelastic analysis to deliver highly spatial-localized biofilm properties within a wide time-frequency window. By exploiting the use of static force spectroscopy in combination with an appropriate viscoelastic framework, we highlight the intensive amount of time-dependent information experimentally available that has been largely overlooked. It is shown that this technique provides a detailed nanorheological signature of the biofilms even at the single-cell level. We share the computational routines that would allow any user to perform the analysis from experimental raw data. The detailed localization of mechanical properties in space and in time-frequency domain provides insights on the understanding of biofilm stability, cohesiveness, dispersal, and control.

This paper explores the effect of the amplitude ratio of the higher to the fundamental eigenmode in bimodal atomic force microscopy (AFM) on the phase contrast and the dissipated power contrast of the higher eigenmode. We explore the optimization of the amplitude ratio in order to maximize the type of contrast that is most relevant to the particular study. Specifically, we show that the trends in the contrast range behave differently for different quantities, especially the dissipated power and the phase, with the former being more meaningful than the latter (a similar analysis can be carried out using the virial, for which we also provide a brief example). Our work is based on numerical simulations using two different conservative-dissipative tip-sample models, including the standard linear solid and the combination of a dissipation coefficient with a conservative model, as well as experimental images of thin film Nafion V R proton exchange polymers. We focus on the original bimodal AFM method, where the higher eigenmode is driven with constant amplitude and frequency (i.e., in "open loop"). V C 2014 AIP Publishing LLC.