A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques.

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.

On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges.

Atomic force microscopy (AFM) is a widely use technique to acquire topographical, mechanical, or electromagnetic properties of surfaces, as well as to induce surface modifications at the micrometer and nanometer scale. Viscoelastic materials, examples of which include many polymers and biological materials, are an important class of systems, the mechanical response of which depends on the rate of application of the stresses imparted by the AFM tip. The mechanical response of these materials thus depends strongly on the frequency at which the characterization is performed, so much so that important aspects of behavior may be missed if one chooses an arbitrary characterization frequency regardless of the materials properties. In this paper we present a linear viscoelastic analysis of intermittent-contact, nearly resonant dynamic AFM characterization of such materials, considering the possibility of multiple characteristic times. We describe some of the intricacies observed in their mechanical response and alert the reader about situations where mischaracterization may occur as a result of probing the material at frequency ranges or with probes that preclude observation of its viscoelastic behavior. While we do not offer a solution to the formidable problem of inverting the frequency-dependent viscoelastic behavior of a material from dynamic AFM observables, we suggest that a partial solution is offered by recently developed quasi-static force-distance characterization techniques, which incorporate viscoelastic models with multiple characteristic times and can help inform dynamic AFM characterization.

Few-cycle Regime Atomic Force Microscopy.

Traditionally, dynamic atomic force microscopy (AFM) techniques are based on the analysis of the quasi-steady state response of the cantilever deflection in terms of Fourier analysis. Here we describe a technique that instead exploits the often disregarded transient response of the cantilever through a relatively modern mathematical tool, which has caused important developments in several scientific fields but that is still quite unknown in the AFM context: the wavelet analysis. This tool allows us to localize the time-varying spectral composition of the initial oscillations of the cantilever deflection when an impulsive excitation is given (as in the band excitation method), a mode that we call the few-cycle regime. We show that this regime encodes very meaningful information about the tip-sample interaction in a unique and extremely sensitive manner. We exploit this high sensitivity to gain detailed insight into multiple physical parameters that perturb the dynamics of the AFM probe, such as the tip radius, Hamaker constant, sample's elastic modulus and height of an adsorbed water layer. We validate these findings with experimental evidence and computational simulations and show a feasible path towards the simultaneous retrieval of multiple physical parameters.

Acquisition of time-frequency localized mechanical properties of biofilms and single cells with high spatial resolution.

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 investigate 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 develop a powerful technique that combines the high spatial resolution of an 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 into the understanding of biofilm stability, cohesiveness, dispersal, and control.

Visible-Light-Responsive Photocatalyst of Graphitic Carbon Nitride for Pathogenic Biofilm Control.

Pathogenic biofilms raise significant health and economic concerns, because these bacteria are persistent and can lead to long-term infections in vivo and surface contamination in healthcare and industrial facilities or devices. Compared with conventional antimicrobial strategies, photocatalysis holds promise for biofilm control because of its broad-spectrum effectiveness under ambient conditions, low cost, easy operation, and reduced maintenance. In this study, we investigated the performance and mechanism of Staphylococcus epidermidis biofilm control and eradication on the surface of an innovative photocatalyst, graphitic carbon nitride (g-C3N4), under visible-light irradiation, which overcame the need for ultraviolet light for many current photocatalysts (e.g., titanium dioxide (TiO2)). Optical coherence tomography and confocal laser scanning microscopy (CLSM) suggested that g-C3N4 coupons inhibited biofilm development and eradicated mature biofilms under the irradiation of white light-emitting diodes. Biofilm inactivation was observed occurring from the surface toward the center of the biofilms, suggesting that the diffusion of reactive species into the biofilms played a key role. By taking advantage of scanning electron microscopy, CLSM, and atomic force microscopy for biofilm morphology, composition, and mechanical property characterization, we demonstrated that photocatalysis destroyed the integrated and cohesive structure of biofilms and facilitated biofilm eradication by removing the extracellular polymeric substances. Moreover, reactive oxygen species generated during g-C3N4 photocatalysis were quantified via reactions with radical probes and 1O2 was believed to be responsible for biofilm control and removal. Our work highlights the promise of using g-C3N4 for a broad range of antimicrobial applications, especially for the eradication of persistent biofilms under visible-light irradiation, including photodynamic therapy, environmental remediation, food-industry applications, and self-cleaning surface development.

Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy.

In this short paper we explore the use of higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy (AFM) for the small-indentation imaging of soft viscoelastic materials. In viscoelastic materials, whose response depends on the deformation rate, the tip-sample forces generated as a result of sample deformation increase as the tip velocity increases. Since the eigenfrequencies in a cantilever increase with eigenmode order, and since higher oscillation frequencies lead to higher tip velocities for a given amplitude (in viscoelastic materials), the sample indentation can in some cases be reduced by using higher eigenmodes of the cantilever. This effect competes with the lower sensitivity of higher eigenmodes, due to their larger force constant, which for elastic materials leads to greater indentation for similar amplitudes, compared with lower eigenmodes. We offer a short theoretical discussion of the key underlying concepts, along with numerical simulations and experiments to illustrate a simple recipe for imaging soft viscoelastic matter with reduced indentation.

Theory of Single-Impact Atomic Force Spectroscopy in liquids with material contrast.

Scanning probe microscopy has enabled nanoscale mapping of mechanical properties in important technological materials, such as tissues, biomaterials, polymers, nanointerfaces of composite materials, to name only a few. To improve and widen the measurement of nanoscale mechanical properties, a number of methods have been proposed to overcome the widely used force-displacement mode, that is inherently slow and limited to a quasi-static regime, mainly using multiple sinusoidal excitations of the sample base or of the cantilever. Here, a different approach is put forward. It exploits the unique capabilities of the wavelet transform analysis to harness the information encoded in a short duration spectroscopy experiment. It is based on an impulsive excitation of the cantilever and a single impact of the tip with the sample. It performs well in highly damped environments, which are often seen as problematic in other standard dynamic methods. Our results are very promising in terms of viscoelastic property discrimination. Their potential is oriented (but not limited) to samples that demand imaging in liquid native environments and also to highly vulnerable samples whose compositional mapping cannot be obtained through standard tapping imaging techniques.

Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times.

We explore the contact problem of a flat-end indenter penetrating intermittently a generalized viscoelastic surface, containing multiple characteristic times. This problem is especially relevant for nanoprobing of viscoelastic surfaces with the highly popular tapping-mode AFM imaging technique. By focusing on the material perspective and employing a rigorous rheological approach, we deliver analytical closed-form solutions that provide physical insight into the viscoelastic sources of repulsive forces, tip-sample dissipation and virial of the interaction. We also offer a systematic comparison to the well-established standard harmonic excitation, which is the case relevant for dynamic mechanical analysis (DMA) and for AFM techniques where tip-sample sinusoidal interaction is permanent. This comparison highlights the substantial complexity added by the intermittent-contact nature of the interaction, which precludes the derivation of straightforward equations as is the case for the well-known harmonic excitations. The derivations offered have been thoroughly validated through numerical simulations. Despite the complexities inherent to the intermittent-contact nature of the technique, the analytical findings highlight the potential feasibility of extracting meaningful viscoelastic properties with this imaging method.

Optimization of the excitation frequency for high probe sensitivity in single-eigenmode and bimodal tapping-mode AFM.

The cantilever excitation frequency and tip free oscillation amplitude are two critical imaging parameters in amplitude-modulation atomic force microscopy (AM-AFM, often referred to as tapping-mode AFM). In general, the excitation frequency is selected to be 'near' the measured resonance frequency of the probe, but there is no established systematic approach for making that choice. In this work we show that the choice of excitation frequency can play a very significant role in the characterization of viscoelastic materials, even when considering small deviations with respect to the resonance frequency. Additionally, we offer an analytical expression, verified through experiments and numerical simulations, which offers guidance for selecting the drive frequency that maximizes probe sensitivity. Our approach is illustrated experimentally through single-eigenmode and bimodal AFM measurements performed on spin-coated Nafion(®) proton exchange thin films. We find that very often, the phase contrast channel is optimized by selecting an excitation frequency that is not necessarily at or near the free resonance frequency.

Modeling viscoelasticity through spring-dashpot models in intermittent-contact atomic force microscopy.

We 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).