Unlocking higher harmonics in atomic force microscopy with gentle interactions

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

Atomic force microscopy (AFM) is an important tool for measuring a variety of nanoscale surface properties, such as topography, viscoelasticity, electrical potential and conductivity. Some of these properties are measured using contact methods (static contact or intermittent contact), while others are measured using noncontact methods. Some properties can be measured using different approaches. Conductivity, in particular, is mapped using the contact-mode method. However, this modality can be destructive to delicate samples, since it involves continuously dragging the cantilever tip on the surface during the raster scan, while a constant tip-sample force is applied. In this paper we discuss a possible approach to develop an intermittent-contact conductive AFM mode based on Fourier analysis, whereby the measured current response consists of higher harmonics of the cantilever oscillation frequency. Such an approach may enable the characterization of soft samples with less damage than contact-mode imaging. To explore its feasibility, we derive the analytical form of the tip-sample current that would be obtained for attractive (noncontact) and repulsive (intermittent-contact) dynamic AFM characterization, and compare it with results obtained from numerical simulations. Although significant instrumentation challenges are anticipated, the modelling results are promising and suggest that Fourier-based higher-harmonics current measurement may enable the development of a reliable intermittent-contact conductive AFM method.

Quantification of nanomechanical properties of surfaces by higher harmonic monitoring in amplitude modulated AFM imaging

The determination of nanomechanical properties is an intensive topic of study in several fields of nanophysics, from surface and materials science to biology. At the same time, amplitude modulation force microscopy is one of the most established techniques for nanoscale characterization. In this work, we combine these two topics and propose a method able to extract quantitative nanomechanical information from higher harmonic amplitude imaging in atomic force microscopy. With this method it is possible to discriminate between different materials in the stiffness range of 1-3 GPa, in our case thin films of PS-PMMA based block copolymers. We were able to obtain a critical lateral resolution of less than 20 nm and discriminate between materials with less than a 1 GPa difference in modulus. We show that within this stiffness range, reliable values of the Young's moduli can be obtained under usual imaging conditions and with standard dynamic AFM probes.

Identification of HIV-1-Based Virus-like Particles by Multifrequency Atomic Force Microscopy

Virus-like particles (VLPs) have become a promising platform for vaccine production. VLPs are formed by structural viral proteins that inherently self-assemble when expressed in a host cell. They represent a highly immunogenic and safe vaccine platform, due to the absence of the viral genome and its high protein density. One of the most important parameters in vaccine production is the quality of the product. A related bottleneck in VLP-based products is the presence of cellular vesicles as a major contaminant in the preparations, which will require the set up of techniques allowing for specific discrimination of VLPs from host vesicular bodies. In this work novel, to our knowledge, multifrequency (MF) atomic force microscopy (AFM) has permitted full structural nanophysical characterization by its access to the virus capsid of the HIV-based VLPs. The assessment of these particles by advanced amplitude modulation-frequency modulation (AM-FM) viscoelastic mapping mode has enhanced the imaging resolution of their nanomechanical properties, opening a new window for the study of the biophysical attributes of VLPs. Finally, the identification and differentiation of HIV-based VLPs from cellular vesicles has been performed under ambient conditions, providing, to our knowledge, novel methodology for the monitoring and quality control of VLPs.

Divergent surface properties of multidimensional sp (2) carbon allotropes: the effect of aging phenomena

Despite the current interest in the scientific community in exploiting divergent surface properties of graphitic carbon allotropes, conclusive differentiation remains elusive even when dealing with parameters as fundamental as adhesion. Here, we set out to provide conclusive experimental evidence on the time evolution of the surface properties of highly oriented pyrolytic graphite (HOPG), graphene monolayer (GML) and multiwalled carbon nanotubes (MWCNTs) as we expose these materials to airborne contaminants, by providing (1) statistically significant results based on large datasets consisting of thousands of force measurements, and (2) errors sufficiently self-consistent to treat the comparison between datasets in atomic force microscopy (AFM) measurements. We first consider HOPG as a model system and then employ our results to draw conclusions from the GML and MWCNT samples. We find that the surface properties of aged HOPG are indistinguishable from those of aged GML and MWCNT, while being distinct from those of cleaved HOPG. Herein, we provide a sufficient body of evidence to disregard any divergence in surface properties for multidimensional sp (2) carbon allotropes that undergo similar aging processes.

Reconstruction of height of sub-nanometer steps with bimodal atomic force microscopy

Obtaining topographic images of surfaces presenting terraces with heights in the nanometer and sub-nanometer range has become routine since the advent of atomic force microscopy (AFM). There remain however several open questions regarding the validity of direct topographic measurements. Here we turn to recent advances in AFM to correct the height of nanometric terraces by exploiting the four observables of bimodal AFM operated in the non-invasive attractive regime. We first derive expressions based on the van der Waals theory and then image model terraces in air in standard bimodal AFM while simultaneously correcting and decoupling the sources of loss/gain of height.

Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

The nonlinear interaction between an AFM tip and a sample gives rise to oscillations of the cantilever at integral multiples (harmonics) of the fundamental resonance frequency. The higher order harmonics have long been recognized to hold invaluable information on short range interactions but their utilization has thus far been relatively limited due to theoretical and experimental complexities. In particular, existing approximations of the interaction force in terms of higher harmonic amplitudes generally require simultaneous measurements of multiple harmonics to achieve satisfactory accuracy. In the present letter we address the mathematical challenge and derive accurate, explicit formulae for both conservative and dissipative forces in terms of an arbitrary single harmonic. Additionally, we show that in frequency modulation-AFM (FM-AFM) each harmonic carries complete information on the force, obviating the need for multi-harmonic analysis. Finally, we show that higher harmonics may indeed be used to reconstruct short range forces more accurately than the fundamental harmonic when the oscillation amplitude is small compared with the interaction range.

Probing viscoelastic surfaces with bimodal tapping-mode atomic force microscopy: Underlying physics and observables for a standard linear solid model

This paper presents computational simulations of single-mode and bimodal atomic force microscopy (AFM) with particular focus on the viscoelastic interactions occurring during tip-sample impact. The surface is modeled by using a standard linear solid model, which is the simplest system that can reproduce creep compliance and stress relaxation, which are fundamental behaviors exhibited by viscoelastic surfaces. The relaxation of the surface in combination with the complexities of bimodal tip-sample impacts gives rise to unique dynamic behaviors that have important consequences with regards to the acquisition of quantitative relationships between the sample properties and the AFM observables. The physics of the tip-sample interactions and its effect on the observables are illustrated and discussed, and a brief research outlook on viscoelasticity measurement with intermittent-contact AFM is provided.