Intermodal coupling spectroscopy of mechanical modes in microcantilevers.

Atomic force microscopy (AFM) is highly regarded as a lens peering into the next discoveries of nanotechnology. Fundamental research in atomic interactions, molecular reactions, and biological cell behaviour are key focal points, demanding a continuous increase in resolution and sensitivity. While renowned fields such as optomechanics have marched towards outstanding signal-to-noise ratios, these improvements have yet to find a practical way to AFM. As a solution, we investigate here a mechanism in which individual mechanical eigenmodes of a microcantilever couple to one another, mimicking optomechanical techniques to reduce thermal noise. We have a look at the most commonly used modes in AFM, starting with the first two flexural modes of cantilevers and asses the impact of an amplified coupling between them. In the following, we expand our investigation to the sea of eigenmodes available in the same structure and find a maximum coupling of 9.38 × 103 Hz/nm between two torsional modes. Through such findings we aim to expand the field of multifrequency AFM with innumerable possibilities leading to improved signal-to-noise ratios, all accessible with no additional hardware.

Temperature Dependence of Water Contact Angle on Teflon AF1600.

In this work, we investigate the change of contact angle (CA) of a water droplet during evaporation on a Teflon AF1600 surface in the temperature range between 20 and 80 °C under standard laboratory conditions. An almost constant initial CA and a significant increase of the stabilized CA have been observed. The results reveal a temperature-dependent CA change, mainly due to water adsorption on the solid surface. Soaking experiments indicate that besides adsorption, a temperature-independent friction-like force contributes to the pinning of triple-line and therefore to the CA change. We propose an adsorption coverage parameter and a friction-like force to describe the CA change. Furthermore, we describe a reproducible process to produce smooth and homogeneous Teflon AF1600 thin films, minimizing the influence of roughness and local heterogeneity on the CA.

Multi-scale characterisation of a ferroelectric polymer reveals the emergence of a morphological phase transition driven by temperature.

Ferroelectric materials exhibit a phase transition to a paraelectric state driven by temperature - called the Curie transition. In conventional ferroelectrics, the Curie transition is caused by a change in crystal symmetry, while the material itself remains a continuous three-dimensional solid crystal. However, ferroelectric polymers behave differently. Polymeric materials are typically of semi-crystalline nature, meaning that they are an intermixture of crystalline and amorphous regions. Here, we demonstrate that the semi-crystalline morphology of the ferroelectric copolymer of vinylidene fluoride and trifluoroethylene (P(VDF-TrFE)) strongly affects its Curie transition, as not only a change in crystal symmetry but also in morphology occurs. We demonstrate, by high-resolution nanomechanical measurements, that the semi-crystalline microstructure in the paraelectric state is formed by crystalline domains embedded into a softer amorphous phase. Using in situ X-ray diffraction measurements, we show that the local electromechanical response of the crystalline domains is counterbalanced by the amorphous phase, effectively masking its macroscopic effect. Our quantitative multi-scale characterisations unite the nano- and macroscopic material properties of the ferroelectric polymer P(VDF-TrFE) through its semi-crystalline nature.

Insights into Nano-Scale Physical and Mechanical Properties of Epoxy/Boehmite Nanocomposite Using Different AFM Modes.

Understanding the interaction between nanoparticles and the matrix and the properties of interphase is crucial to predict the macroscopic properties of a nanocomposite system. Here, we investigate the interaction between boehmite nanoparticles (BNPs) and epoxy using different atomic force microscopy (AFM) approaches. We demonstrate benefits of using multifrequency intermodulation AFM (ImAFM) to obtain information about conservative, dissipative and van der Waals tip-surface forces and probing local properties of nanoparticles, matrix and the interphase. We utilize scanning kelvin probe microscopy (SKPM) to probe surface potential as a tool to visualize material contrast with a physical parameter, which is independent from the mechanics of the surface. Combining the information from ImAFM stiffness and SKPM surface potential results in a precise characterization of interfacial region, demonstrating that the interphase is softer than epoxy and boehmite nanoparticles. Further, we investigated the effect of boehmite nanoparticles on the bulk properties of epoxy matrix. ImAFM stiffness maps revealed the significant stiffening effect of boehmite nanoparticles on anhydride-cured epoxy matrix. The energy dissipation of epoxy matrix locally measured by ImAFM shows a considerable increase compared to that of neat epoxy. These measurements suggest a substantial alteration of epoxy structure induced by the presence of boehmite.

Probing viscoelastic response of soft material surfaces at the nanoscale.

We study the interaction between an AFM tip and a soft viscoelastic surface. Using a multifrequency method we measure the amplitude-dependence of the cantilever dynamic force quadratures, which clearly show the effect of finite relaxation time of the viscoelastic surface. A model is introduced which treats the tip and surface as a two-body dynamic problem with a nonlinear interaction depending on their separation. We find good agreement between simulations of this model and experimental data on polymer blend samples for a variety of materials and measurement conditions.

Polynomial force approximations and multifrequency atomic force microscopy.

We present polynomial force reconstruction from experimental intermodulation atomic force microscopy (ImAFM) data. We study the tip-surface force during a slow surface approach and compare the results with amplitude-dependence force spectroscopy (ADFS). Based on polynomial force reconstruction we generate high-resolution surface-property maps of polymer blend samples. The polynomial method is described as a special example of a more general approximative force reconstruction, where the aim is to determine model parameters that best approximate the measured force spectrum. This approximative approach is not limited to spectral data, and we demonstrate how it can be adapted to a force quadrature picture.

Interpreting motion and force for narrow-band intermodulation atomic force microscopy.

Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip-surface force by measurement of the mixing of multiple modes in a frequency comb. A high-quality factor cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show, by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time-domain perspective, we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip-surface force that are in-phase with the tip motion (F(I)) and quadrature to the motion (F(Q)). Traditionally, these force components have been considered as a function of the static-probe height only. Here we show that F(I) and F(Q) actually depend on both static-probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of F(I) and F(Q) from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe-height dependence of the force components F(I) and F(Q), providing deeper insight into the tip-surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.

Interaction imaging with amplitude-dependence force spectroscopy.

Knowledge of surface forces is the key to understanding a large number of processes in fields ranging from physics to material science and biology. The most common method to study surfaces is dynamic atomic force microscopy (AFM). Dynamic AFM has been enormously successful in imaging surface topography, even to atomic resolution, but the force between the AFM tip and the surface remains unknown during imaging. Here we present a new approach that combines high-accuracy force measurements and high-resolution scanning. The method, called amplitude-dependence force spectroscopy (ADFS), is based on the amplitude dependence of the cantilever's response near resonance and allows for separate determination of both conservative and dissipative tip-surface interactions. We use ADFS to quantitatively study and map the nano-mechanical interaction between the AFM tip and heterogeneous polymer surfaces. ADFS is compatible with commercial atomic force microscopes and we anticipate its widespread use in taking AFM toward quantitative microscopy.

The role of nonlinear dynamics in quantitative atomic force microscopy.

Various methods of force measurement with the atomic force microscope are compared for their ability to accurately determine the tip-surface force from analysis of the nonlinear cantilever motion. It is explained how intermodulation, or the frequency mixing of multiple drive tones by the nonlinear tip-surface force, can be used to concentrate the nonlinear motion in a narrow band of frequency near the cantilever's fundamental resonance, where accuracy and sensitivity of force measurement are greatest. Two different methods for reconstructing tip-surface forces from intermodulation spectra are explained. The reconstruction of both conservative and dissipative tip-surface interactions from intermodulation spectra are demonstrated on simulated data.

Note: The intermodulation lockin analyzer.

Nonlinear systems can be probed by driving them with two or more pure tones while measuring the intermodulation products of the drive tones in the response. We describe a digital lockin analyzer which is designed explicitly for this purpose. The analyzer is implemented on a field-programmable gate array, providing speed in analysis, real-time feedback, and stability in operation. The use of the analyzer is demonstrated for intermodulation atomic force microscopy. A generalization of the intermodulation spectral technique to arbitrary drive waveforms is discussed.

Reconstructing nonlinearities with intermodulation spectroscopy.

We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives, resulting in a complicated spectral response. Analysis of this spectrum allows one to approximate the nonlinearity. The method, which is generally applicable to measurements based on resonant detection, increases the information content of the measurement without requiring a large detection bandwidth, and optimally uses the enhanced sensitivity near resonance to extract information and minimize error due to detector noise.

Phase imaging with intermodulation atomic force microscopy.

Intermodulation atomic force microscopy (IMAFM) is a dynamic mode of atomic force microscopy (AFM) with two-tone excitation. The oscillating AFM cantilever in close proximity to a surface experiences the nonlinear tip-sample force which mixes the drive tones and generates new frequency components in the cantilever response known as intermodulation products (IMPs). We present a procedure for extracting the phase at each IMP and demonstrate phase images made by recording this phase while scanning. Amplitude and phase images at intermodulation frequencies exhibit enhanced topographic and material contrast.