One of the key goals in atomic force microscopy (AFM) imaging is to enhance material property contrast with high resolution. Bimodal AFM, where two eigenmodes are simultaneously excited, confers significant advantages over conventional single-frequency tapping mode AFM due to its ability to provide contrast between regions with different material properties under gentle imaging conditions. Bimodal AFM traditionally uses the first two eigenmodes of the AFM cantilever. In this work, the authors explore the use of higher eigenmodes in bimodal AFM (e.g., exciting the first and fourth eigenmodes). It is found that such operation leads to interesting contrast reversals compared to traditional bimodal AFM. A series of experiments and numerical simulations shows that the primary cause of the contrast reversals is not the choice of eigenmode itself (e.g., second versus fourth), but rather the relative kinetic energy between the higher eigenmode and the first eigenmode. This leads to the identification of three distinct imaging regimes in bimodal AFM. This result, which is applicable even to traditional bimodal AFM, should allow researchers to choose cantilever and operating parameters in a more rational manner in order to optimize resolution and contrast during nanoscale imaging of materials.
atomic force microscopy; bimodal AFM; cantilever eigenmodes; polymer characterization
We present an overview of the bimodal amplitude–frequency-modulation (AM-FM) imaging mode of atomic force microscopy (AFM), whereby the fundamental eigenmode is driven by using the amplitude-modulation technique (AM-AFM) while a higher eigenmode is driven by using either the constant-excitation or the constant-amplitude variant of the frequency-modulation (FM-AFM) technique. We also offer a comparison to the original bimodal AFM method, in which the higher eigenmode is driven with constant frequency and constant excitation amplitude. General as well as particular characteristics of the different driving schemes are highlighted from theoretical and experimental points of view, revealing the advantages and disadvantages of each. This study provides information and guidelines that can be useful in selecting the most appropriate operation mode to characterize different samples in the most efficient and reliable way.
amplitude-modulation; atomic force microscopy; frequency-modulation; phase-locked loop; spectroscopy
This paper illustrates through numerical simulation the complexities encountered in high-damping AFM imaging, as in liquid enviroments, within the specific context of multifrequency atomic force microscopy (AFM). The focus is primarily on (i) the amplitude and phase relaxation of driven higher eigenmodes between successive tip–sample impacts, (ii) the momentary excitation of non-driven higher eigenmodes and (iii) base excitation artifacts. The results and discussion are mostly applicable to the cases where higher eigenmodes are driven in open loop and frequency modulation within bimodal schemes, but some concepts are also applicable to other types of multifrequency operations and to single-eigenmode amplitude and frequency modulation methods.
amplitude-modulation; bimodal; frequency-modulation; liquids; multifrequency atomic force microscopy
Bimodal atomic force microscopy is a force-microscopy method that requires the simultaneous excitation of two eigenmodes of the cantilever. This method enables the simultaneous recording of several material properties and, at the same time, it also increases the sensitivity of the microscope. Here we apply fractional calculus to express the frequency shift of the second eigenmode in terms of the fractional derivative of the interaction force. We show that this approximation is valid for situations in which the amplitude of the first mode is larger than the length of scale of the force, corresponding to the most common experimental case. We also show that this approximation is valid for very different types of tip–surface forces such as the Lennard-Jones and Derjaguin–Muller–Toporov forces.
AFM; atomic force microscopy; bimodal AFM; frequency shift; integral calculus applications
The resonance frequency, amplitude, and phase response of the first two eigenmodes of two contact-resonance atomic force microscopy (CR-AFM) configurations, which differ in the method used to excite the system (cantilever base vs sample excitation), are analyzed in this work. Similarities and differences in the observables of the cantilever dynamics, as well as the different effect of the tip–sample contact properties on those observables in each configuration are discussed. Finally, the expected accuracy of CR-AFM using phase-locked loop detection is investigated and quantification of the typical errors incurred during measurements is provided.
contact-resonance AFM; dynamic AFM; frequency modulation; phase-locked loop; viscoelasticity
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.
atomic force microscopy; AFM; frequency combs; force spectroscopy; high-quality-factor resonators; intermodulation; multifrequency
In this work, we investigated the bulk phase distinguishing of the poly(ε-caprolactone)-polybutadiene-poly(ε-caprolactone) (PCL-PB-PCL) triblock copolymer blended in epoxy resin by tapping mode atomic force microscopy (TM-AFM). We found that at a set-point amplitude ratio (rsp) less than or equal to 0.85, a clear phase contrast could be obtained using a probe with a force constant of 40 N/m. When rsp was decreased to 0.1 or less, the measured size of the PB-rich domain relatively shrank; however, the height images of the PB-rich domain would take reverse (translating from the original light to dark) at rsp = 0.85. Force-probe measurements were carried out on the phase-separated regions by TM-AFM. According to the phase shift angle vs. rsp curve, it could be concluded that the different force exerting on the epoxy matrix or on the PB-rich domain might result in the height and phase image reversion. Furthermore, the indentation depth vs. rsp plot showed that with large tapping force (lower rsp), the indentation depth for the PB-rich domain was nearly identical for the epoxy resin matrix.
tapping mode AFM; PCL-PB-PCL; phase image; force-probe
The structural evolution of low-molecular-weight poly(ethylene oxide)-block-polystyrene (PEO-b-PS) diblock copolymer thin film with various initial film thicknesses on silicon substrate under thermal annealing was investigated by atomic force microscopy, optical microscopy, and contact angle measurement. At film thickness below half of the interlamellar spacing of the diblock copolymer (6.2 nm), the entire silicon is covered by a polymer brush with PEO blocks anchored on the Si substrate due to the substrate-induced effect. When the film is thicker than 6.2 nm, a dense polymer brush which is equal to half of an interlamellar layer was formed on the silicon, while the excess material dewet this layer to form droplets. The droplet surface was rich with PS block and the PEO block crystallized inside the bigger droplet to form spherulite.
The surface properties of patterned surfaces made by a combination of photolithography and oxygen plasma treatment of polystyrene (PS) were investigated. PS and plasma-treated PS (PSox) were first characterized using X-ray photoelectron spectroscopy and the study of wetting dynamics (Wilhelmy plate method) in water and in solutions of different pH. The results indicated that the PSox surface may be viewed as covered with a polyelectrolyte-like gel, which swells depending on pH. It was then shown, using atomic force microscopy (AFM), that the adhesion force measured on PS with a silicon tip in water was higher compared with that measured on PSox. This feature allowed imaging of the oxidation patterns using the adhesion mapping mode. The origin of the pulloff force contrast, which could not be explained by combining Johnson–Kendall–Roberts theory and thermodynamic considerations, was attributed to repulsion between the tip and hydrated polymer chains present on the oxidized surface. Imaging was also performed in the lateral force mode, a higher friction being recorded On PS than On PSOX.
atomic force microscopy; plasma treatment; polystyrene; Wilhelmy plate method; Johnson–Kendall–Roberts model; surface forces
Atomic force microscopy (AFM) in contact mode and tapping mode is employed for high resolution studies of soft organic molecules (fetal bovine serum proteins) on hard inorganic diamond substrates in solution and air. Various effects in morphology and phase measurements related to the cantilever spring constant, amplitude of tip oscillations, surface approach, tip shape and condition are demonstrated and discussed based on the proposed schematic models. We show that both diamond and proteins can be mechanically modified by Si AFM cantilever. We propose how to choose suitable cantilever type, optimize scanning parameters, recognize and minimize various artifacts, and obtain reliable AFM data both in solution and in air to reveal microscopic characteristics of protein-diamond interfaces. We also suggest that monocrystalline diamond is well defined substrate that can be applicable for fundamental studies of molecules on surfaces in general.
The instantaneous displacement, velocity and acceleration of a cantilever tip impacting onto a graphite surface are reconstructed. The total dissipated energy and the dissipated energy per cycle of each excited flexural mode during the tip interaction is retrieved. The tip dynamics evolution is studied by wavelet analysis techniques that have general relevance for multi-mode atomic force microscopy, in a regime where few cantilever oscillation cycles characterize the tip–sample interaction.
band excitation; multifrequency atomic force microscopy (AFM); phase reference; wavelet transforms
We present quantitative, high spatially resolved magnetic force microscopy imaging of samples based on 11 nm diameter superparamagnetic iron oxide nanoparticles in air at room temperature. By a proper combination of the cantilever resonance frequency shift, oscillation amplitude and phase lag we obtain the tip-sample interaction maps in terms of force gradient and energy dissipation. These physical quantities are evaluated in the frame of a tip-particle magnetic interaction model also including the tip oscillation amplitude. Magnetic nanoparticles are characterized both in bare form, after deposition on a flat substrate, and as magnetically assembled fillers in a polymer matrix, in the form of nanowires. The latter approach makes it possible to reveal the magnetic texture in a composite sample independently of the surface topography.
We introduce drive-amplitude-modulation atomic force microscopy as a dynamic mode with outstanding performance in all environments from vacuum to liquids. As with frequency modulation, the new mode follows a feedback scheme with two nested loops: The first keeps the cantilever oscillation amplitude constant by regulating the driving force, and the second uses the driving force as the feedback variable for topography. Additionally, a phase-locked loop can be used as a parallel feedback allowing separation of the conservative and nonconservative interactions. We describe the basis of this mode and present some examples of its performance in three different environments. Drive-amplutide modulation is a very stable, intuitive and easy to use mode that is free of the feedback instability associated with the noncontact-to-contact transition that occurs in the frequency-modulation mode.
atomic force microscopy; control systems; dissipation; frequency modulation; noncontact
The recent achievement of atomic resolution with dynamic atomic force microscopy (dAFM) [Fukuma et al., Appl. Phys. Lett.
2005, 87, 034101], where quality factors of the oscillating probe are inherently low, challenges some accepted beliefs concerning sensitivity and resolution in dAFM imaging modes. Through analysis and experiment we study the performance metrics for high-resolution imaging with dAFM in liquid media with amplitude modulation (AM), frequency modulation (FM) and drive-amplitude modulation (DAM) imaging modes. We find that while the quality factors of dAFM probes may deviate by several orders of magnitude between vacuum and liquid media, their sensitivity to tip–sample forces can be remarkable similar. Furthermore, the reduction in noncontact forces and quality factors in liquids diminishes the role of feedback control in achieving high-resolution images. The theoretical findings are supported by atomic-resolution images of mica in water acquired with AM, FM and DAM under similar operating conditions.
atomic force microscopy; dAFM; high-resolution; liquids
The coupling of distinct systems underlies nearly all physical phenomena. A basic instance is that of interacting harmonic oscillators, giving rise to, for example, the phonon eigenmodes in a lattice. Of particular importance are the interactions in hybrid quantum systems, which can combine the benefits of each part in quantum technologies. Here we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering of entangled motional states.
Optomechanical systems allow for the exploration of macroscopic behaviour at or near the quantum limit. Massel et al. use micromechanical resonators to study the hybridisation of one photonic and two phononic modes with phonon numbers down to 1.8, showing a coupling between all three degrees of freedom.
Atomic force microscopy (AFM) is widely used in the biological sciences. Despite 25 years of technical developments, two popular modes of bioAFM, imaging and single molecule force spectroscopy, remain hindered by relatively poor force precision and stability. Recently, we achieved both sub-pN force precision and stability under biologically useful conditions (in liquid at room temperature). Importantly, this sub-pN level of performance is routinely accessible using a commercial cantilever on a commercial instrument. The two critical results are that (i) force precision and stability were limited by the gold coating on the cantilevers, and (ii) smaller yet stiffer cantilevers did not lead to better force precision on time scales longer than 25 ms. These new findings complement our previous work that addressed tip-sample stability. In this review, we detail the methods needed to achieve this sub-pN force stability and demonstrate improvements in force spectroscopy and imaging when using uncoated cantilevers. With this improved cantilever performance, the widespread use of nonspecific biomolecular attachments becomes a limiting factor in high-precision studies. Thus, we conclude by briefly reviewing site-specific covalent-immobilization protocols for linking a biomolecule to the substrate and to the AFM tip.
Atomic force microscopy; scanning probe microscopy; single molecule force spectroscopy; drift; overstretching DNA; cantilever; imaging
Block copolymer-based vesicles have recently garnered a great deal of interest as nanoplatforms for drug delivery and molecular imaging applications due to their unique structural properties. These nanovesicles have been shown to direct their cargo to disease sites either through enhanced permeability and retention or even more efficiently via active targeting. Here we show that the efficacy of nanovesicle targeting can be significantly improved when prepared from polymer-lipid blends compared with block copolymer alone. Polymer-lipid hybrid nanovesicles were produced from the aqueous co-assembly of the diblock copolymer, poly(ethylene oxide)-block-polybutadiene (PEO-PBD), and the phospholipid, hydrogenated soy phosphatidylcholine (HSPC). The PEG-based vesicles, 117 nm in diameter, were functionalized with either folic acid or anti-HER2/neu affibodies as targeting ligands to confer specificity for cancer cells. Our results revealed that nanovesicles prepared from polymer-lipid blends led to significant improvement in cell binding compared to nanovesicles prepared from block copolymer alone in both in vitro cell studies and murine tumor models. Therefore, it is envisioned that nanovesicles composed of polymer-lipid blends may constitute a preferred embodiment for targeted drug delivery and molecular imaging applications.
Diblock copolymer; phospholipids; PEG; tumor targeting; polymersome
Measurements of the frequency shift versus distance in noncontact atomic force microscopy (NC-AFM) allow measurements of the force gradient between the oscillating tip and a surface (force-spectroscopy measurements). When nonconservative forces act between the tip apex and the surface the oscillation amplitude is damped. The dissipation is caused by bistabilities in the potential energy surface of the tip–sample system, and the process can be understood as a hysteresis of forces between approach and retraction of the tip. In this paper, we present the direct measurement of the whole hysteresis loop in force-spectroscopy curves at 77 K on the PTCDA/Ag/Si(111) √3 × √3 surface by means of a tuning-fork-based NC-AFM with an oscillation amplitude smaller than the distance range of the hysteresis loop. The hysteresis effect is caused by the making and breaking of a bond between PTCDA molecules on the surface and a PTCDA molecule at the tip. The corresponding energy loss was determined to be 0.57 eV by evaluation of the force–distance curves upon approach and retraction. Furthermore, a second dissipation process was identified through the damping of the oscillation while the molecule on the tip is in contact with the surface. This dissipation process occurs mainly during the retraction of the tip. It reaches a maximum value of about 0.22 eV/cycle.
atomic force microscopy; energy dissipation; force spectroscopy; hysteresis loop; PTCDA/Ag/Si(111) √3 × √3
Atomic force microscopy (AFM) allows for the visualizing of individual proteins, DNA
molecules, protein-protein complexes, and DNA-protein complexes. On the end of the
microscope's cantilever is a nano-scale probe, which traverses image areas ranging from
nanometers to micrometers, measuring the elevation of macromolecules resting on the
substrate surface at any given point. Electrostatic forces cause proteins, lipids, and
nucleic acids to loosely attach to the substrate in random orientations and permit
imaging. The generated data resemble a topographical map, where the macromolecules resolve
as three-dimensional particles of discrete sizes (Figure 1) 1,2.
Tapping mode AFM involves the repeated oscillation of the cantilever, which permits
imaging of relatively soft biomaterials such as DNA and proteins. One of the notable
benefits of AFM over other nanoscale microscopy techniques is its relative adaptability to
visualize individual proteins and macromolecular complexes in aqueous buffers, including
near-physiologic buffered conditions, in real-time, and without staining or coating the
sample to be imaged.
The method presented here describes the imaging of DNA and an immunoadsorbed
transcription factor (i.e. the glucocorticoid receptor, GR) in buffered solution
(Figure 2). Immunoadsorbed proteins and protein complexes can be separated
from the immunoadsorbing antibody-bead pellet by competition with the antibody epitope and
then imaged (Figure 2A). This allows for biochemical manipulation of the
biomolecules of interest prior to imaging. Once purified, DNA and proteins can be mixed
and the resultant interacting complex can be imaged as well. Binding of DNA to mica
requires a divalent cation 3,such as Ni2+ or Mg2+, which
can be added to sample buffers yet maintain protein activity. Using a similar approach,
AFM has been utilized to visualize individual enzymes, including RNA polymerase
4 and a repair enzyme 5, bound to individual DNA strands. These
experiments provide significant insight into the protein-protein and DNA-protein
biophysical interactions taking place at the molecular level. Imaging individual
macromolecular particles with AFM can be useful for determining particle homogeneity and
for identifying the physical arrangement of constituent components of the imaged
particles. While the present method was developed for visualization of GR-chaperone
protein complexes 1,2 and DNA strands to which the GR can bind, it can be
applied broadly to imaging DNA and protein samples from a variety of sources.
In frequency-modulation atomic force microscopy the direct observable is the frequency shift of an oscillating cantilever in a force field. This frequency shift is not a direct measure of the actual force, and thus, to obtain the force, deconvolution methods are necessary. Two prominent methods proposed by Sader and Jarvis (Sader–Jarvis method) and Giessibl (matrix method) are investigated with respect to the deconvolution quality. Both methods show a nontrivial dependence of the deconvolution quality on the oscillation amplitude. The matrix method exhibits spikelike features originating from a numerical artifact. By interpolation of the data, the spikelike features can be circumvented. The Sader–Jarvis method has a continuous amplitude dependence showing two minima and one maximum, which is an inherent property of the deconvolution algorithm. The optimal deconvolution depends on the ratio of the amplitude and the characteristic decay length of the force for the Sader–Jarvis method. However, the matrix method generally provides the higher deconvolution quality.
frequency-modulation atomic force microscopy; force deconvolution; numerical implementation
Microcantilevers were first introduced as imaging probes in Atomic Force Microscopy (AFM) due to their extremely high sensitivity in measuring surface forces. The versatility of these probes, however, allows the sensing and measurement of a host of mechanical properties of various materials. Sensor parameters such as resonance frequency, quality factor, amplitude of vibration and bending due to a differential stress can all be simultaneously determined for a cantilever. When measuring the mechanical properties of materials, identifying and discerning the most influential parameters responsible for the observed changes in the cantilever response are important. We will, therefore, discuss the effects of various force fields such as those induced by mass loading, residual stress, internal friction of the material, and other changes in the mechanical properties of the microcantilevers. Methods to measure variations in temperature, pressure, or molecular adsorption of water molecules are also discussed. Often these effects occur simultaneously, increasing the number of parameters that need to be concurrently measured to ensure the reliability of the sensors. We therefore systematically investigate the geometric and environmental effects on cantilever measurements including the chemical nature of the underlying interactions. To address the geometric effects we have considered cantilevers with a rectangular or circular cross section. The chemical nature is addressed by using cantilevers fabricated with metals and/or dielectrics. Selective chemical etching, swelling or changes in Young's modulus of the surface were investigated by means of polymeric and inorganic coatings. Finally to address the effect of the environment in which the cantilever operates, the Knudsen number was determined to characterize the molecule-cantilever collisions. Also bimaterial cantilevers with high thermal sensitivity were used to discern the effect of temperature variations. When appropriate, we use continuum mechanics, which is justified according to the ratio between the cantilever thickness and the grain size of the materials. We will also address other potential applications such as the ageing process of nuclear materials, building materials, and optical fibers, which can be investigated by monitoring their mechanical changes with time. In summary, by virtue of the dynamic response of a miniaturized cantilever shaped material, we present useful measurements of the associated elastic properties.
Microcantilever; mechanics; ageing; environment; stress; gas; materials; sensor; pressure; temperature
We critically discuss the extraction of intrinsic cantilever properties, namely eigenfrequency f
n, quality factor Q
n and specifically the stiffness k
n of the nth cantilever oscillation mode from thermal noise by an analysis of the power spectral density of displacement fluctuations of the cantilever in contact with a thermal bath. The practical applicability of this approach is demonstrated for several cantilevers with eigenfrequencies ranging from 50 kHz to 2 MHz. As such an analysis requires a sophisticated spectral analysis, we introduce a new method to determine k
n from a spectral analysis of the demodulated oscillation signal of the excited cantilever that can be performed in the frequency range of 10 Hz to 1 kHz regardless of the eigenfrequency of the cantilever. We demonstrate that the latter method is in particular useful for noncontact atomic force microscopy (NC-AFM) where the required simple instrumentation for spectral analysis is available in most experimental systems.
AFM; cantilever; noncontact atomic force microscopy (NC-AFM); Q-factor; thermal excitation; resonance; spectral analysis; stiffness
Atomic force microscope (AFM) probe with a long and rigid needle tip was fabricated and studied for high Q factor dynamic (tapping mode) AFM imaging of samples submersed in liquid. The extended needle tip over a regular commercially-available tapping mode AFM cantilever was sufficiently long to keep the AFM cantilever from submersed in liquid, which significantly minimized the hydrodynamic damping involved in dynamic AFM imaging of samples in liquid. Dynamic AFM imaging of samples in liquid at an intrinsic Q factor of over 100 and an operation frequency of over 200 kHz was demonstrated. The method has the potential to be extended to acquire viscoelastic materials properties and provide truly gentle imaging of soft biological samples in physiological environments.
In contrast to incompressible liquid solutions, compressible near-critical solutions of block copolymers allow for controlling rapid structure transformations with pressure alone. For example, when dissolved in near-critical propane, polystyrene-block-polybutadiene can form a random molecular solution at high pressures, a micellar solution at moderate pressures, and a solvent-free precipitate at low pressures. In contrast to the unstructured virgin copolymer, such a propane-treated precipitate rapidly self assembles toward structures characteristic of equilibrated block copolymers, such as lamellae, spheres or cylinders, which depend on the block ratio rather than on the decompression rate or temperature, at least within the rate and temperature ranges investigated in this work. At lower temperatures, however, say below 40 °C, glass transition of the styrene-butadiene diblocks can inhibit independent structure formation while crystallization of their hydrogenated-butadiene analogs can preserve the micellar-solution structure.
TEM; block copolymer; supercritical solution; self-assembly; crystallization
Surface modification of medical polymers can improve biocompatibility. Pure polystyrene is hydrophobic and cannot provide a suitable environment for cell cultures. The conventional method for surface modification of polystyrene is treatment with plasma. In this study, conventional polystyrene was exposed to microwave plasma treatment with oxygen and argon gases for 30, 60, and 180 seconds.
Methods and results:
Attenuated total reflection Fourier transform infrared spectra investigations of irradiated samples indicated clearly the presence of functional groups. Atomic force microscopic images of samples irradiated with inert and active gases indicated nanometric surface topography. Samples irradiated with oxygen plasma showed more roughness (31 nm) compared with those irradiated with inert plasma (16 nm) at 180 seconds. Surface roughness increased with increasing duration of exposure, which could be due to reduction of the contact angle of samples irradiated with oxygen plasma. Contact angle analysis showed reduction in samples irradiated with inert plasma. Samples irradiated with oxygen plasma showed a lower contact angle compared with those irradiated by argon plasma.
Cellular investigations with unrestricted somatic stem cells showed better adhesion, cell growth, and proliferation for samples radiated by oxygen plasma with increasing duration of exposure than those of normal samples.
surface topography; polystyrene; plasma treatment; argon; oxygen