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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
About 40 % of current atomic force microscopy (AFM) research is performed in liquids, making liquid-based AFM a rapidly growing and important tool for the study of biological materials. This book focuses on the underlying principles and experimental aspects of AFM under liquid, with an easy-to-follow organization intended for new AFM scientists. The book also serves as an up-to-date review of new AFM techniques developed especially for biological samples. Aimed at physicists, materials scientists, biologists, analytical chemists, and medicinal chemists. An ideal reference book for libraries. From the contents: Part I: General Atomic Force Microscopy * AFM: Basic Concepts * Carbon Nanotube Tips in Atomic Force Microscopy with * Applications to Imaging in Liquid * Force Spectroscopy * Atomic Force Microscopy in Liquid * Fundamentals of AFM Cantilever Dynamics in Liquid * Environments * Single-Molecule Force Spectroscopy * High-Speed AFM for Observing Dynamic Processes in Liquid * Integration of AFM with Optical Microscopy Techniques Part II: Biological Applications * DNA and Protein-DNA Complexes * Single-Molecule Force Microscopy of Cellular Sensors * AFM-Based Single-Cell Force Spectroscopy * Nano-Surgical Manipulation of Living Cells with the AFM
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Seitenzahl: 697
Veröffentlichungsjahr: 2012
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The Editors
Prof. Arturo M. Baró
Instituto de Ciencia de Materials
de Madrid (CSIC)
Sor Inés de la Cruz
Madrid 28049
Spain
Prof. Ronald G. Reifenberger
Purdue University
Department of Physics
525, Northwestern Avenue
West Lafayette, IN 47907-2036
USA
All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
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© 2012 Wiley-VCH Verlag & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
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Contents
Preface
List of Contributors
Part I General Atomic Force Microscopy
1 AFM: Basic Concepts
Fernando Moreno-Herrero and Julio Gomez-Herrero
1.1 Atomic Force Microscope: Principles
1.2 Piezoelectric Scanners
1.3 Tips and Cantilevers
1.4 Force Detection Methods for Imaging in Liquids
1.5 AFM Operation Modes: Contact, Jumping/Pulsed, Dynamic
1.6 The Feedback Loop
1.7 Image Representation
1.8 Artifacts and Resolution Limits
Acknowledgments
References
2 Carbon Nanotube Tips in Atomic Force Microscopy with Applications to Imaging in Liquid
Edward D. de Asis, Jr., Joseph Leung, and Cattien V. Nguyen
2.1 Introduction
2.2 Fabrication of CNT AFM Probes
2.3 Chemical Functionalization
2.4 Mechanical Properties of CNTs in Relation to AFM Applications
2.5 Dynamics of CNT Tips in Liquid
2.6 Performance and Resolution of CNT Tips in Liquid
References
3 Force Spectroscopy
Arturo M. Baró
3.1 Introduction
3.2 Measurement of Force Curves
3.3 Measuring Surface Forces by the Surface Force Apparatus
3.4 Forces between Macroscopic Bodies
3.5 Theory of DLVO Forces between Two Surfaces
3.6 Van der Waals Forces – the Hamaker Constant
3.7 Electrostatic Force between Surfaces in a Liquid
3.8 Spatially Resolved Force Spectroscopy
3.9 Force Spectroscopy Imaging of Single DNA Molecules
3.10 Solvation Forces
3.11 Hydrophobic Forces
3.12 Steric Forces
3.13 Conclusive Remarks
Acknowledgments
References
4 Dynamic-Mode AFM in Liquid
Takeshi Fukuma and Michael J. Higgins
4.1 Introduction
4.2 Operation Principles
4.3 Instrumentation
4.4 Quantitative Force Measurements
4.5 High-Resolution Imaging
4.6 Summary and Future Prospects
References
5 Fundamentals of AFM Cantilever Dynamics in Liquid Environments
Daniel Kiracofe, John Melcher, and Arvind Raman
5.1 Introduction
5.2 Review of Fundamentals of Cantilever Oscillation
5.3 Hydrodynamics of Cantilevers in Liquids
5.4 Methods of Dynamic Excitation
5.5 Dynamics of Cantilevers Interacting with Samples in Liquids
5.6 Outlook
References
6 Single-Molecule Force Spectroscopy
Albert Galera-Prat, Rodolfo Hermans, Rubén Hervás, Àngel Gómez-Sicilia, and Mariano Carrión-Vázquez
6.1 Introduction
6.2 AFM-SMFS Principles
6.3 Dynamics of Adhesion Bonds
6.4 Specific versus Other Interactions
6.5 Steered Molecular Dynamics Simulations
6.6 Biological Findings Using AFM–SMFS
6.7 Concluding Remarks
Acknowledgments
Disclaimer
References
7 High-Speed AFM for Observing Dynamic Processes in Liquid
Toshio Ando, Takayuki Uchihashi, Noriyuki Kodera, Mikihiro Shibata, Daisuke Yamamoto, and Hayato Yamashita
7.1 Introduction
7.2 Theoretical Derivation of Imaging Rate and Feedback Bandwidth
7.3 Techniques Realizing High-Speed Bio-AFM
7.4 Substrate Surfaces
7.5 Imaging of Dynamic Molecular Processes
7.6 Future Prospects of High-Speed AFM
7.7 Conclusion
References
8 Integration of AFM with Optical Microscopy Techniques
Zhe Sun, Andreea Trache, Kenith Meissner, and Gerald A. Meininger
8.1 Introduction
8.2 Combining AFM with IRM and TIRF microscopy
8.3 Combining AFM and FRET
8.4 FRET-AFM
8.5 Sample Preparation and Experiment Setup
References
Part II Biological Applications
9 AFM Imaging in Liquid of DNA and Protein–DNA Complexes
Yuri L. Lyubchenko
9.1 Overview: the Study of DNA at Nanoscale Resolution
9.2 Sample Preparation for AFM Imaging of DNA and Protein–DNA Complexes
9.3 AFM of DNA in Aqueous Solutions
9.4 AFM Imaging of Alternative DNA Conformations
9.5 Dynamics of Protein–DNA Interactions
9.6 DNA Condensation
9.7 Conclusions
Acknowledgments
References
10 Stability of Lipid Bilayers as Model Membranes: Atomic Force Microscopy and Spectroscopy Approach
Lorena Redondo-Morata, Marina Inés Giannotti, and Fausto Sanz
10.1 Biological Membranes
10.2 Mechanical Characterization of Lipid Membranes
10.3 Future Perspectives
References
11 Single-Molecule Atomic Force Microscopy of Cellular Sensors
Jürgen J. Heinisch and Yves F. Dufrêne
11.1 Introduction
11.2 Methods
11.3 Probing Single Yeast Sensors in Live Cells
11.4 Conclusions
Acknowledgments
References
12 AFM-Based Single-Cell Force Spectroscopy
Clemens M. Franz and Anna Taubenberger
12.1 Introduction
12.2 Cantilever Choice
12.3 Cantilever Functionalization
12.4 Cantilever Calibration
12.5 Cell Attachment to the AFM Cantilever
12.6 Recording a Force–Distance Curve
12.7 Processing F–D Curves
12.8 Quantifying Overall Cell Adhesion by SCFS
12.9 SFCS with Single-Molecule Resolution
12.10 Dynamic Force Spectroscopy
12.11 Measuring Cell–Cell Adhesion
12.12 Conclusions and Outlook
References
13 Nanosurgical Manipulation of Living Cells with the AFM
Atsushi Ikai, Rehana Afrin, Takahiro Watanabe-Nakayama, and Shin-ichi Machida
13.1 Introduction: Mechanical Manipulation of Living Cells
13.2 Basic Mechanical Properties of Proteins and Cells
13.3 Hole Formation on the Cell Membrane
13.4 Extraction of mRNA from Living Cells
13.5 DNA Delivery and Gene Expression
13.6 Mechanical Manipulation of Intracellular Stress Fibers
13.7 Cellular Adaptation to Local Stresses
13.8 Application of Carbon Nanotube Needles
13.9 Use of Fabricated AFM Probes with a Hooking Function
13.10 Membrane Protein Extraction
13.11 Future Prospects
Acknowledgments
References
Index
Preface
The atomic force microscope (AFM) is a member of the broad family of scanning probe microscopes and arguably has become the most widely used scanning probe instrument in the world. The high image resolution coupled with a new class of spectroscopic tools has enabled AFMs to perform real-time dynamic studies as well as controlled nanomanipulation, resulting in significant breakthroughs in many different realms of science and engineering.
The book Atomic Force Microscopy in Liquid: Biological Applications broadly focuses on phenomena relevant to AFM studies at a solid–liquid interface, with an emphasis on biological applications ranging from small biomolecules to living cells. As far as we know, there are no books closely related to this one. The ability of an AFM to study samples in a liquid environment provides a significant advantage when compared to other microscopies such as SEM and TEM. This unique capability allows measurements of native biological samples in aqueous environments under physiologically relevant conditions. The weakness of van der Waals interactions and the absence of capillary forces in liquid drastically reduce the tip–sample interaction, resulting in little damage to soft biological samples. The highly local character of AFM that directly results from probe proximity to the sample coupled with tip sharpness not only allows high-resolution images but also permits laterally resolved spectroscopic measurements capable of reaching the level of a single molecule, as, for example, in single molecule force spectroscopy applications.
This book provides a thorough description of AFM operation in liquid environments and will serve as a useful reference for all AFM groups. It is organized into two sections in an effort to be especially useful for new researchers who desire to start bio-related studies. The first part of the book is focused on the study of features unique to AFM including instrumentation, force spectroscopic analysis, general imaging and spectroscopy considerations, single molecule force spectroscopy, operational modes, electrostatic forces in liquids containing ions, high-speed imaging, nanomanipulation, and lithography. Historically, there have been a number of AFM studies on biological systems in liquid by contact-mode AFM. Recently, dynamic force spectroscopy (DFS) experiments have appeared that utilize noncontact imaging, further reducing sample damage. Therefore, DFS is discussed in two chapters, one connected with experimental work and a second that deals with the theory of dynamic AFM. We also include a chapter on the combination of AFM with more traditional optical techniques such as fluorescence. A growing trend will be the simultaneous utilization of one or more auxiliary techniques with AFM to exploit the many advantages when complementary techniques are combined.
The second part of the book deals with applications of AFM to the study of biological materials ranging from the smallest biomolecules (phospholipids, proteins, DNA, RNA, and protein complexes) to subcellular structures (e.g., membranes), and finally culminating with studies of living microbial cells. Single cell force spectroscopy and the manipulation of biological material with an AFM are also included. The goal is to feature recent advances that emphasize in vivo experiments.
This book is timely and up-to-date. It is aimed at a mixed audience that includes starting graduate students, young researchers, and established scientists. Physicists need to learn how to handle/prepare biological samples; biologists need to understand the important issues related to imaging of complex samples in liquid. We hope the book is useful, especially for those who enjoy breaking ground in a new and interdisciplinary field.
We would like to thank all the distinguished scientists and their coauthors for their timely and well-referenced contributions. Grateful acknowledgments are offered to the Wiley-VCH editorial staff, in particular Lesley Belfit, Project Editor, and Publisher Dr. Gudrun Walter.
UAM, Madrid
Purdue University
Arturo M. Baró
Ronald G. Reifenberger
List of Contributors
Part I
General Atomic Force Microscopy
Chapter 1
AFM: Basic Concepts
Fernando Moreno-Herrero and Julio Gomez-Herrero
1.1 Atomic Force Microscope: Principles
A conceptually new family of microscopes emerged after the invention of the scanning tunneling microscope (STM) by Binnig and Rohrer in 1982 [1]. This family of instruments called scanning probe microscopes (SPMs) is based on the strong distance-dependent interaction between a sharp probe or tip and a sample. The atomic force microscope therefore uses the force existing between the probe and the sample to build an image of an object [2, 3]. AFMs can operate in almost any environment including aqueous solution, and that opened myriad uses in biology [4, 5]. When thinking about how an AFM works, all notions of conventional microscope design need to be disregarded, since there are no lenses through which the operator looks at the sample. In AFM, images are obtained by sensing with the probe rather than by seeing.
The central part of an AFM is therefore the tip that literally feels the sample. A nanometer-sharp AFM tip made by microfabricating technology is grown at the free end of a flexible cantilever that is used as the transductor of the interaction between the tip and sample. The reflection of a laser beam focused at the back side of the cantilever is frequently used by most AFMs to amplify and measure the movement of the cantilever, although other detection methods may also be used (Section 1.4). The reflected beam is directed to a photodiode that provides a voltage depending on the position of the laser beam. For imaging, the tip is scanned over the sample, or as in some designs, it is the sample that moves with respect to the fixed tip, which is only allowed to move in the vertical direction. In both cases, the fine movements of the tip and sample are provided by piezoelectric materials that can move with subnanometer precision. At each position, the cantilever deflection is measured, from which a topography map can be constructed. This scanning technique in which the tip is brought into mechanical contact with the sample surface is known as contact mode, and it was first described by Binnig and coworkers [2]. Both the tip and scanner are the key features in any AFM setup.
Figure 1.1 Components of a standard atomic force microscope. 1. The AFM head and the piezoelectric stage. The cantilever and its detection system as well as the sample movement are the main parts of this component. From the photodiode, the signals related to the normal and lateral forces (FN and FL) as well as the total intensity of light (∑) are obtained and transferred to the high voltage electronics. 2. The high voltage electronics. This component amplifies voltages from the digital signal processor to perform the movement of the piezotube (XYZ voltages). It also collects signals from the photodiode (FN, FL, and ∑) and transfers them to the DSP. 3. The computer, DSP, and software that controls the AFM setup.
One of the most common models of AFM is schematically depicted in Figure 1.1. In this model, the sample is scanned over the tip, but the opposite is also possible. The latter are the so-called stand-alone AFMs that are commonly used combined with an inverted optical microscope to image biological samples in liquid. In either case, a standard AFM setup consists of three main components. (i) the AFM head and base stage: The AFM head contains the tip holder, the laser, and the photodiode. It also includes positioning mechanisms for focusing the laser beam on the back side of the cantilever and photodiode and small electronics for processing the signals coming from the photodiode. From this, the vertical (FN) and lateral (FL) deflections of the laser beam and its total intensity (Σ) are obtained. The AFM head is placed over a base stage that holds the piezoelectric scanner that moves the sample, and also a coarse, micrometer-ranged approaching mechanism, usually based on step motors.1) (ii) Thehigh voltage (HV) electronics: It amplifies the signals coming from the digital signal processor (DSP) (XYZ low voltage) to drive the piezoelectric scanner with voltages of about 100 V (XYZ HV). The electronics also transfers the analog voltage signals from the photodiode (FN, FL, ∑) to the DSP. The HV electronics must be able to amplify small signals from the computer (of some volts) to hundreds of volts needed to move the piezoelectric tube over micrometer distances. It is therefore essential that this amplification does not introduce electrical noises that may affect the resolution of the AFM. (iii) The DSP, the computer, and the software: The DSP performs all the signal processing and calculations involved in the real-time operation of the AFM. The DSP is mainly located in a board plugged in the computer. It contains the chips to perform the translation from digital to analog signals (digital to analog converters (DACs)), which are further managed by the HV electronics. Analog signals from the HV amplifier are converted to digital signals also at the DSP board using analog to digital converters (ADCs). Finally, all computer-based systems need software to run the setup. Nearly all AFMs in the market come with purpose-made acquisition software. Raw images can later be processed with any of the many imaging-processing freeware available in the Internet.
Operating the AFM in liquid conditions requires modifications of some parts to prevent wetting of electrical components such as piezoelectric ceramics. For instance, the sample holder must be large enough to accommodate the sample and the buffer in which it is immersed. Some authors simply use a small droplet of some tens of microliters, which covers the sample; others use a small container filled with several milliliters of buffer. The first approach has the advantage of a smaller mass (droplet) added to the piezo, but experiments suffer from evaporation, which results in a change in the concentration of solvents. On the other hand, using the container approach, concentrations are kept roughly constant, but a considerable mass must be moved by the piezo scanner, which reduces its resonance frequency and therefore the range of imaging speeds. The tip holder, also known as liquid cell (Section 1.4.2.1), must be designed to prevent contact between the liquid and the small piezo that drives movement of the cantilever. Finally, in some AFMs, the piezo tube is protected and covered to prevent wetting in case of liquid spill (Section 1.2.1).
1.2 Piezoelectric Scanners
Piezoelectric ceramic transducers are used to accurately position the tip and sample in AFMs. The direct piezoelectric effect consists of the generation of a potential difference across the opposite faces of certain nonconductive crystals as a result of the application of stress. The reverse piezoelectric effect is also possible because of a change in dimensions of the crystal as a consequence of the application of a potential difference between two faces of the piezoelectric material. This method is used to position the tip and sample with respect to each other with subnanometer precision since piezoelectric ceramic transducers are highly sensitive, stable, and reliable. Regardless, if the tip is moved over the sample or vice versa, the scan in AFM is performed using piezoelectric transducers.
Figure 1.2 Piezoelectric scanners. (a) Piezotube architecture based on four sectors. Voltages are applied between opposite sides, and as a consequence, movement of the piezo is generated. (b) Sequence of voltages applied to X (fast scan) and Y (slow scan) to generate an image scan. Each step in y-axis is associated with the change of an imaging line. (c,d)Two typical problems of piezotube scanners. (c) The plane where the sample is situated describes an arc rather than a straight line. (d) Clear effect of piezo hysteresis when imaging DNA molecules.
Many AFMs use piezoelectric tube scanners such as the one shown in Figure 1.2a. They consist of a thin-walled hard piezoelectric ceramic, which is polarized radially [6]. The external face of the tube is divided into four longitudinal segments of equal size and electrodes are welded to the internal and external faces of the tube. To achieve extension or contraction, a bias voltage is applied between the inner and all the outer electrodes. The scan movement is performed by applying a bias voltage to one of the segments of the outer wall. To amplify this bending effect by a factor of two, a voltage with opposite sign is applied to the opposite segment. With a correct synchronization of applied voltages ( ± x and ± y), a sequential scan can be generated (Figure 1.2b). Typically, tube scanners of 10 × 10 μm range have sensitivities of ∼40 nm/V. This means that voltages up to ±125 V must be generated with submilivolts precision to achieve a basal noise of ∼0.01 nm. This operation is performed by the HV electronics.
Tube scanners have some drawbacks. For instance, the plane in which the sample is located describes an arc rather than a straight line. This effect is more pronounced when large areas are scanned and the height of the objects to be imaged is small compared to the scan area. For instance, Figure 1.2c shows a profile of a flat surface with adsorbed DNA molecules. The effect of the arc trajectory described by the piezo is clearly visible, and the detection of small molecules such as DNA (height < 1 nm) is challenging. This effect can easily be corrected by subtracting a polynomial function to each scan line or to the overall surface. Piezo tubes have relatively low resonance frequencies, of the order of kilohertz, which limits the scan speed. Recently, some manufacturers have employed small stacks of piezoelectric ceramics to increase the resonance frequency of these devices and therefore the imaging speed. However, stacked piezos have a quite limited scan range.
A different approach used to move the sample is based on stick-slip motion. These positioners rely on the controllable use of the inertia of a sliding block. In brief, a sliding block slips along a guided rod, which is otherwise clamped in frictional engagement. A net step is obtained by first accelerating very rapidly the guiding rod over a short period (typically microseconds) so that the inertia of the sliding block overcomes the friction. The sliding block disengages from the accelerated rod and remains nearly nondisplaced. Then, the guiding rod moves back to its initial position slowly enough so that the sliding block sticks to it and thus makes a net step. Periodic repetition of this sequence leads to a step-by-step motion of the sliding block in one direction. The movement of the guiding rod is performed by a piezoelectric ceramic, which can pull or push as required. Stick-slip positioners have long travel ranges of several millimeters, but their performance is dependent on the mass to be moved, which can be significant in liquid imaging. These devices also have the limitation of a relatively large step (few nanometers) and a low resonance frequency (much lower than that of stacked piezos). Hence the main use of these devices is as nanopositioners rather than as fast scanners.
Piezoelectric scanners are inherently nonlinear, and this nonlinearity becomes quite significant at large scans. Typical piezos suffer from hysteresis in the forward and backward traces. This effect can be clearly seen in the forward and backward profiles shown in Figure 1.2d. Piezo scanners are also subjected to creep after changing the polarity (direction) of the scan or just after setting the voltage to zero. This is due to some sort of relaxation, which occurs under constant stress. It has an effect on the images distorting the dimensions of the objects to be imaged. In general, this problem can be solved by repeating the scan, allowing the piezo to relax. To minimize unwanted motions in the piezoactuator, some AFMs incorporate a combination of piezoactuators and metal springs. These devices have flexure-guided stages, acting as springs and restricted to move only in one direction. A piezoactuator pulls against the spring, and therefore a forward and backward movement of the flexure guide can be achieved by changing the voltage in the piezoactuator. This combination effectively decouples the unwanted motions in the piezoactuator and produces a pure linear translation while keeping high resonance frequencies at relatively high loads (∼2 kHz for a 100 g load). Finally, many AFMs have capacitive sensors incorporated in their piezos that allow for measuring the position independent of the applied voltage. With this feature, a closed-loop circuit can be designed, being able to cancel any hysteresis, creep, or nonlinearity by applying additional correction voltages.
1.2.1 Piezoelectric Scanners for Imaging in Liquids
In many AFMs, the piezoelectric used to image in air is the same as that used to image in liquids, but some precautions must be taken. The main concern is related to the electrical isolation of the piezo to avoid any shortcut due to wetting. HVs (hundreds of volts) are applied to the piezo, and if any water gets into it, the expensive piezo tube will almost certainly be destroyed. Therefore, some caution must be taken when imaging in liquids to avoid any spill of water into the piezo. In most AFMs, some silicone or rubber is added to prevent any liquid from getting into the piezo.
For imaging in liquids, it is often recommended to move the tip relative to the sample instead of keeping the tip fixed and move the sample. In the latter scenario, volumes of milliliters should be moved at kilohertz frequencies, affecting the mechanical stability of the piezo. This is equivalent to considering an effective mass in Eq. (1.3). That will lower the piezo resonant frequency and will slow down the imaging speed of the AFM. Instead, when moving the tip relative to the sample in liquids, the added effective mass is small because only the tip and parts of the tip holder are immersed in the buffer container. When imaging in environments with large viscosity such as liquids, it is important to keep the mass of moving objects as low as possible. This is also important for oscillating the tip; a need in dynamic modes. Some users oscillate the complete tip holder, exciting many mechanical vibrations in the buffer container, which hide the genuine mechanical resonance of the cantilever (Section 1.5.3.1).
1.3 Tips and Cantilevers
In contact mode, to be able to feel the surface with atom resolution, the stiffness of an AFM cantilever should be much smaller than the spring constant that maintains the atoms confined together on the surface. This bonding force constant in a crystalline lattice is of the order of 1 N m−1 [7], meaning that to use the AFM in contact mode (Section 1.5.1), the spring constant of the cantilevers (k) should be much smaller than 1 N m−1. To achieve this value of k, a beamlike cantilever made of silicon or silicon nitride should have micrometer dimensions if one considers the formula for the spring constant of a cantilever
(1.1)
where E is the Young's modulus of the material (i.e., for silicon nitride E = 1.5 × 1011 N m−2) and t, w, and l are the thickness, width, and length of the cantilever, respectively. For example, a silicon nitride cantilever of dimensions (t, w, l) = (0.3, 10, 100) μm will yield a value of k of 0.01 N m−1, well below the spring constant of the atoms in a crystalline lattice. In principle, one could think that it may be advantageous for imaging soft materials such as proteins to fabricate cantilevers with an arbitrarily low constant. However, there is a fundamental limitation for lowering k. A cantilever in thermodynamic equilibrium with a thermal bath at temperature T has a thermal energy kBT, kB being the Boltzmann's constant. Considering the cantilever as a system with just one degree of freedom (it can move only up and down), the thermal energy increases the elastic energy stored in the cantilever as
(1.2)
(1.3)
Equation (1.3) combines the resonance frequency of a harmonic oscillator with the stiffness values of a cantilever. It should be noted that Eq. (1.3) is only exact for a point mass particle, but it is generally considered a good approximation for a continuum mass such as a cantilever. A cantilever of the abovementioned dimensions will have a mass of ∼1 ng (considering a density of 3.44 g cm−3 and not taking into account the mass of the tip) and a resonant frequency of approximately few kilohertz, well above the mechanical resonances of the building, for instance. The resonant frequency of the cantilever has important implications related to the imaging speed of the AFM. Let us assume a surface with a corrugation that can be approximated to a sinusoidal function with a wavelength of 2 nm. This means that the cantilever should move up and down at a frequency of ∼5 kHz when imaging a surface of size 10 μm × 10 μm at a speed of 1 line per second (a typical value for AFM). In other words, a wavelength translates to a time period when the cantilever scans the surface at a given speed. In order to respond to such a corrugation, the resonance frequency of the cantilever should be well above the frequency associated with the corrugation. Therefore, it turns out that the use of cantilevers with high resonant frequencies and low stiffness is highly advantageous for fast imaging of soft materials.
The offer provided by several manufacturers of different tips, cantilevers, and materials is very extensive. This large offer has opened the AFM field to multiple applications, such as noncontact AFM (NC-AFM) and dynamic modes, conductive AFM, electrostatic AFM, and so on, and has also given the possibility to image in different environments. The criterion to choose the most appropriate tip and cantilever depends on the application. In general, soft cantilevers are used in contact mode to avoid damage to the sample. On the other hand, stiff cantilevers are preferred for imaging in dynamic mode to overcome capillary forces. Ideally, cantilevers of high resonant frequency and low spring constant are preferred, but this is only possible by reducing the cantilever dimensions, which turns out to be complicated. However, recently, some manufacturers have presented new small cantilevers that are meant to meet the expectations of demanding users. Table 1.1 gives an overview of cantilever properties and their uses in the different imaging modes (see Section 1.5 for reference to imaging modes).
Table 1.1 Standard properties of cantilever used for each imaging mode and for liquids and air.a
a Data extracted from manufacturers: Nanosensors and Olympus. www.nanosensors.com and http://probe.olympus-global.com/en/.
1.3.1 Cantilever Calibration
For some quantitative AFM applications, for instance, force–distance spectroscopy, the spring constant of the cantilever must be precisely determined since the quoted value provided by the manufacturer is only an approximation based on the dimensions of the cantilevers. In some cases, the spring constant of the cantilever can be over 20% off from the quoted value.
Equation (1.3) can be used to calculate the cantilever spring constant if its mass is known. However, the AFM cantilever beam is not a simple point mass added at the end of a spring but has its weight distributed along its length, so Eq. (1.3) is usually modified by considering an effective mass, m0. In any case, measuring the effective mass of a cantilever is rather complicated, and Cleveland and coworkers [8] proposed a method based on measuring the changes in resonant frequency, f, as small masses, m*, were added to the cantilever (Eq. ((1.4))).
(1.4)
A plot of added mass, m*, versus ω−2 has a slope equal to k, and an intercept equal to the effective cantilever mass m0. By carefully performing the measurements described in [8], Cleveland and coworkers derived the following equation, which allows calculation of k with reasonable accuracy by just measuring the unloaded resonant frequency of the cantilever, assuming that one has accurate information on the length and the width of the cantilever.
(1.5)
where l is the length of the cantilever, w its width, ρ is the density of the material, E the elastic modulus or Young's modulus, and f the measured resonant frequency.
A more accurate method was proposed in 1995 by Sader et al. [9], and it was improved and applied to rectangular cantilevers in 1999 [10]. This method required to know the width and length of the cantilever, the experimentally measured resonant frequency and quality factor of the cantilever, and the density and viscosity of the fluid (properties of air: density ρair = 1.18 kg m−3 and viscosity ηair = 1.86 × 10−5 kg m−1 s−1). Sader's method was extended to enable simultaneous calibration of the torsional spring constant of rectangular cantilevers in 2004 [11]. The advantages of these methods are that the thickness, density, and resonant frequency in vacuum of the cantilever are not needed. In addition, they are rapid to use, simple to implement experimentally, noninvasive, and nondestructive (http://www.ampc.ms.unimelb.edu.au/afm/calibration.html).
1.3.2 Tips and Cantilevers for Imaging in Liquids
In solution, the charge of an object (i.e., of the tip and cantilever) is normally screened by mobile ions in the surrounding electrolyte. Coions (ions with the same sign of charge) are repelled from the surroundings of the object. Counterions (ions with opposite charge) are electrostatically attracted to the object, but this attraction diminishes their entropy. Their spatial distribution is a compromise between these two opposite tendencies. The resulting arrangement of screening charges around the object is known as the electric double layer, and its structure has a major impact on interactions between charged objects in solution [12]. Therefore, in contrast to air imaging, where capillary forces play a central role in the tip–surface interaction, in liquid imaging, electrostatic interactions are the most relevant ones. This means that resolution, which is closely related to tip–sample distance, depends on the arrangement and screening of charges in solution, and therefore, high resolution in buffer can only be achieved if contact takes place between the tip and sample. The fact that imaging in buffer at high resolution requires contact is a major issue when imaging soft samples because soft cantilevers are needed. Originally, soft cantilevers could only be used in contact mode because of their low resonant frequency. Imaging in contact mode implies the presence of shear and lateral forces that could damage soft samples or drag objects along the surface. This problem was partially overcome with the use of pulsed modes such as jumping mode, pulsed force mode, or force volume mode that minimized lateral forces. Recently, some cantilever manufacturers have developed cantilevers designed for imaging soft samples in buffer with low spring constants and reasonably high resonant frequencies, thus allowing the use of dynamic modes. This has increased the range of measurements and has minimized shear and lateral forces. However, fine tuning of electrolyte concentrations is still required to minimize the distance of electrostatic interactions between the tip and sample and to achieve high resolution.
Figure 1.3 exemplifies the relevance of proper tuning of the amount of monovalent and divalent ions when operating in liquids. It shows experimental data of force (cantilever deflection) as a function of piezo extension obtained in different liquids using a soft cantilever of 0.08 N m−1 and freshly cleaved mica as a surface. The deflection or force is zero until an attractive (negative) force pulls the cantilever toward the mica. Once the cantilever is in contact with the surface, the deflection follows the piezo movement. When using water (black curve), this attractive force is over 0.5 nN, a rather large force when imaging biological materials. Data obtained using 25 mM tris-acetate (pH 7.5), 50 mM KCl, 50 mM MgOAc (dark yellow curve) shows an effective absence of adhesion and attractive force.
Figure 1.3 Approaching (a) and withdrawing (b) force-extension curves for a mica surface immersed in different buffers. The cantilever used had a force constant of 0.08 Nm-1, and Buffer A is 25 mM tris-acetate pH (7.5) and 2 mM MgOAc supplemented with KCl or extra MgOAc when stated.
1.3.3 Cantilever Dynamics in Liquids
According to Eq. (1.1), the spring constant k only depends on the material properties of the cantilever and its geometrical dimensions. This means that k is independent of the surrounding environment in which the cantilever may be immersed. However, viscosity of the surrounding media does affect the mechanical response of the cantilever, and this is important when operating in liquids. Equation (1.3) already indicates that moving the cantilever from air to a more dense fluidlike liquid will have an immediate effect on its resonant frequency, which is reduced because it has to move an extra mass [13]. In addition, the liquid viscosity is much higher than the viscosity of air. The movement of a cantilever driven by an external oscillatory force F(t) = F0cos(ωt) can be described as a forced harmonic oscillator with damping [14].
(1.6)
(1.7)
(1.8)
Here, z describes the vertical movement of the cantilever, m is its mass (note that an effective mass m* can substitute m in all these equations), ω0 is its free (vacuum) resonant frequency and ωr its resonance frequency in a fluid, Q is the quality factor, γ the damping coefficient, and F0 the amplitude of the oscillatory force at a time t.
The solution of Eq. (1.6) has a transient term and a steady term [15].
(1.9)
The transient term is reduced by a factor of 1/e, after a time 1/α = 2Q/ω0. From then, the motion of the tip is dominated by the steady term. The steady term is a harmonic function with a phase lag with respect to the external excitation force. Amplitude and phase lag can be calculated with the following equations:
(1.10)
(1.11)
Examples of amplitudes and phase lags are shown in Figure 1.4 for different values of Q.
Figure 1.4 Plots of Eqs. (1.9) and (1.10) highlighting the role of the quality factor Q in a harmonic oscillator.
The oscillation of a cantilever in liquid has important differences compared with its oscillation in air or in vacuum. First, as a consequence of the large density of the surrounding liquid compared with the density of air, the cantilever suffers an increase of the effective mass by a factor of 10–40 and a corresponding decrease of the resonant frequency (Eq. (1.3)). Resonance and natural frequencies are related by Eq. (1.8). Therefore as a second consequence, the strong hydrodynamic interaction between the cantilever and the liquid produces a very low quality factor Q. Typically, Q in liquids can be about two orders of magnitude lower than in air (Figure 1.5) [16]. The decrease in resonant frequency and Q has important consequences on the cantilever oscillation and therefore affects the performance of dynamic modes. First, the cantilever oscillation is inharmonic and asymmetric in liquids [17], in contrast with its performance in air where the oscillation is sinusoidal and symmetric [18]. In addition, the low quality factor of the cantilever in liquid implies high forces between the tip and sample [19]. Dynamic modes use as a control signal, the amplitude of the oscillation that reflects the interaction between the tip and the sample. A shift in the resonant frequency of the cantilever due to tip–sample interaction produces an amplitude damping at resonance, which is proportional to the quality factor of the cantilever. Some authors developed an AFM technique for liquids in which the cantilever response is controlled by adding an active feedback system that increases the quality factor up to three orders of magnitude [16]. Alternatively, use of cantilevers of high resonance frequency in liquids should improve the performance of dynamic modes, although high frequencies are achieved at the expense of increasing the force constant, which is not convenient for imaging soft materials. Although cantilevers of low k and high f are preferable, molecular resolution has been obtained in buffer using cantilevers of k ∼ 0.08 N m−1 and f ∼ 7 kHz as can be seen in Figure 1.5 [20].
Figure 1.5 (a) Oscillation of the cantilever in air and in liquids. The thermal spectrum of the cantilever (Olympus BL-RC-150VB, k ∼ 0.03 N m−1) illustrates the reduction in resonant frequency and Q in liquids. (b,c) Examples of images of biomolecules obtained in liquids using dynamic modes and soft cantilevers (Olympus TR400PSA, k ∼ 0.08 N m−1). (b) DNA molecules imaged in 10 mM tris-HCl (pH 8.0), 5 mM MgCl2. (c) Rad50/Mre11 protein complex in 25 mM tris-HCl (pH 8.0), 125 mM KCl and 10% Glicerol. (a) Adapted from Ref. [19].
1.4 Force Detection Methods for Imaging in Liquids
The heart of an AFM is a sharp tip that interacts with a force at the surface of a sample. As seen before, the tip is mounted on a flexible beam whose geometrical and material properties makes it possible to probe the force with high sensitivity. The role of the beam is to translate the force acting on the tip into a deflection that can subsequently be monitored by various means. Among these, tunneling of electrons (the original scheme invented by Binnig and coworkers), capacitance, piezoelectric cantilevers and tuning forks, optical interferometry, and optical beam deflection have been developed to a high degree of sophistication. The interaction force is proportional to the deflection of the cantilever following Hooke's law. Electrical methods such as electron tunneling or capacitance were historically the first used to detect the small movement of the cantilever, but they are not applicable to in-liquid imaging. Interferometry has very high sensitivity and signal-to-noise ratio, but the instrument is difficult to set up and gets quickly misaligned. For this reason, it is not used in liquid AFM. For liquid operation, most AFMs use the laser beam deflection method, but piezoelectric cantilevers and tuning forks can also be employed. In the following section, we introduce both methods.
1.4.1 Piezoelectric Cantilevers and Tuning Forks
The piezoelectric cantilever detection method [21] uses a cantilever with an additional piezoelectric thin film containing electrical connections. As the cantilever bends, the piezoelectric layer is stressed and deformed, altering the charge distribution at both sides of the layer (direct piezoelectric effect). By making proper contacts at both sides of the layer and using a simple preamplifier circuit, it is very easy to obtain a voltage proportional to the cantilever deflection (Figure 1.6a). This method has the advantage that the same connections used to detect deflection can be used to oscillate the cantilever by applying an AC voltage to the piezoelectric film. Piezoelectric cantilevers are also convenient for dynamic operation in liquids. When a cantilever is oscillated in liquid using acoustic excitation, a number of spurious resonances, which are related to the mechanics of the experimental setup, make it very difficult to identify the true cantilever resonant frequency (see discussion in Section 1.5.3.1). In the case of self-oscillated cantilevers, since the only moving object is the cantilever itself, the response of the system does not exhibit the spurious peaks associated with an external drive [22]. On the other hand, electrical contacts in liquids are tricky and may cause unstable oscillation of the cantilever. In addition, this method requires rather expensive cantilevers, often custom manufactured, and their sensitivity is not as good as in optical detection systems.
Figure 1.6 (a) Piezoelectric cantilever method and (b) tuning fork method.
A similar self-oscillating and detection approach uses a tuning fork for detection of the tip–sample distance (Figure 1.6b). In general, an AFM tip is glued onto one leg of a small quartz tuning fork and it is forced to oscillate. Damping of the amplitude by tip–sample interaction forces is monitored and/or used as a feedback signal. The force resolution of this technique is typically 0.1 pN. This method is employed for NC-AFM [23] (see dynamic modes, Section 1.5.3) and has the advantage that the probe does not touch the sample surface, and therefore damage to the sample by the probe can be avoided. However, many problems must be overcome for the successful application of NC-AFM to biomaterials or biosystems. First, the large oscillation amplitude of the order of 10 or 100 Å used to attain a sufficient signal-to-noise ratio makes interpretation of the force curve difficult. This problem can be solved by using a stiffer force sensor compared to the conventional ones. Second, in liquids, sufficient Q-value required for NC-AFM measurement is hardly implemented because of the viscosity of the liquid.
1.4.2 Laser Beam Deflection Method
Laser beam deflection is the most common detection method used in modern commercial AFMs and was pioneered by Meyer and Amer [24, 25]. The cartoon in Figure 1.7a describes its functioning principle. The cantilever deflection is measured by monitoring the position of a laser beam reflecting from the cantilever and directed to a quadrant photodiode. The photodiode is a semiconductor device that turns the intensity of light falling on it into an electrical voltage signal. The photodiode is usually split into four sections, enabling both vertical and lateral movements of the cantilever to be differentiated. Vertical movement of the cantilever is measured as the difference in voltage between upper and lower quadrants of the photodiode. Similarly, torsional motion of the cantilever is measured as the difference in voltage between the left and right quadrants of the photodiode. Vertical movement of the cantilever originates from the so-called normal forces. The origin of torsional movement of the cantilever arises from frictional forces that originate by the lateral motion of the tip with respect to the sample during the scan [26]. The accuracy of the beam deflection method can be as high as 0.1 Å and is generally limited by random thermal excitation of the cantilever on which the tip is mounted.
Figure 1.7 Beam deflection method. (a) Cartoon showing the principle of the beam deflection method. A laser beam is focused on the back side of the cantilever and its reflection is directed to a photodiode that records the vertical and lateral movements of the cantilever. (b) A side view of the setup with the relevant dimensions.
It can be shown that the angle at the end of a lever in the presence of a force F acting at this point is [27] (Figure 1.7b)
(1.12)
where E is the Young's Modulus and I the area moment of inertia. For a rectangular cantilever, EI = kl3/3, where k is the spring constant fulfilling F = kz and l is the cantilever length. Then we get
(1.13)
And since for small deflections tan θ ∼ θ and tan θ = D/S
(1.14)
This is a large amplification of the movement because for a cantilever of l ∼ 200 μm at a distance S ∼ 5 cm, this method amplifies the movement of the cantilever by a factor of 375. In general, the beam deflection method is less sensitive than other electronic methods, but the simplicity of the implementation makes it the preferred method to detect the cantilever deflection in air and in liquids.
1.4.2.1 Liquid Cells and Beam Deflection
The experimental device that allows the laser beam to propagate without suffering scattering in the liquid surface is known as liquid cell. The importance of this device is illustrated in Figure 1.8. In almost any air–liquid interface, small mechanical instabilities give rise to surface waves in the liquid that scatter the light coming from a laser beam, producing a noisy spot that is useless for detecting the cantilever deflection (Figure 1.8, left). This problem is solved by creating a well-defined solid–liquid interface with a transparent window. The incoming laser beam (right red line) is transmitted in the liquid without being affected by any surface wave, resulting in a stable spot suitable for detecting the cantilever deflection (Figure 1.8, middle).
The degree of sophistication of a liquid cell depends on the imaging mode employed. We discuss later that there are imaging modes in which the cantilever is oscillated at a particular frequency, and that complicates the design of a liquid cell. Precisely, to oscillate a standard cantilever, most liquid cells incorporate a piezoelectric ceramic, which is isolated to prevent wetting. Some liquid cells use magnetic cantilevers and then there is no need for using piezoelectrics since the cantilever oscillation is achieved with an external magnetic field. Often, the liquid has to be changed in the course of an experiment. Some liquid cells incorporate two holes (Figure 1.8, right) at the tip mount. This permits to flow the required solution in and out of the bath, allowing a constant renewal of the liquid environment. The exchange of buffer may cause turbulences in the surrounding of the cantilever. Therefore, to prevent tip damaging, it is recommended to perform this operation with the tip out of contact. Once the old buffer is replaced, the tip can again be approached and set in range for imaging.
Figure 1.8 Need of a liquid cell device for imaging in liquids. The incoming laser beam (red line) continuously changes direction due to surface waves at the gas–liquid interface. As a consequence, a nonsteady spot is obtained (left). By using a transparent glass window, a well-defined interface is created and the laser light is transmitted without scattering in the liquid (middle). By means of two holes, liquid can be exchanged in the course of an experiment (right).
1.5 AFM Operation Modes: Contact, Jumping/Pulsed, Dynamic
Imaging modes in AFM are generally classified as static or dynamic modes. This classification is related to the oscillation of the tip during imaging. In static mode, the tip does not oscillate, and in dynamic mode, the tip is forced to oscillate at or near its resonant frequency. Static modes mainly include contact and jumping or pulsed force modes, while dynamic modes include, among others, amplitude-modulation atomic force microscopy (AM-AFM) and frequency-modulation atomic force microscopy (FM-AFM). In the following sections, a general description of the most important ones is given.
1.5.1 Contact Mode
Contact mode atomic force microscopy (CM-AFM) is the oldest and simplest AFM imaging mode in which the tip is brought into direct contact with the surface, deflecting the cantilever (repulsive force) [2]. This deflection is measured in liquid by any of the methods described in Section 1.4 and controlled by a feedback system that keeps it constant. In practice, most AFMs use the beam deflection method, and therefore, the signal used as control is the one given by the photodiode that corresponds to vertical deflection of the cantilever. The value at which images are taken (usually known as the feedback set point) is chosen by the operator depending on the conditions of the experiment. As the tip scans the surface, the Z-scanner is automatically adjusted maintaining the normal signal from the photodiode equal to the set point (see later the feedback loop Section 1.6). First applications of AFM in liquids used this operation mode [5]. AFM was used in contact mode to investigate membrane-bound proteins ordered in 2D arrays [28] and to image the chaperonins GroEL and GroES from Escherichia coli [29]. However, these first approaches to AFM in biology soon evidenced that contact mode imaging had several drawbacks. First, the set point given by the operator is related to a certain position of the deflected beam in the photodiode and may not reflect a constant force applied to the sample. This is because the photodiode signal that corresponds to free cantilever deflection (out of contact, zero force) may drift with time. As a consequence, while images are taken at constant deflection, they may not be taken at constant force. Second, the normal force in combination with the lateral motion during scanning introduces high lateral forces (friction) that can damage or move the sample. This is particularly relevant for the case of soft biological materials weakly attached to a surface (DNA, proteins, viruses, etc.). In order to minimize shear forces and to accurately control the force applied while imaging, several methods have been developed, and a brief description is given below.
1.5.2 Jumping and Pulsed Force Mode
Jumping mode atomic force microscopy (JM-AFM) [30] combines features of contact and dynamic modes (Section 1.5.3) and is very similar to pulsed force microscopy [31]. It was originally developed as a scanning mode to minimize shear forces and to accurately control the force applied on an image, while the tip is in contact. In JM-AFM, a force-extension measurement is performed on each of the pixels of the image. JM-AFM mode operation can be described as a cycle repeated at each image point with the following four steps: (1) tip–sample separation (moving from point A to B and C in Figure 1.9), (2) lateral tip motion at the largest tip–sample distance, (3) tip–sample approach (moving from point C to D and A in Figure 1.9), and (4) feedback enabled, which is generally performed on the cantilever deflection (point A in Figure 1.9). From this cycle it is clear that shear forces are minimized because lateral motion is always performed out of contact and that the applied force is controlled because the zero-force level is known and adjusted for each cycle.
JM-AFM solved some of the technical problems occurring in contact mode, for instance, the drift in the zero-force level, but its performance is still seriously affected by the environment used for imaging because of the presence of contact between the tip and sample. In air, the strong adhesion force arising from van der Waals and capillary forces makes it difficult to obtain reproducible images of biomolecules because forces of hundreds of picoNewtons are induced by the mere contact with the sample (Figure 1.10). In liquids, however, the absence of both capillary forces and low van der Waals forces dramatically decreases the magnitude of the applied forces. This benefits imaging in JM-AFM in liquids, as it has been shown for imaging DNA molecules and viral capsids [17, 32, 33]. Moreover, this method can be used to get information on the mechanical properties of the sample by performing force-extension curves at each image point. For instance, mechanical properties of virus [33, 34] and unfolding of proteins [35] have been investigated. However, JM-AFM has some drawbacks as, for example, the low imaging rate because of the time consumed during its operating cycle.
Figure 1.9 Jumping mode oscilloscope signals. (1) Normal force signal or cantilever deflection. (2) Piezoelectric Z (vertical) signal. (3) Piezoelectric (X) lateral displacement as a function of time. In the inset, a force (signal 1) versus extension (signal 2) curve is shown including main points of interest. (A) Region with feedback on. (B) Jump-off point or point of maximum negative deflection of the cantilever (adhesion force). (C) Largest tip–sample distance. (D) Jump-in point or position where tip–sample contact is established. Adapted from Ref. [30].
Figure 1.10 Force-extension curves in air and in liquids, enhancing the role of van der Waals and capillary forces in both environments.
1.5.3 Dynamic Modes
The common feature of dynamic modes is that the cantilever is driven at, or close to, its free (far from the surface) resonant frequency f0. There are two major dynamic AFM modes, AM-AFM and FM-AFM, which are classified according to the signal used as feedback: amplitude and frequency of the oscillating cantilever, respectively. In AM-AFM, the cantilever is excited at ∼ f0 with a given oscillation amplitude A0 (Figure 1.11a,b). Then, the oscillating tip and sample are approached as the amplitude signal is monitored. The amplitude of the cantilever can be measured with a lock-in amplifier or with a much simpler root-mean-square (RMS) detector. At some point, the tip starts feeling the interaction with the surface and as a consequence, the amplitude decreases linearly with the distance between the tip and surface. A naive way of surface feeling is to imagine the tip to be in intermittent contact with the surface, as if one taps the surface with a finger (Figure 1.11c,d). This is why AM-AFM is usually known as tapping mode [36–38]. Generally speaking, the degree of reduction of the amplitude in the tapping region with respect to the free amplitude defines the force applied on the sample and in many occasions, the quality of the image.
Figure 1.11 Principles of dynamic-mode AFM. (a) Cantilever driven at its free resonance frequency f0 with amplitude A0. (b) Rendering of the cantilever deflection as a function of time using, for instance, the beam deflection method. (c) The cantilever is approached to the sample surface and the oscillation amplitude is reduced to A. (d) Same as in (b) but with the cantilever near the surface.
In FM-AFM, the cantilever is kept oscillating with a fixed amplitude at its resonant frequency [39, 40]. An image is formed by scanning at a constant frequency shift (difference between current frequency and the free resonant frequency). FM-AFM is the preferred imaging mode in ultrahigh vacuum (UHV), but recently, true atomic resolution on mica has been reported using this method in liquids [41]. Some authors are now using FM-AFM in liquids as a method to obtain the highest resolution [42].
Despite the superior performance of dynamic modes in air with respect to contact or jumping/pulsed mode, in liquids, both methods yield comparable results. In liquids, van der Waals forces are very weak and there are no capillary forces. As a consequence, in dynamic modes in liquid, contact between tip and sample takes place and forces involved in the working cycle of dynamic and jumping modes are very similar. Nevertheless, there is still an obvious difference between both operating modes, namely, the time consumed in performing each cycle per image point: approximately milliseconds in the case of jumping/pulsed and <0.1 ms in dynamic modes. This affects the imaging rate and gives advantage to dynamic modes compared to others. However, there is still room for improvement because owing to the large effective mass of the cantilever in liquid, its resonant frequency drops and the high damping strongly reduces the Q factor of the system, which in turn means a reduction of the sensitivity of the technique.
1.5.3.1 Liquid Cells and Dynamic Modes
For working in static modes (contact, jumping, or pulse force mode), a liquid cell is almost nothing else but what is shown in Figure 1.8. However, working in liquids in dynamic modes, where the cantilever has to oscillate at or near its resonant frequency, involves a higher degree of sophistication in the liquid cell design. The most common way to oscillate a cantilever in air or vacuum is to use acoustic driving, in which a small piezoelectric element with a very high resonant frequency is located right below the cantilever chip. When working in liquid, this is not so simple because the liquid can easily get in contact with the piezoelectric, creating shortcuts and potential leaks. A simple way to avoid this problem is to locate the small piezo element far away from the liquid. In the liquid cell shown in Figure 1.12, the piezoelectric is located under one of the supporting balls. This solution has an important drawback as the piezo element excites many different mechanical resonances of the liquid cell, thus producing a forest of resonances
