Force measurements with the atomic force microscope: Technique, interpretation and applications

https://doi.org/10.1016/j.surfrep.2005.08.003Get rights and content

Abstract

The atomic force microscope (AFM) is not only a tool to image the topography of solid surfaces at high resolution. It can also be used to measure force-versus-distance curves. Such curves, briefly called force curves, provide valuable information on local material properties such as elasticity, hardness, Hamaker constant, adhesion and surface charge densities. For this reason the measurement of force curves has become essential in different fields of research such as surface science, materials engineering, and biology.

Another application is the analysis of surface forces per se. Some of the most fundamental questions in colloid and surface science can be addressed directly with the AFM: What are the interactions between particles in a liquid? How can a dispersion be stabilized? How do surfaces in general and particles in particular adhere to each other? Particles and surfaces interactions have major implications for friction and lubrication. Force measurements on single molecules involving the rupture of single chemical bonds and the stretching of polymer chains have almost become routine. The structure and properties of confined liquids can be addressed since force measurements provide information on the energy of a confined liquid film.

After the review of Cappella [B. Cappella, G. Dietler, Surf. Sci. Rep. 34 (1999) 1–104] 6 years of intense development have occurred. In 1999, the AFM was used only by experts to do force measurements. Now, force curves are used by many AFM researchers to characterize materials and single molecules. The technique and our understanding of surface forces has reached a new level of maturity. In this review we describe the technique of AFM force measurements. Important experimental issues such as the determination of the spring constant and of the tip radius are discussed. Current state of the art in analyzing force curves obtained under different conditions is presented. Possibilities, perspectives but also open questions and limitations are discussed.

Introduction

The atomic force microscopy (AFM) belongs to a series of scanning probe microscopes invented in the 1980s. This series started with the scanning tunnelling microscope (STM), which allowed the imaging of surfaces of conducting and semiconducting materials [1], [2]. With the STM it became possible to image single atoms on “flat” (i.e., not a tip) surfaces. In parallel the scanning near-field optical microscope (SNOM) was invented which allowed microscopy with light below the optical resolution limit [3], [4]. The last one of the series is the AFM, invented by Binnig et al. [5]. The AFM with its “daughter” instruments such as the magnetic force microscope and the Kelvin probe microscope has become the most important scanning probe microscope. The AFM allowed the imaging of the topography of conducting and insulating surfaces, in some cases with atomic resolution.

In the AFM (Fig. 1) the sample is scanned by a tip, which is mounted to a cantilever spring. While scanning, the force between the tip and the sample is measured by monitoring the deflection of the cantilever. A topographic image of the sample is obtained by plotting the deflection of the cantilever versus its position on the sample. Alternatively, it is possible to plot the height position of the translation stage. This height is controlled by a feedback loop, which maintains a constant force between tip and sample.

Image contrast arises because the force between the tip and sample is a function of both tip–sample separation and the material properties of tip and sample. To date, in most applications image contrast is obtained from the very short range repulsion, which occurs when the electron orbitals of tip and sample overlap (Born repulsion). However, further interactions between tip and sample can be used to investigate properties of the sample, the tip, or the medium in between. These measurements are usually known as “force measurements”. In an AFM force measurement the tip attached to a cantilever spring is moved towards the sample in normal direction. Vertical position of the tip and deflection of the cantilever are recorded and converted to force-versus-distance curves, briefly called “force curves”.

In the first few years force measurements with the AFM were driven by the need to reduce the total force between tip and sample in order to be able to image fragile, e.g. biological structures. Therefore it was obligatory to understand the different components of the force. In addition, microscopists tried to understand the contrast mechanism of the AFM to interpret images correctly. One prominent example was the observation of meniscus forces under ambient conditions by Weisenhorn et al. [6] in 1989. Weisenhorn et al. did not only detect meniscus forces but they also realized that imaging in liquid could significantly reduce the interaction between tip and sample in AFM imaging and thus increase the resolution.

Another important motivation was the computer industry with its demand to produce hard discs and other storage devices with high data density. This stimulated the measurement of magnetic [7], [8], [9], [10] and electrostatic forces [11], [12], [13] and led to the development of magnetic force, electric force, and Kelvin probe microscopy [14]. The goal was not so much to understand the force but to image the distribution of magnetization, charge, or surface potential, respectively.

The main focus of AFM force measurements today is to study surface forces per se. The interaction between two surfaces across a medium is one of the fundamental issues in colloid and surface science. It is not only of fundamental interest but also of direct practical relevance when it comes to dispersing solid particles in a liquid. One major step to measure surface forces quantitatively was the introduction of the colloidal probe technique [15], [16]. In the colloidal probe technique a spherical particle of typically 2–20 μm diameter is attached to the end of the cantilever. Then the force between this microsphere and a flat surface is measured. Since the radius of the microsphere can easily be determined, surface forces can be measured quantitatively. For imaging, a microsphere is of course not suitable.

The AFM is not the only device to measure forces between solid surfaces. During the last decades several techniques and devices have been developed [17]. One important device is the surface forces apparatus (SFA). The SFA allows to measure directly the force law in liquids and vapors at angstrom resolution level [18], [19]. The SFA contains two crossed atomically smooth mica cylinders of roughly 1 cm radius between which the interaction forces are measured. One mica cylinder is mounted to a piezoelectric translator. With this translator the distance is adjusted. The other mica surface is mounted to a spring of known and adjustable spring constant. The separation between the two surfaces is measured by use of an optical technique using multiple beam interference fringes. Knowing the position of one cylinder and the separation to the surface of the second cylinder, the deflection of the spring and the force can be calculated.

Another important, although less direct, technique for measuring forces between macromolecules or lipid bilayers is the osmotic stress method [20], [21], [22]. In the osmotic stress method a dispersion of vesicles or macromolecules is equilibrated with a reservoir solution containing water and other small solutes, which can freely exchange with the dispersion phase. The reservoir also contains a polymer which cannot diffuse into the dispersion. The polymer concentration determines the osmotic stress acting on the dispersion. The spacing between the macromolecules or vesicles is measured by X-ray diffraction. In this way one obtains pressure-versus-distance curves.

During the last 10–15 years a new technique called total internal reflection microscopy (TIRM) was developed [23]. Using TIRM the distance between a single microscopic sphere immersed in a liquid and a transparent plate can be monitored with typically 1 nm resolution. The distance is calculated from the intensity of light scattered by the sphere when illuminated by an evanescent wave through the plate. From the equilibrium distribution of distances sampled by Brownian motions the potential energy-versus-distance can be determined. TIRM complements force measurements with the AFM and the SFA because it covers a lower force range.

These techniques have allowed accurate measurement of surface and intermolecular forces and led to improved understanding in this field. However, only a limited number of systems could be investigated because of restrictions to the material properties and the complexity of the equipment. In contrast, the AFM is relatively easy to use. Since many people use the AFM for imaging it is relatively common and the technology is refined. Due to its high lateral resolution small samples can be used and material non-homogeneities can be mapped. Having small contact areas also reduces the danger of contamination and surface roughness.

In 1994 another type of AFM force measurements emerged, that of single molecule experiments. Forces to stretch single polymer molecules or to break single bonds had been measured before, but the ease and accuracy greatly stimulated the field (for a review, see Ref. [24]). The wealth of experimental results has also triggered the development of a much refined theory of bonding and bond breaking.

The aim of this review is to provide the reader with a comprehensive description of how to measure and analyze AFM force experiments. It is written for researchers who intend to use the AFM or already use it for measure forces. These can be microscopists with a background in imaging who intend to expand their possibilities by taking force curves. It also concerns colloidal and interface scientists who want to use the AFM to study interparticle and surface forces. The review highlights the contribution the AFM made to our knowledge of surface forces. We describe the technique and analysis, the advantages and scientific achievements but also the problems, limits, and pitfalls. We believe that AFM force experiments have reached such a maturity, that a comprehensive review is helpful.

Section snippets

Overview

In a force measurement the sample is moved up and down by applying a voltage to the piezoelectric translator, onto which the sample is mounted, while measuring the cantilever deflection (Fig. 2). In some AFMs the chip to which the cantilever is attached is moved by the piezoelectric translator rather than the sample. This does not change the description at all, for simplicity we assume that the sample is moved. The sample is usually a material with a planar, smooth surface. It is one of the two

Conversion of force curves and the problem of zero distance

The direct result of a force measurement is a measure of the photodiode current IPSD versus height position of the piezoelectric translator Zp. To obtain a force-versus-distance curve, IPSD and Zp have to be converted into force and distance (see also [197]). Therefore two parameters need to be known: the sensitivity and the zero distance. In atomic force microscopy both parameters must be inferred from the force curve itself and not through an independent method. Practically, the linear part

Overview

From the contact lines of force–displacement curves it is possible to draw information about the elastic–plastic behavior of materials. In fact, the first force curves taken with the AFM were aimed at analyzing the nanomechanical properties of solid surfaces. Meyer et al. [108] measured force curves between diamond shards and LiF and HOPG. Mate et al. [236] measured the force-versus-distance between a Pt–Rh wire, which was bent like a cantilever and whose deflection was detected via optical

Theory

In this section only some basic equations, necessary for the comprehension of the experimental sections, are summarized. An general introduction on van der Waals force can be found in Ref. [309]. The van der Waals force between atoms and/or molecules is the sum of three different forces, all proportional to 1/r6, where r is the distance between the atoms or molecules. The corresponding potentials are the orientation or Keesom potential wK(r), the induction or Debye potential wD(r), and the

Electrostatic double-layer force and DLVO theory

At the end of the 19th century it was well known that many colloids in aqueous medium coagulate after the addition of salt. It was even known that di- or trivalent ions are much more efficient in destabilizing dispersions than monovalent ions. The explanation for this behavior was eventually given in a quantitative way with the DLVO theory, named after Derjaguin, Landau, Verwey, and Overbeek [394], [395]. In DLVO theory the interaction between two particles is assumed to consist of two

Adhesion

When retracting the tip from the sample surface, the tip stays in contact with the surface until the cantilever force overcomes the adhesive tip–sample interaction. First measurements of this pull-off force or adhesion force Fad were performed by Martin et al. [551] and Erlandson et al. [552]. In the most general case the adhesion force Fad is a combination of the electrostatic force Fel, the van der Waals force FvdW, the meniscus or capillary force Fcap and forces due to chemical bonds or

Overview

Often the liquid structure close to an interface is different from that in the bulk. For many fluids the density profile normal to a solid surface oscillates about the bulk density with a periodicity of about one molecular diameter, close to the surface. This region typically extends over a few molecular diameters and is particularly pronounced for a strong liquid–wall interaction. In this range the molecules are ordered in layers. When two such surfaces approach each other, layer after layer

Particle–bubble interaction

While the electric double layer on a solid surface is relatively well understood and theories are able to account for colloidal stability and coagulation kinetics quite well, there has been much less success in understanding the double-layer structure at liquid–liquid or liquid–gas interfaces. This is despite the fact that the stability of emulsions or dispersion of particles and gas bubbles play a central role in many industrial processes such as flotation or the deinking of paper. With the

Single molecules

The unique capability of the AFM to acquire forces locally and with high sensitivity makes it possible to get information about the interactions of a single molecular pair. This kind of experiments is known as “force spectroscopy” (for reviews see Refs. [24], [1046]). Two main fields of interest have emerged in recent years: Molecule stretching [1047], [1048], [1049] and specific interactions between biological pairs [1050], [1051], [1052]. Accordingly, two relevant classes of models have been

Force volume mode

Instead of taking forces-distance curves only on selected points of the sample, one can also acquire force–distance curves in every point corresponding to a pixel of the AFM image. Since the tip is scanned not only along the surface, but travels also in the Z-direction perpendicular to the surface, the term “force volume mode” has been coined for this mode of operation. From the array of force–distance curves the spatial variation of interactions throughout the sample surface can be obtained.

Conclusions and perspectives

The field of force measurements with the AFM has reached a state of maturity. The basic mathematics to describe the cantilever and tip and the theory to describe forces acting on the tip have been developed for many applications. For example, the calibration of the elastic constant of the cantilever, playing a key role for quantitative force measurements, is nowadays a standard opportunity in commercial AFMs. Also the exact knowledge of tip shape and dimensions is necessary for quantitative and

References (1253)

  • A. Lewis et al.

    Ultramicroscopy

    (1984)
  • S. Porthun et al.

    J. Magn. Magn. Mater.

    (1998)
  • M.R. Koblischka et al.

    Ultramicroscopy

    (2003)
  • H.-J. Butt

    Biophys. J.

    (1991)
  • P.M. Claesson et al.

    Adv. Colloid Interf. Sci.

    (1996)
  • V.A. Parsegian et al.

    Meth. Enzymol.

    (1986)
  • D.C. Prieve

    Adv. Colloid Interf. Sci.

    (1999)
  • H.-J. Butt et al.

    J. Struct. Biol.

    (1993)
  • M. Hegner et al.

    Surf. Sci.

    (1993)
  • H.-J. Butt

    J. Colloid Interf. Sci.

    (1996)
  • R. Garcia et al.

    Surf. Sci. Rep.

    (2002)
  • R. Boisgard et al.

    Surf. Sci.

    (1998)
  • T. Okajima et al.

    Appl. Surf. Sci.

    (2003)
  • H.-J. Butt

    J. Colloid Interf. Sci.

    (1994)
  • R.W. Stark et al.

    Ultramicroscopy

    (2001)
  • J.L. Hazel et al.

    Thin Solid Films

    (1999)
  • G. Binnig et al.

    Phys. Rev. Lett.

    (1982)
  • G. Binnig et al.

    Phys. Rev. Lett.

    (1983)
  • D.W. Pohl et al.

    Appl. Phys. Lett.

    (1984)
  • G. Binnig et al.

    Phys. Rev. Lett.

    (1986)
  • A.L. Weisenhorn et al.

    Appl. Phys. Lett.

    (1989)
  • Y. Martin et al.

    Appl. Phys. Lett.

    (1987)
  • J.J. Sáenz et al.

    J. Appl. Phys.

    (1987)
  • Y. Martin et al.

    J. Appl. Phys.

    (1987)
  • J.E. Stern et al.

    Appl. Phys. Lett.

    (1988)
  • R. Erlandsson et al.

    J. Vac. Sci. Technol. A

    (1988)
  • M. Rohwerder, P. Leblanc, G.S. Frankel, M. Stratmann, in: P. Marcus (Ed.), Analytical Methods for Corrosion Science and...
  • W.A. Ducker et al.

    Nature

    (1991)
  • D. Tabor et al.

    Nature

    (1968)
  • J.N. Israelachvili et al.

    Proc. R. Soc. London A

    (1972)
  • D.M. LeNeveu et al.

    Nature

    (1976)
  • V.A. Parsegian et al.

    Proc. Natl. Acad. Sci. U.S.A.

    (1979)
  • A. Janshoff et al.

    Angew. Chem. Int. Ed.

    (2000)
  • L. Meagher et al.

    Langmuir

    (1995)
  • G. Meyer et al.

    Appl. Phys. Lett.

    (1988)
  • S. Alexander et al.

    J. Appl. Phys.

    (1989)
  • S.M. Hues et al.

    Rev. Sci. Instrum.

    (1994)
  • M. Preuss et al.

    Langmuir

    (1998)
  • K.O. van der Werf et al.

    Appl. Phys. Lett.

    (1994)
  • A. Rosa

    Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem.

    (1996)
  • T. Miyatani et al.

    Appl. Phys. Lett.

    (1997)
  • A. Rosa-Zeiser et al.

    Meas. Sci. Technol.

    (1997)
  • D. Sarid

    Scanning Force Microscopy

    (1991)
  • G.Y. Chen et al.

    Rev. Sci. Instrum.

    (1994)
  • T.R. Albrecht et al.

    J. Vac. Sci. Technol. A

    (1990)
  • H.-J. Butt et al.

    J. Microsc.

    (1993)
  • T. Thundat et al.

    Appl. Phys. Lett.

    (1994)
  • J.E. Sader

    Rev. Sci. Instrum.

    (1995)
  • D.A. Walters et al.

    Rev. Sci. Instrum.

    (1996)
  • M.B. Viani

    Rev. Sci. Instrum.

    (1999)
  • Cited by (3069)

    • Mitigation mechanisms of silica scaling on different organic-fouled nanofiltration membrane surface

      2024, Colloids and Surfaces A: Physicochemical and Engineering Aspects
    View all citing articles on Scopus
    View full text