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Force Measurements with the Atomic Force Microscope Surface Science Reports 59 (2005) 1–152 www.elsevier.com/locate/surfrep Force measurements with the atomic force microscope: Technique, interpretation and applications Hans-Ju¨rgen Butt a, Brunero Cappella b,*, Michael Kappl a a Max-Planck-Institute for Polymer Research, D-55128 Mainz, Germany b Federal Institute for Material Research and Testing, D-12205 Berlin, Germany Accepted 1 August 2005 Abbreviations: AFM, atomic force microscope; AOT, bis(2-ethylhexyl)sulfosuccinate; BSA, bovine serum albumin; CMC, critical micellar concentration (mol/L); CSH, calcium silicate hydrate; CTAB, cetyltrimethylammonium bromide (=hexade- cyltrimethylammonium bromide); DDAB, didodecyl dimethylammonium bromide; DDAPS, N-dodecyl-N,N-dimethyl-3- ammonio-1-propanesulfonate; DGDG, digalactosyldiglyceride; DLVO, Derjaguin–Landau–Verwey–Overbeek theory; DMA, dynamical mechanical analysis; DMT, Derjaguin–Mu¨ller–Toporov theory of mechanical contact; DNA, desoxy- ribonucleic acid; DODAB, dimethyl-dioctadecylammonium bromide; DOPC, 1,2-dioleoyl-sn-glycero-3-phosphocholine; DOPE, 1,2-dioleoyl-sn-glycero-3-phosphodylethanolamine; DOPS, 1,2-dioleoyl-sn-glycero-3-phospho-l-serine; DOTAP, 1,2-dioleoyl-3-trimethylammonium-propane chloride; DTAB, dodecyltrimethylammonium bromide; DSCG, disodium cromo- glycate; DSPE, 1,2-distearoyl-sn-glycero-3-phosphoethanolamine; EDTA, ethylenediaminetetraacetic acid; FJC, freely jointed chain; HOPG, highly oriented pyrolytic graphite; HSA, human serum albumin; JKR, Johnson–Kendall–Roberts theory of mechanical contact; LPS, lipopolysaccharides; MD, molecular dynamics; MEMS, micro-electromechanical systems; MF, melamine formaldehyde; MGDG, monogalactosyldiacylglycerol; OMCTS, octamethylcyclotetrasiloxane, ((CH2)2SiO)4; OTS, octadecyltrichlorosilane; PAA, poly(acrylic acid); PAH, poly(allyl amine hydrochloride); PBA, parallel beam approximation; PBMA, poly(n-butyl methacrylate), –(CH2CC4H9COOCH3)n–; PDADMAC, poly(diallyl-dimethyl-ammonium chloride); PDMS, poly(dimethylsiloxane); PEG, polyethylene glycol; PEI, polyethyleneimine; PEO, polyethyleneoxide, – (OCH2CH2)n–; PFM, pulsed force mode; PLA, polylactic acid; PMAA, poly(methacrylic acid), –(CH2CHCOOH)n–; PMC, polyelectrolyte microcapsules; PMMA, poly(methyl methacrylate), –(CH2CCH3COOCH3)n–; PP, poly(propylene), – (CH2CHCH3)n–; PS, polystyrene, –(CH2–CH(C6H5))n–; PSD, position sensitive detector; PSS, poly(sodium styrenesulfonate); PSU, polysulfonate; PTFE, poly(tetrafluoroethylene); PVD, physical vapor deposition; PVP, poly(vinylpyridine), – (CH2CHC5NH4)n–; SAM, self-assembled monolayer; SDS, sodium dodecylsulfate; SEDS, solution-enhanced dispersion by supercritical fluids; SEM, scanning electron microscope; SFA, surface forces apparatus; SNOM, scanning near-field optical microscope; STM, scanning tunneling microscope; TEM, transmission electron microscope; TIRM, total internal reflection microscopy; TTAB, tetradecyl trimethylammonium bromide; UHV, ultra-high vacuum; WLC, wormlike chain; XPS, X-ray photoelectron spectroscopy * Corresponding author. E-mail address: [email protected] (B. Cappella). 0167-5729/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.surfrep.2005.08.003 2 H.-J. Butt et al. / Surface Science Reports 59 (2005) 1–152 Nomenclature a contact radius (m) aHertz contact radius in the Hertz theory A area (m2) AH Hamaker constant (J) A1 area between the two contact lines above the axis F =0 A2 area between the retraction contact lines and the axis F =0 b slip length (m) c speed of light in vacuum (2.998 Â 108 m/s), concentration (mol/L) C capacitance of tip and sample (F); constant of the atom–atom pair potential (J m6) 6 CK, CD, CL Keesom, Debye, and London coefficients (J m ) d distance between end of cantilever and PSD D tip–sample distance (m) Djtc tip–sample distance at which the jump-to-contact occurs (m) D0 typical interatomic spacing (m) e unit charge (1.602 Â 10À19 C) E Young’s modulus (Pa) EF, ES Young’ modulus of film and substrate (Pa) Et, Es Young’s modulus of tip and sample material (Pa) Etot reduced Young’s modulus Eq. (4.4) (Pa) f force per unit area (Pa) f* dimensionless correction factor F force (N) Fad adhesion force (N) Fav average force (N) Fcap capillary force (N) Fel double-layer force (N) FH hydrodynamic force (N) Fsurf distance-dependent surface force (N) F0 mean rupture force (N) h Planck’s constant (6.626 Â 10À34 J s); thickness of a film on a substrate (m) H height of tip (m); hardness (Pa) Hd height of a deformed polyelectrolyte microcapsule (m) 3 4 I wtc =12, moment of inertia of a cantilever (m ) IPSD photosensor current (A) J relative Young’ modulus, Eq. (4.12) À23 kB Boltzmann constant (1.381 Â 10 J/K) kc spring constant of cantilever (N/m) keff =kcks/(kc + ks) effective spring constant (N/m) ks sample stiffness (N/m) k0 frequency of spontaneous hole formation (Hz) l length of one segment in a linear polymer (m) H.-J. Butt et al. / Surface Science Reports 59 (2005) 1–152 3 lK Kuhn length (m) lp persistence length (m) L length of cantilever (m) L0 equilibrium thickness of a polymer brush (m) mc mass of the cantilever (g) mM ratio between the contact radius a and an annular region, where the adhesion is taken into account mt mass of the tip (g) m* effective mass of the cantilever (g) n number of carbon atoms in an alkyl chain; number of segments in a linear polymer; parameter; refractive index ni refractive index nav average number of bonds n1 bulk concentration of salt in a solvent (molecules per volume) p permanent plastic deformation (m) p0 intercept between the axis F = 0 and the tangent to the unloading curve for very high loads P pressure (N/m2); probability to find the tip on top of a molecular layer; binding probability Q quality factor of the cantilever r radial distance or distance between molecules (m) rms root mean square roughness (m) R tip radius or radius of microsphere (m) Re Reynolds number Rg radius of gyration of a polymer (m) Rm molecular radius (m) R0 radius of not deformed polyelectrolyte microcapsule s surface stress (N/m) S order parameter; spreading pressure t time (s) tc thickness of the cantilever (m) ts thickness of the shell of a polyelectrolyte capsule T temperature (K) u1, u2 dipole moment of molecules (C m) U potential energy between tip and sample (J) 2 UA potential energy per unit area between two planar, parallel surfaces (J/m ) Uc Hooke’s elastic potential of the cantilever (J) Ucs tip–sample interaction potential (J) Us Hooke’s elastic potential of the sample (J) U0 activation energy (J) v velocity of the tip or particle (m/s) vx fluid velocity parallel to a surface (m/s) v0 vertical scan rate, identical to velocity of the base of the cantilever (m/s) V voltage (V) Vm molar volume of a liquid 4 H.-J. Butt et al. / Surface Science Reports 59 (2005) 1–152 w width of cantilevers (m) wK; wD; wL; wvdW Keesom, Debye, London, and total van der Waals potentials between molecules W work of adhesion at contact per unit area (J/m2) Wad work of adhesion at contact (J) x distance in gap between two planar, parallel walls (m); relative extension of a polymer X horizontal coordinate originating at the base of the cantilever (m) z coordinate normal to a surface (m) Z cantilever deflection (m) at a certain horizontal coordinate Zc deflection of the cantilever at its end (m) (Zc)jtc deflection of the cantilever at the jump to contact (m) Zi valency of ion Zp height position of the piezoelectric translator (m) Z0 amplitude of cantilever vibration (m) Greek letters a opening angle of V-shaped cantilever; endslope of cantilever; parameter in contact theory; immersion angle ai parameters describing the eigenmodes of rectangular cantilevers 2 2 a01, a02 electronic polarizabilities of molecules (C m /J) b, b* correction factor, parameter b1, b2 parameters to describe plastic contact g surface tension of a liquid (N/m) or surface energy gD damping coefficient (kg/s) g0 surface tension of a pure liquid (N/m) gAB acid–base surface energy gLW Lifshitz–van der Waals surface energy g+, gÀ electron acceptor and electron donor components of the acid–base surface energy G surface excess (mol/m2); grafting density (number/m2) Gi imaginary part of the so-called ‘‘hydrodynamic function’’ d indentation (m) dmax maximal indentation (m) DPSD distance the laser spot moves on the PSD (m) e, ei dielectric constant of the medium À12 À1 À1 e0 vacuum permittivity (8.854 Â 10 AsV m ) h viscosity (Pa s) u, ua, ur contact angle (advancing and receding) Q half opening angle of a conical tip W tilt of the cantilever with respect to the horizontal k line tension (N); bending rigidity (J) l Maugis parameter lD Debye length (m) lH Decay length of hydration force (m) li wavelengths of the eigenmodes of rectangular cantilevers H.-J. Butt et al. / Surface Science Reports 59 (2005) 1–152 5 lS Decay length of solvation force (m) m chemical potential (J/mol) n Poisson’s ratio ne mean absorption frequency (Hz) nF, nS Poisson’s ratio of film and substrate (Pa) nt, ns Poisson’s ratio of tip and sample material (Pa) n0 resonance frequency of cantilever (Hz) n1, n2 ionization frequencies (Hz) j relative deformation of a polyelectrolyte microcapsule r density (kg/m3) 3 rf density of fluid surrounding the cantilever (kg/m ) s molecular diameter (m) 2 sS surface charge density of sample in aqueous medium (C/m ) 2 sT surface charge density of tip in aqueous medium (C/m ) 2 2 sF ðsnÞ force variance, number of bonds variance t inverse of vibration frequency (s) w phase c electric potential (V) cP plasticity index, Eq. (4.9) cS electric surface potential of sample in aqueous medium (V) cT electric surface potential of tip in aqueous medium (V) v angular frequency (Hz) v0 angular resonance frequency of the cantilever, v0 =2pn0 (Hz) V frequency factor (number of attempts of the tip to penetrate through a layer) Abstract The atomic force microscope (AFM) is not only a tool to image the topography of solid surfaces at high resolution.
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