Quantitative force microscopy from a dynamic point of view

We discuss the physical origin and measurement of force between an atomic force microscope tip and a soft material surface. Quasi-static and dynamic measurements are contrasted and similarities are revealed by analyzing the dynamics in the frequency domain. Various dynamic methods using single and multiple excitation frequencies are described. Tuned multifrequency lockin detection with one reference oscillation gives a great deal of information from which one can reconstruct the tip–surface interaction. Intermodulation in a weakly perturbed high Q resonance enables the measurement of a new type of dynamic force curve, offering a physically intuitive way to visualize both elastic and viscous forces.     

Role of hydration force in the self-assembly of collagens and amyloid steric zipper filaments

In protein self-assembly, types of surfaces determine the force between them. Yet the extent to which the surrounding water contributes to this force remains as a fundamental question. Here we study three self-assembling filament systems that respectively have hydrated (collagen), dry nonpolar, and dry polar (amyloid) interfaces. Using molecular dynamics simulations, we calculate and compare local hydration maps and hydration forces. We find that the primary hydration shells are formed all over the surface, regardless of the types of the underlying amino acids. The weakly oscillating hydration force arises from coalescence and depletion of hydration shells as two filaments approach, whereas local water diffusion, orientation, or hydrogen-bonding events have no direct effect. Hydration forces between hydrated, polar, and nonpolar interfaces differ in the amplitude and phase of the oscillation relative to the equilibrium surface separation. Therefore, water-mediated interactions between these protein surfaces, ranging in character from "hydrophobic" to "hydrophilic", have a common molecular origin based on the robustly formed hydration shells, which is likely applicable to a broad range of biomolecular assemblies whose interfacial geometry is similar in length scale to those of the present study.     

Effect of solution concentration, surface bias and protonation on the dynamic response of amplitude-modulated atomic force microscopy in water

The dynamic response of amplitude-modulated atomic force microscopy (AM-AFM) is studied at the solid/water interface with respect to changes in ionic concentration, applied surface potential, and surface protonation. Each affects the electric double layer in the solution, charge on the tip and the sample surface, and thus the forces affecting the dynamic response. A theoretical model is developed to relate the effective stiffness and hydrodynamic damping of the AFM cantilever that is due to the tip/surface interaction with the phase and amplitude signals measured in the AM-AFM experiments. The phase and amplitude of an oscillating cantilever are measured as a function of tip-sample distance in three experiments: mica surface in potassium nitrate solutions with different concentrations, biased gold surface in potassium nitrate solution, and carboxylic acid-terminated self-assembled monolayers (SAMs) on gold in potassium nitrate pH buffers. Results show that, over the range where the higher harmonic modes of the oscillation are negligible, the effective stiffness of the AFM cantilever increases to a maximum as the tip approaches the surface before declining again as a result of the repulsive electrical double layer interaction. For attractive electrical double-layer interactions, the effective stiffness declines monotonically as the tip approaches the surface. Similarly, the hydrodynamic damping of the tip increases and then decreases as the tip approaches the solid/water interface, with the magnitude depending on the species present in the solution.     

Chemical force spectroscopy in heterogeneous systems: intermolecular interactions involving epoxy polymer,mixed monolayers,and polar solvents

We used chemical force microscopy (CFM) to study adhesive forces between surfaces of epoxy resin and self-assembled monolayers (SAMs) capable of hydrogen bonding to different extents. The influence of the liquid medium in which the experiments were carried out was also examined systematically. The molecular character of the tip, polymer, and liquid all influenced the adhesion. Complementary macroscopic contact angle measurements were used to assist in the quantitative interpretation of the CFM data. A direct correlation between surface free energy and adhesion forces was observed in mixed alcohol-water solvents. An increase in surface energy from 2 to 50 mJ/m(2) resulted in an increase in adhesion from 4-8 nN to 150-300 nN for tips with radii of 50-150 nm. The interfacial surface energy for identical nonpolar surface groups of SAMs was found not to exceed 2 mJ/m(2). An analysis of adhesion data suggests that the solvent was fully excluded from the zone of contact between functional groups on the tip and sample. With a nonpolar SAM, the force of adhesion increased monotonically in mixed solvents of higher water content; whereas, with a polar SAM (one having a hydrogen bonding component), higher water content led to decreased adhesion. The intermolecular force components theory was used for the interpretation of adhesion force measurements in polar solvents. Competition between hydrogen bonding within the solvent and hydrogen bonding of surface groups and the solvent was shown to provide the main contribution to adhesion forces. We demonstrate how the trends in the magnitude of the adhesion forces for chemically heterogeneous systems (solvents and surfaces) measured with CFM can be quantitatively rationalized using the surface tension components approach. For epoxy polymer, inelastic deformations also contributed heavily to measured adhesion forces.     

Adhesion forces in liquid media: effect of surface topography and wettability

This work was motivated by the unexpected values of adhesion forces measured between an atomic force microscopy tip and the hydrophobic surface of ultra-high-molecular-weight polyethylene. Two types of samples with different roughness but similar wettability were tested. Adhesion forces of similar magnitude were obtained in air and in polar liquids (water and Hank's Balanced Salt Solution, a saline solution) with the rougher sample. In contrast, the adhesion forces measured on the smoother sample in air were much higher than those measured in water or in the aqueous solution. Those experimental results suggested the presence of nanobubbles at the interface between the rough sample and the polar liquids. The existence of the nanobubbles was further confirmed by the images of the interface obtained in noncontact tapping mode. The adhesion forces measured in a nonpolar liquid (hexadecane) were small and of the same order of magnitude for both samples and their values were in good agreement with the predictions of the London-Hamaker approach for the van der Waals interactions. Finally, we correlate the appearance of nanobubbles with surface topography. The conclusion of this work is that adhesion forces measured in aqueous media may be strongly affected by the presence of nanobubbles if the surface presents topographical accidents.     

Molecular dynamics simulation of nanocolloidal amorphous silica particles: Part I

Explicit molecular dynamics simulations were applied to a pair of amorphous silica nanoparticles in aqueous solution, with diameter of 4.4 nm and with four different background electrolyte concentrations, to extract the mean force acting between the two silica nanoparticles. Dependences of the interparticle forces on the separation and the background electrolyte concentration were demonstrated. The nature of the interaction of the counterions with charged silica surface sites (deprotonated silanols) was investigated. A "patchy" double layer of adsorbed sodium counterions was observed. Dependences of the interparticle potential of mean force on the separation and the background electrolyte concentration were demonstrated. Direct evidence of the solvation forces is presented in terms of changes of the water ordering at the surfaces of the isolated and double nanoparticles. The nature of the interaction of the counterions with charged silica surface sites (deprotonated silanols) was investigated in terms of quantifying the effects of the number of water molecules separately inside each pair of nanoparticles by defining an impermeability measure. A direct correlation was found between the impermeability (related to the silica surface "hairiness") and the disruption of water ordering. Differences in the impermeability between the two nanoparticles are attributed to differences in the calculated electric dipole moment.     

Adhesion of spherical polyelectrolyte brushes on mica: an in situ AFM investigation

We demonstrate that the adsorption of cationic spherical polyelectrolyte brushes (SPB) on negatively charged mica substrates can be controlled in situ by the ionic strength of the suspension. The SPB used in our experiments consist of colloidal core particles made of polystyrene. Long cationic polyelectrolyte chains are grafted onto these cores that have diameters in the range of 100 nm. These particles are suspended in aqueous solution with a fixed ionic strength. Atomic force microscopy (AFM) in suspension as well as in air was used for surface characterization. In pure water the polymer particles exhibit a strong adhesion to the mica surface. AFM investigations of the dry samples show that the particles occupy the identical positions as they did in liquid. They were not removed by the capillary forces within the receding water front during the drying process. The strong interaction between the particles and the mica surface is corroborated by testing the adhesion of individual particles on the dried surface by means of the AFM tip: after a stepwise increase of the force applied to the surface by the AFM tip, the polymer particles still were not removed from the surface, but they were cut through and remained on the substrate. Moreover, in situ AFM measurements showed that particles which adsorb under liquid in a stable manner are easily desorbed from the surface after electrolyte is added to the suspension. This finding is explained by a decreasing attractive particle-substrate interaction, and the removal of the particles from the surface is due to the significant reduction of the activation barrier of the particle desorption. All findings can be explained in terms of the counterion release force.     

Attractive surface force in the presence of dissolved gas: a molecular approach

Despite widespread evidence of the influence of dissolved air on hydrophobic interaction, the mechanisms of observed effects are still unknown. Although some experiments indicate that adsorbed gases can modify the structure of water next to hydrophobic surfaces, gas effects on measured forces have been observed only at large surface separations. Gas-specific depletion of water at a hydrophobic surface has been detected but was not reproduced in subsequent measurements. We use computer simulations to study short-ranged hydrophobic attraction in the absence and presence of dissolved gas and monitor gas adsorption at molecular resolution inaccessible in experiments. Although we observe a significant accumulation of dissolved gases at hydrophobic surfaces, even in supersaturated gas solutions surface concentrations remain too low to induce any significant change in the local structure of water and short-range surface forces. We present direct calculations of the hydrophobic force between model hydrocarbon plates at separations between 1.5 and 4 nm. Although stronger, the calculated solvation force has a similar decay rate as deduced from recent surface force apparatus measurements at a somewhat lower contact angle. Within the statistical uncertainty, short-range attraction is not affected by the presence of dissolved nitrogen, even in supersaturated solution with a gas fugacity as high as 30 atm. Comparisons of the adsorption behavior of N2, O2, CO2, and Ar reveal similar features in contrast to the peculiar suppression of water depletion reported for an Ar solution in a neutron reflectivity experiment. Our calculations reveal a notable difference between pathways to the capillary evaporation of pure water and gas-phase nucleation in confined supersaturated gas solutions.     

Transport mechanisms in capillary condensation of water at a single-asperity nanoscopic contact

Transport mechanisms involved in capillary condensation of water menisci in nanoscopic gaps between hydrophilic surfaces are investigated theoretically and experimentally by atomic force microscopy (AFM) measurements of capillary force. The measurements showed an instantaneous formation of a water meniscus by coalescence of the water layers adsorbed on the AFM tip and sample surfaces, followed by a time evolution of meniscus toward a stationary state corresponding to thermodynamic equilibrium. This dynamics of the water meniscus is indicated by time evolution of the meniscus force, which increases with the contact time toward its equilibrium value. Two water transport mechanisms competing in this meniscus dynamics are considered: (1) Knudsen diffusion and condensation of water molecules in the nanoscopic gap and (2) adsorption of water molecules on the surface region around the contact and flow of the surface water toward the meniscus. For the case of very hydrophilic surfaces, the dominant role of surface water transportation on the meniscus dynamics is supported by the results of the AFM measurements of capillary force of water menisci formed at sliding tip-sample contacts. These measurements revealed that fast movement of the contact impedes on the formation of menisci at thermodynamic equilibrium because the flow of the surface water is too slow to reach the moving meniscus.     

Influence of attractive force on imaging micro‐droplets of water by atomic force microscope

The shape of micro‐droplets of water on a pure copper surface was investigated using the a.c. non‐contact mode of an atomic force microscope (AFM) by applying different attractive forces between the cantilever tip and the liquid surface. The forces largely influenced the observed radii of micro‐droplets; the influence can be reduced significantly by reducing the force. The same attractive force between the cantilever tip and the micro‐droplets is necessary when comparing the contact angles of micro‐droplets on different surfaces. Furthermore, the values of the contact angles of the micro‐droplets should be the average of those on at least four sides of the droplets. Copyright © 2005 John Wiley & Sons, Ltd.     

Probing colloidal forces between a Si3N4 AFM tip and single nanoparticles of silica and alumina

The atomic force microscope (AFM) has been used to measure surface forces between silicon nitride AFM tips and individual nanoparticles deposited on substrates in 10(-4) and 10(-2) M KCl solutions. Silica nanoparticles (10 nm diameter) were deposited on an alumina substrate and alumina particles (5 to 80 nm diameter) were deposited on a mica substrate using aqueous suspensions. Ionic concentrations and pH were used to manage attractive substrate-particle electrostatic forces. The AFM tip was located on deposited nanoparticles using an operator controlled offset to achieve stepwise tip movements. Nanoparticles were found to have a negligible effect on long-range tip-substrate interactions, however, the forces between the tip and nanoparticle were detectable at small separations. Exponentially increasing short-range repulsive forces, attributed to the hydration forces, were observed for silica nanoparticles. The effective range of hydration forces was found to be 2-3 nm with the decay length of 0.8-1.3 nm. These parameters are in a good agreement with the results reported for macroscopic surfaces of silica obtained using the surface force apparatus suggesting that hydration forces for the silica nanoparticles are similar to those for flat silica surfaces. Hydration forces were not observed for either alumina substrates or alumina nanoparticles in both 10(-4) M KCl solution at pH 6.5 and 10(-2) M KCl at pH 10.2. Instead, strong attractive forces between the silicon nitride tip and the alumina (nanoparticles and substrate) were observed.     

Dynamic simulations of adhesion and friction in chemical force microscopy

A hybrid molecular simulation approach has been applied to investigate dynamic adhesion and friction between a chemical force microscope (CFM) tip and a substrate, both modified by self-assembled monolayers (SAMs) with hydrophobic methyl (CH(3)) or hydrophilic hydroxyl (OH) terminal groups. The method combines a dynamic model for the CFM tip-cantilever system and a molecular dynamics (MD) relaxation technique for SAMs on Au(111) at room temperature. The hybrid simulation method allows one to simulate force-distance curves (or adhesion) and friction loops (or friction coefficient) in the CFM on the experimental time scale for the first time. The simulation results also provide valuable molecular information at the interface that is not accessible in CFM experiments, such as the actual tip position with respect to the cantilever support position, molecular and hydrogen-bonding structures at the interface, and load distributions among different molecular chains (or single-molecule forces). Results show that the adhesion force and friction coefficient for the OH/OH contact pair are much larger than those for the CH(3)/CH(3) pair due to the formation of hydrogen bonds. During the retraction of a CFM tip from a surface, the CFM tip is away from the sample surface slightly while the spring undergoes dramatic elongation in the normal direction before rupture occurs. Single-molecule forces are distributed unevenly at the contact area. Surface energies calculated for functionalized surfaces compare well with those determined by experiments.     

Forces between surfaces in liquids

The results and implications of direct force measurements between molecularly smooth mica surfaces in liquids are reviewed. These discussions include four interactions fundamental to colloid science: van der Waals forces, double layer forces, adhesion forces and structural or solvation forces (e.g. hydration forces). Also considered are the effects of preferential surface adsorption of solute molecules on these interactions, e.g. surfactant adsorptions from aqueous solutions and water condensation from non-aqueous solvents.In aqueous media it is apparent that the DLVO theory is valid at all surface separations down to the “force barrier”, but that under certain conditions hydration forces can become significant at distances below 30 Å.The measured adhesion force between two solid surfaces can be simply related to their surface energies and where meniscus forces are also present due to “capillary condensation” from vapor solvent, their effect on adhesion can be understood in terms of straightforward bulk thermodynamic principles. Here, too, it is concluded that structural forces cannot be ignored.Our results suggest that structural forces may either very monotonically with distance or be oscillatory with a periodicity equal to the molecular size. Their origin, nature, mode of action and importance for particle interactions will no doubt take many years to sort out.     

Direct measurements of the interaction between pyrene and graphite in aqueous media by single molecule force spectroscopy: understanding the pi-pi interactions

Pyrene derivatives can absorb onto the surface of carbon nanotubes and graphite particles through pi-pi interactions to functionalize these inorganic building blocks with organic surface moieties. Using single molecule force spectroscopy, we have demonstrated the first direct measurement of the interaction between pyrene and a graphite surface. In particular, we have connected a pyrene molecule onto an AFM tip via a flexible poly(ethylene glycol) (PEG) chain to ensure the formation of a molecular bridge. The pi-pi interaction between pyrene and graphite is thus indicated to be approximately 55 pN with no hysteresis between the desorption and adhesion forces.     

Nanoscale repulsive forces between mica and silica surfaces in aqueous solutions

Nanoscale repulsive forces between mineral surfaces in aqueous solutions were measured for the asymmetric mica-silica system. The force measured with an atomic force microscope (AFM) has universal character in the short range, less than ～1 nm or about 3-4 water molecules, independent of solution conditions, that is, electrolyte ion (Na, Ca, Al), concentration (10(-6)-10(-2)M), and pH (3.9-8.2). Notably, the force is essentially the same as for the glass-silica system. Single force curves for a mica-silica system in a 10(-4)M aqueous NaCl solution at pH ～ 5.1 show oscillations with a period of about 0.25 nm, roughly the diameter of a water molecule, a consequence of a layer-by-layer dehydration of the surfaces when pushed together. This result provides additional support to the idea that nanoscale repulsive forces between mineral surfaces in aqueous solutions arise from a surface-induced water effect; the water between two mineral plates that are pushed together becomes structured and increasingly anchored to the surface of the plates by the creation of a hydrogen-bonding network that prevents dehydration of the surfaces.     

Measurement of polyamide and polystyrene adhesion with coated-tip atomic force microscopy

This work presents atomic force microscopy (AFM) measurements of adhesion forces between polyamides, polystyrene and AFM tips coated with the same materials. The polymers employed were polyamide 6 (PA6), PA66, PA12 and polystyrene (PS). All adhesion forces between the various unmodified or modified AFM tips and the polymer surfaces were in the range -1.5 to -8 nN. The weakest force was observed for an unmodified AFM tip with a PS surface and the strongest was between a PS-coated tip and PS surface. The results point to both the benefits and drawbacks of coated-tip AFM force-distance measurements. Adhesion forces between the two most dissimilar (PA6-PS and PA66-PS) materials were significantly asymmetric, e.g., the forces were different depending on the relative placement of each polymer on the AFM tip or substrate. Materials with similar chemistry and intermolecular interactions yielded forces in close agreement regardless of placement on tip or substrate. Using experimental forces, we calculated the contact radii via four models: Derjaguin, Muller, and Toporov; Johnson, Kendall, and Roberts; parametric tip-force-distance relation; and a square pyramid-flat surface (SPFS) model developed herein. The SPFS model gave the most reasonable contact tip radius estimate. Hamaker constants calculated from the SPFS model using this radius agreed in both magnitude and trends with experiment and Lifshitz theory.     

Conformation of poly(styrene sulfonate) layers physisorbed from high salt solution studied by force measurements on two different length scales

The conformation of poly(styrene sulfonate) (PSS) layers physisorbed from 1 M NaCl is determined by force measurements and imaging on two length scales. With colloidal probe technique steric forces as predicted for neutral grafted brushes are observed. On decrease and increase of the NaCl concentration, the grafting density remains constant, yet the brush thickness swells and shrinks reversibly with the salt concentration with an exponent of -0.3. At low salt conditions, the brush length amounts to 30% of the contour length, a behavior known for polyelectrolyte brushes and attributed to the entropy of the counterions trapped in the brush. Between a PSS layer and a pure colloidal silica sphere, the same steric forces are observed, and additionally at large separations (beyond the range of the steric repulsion) an electrostatic force is found. A negatively charged AFM tip penetrates the brush--a repulsive electrostatic force between the tip and surface is found, and single chains can be imaged. Thus, with the nanometer-sized AFM tip, the flatly adsorbed fraction of the PSS chains is seen, whereas the micrometer-sized colloidal probe interacts with the fraction of the chains penetrating into solution.     

In situ hydrodynamic lateral force calibration of AFM colloidal probes

Lateral force microscopy (LFM) is an application of atomic force microscopy (AFM) to sense lateral forces applied to the AFM probe tip. Recent advances in tissue engineering and functional biomaterials have shown a need for the surface characterization of their material and biochemical properties under the application of lateral forces. LFM equipped with colloidal probes of well-defined tip geometries has been a natural fit to address these needs but has remained limited to provide primarily qualitative results. For quantitative measurements, LFM requires the successful determination of the lateral force or torque conversion factor of the probe. Usually, force calibration results obtained in air are used for force measurements in liquids, but refractive index differences between air and liquids induce changes in the conversion factor. Furthermore, in the case of biochemically functionalized tips, damage can occur during calibration because tip-surface contact is inevitable in most calibration methods. Therefore, a nondestructive in situ lateral force calibration is desirable for LFM applications in liquids. Here we present an in situ hydrodynamic lateral force calibration method for AFM colloidal probes. In this method, the laterally scanned substrate surface generated a creeping Couette flow, which deformed the probe under torsion. The spherical geometry of the tip enabled the calculation of tip drag forces, and the lateral torque conversion factor was calibrated from the lateral voltage change and estimated torque. Comparisons with lateral force calibrations performed in air show that the hydrodynamic lateral force calibration method enables quantitative lateral force measurements in liquid using colloidal probes.     

Generation of nanostructures of mica supported lysozyme molecules in aqueous solution by atomic force microscopy

Nanostructures of lysozyme molecules adsorbed to mica were generated by the tip of an atomic force microscope in contact, tapping, and force-distance mode in aqueous solution. In contact mode at high ionic strength and adjusted lysozyme concentration a monolayer of defined pattern and orientation could be formed by the scan process of the tip. A lysozyme monolayer with minimal pattern size of about 60 nm was achieved by line scan. At larger loading forces besides a monolayer also 3D-aggregates of lysozyme molecules could be generated. In force-distance mode the volume of 3D-aggregates grows with increasing generation time, lysozyme concentration in the bulk phase, loading force, and frequency of up- and down-movement of the substrate toward the fixed cantilever. In tapping mode 3D-aggregates could be generated as well. It is postulated that reduction of electrostatic interaction between the oppositely charged lysozyme molecules and mica surface by sufficient high ionic strength is essential for monolayer formation. It is discussed that for the underlying mechanism of monolayer generation in contact mode lysozyme molecules of the bulk phase adsorb to the tip, become pulled off and attach to the mica surface by the scan process of the tip.     

Changes in the interaction characteristics of polyelectrolyte complex covered silica surfaces

The adsorption of polyelectrolyte complexes, PEC, made from the cationic poly (diallyldimethylammonium) chloride (PDADMAC) and the anionic maleic acid-co-propene copolymer (MA-P) on a Si-wafer surface has been studied. The application of highly diluted colloidally dispersed PEC solutions led to the deposition of single PEC particles onto the surface of the Si-wafer. The interaction forces of the heterogeneously covered surface were monitored by direct force measurements with an atomic force microscope (AFM) in the force volume mode. On the surface of a single PEC particle drastic changes in the interaction forces were found in comparison with the unmodified Si-wafer: in all force vs. distance curves a strong increase of the adhesion was measured that can be attributed to the formation of electrostatic bonds between the negatively charged Si₃N₄-tip and the cationic excess charge of the PEC. Additionally, the behavior during approach of both surfaces has been distinct: at pH 6.1 we see a long range electrostatic attraction between the tip and the PEC particle. The attraction becomes even stronger at pH 4.1, because of an increased positive net charge. Generally, a heterogeneous surface with a wide variety of interaction features can be created by the adsorption of PEC particles.