Dynamics of a disturbed sessile drop measured by atomic force microscopy (AFM)

A new method for studying the dynamics of a sessile drop by atomic force microscopy (AFM) is demonstrated. A hydrophobic microsphere (radius, r ～ 20-30 μm) is brought into contact with a small sessile water drop resting on a polytetrafluoroethylene (PTFE) surface. When the microsphere touches the liquid surface, the meniscus rises onto it because of capillary forces. Although the microsphere volume is 6 orders of magnitude smaller than the drop, it excites the normal resonance modes of the liquid interface. The sphere is pinned at the interface, whose small (<100 nm) oscillations are readily measured with AFM. Resonance oscillation frequencies were measured for drop volumes between 5 and 200 μL. The results for the two lowest normal modes are quantitatively consistent with continuum calculations for the natural frequency of hemispherical drops with no adjustable parameters. The method may enable sensitive measurements of volume, surface tension, and viscosity of small drops.     

Volume of a nanoscale water bridge

Water bridges formed through capillary condensation at nanoscale contacts first stretch and then break during contact rupture. Atomic force microscopy (AFM) pull-off experiments performed in air with hydrophilic tips and samples show that stretched nanoscopic water bridges are in mechanical equilibrium with the external pull-off force acting at the contact but not in thermodynamic equilibrium with the water vapor in air. The experimental findings are explained by a theoretical model that considers constant water volume and decrease of water meniscus curvature during meniscus stretching. The model predicts that the water bridge breakup distance will be roughly equal to the cubic root of the water bridge volume. A thermodynamic instability was noticed for large water bridges formed at the contact of a blunt AFM tip (curvature radius of 400 nm) with a flat sample. In this case, experiments showed rise and stabilization of the volume of the water at the contact in about 1 s. For sharp AFM tips (curvature radius below 50 nm), the experiments indicated that formation of stable water bridges occurs in a much shorter time (below 5 ms).     

Capillary forces between two spheres with a fixed volume liquid bridge: theory and experiment

Capillary forces are commonly encountered in nature because of the spontaneous condensation of liquid from surrounding vapor, leading to the formation of a liquid bridge. In most cases, the advent of capillary forces by condensation leads to undesirable events such as an increase in the strength of granules, which leads to flow problems and/or caking of powder samples. The prediction and control of the magnitude of capillary forces is necessary for eliminating or minimizing these undesirable events. The capillary force as a function of the separation distance, for a liquid bridge with a fixed volume in a sphere/plate geometry, was calculated using different expressions reported previously. These relationships were developed earlier, either on the basis of the total energy of two solid surfaces interacting through the liquid and the ambient vapor or by direct calculation of the force as a result of the differential gas pressure across the liquid bridge. It is shown that the results obtained using these methodologies (total energy or differential pressure) agree, confirming that a total-energy-based approach is applicable, despite the thermodynamic nonequilibrium conditions of a fixed volume bridge rupture process. On the basis of the formulas for the capillary force between a sphere and a plane surface, equations for the calculation of the capillary force between two spheres are derived in this study. Experimental measurements using an atomic force microscope (AFM) validate the formulas developed. The most common approach for transforming interaction force or energy from that of sphere/plate geometry to that of sphere/sphere geometry is the Derjaguin approximation. However, a comparison of the theoretical formulas derived in this study for the interaction of two spheres with those for sphere/plate geometry shows that the Derjaguin approximation is only valid at zero separation distance. This study attempts to explain the inapplicability of the Derjaguin approximation at larger separation distances. In particular, the area of a liquid bridge changes with the separation distance, H, and thereby does not permit the application of the "integral method," as used in the Derjaguin approximation.     

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.     

Particle-surface capillary forces with disjoining pressure

A new, atomic force microscopy (AFM) based experimental setup for the continuous acquisition of friction force data as a function of humidity has been developed. The current model of interactions between wet contacts under the influence of capillary effects, has been amended to include a vertical component due to the disjoining pressure and takes into account the influence of liquid films adsorbed on the surface. This is a 'switching' model, i.e. the contact between nanometer-sized sphere and a flat surface can exist in two distinct states due to capillary bridge formation/destruction as the humidity is varied. The model has been qualitatively verified on samples of differing wettability produced by UV-ozone treatment of polystyrene (PS). Results of AFM analysis of the friction vs. vapor pressure curves collected from the surface are presented. Correlation between important surface properties such as wettability, adsorption, and contact angle and friction force under varying humidity were found and discussed.     

Micro-wilhelmy and related liquid property measurements using constant-diameter nanoneedle-tipped atomic force microscope probes

The micro-Wilhelmy method is a well-established method of determining surface tension by measuring the force of withdrawing a tens of microns to millimeters in diameter cylindrical wire or fiber from a liquid. A comparison of insertion force to retraction force can also be used to determine the contact angle with the fiber. Given the limited availability of atomic force microscope (AFM) probes that have long constant diameter tips, force-distance (F-D) curves using probes with standard tapered tips have been difficult to relate to surface tension. In this report, constant diameter metal alloy nanowires (referred to as "nanoneedles") between 7.2 and 67 microm in length and 108 and 1006 nm in diameter were grown on AFM probes. F-D and Q damping AFM measurements of wetting and drag forces made with the probes were compared against standard macroscopic models of these forces on slender cylinders to estimate surface tension, contact angle, meniscus height, evaporation rate, and viscosity. The surface tensions for several low molecular weight liquids that were measured with these probes were between -4.2% and +8.3% of standard reported values. Also, the F-D curves show well-defined stair-step events on insertion and retraction from partial wetting liquids, compared to the continuously growing attractive force of standard tapered AFM probe tips. In the AFM used, the stair-step feature in F-D curves was repeatably monitored for at least 0.5 h (depending on the volatility of the liquid), and this feature was then used to evaluate evaporation rates (as low as 0.30 nm/s) through changes in the surface height of the liquid. A nanoneedle with a step change in diameter at a known distance from its end produced two steps in the F-D curve from which the meniscus height was determined. The step features enable meniscus height to be determined from distance between the steps, as an alternative to calculating the height corresponding to the AFM measured values of surface tension and contact angle. All but one of the eight measurements agreed to within 13%. The constant diameter of the nanoneedle also is used to relate viscous damping of the vibrating cantilever to a macroscopic model of Stokes drag on a long cylinder. Expected increases in drag force with insertion depth and viscosity are observed for several glycerol-water solutions. However, an additional damping term (associated with drag of the meniscus on the sidewalls of the nanoneedle) limits the sensitivity of the measurement of drag force for low-viscosity solutions, while low values of Q limit the sensitivity for high-viscosity solutions. Overall, reasonable correspondence is found between the macroscopic models and the measurements with the nanoneedle-tipped probes. Tighter environmental control of the AFM and treatments of needles to give them more ideal surfaces are expected to improve repeatability and make more evident subtle features that currently appear to be present on the F-D and Q damping curves.     

Wetting in the nanoscale: a continuum mechanics approach

A continuum mechanics model has been developed to study the equilibrium shape of nanometric droplets on a planar solid substrate and how, in this scale, the contact angle depends on the drop size. The drop is modeled as a liquid volume enclosed in an inextensible membrane, subject to an isotropic tension (the surface tension) and to a field of surface forces including, in the proximity of the solid, the liquid-to-solid interactions, envisaged as a generic potential force per unit surface directed normally to the solid surface (i.e. vertically). The only conditions required to solve the problem are those of mechanical and thermodynamic equilibrium. The predictions of the model are discussed in comparison with data on nanodrops retrieved by a special AFM device for a number of different liquid–solid systems.     

Parameters ruling capillary forces at the submillimetric scale

This paper reviews the way to compute capillary forces between two solids by numerically integrating the Laplace equation describing the shape of an axially symmetric meniscus at equilibrium. The numerical results of the proposed model have been experimentally validated with a test bed able to measure forces of about 1 mN with an accuracy of about 1 microN. Thanks to the simulation tool and the test bed, the influence of the following parameters has been studied: surface tension, solid geometry, volume of liquid, materials, separation distance between both solids, and surrounding environment. The way to compute the force from a given meniscus geometry has been clarified as far as the "Laplace" and "tension" contributions are concerned.     

Chemical Force Microscopy Study of Adhesion and Friction between Surfaces Functionalized with Self-Assembled Monolayers and Immersed in Solvents

Adhesive and frictional forces between surfaces modified with self-assembled monolayers (SAMs) and immersed in solvents were measured with chemical force microscopy as functions of surface functionality and solvent. Si/SiO2 substrates were modified with SAMs of alkylsiloxanes (SiCl3(CH2)n-X), and gold-coated AFM tips were modified with SAMs of alkylthiolates (HS-(CH2)n-X). SAMs of alkylsiloxanes terminated in a methyl or oxidized vinyl group; SAMs of alkanethiolates terminated in a methyl or carboxyl group. Adhesive and frictional forces were measured in hexadecane, ethanol, 1,2-propanediol, 1,3-propanediol, and water. The work of adhesion (W) was calculated with the Johnson-Kendall-Roberts theory of adhesive contact. The JKR values agreed well with values derived from the Fowkes-van Oss-Chaudhury-Good surface tension model and from contact angle results. Calculated values of W for all combinations of contacting surfaces and solvents spanned two orders of magnitude. W correlated with the surface tension of the solvent for hydrophobic/hydrophobic interactions; hydrophilic/hydrophilic and hydrophobic/hydrophilic interactions were more complex. Friction forces were fit to a modified form of Amonton's law. For any solvent, friction coefficients were largest for the hydrophilic/hydrophilic contacting surfaces. The friction coefficient for any contacting pair was largest in hexadecane. In polar solvents, friction coefficients scaled with solvent polarity only for hydrophobic/hydrophobic contacting pairs. Copyright 1999 Academic Press.     

Prediction of solid-fluid interfacial tension and contact angle

Two simple equations have been developed using the lattice theory and the regular solution assumption to predict the solid-vapor and solid-liquid interfacial tension. The required parameters are the liquid critical temperature and volume, the solid melting temperature and the molar volume of liquid and solid compounds. To confirm the models, the predicted solid-fluid interfacial tension values have been used to predict the contact angle of the liquid drop on the solid surface applying Young's equation. Agreement of the predicted contact angle with the experimental data reveals the reliability of the developed models.     

Measurement of the surface tension of liquid marbles

The capillary rise and Wilhelmy plate methods have been used to study the "surface tension" of water marbles encapsulated with polytetrafluoroethylene (PTFE) powders of 1-, 35-, and 100-μm particle size. With the capillary rise technique, a glass capillary tube was inserted into a water marble to measure the capillary rise of the water. The Laplace pressure exerted by the water marble was directly measured by comparing the heights of the capillary rise from the marble and from a flat water surface in a beaker. An equation based on Marmur's model was proposed to calculate the water marble surface tension. This method does not require the water contact angle with the supporting solid surface to be considered; it is therefore a simple but efficient method for determining liquid marble surface tension. The Wilhelmy method was used to measure the surface tension of a flat water surface covered by PTFE powder. This method offers a new angle for investigating liquid marble shell properties. A discussion on the nature and the realistic magnitude of liquid marble surface tension is offered.     

Effects of gas adsorption isotherm and liquid contact angle on capillary force for sphere-on-flat and cone-on-flat geometries

This paper explains the origin of the vapor pressure dependence of the asperity capillary force in vapor environments. A molecular adsorbate layer is readily formed on solid surface in ambient conditions unless the surface energy of the solid is low enough and unfavorable for vapor adsorption. Then, the capillary meniscus formed around the solid asperity contact should be in equilibrium with the adsorbate layer, not with the bare solid surface. A theoretical model incorporating the vapor adsorption isotherm into the solution of the Young-Laplace equation is developed. Two contact geometries--sphere-on-flat and cone-on-flat--are modeled. The calculation results show that the experimentally-observed strong vapor pressure dependence can be explained only when the adsorption isotherm of the vapor on the solid surface is taken into account. The large relative partial pressure dependence mainly comes from the change in the meniscus size due to the presence of the adsorbate layer.     

Influence of surface topography on the interactions between nanostructured hydrophobic surfaces

Nanostructured particle coated surfaces, with hydrophobized particles arranged in close to hexagonal order and of specific diameters ranging from 30 nm up to 800 nm, were prepared by Langmuir-Blodgett deposition followed by silanization. These surfaces have been used to study interactions between hydrophobic surfaces and a hydrophobic probe using the AFM colloidal probe technique. The different particle coated surfaces exhibit similar water contact angles, independent of particle size, which facilitates studies of how the roughness length scale affects capillary forces (previously often referred to as "hydrophobic interactions") in aqueous solutions. For surfaces with smaller particles (diameter < 200 nm), an increase in roughness length scale is accompanied by a decrease in adhesion force and bubble rupture distance. It is suggested that this is caused by energy barriers that prevent the motion of the three-phase (vapor/liquid/solid) line over the surface features, which counteracts capillary growth. Some of the measured force curves display extremely long-range interaction behavior with rupture distances of several micrometers and capillary growth with an increase in volume during retraction. This is thought to be a consequence of nanobubbles resting on top of the surface features and an influx of air from the crevices between the particles on the surface.     

Cleaning and hydrophilization of atomic force microscopy silicon probes

The silicon surface of commercial atomic force microscopy (AFM) probes loses its hydrophilicity by adsorption of airborne and package-released hydrophobic organic contaminants. Cleaning of the probes by acid piranha solution or discharge plasma removes the contaminants and renders very hydrophilic probe surfaces. Time-of-flight secondary-ion mass spectroscopy and X-ray photoelectron spectroscopy investigations showed that the native silicon oxide films on the AFM probe surfaces are completely covered by organic contaminants for the as-received AFM probes, while the cleaning methods effectively remove much of the hydrocarbons and silicon oils to reveal the underlying oxidized silicon of the probes. Cleaning procedures drastically affect the results of adhesive force measurements in water and air. Thus, cleaning of silicon surfaces of the AFM probe and sample cancelled the adhesive force in deionized water. The significant adhesive force values observed before cleaning can be attributed to formation of a bridge of hydrophobic material at the AFM tip-sample contact in water. On the other hand, cleaning of the AFM tip and sample surfaces results in a significant increase of the adhesive force in air. The presence of water soluble contaminants at the tip-sample contact lowers the capillary pressure in the water bridge formed by capillary condensation at the AFM tip-sample contact, and this consequently lowers the adhesive force.     

Measurement of dynamical forces between deformable drops using the atomic force microscope. I. Theory

Recent experimental developments have enabled the measurement of dynamical forces between two moving liquid drops in solution using an atomic force microscope (AFM). The drop sizes, interfacial tension, and approach velocities used in the experiments are in a regime where surface forces, hydrodynamics, and drop deformation are all significant. A detailed theoretical model of the experimental setup which accounts for surface forces, hydrodynamic interactions, droplet deformation, and AFM cantilever deflection has been developed. In agreement with experimental observations, the calculated force curves show pseudo-constant compliance regions due to drop flattening, as well as attractive pull-off forces due mainly to hydrodynamic lubrication forces.     

Spreading of nanofluids driven by the structural disjoining pressure gradient

This paper discusses the role of the structural disjoining pressure exerted by nanoparticles on the spreading of a liquid film containing these particles. The origin of the structural disjoining pressure in a confined geometry is due to the layering of the particles normal to the confining plane and has already been traced to the net increase in the entropy of the system in previous studies. In a recent paper, Wasan and Nikolov (Nature, 423 (2003) 156) pointed out that the structural component of the disjoining pressure is strong enough to move a liquid wedge; this casts a new light on many applications-most notably, detergency. While the concept of spreading driven by the disjoining pressure is not new, the importance of the structural disjoining pressure arises from its long-range nature (as compared to the van der Waals' force), making it an important component of the overall force balance near the contact line. In this paper, we report on a parametric study of the spreading phenomena by examining the effects of nanoparticle size, concentration and polydispersity on the displacement of an oil-aqueous interface with the aqueous bulk containing nanoparticles. The solution of the extended Laplace-Young equations for the profile of the meniscus yields the position of the nominal contact line under the action of the structural disjoining pressure. Simulations show that the displacement of the contact line is greater with a high nanoparticle volume fraction, small particles for the same volume fraction, monodispersed (in size) particles rather than polydispersed particles and when the resisting capillary pressure is small, i.e., when the interfacial tension is low and/or the radius of the dispersed phase drop/bubble is large.     

Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA)

Axisymmetric drop-shape analysis-no apex (ADSA-NA) is a recent drop-shape method that allows the simultaneous measurement of contact angles and surface tensions of drop configurations without an apex (i.e., a sessile drop with a capillary protruding into the drop). Although ADSA-NA significantly enhanced the accuracy of contact angle and surface tension measurements compared to that of original ADSA using a drop with an apex, it is still not as accurate as a surface tension measurement using a pendant drop suspended from a holder. In this article, the computational and experimental aspects of ADSA-NA were scrutinized to improve the accuracy of the simultaneous measurement of surface tensions and contact angles. It was found that the results are relatively insensitive to different optimization methods and edge detectors. The precision of contact angle measurement was enhanced by improving the location of the contact points of the liquid meniscus with the solid substrate to subpixel resolution. To optimize the experimental design, the capillary was replaced with an inverted sharp-edged pedestal, or holder, to control the drop height and to ensure the axisymmetry of the drops. It was shown that the drop height is the most important experimental parameter affecting the accuracy of the surface tension measurement, and larger drop heights yield lower surface tension errors. It is suggested that a minimum nondimensional drop height (drop height divided by capillary length) of 1.7 is required to reach an error of less than 0.2 mJ/m(2) for the measured surface tension. As an example, the surface tension of water was measured to be 72.46 ± 0.04 at 24 °C by ADSA-NA, compared to 72.39 ± 0.01 mJ/m(2) obtained with pendant drop experiments.     

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.     

Filling kinetics of liquids in nanochannels as narrow as 27 nm by capillary force

We report the filling kinetics of different liquids in nanofabricated capillaries with rectangular cross-section by capillary force. Three sets of channels with different geometry were employed for the experiments. The smallest dimension of the channel cross-section was respectively 27, 50, and 73 nm. Ethanol, isopropanol, water and binary mixtures of ethanol and water spontaneously filled nanochannels with inner walls exposing silanol groups. For all the liquids the position of the moving liquid meniscus was observed to be proportional to the square root of time, which is in accordance with the classical Washburn kinetics. The velocity of the meniscus decreased both with the dimension of the channel and the ratio between the surface tension and the viscosity. In the case of water, air-bubbles were spontaneously trapped as channels were filled. For a binary mixture of 40% ethanol and water, no trapping of air was observed anymore. The filling rate was higher than expected, which also corresponds to the dynamic contact angle for the mixture being lower than that of pure ethanol. Nanochannels and porous materials share many physicochemical properties, e.g., the comparable pores size and extremely high surface to volume ratio. These similarities suggest that our nanochannels could be used as an idealized model to study mass transport mechanisms in systems where surface phenomena dominate.     

Wetting force measurements on single fibers

Wilhelmy-type wetting force measurements utilizing sensitive instrumentation are being used more and more to quantify the surface energetics of solids generally, and of filaments in particular. This report describes a recommended methodology for such measurements. It is shown that, under certain conditions, advancing and receding contact angles can be obtained from wetting force measurements alone without the need for independent determinations of specimen perimeter or liquid surface tension. Factors that may complicate or interfere with such contact angle determinations are discussed, including corrections for buoyancy, limitations on the magnitude of the contact angle, and specimen geometry requirements. Experiments demonstrating the use, reproducibility, and sensitivity of the methodology are summarized.