Forces between two oil drops in aqueous solution measured by AFM

The surface and hydrodynamic forces between individual oil droplets in solution can provide insight into both emulsion stability and processes such as drop coalescence in liquid-liquid extraction. We present the first measurements of the interaction forces between alkane droplets in aqueous solution using atomic force microscopy. The radii of the droplets were well below the capillary lengths for the system, thus gravity effects are negligible, and interfacial tension and interaction forces governed the system behavior. The effects of modulating electrostatic double-layer interactions and interfacial tension through the presence of an anionic surfactant are demonstrated. Challenges in interpretation of the force data due to drop deformation are also discussed. A range of drop approach and retract speeds was used to determine the regime where hydrodynamic drainage effects had significant impact on the measurement.     

Elastic deformation during dynamic force measurements in viscous fluids

Understanding and harnessing the coupling between lubrication pressure and elasticity provides materials design strategies for applications such as adhesives, coatings, microsensors, and biomaterials. Elastic deformation of compliant solids caused by viscous forces can also occur during dynamic force measurements in instruments such as the surface forces apparatus (SFA) or the atomic force microscope (AFM). We briefly review hydrodynamic interactions in the presence of soft, deformable interfaces in the lubrication limit. More specifically, we consider the scenario of two surfaces approaching each other in a viscous fluid where one or both surfaces is deformable, which is also relevant to many force measurement systems. In this article the basic theoretical background of the elastohydrodynamic problem is detailed, followed by a discussion of experimental validation and considerations, especially for the role of elastic deformation on surface forces measurements. Finally, current challenges to our understanding of soft hydrodynamic interactions, such as the consideration of substrate layering, poroelasticity, viscoelasticity, surface heterogeneity, as well as their implications are discussed.     

Measurement and analysis of forces in bubble and droplet systems using AFM

The use of atomic force microscopy to measure and understand the interactions between deformable colloids - particularly bubbles and drops - has grown to prominence over the last decade. Insight into surface and structural forces, hydrodynamic drainage and coalescence events has been obtained, aiding in the understanding of emulsions, foams and other soft matter systems. This article provides information on experimental techniques and considerations unique to performing such measurements. The theoretical modelling frameworks which have proven crucial to quantitative analysis are presented briefly, along with a summary of the most significant results from drop and bubble AFM measurements. The advantages and limitations of such measurements are noted in the context of other experimental force measurement techniques.     

Deformation and motion of a charged conducting drop in a dielectric liquid under a nonuniform electric field

As a tool for transporting a drop inside another fluid, a charged conducting drop driven by Coulombic force is considered. Specifically, deformation and motion of a charged conducting drop under nonuniform electric fields are studied using the perturbation method. For simplicity in analysis, the applied electric field is assumed to be expressed as the sum of a uniform field and a linear field and the flow is assumed to be in the Stokes flow range. The deformed drop shape due to electrical stress is computed to the first order of the electrical Weber number (W). Then the electric force and the hydrodynamic drag are computed to derive the formula of the translation velocity, which is valid up to O(W). Several important results have also been obtained for the effect of drop deformation on the electric and hydrodynamic forces exerted on the drop.     

Theory of non-equilibrium force measurements involving deformable drops and bubbles

Over the past decade, direct force measurements using the Atomic Force Microscope (AFM) have been extended to study non-equilibrium interactions. Perhaps the more scientifically interesting and technically challenging of such studies involved deformable drops and bubbles in relative motion. The scientific interest stems from the rich complexity that arises from the combination of separation dependent surface forces such as Van der Waals, electrical double layer and steric interactions with velocity dependent forces from hydrodynamic interactions. Moreover the effects of these forces also depend on the deformations of the surfaces of the drops and bubbles that alter local conditions on the nanometer scale, with deformations that can extend over micrometers. Because of incompressibility, effects of such deformations are strongly influenced by small changes of the sizes of the drops and bubbles that may be in the millimeter range. Our focus is on interactions between emulsion drops and bubbles at around 100 μm size range. At the typical velocities in dynamic force measurements with the AFM which span the range of Brownian velocities of such emulsions, the ratio of hydrodynamic force to surface tension force, as characterized by the capillary number, is ~ 10^{− 6} or smaller, which poses challenges to modeling using direct numerical simulations. However, the qualitative and quantitative features of the dynamic forces between interacting drops and bubbles are sensitive to the detailed space and time-dependent deformations. It is this dynamic coupling between forces and deformations that requires a detailed quantitative theoretical framework to help interpret experimental measurements. Theories that do not treat forces and deformations in a consistent way simply will not have much predictive power. The technical challenges of undertaking force measurements are substantial. These range from generating drop and bubble of the appropriate size range to controlling the physicochemical environment to finding the optimal and quantifiable way to place and secure the drops and bubbles in the AFM to make reproducible measurements. It is perhaps no surprise that it is only recently that direct measurements of non-equilibrium forces between two drops or two bubbles colliding in a controlled manner have been possible. This review covers the development of a consistent theory to describe non-equilibrium force measurements involving deformable drops and bubbles. Predictions of this model are also tested on dynamic film drainage experiments involving deformable drops and bubbles that use very different techniques to the AFM to demonstrate that it is capable of providing accurate quantitative predictions of both dynamic forces and dynamic deformations. In the low capillary number regime of interest, we observe that the dynamic behavior of all experimental results reviewed here are consistent with the tangentially immobile hydrodynamic boundary condition at liquid–liquid or liquid–gas interfaces. The most likely explanation for this observation is the presence of trace amounts of surface-active species that are responsible for arresting interfacial flow.     

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.     

Reliable measurements of interfacial slip by colloid probe atomic force microscopy. II. Hydrodynamic force measurements

Here we report a new study on the boundary conditions for the flow of a simple liquid in a confined geometry obtained by measuring hydrodynamic drainage forces with colloid probe atomic force microscopy (AFM). In this work, we provide experimental data obtained using a best practice experimental protocol and fitted with a new theoretical calculation (Zhu, L.; Attard, P.; Neto, C. Langmuir 2010, submitted for publication, preceding paper). We investigated the hydrodynamic forces acting on a silica colloid probe approaching a hydrophobized silicon surface in a single-component viscous Newtonian liquid (di-n-octylphthalate), a partially wetting system. The measured average slip lengths were in the range of 24-31 nm at approach velocities of between 10 and 80 μm/s. Using our experimental approach, the presence of nanoparticle contaminants in the system can be indentified, which is important because it has been shown that nanoparticles lead to a large apparent slip length. Under our stringent control of experimental conditions, the measurement of the slip length is reproducible and independent of the spring constant of the cantilever.     

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.     

Direct measurement of depletion and hydrodynamic forces in solutions of a reversible supramolecular polymer

In this paper, the investigation of surface forces in semidilute solutions of a nonadsorbing hydrogen-bonded reversible supramolecular polymer is described. Colloidal probe atomic force microscopy was used for direct measurement of depletion forces. Hydrodynamic drag on the AFM cantilever with the colloidal probe was measured both far away from and close to the planar substrate surface. The results indicate that the presence of the depletion layer causes slip at the surfaces with a large apparent slip length. Our analysis explains how the presence of slip enables the measurement of (relatively weak) depletion forces in solutions with a high viscosity by significantly reducing the hydrodynamic forces. The range and magnitude of the measured depletion forces are qualitatively in agreement with previous experiments and theoretical predictions. Due to the relatively large experimental error, no quantitative conclusions can be drawn. Depletion-induced phase separation of suspensions of stearylated silica particles was also observed. Phase separation becomes more pronounced with increasing polymer concentration.     

Microdrops on atomic force microscope cantilevers: evaporation of water and spring constant calibration

The evaporation of water drops with radii approximately 20 microm was investigated experimentally by depositing them onto atomic force microscope (AFM) cantilevers and measuring the deflection versus time. Because of the surface tension of the liquid, the Laplace pressure inside the drop, and the change of interfacial stress at the solid-liquid interface, the cantilever is deflected by typically a few hundred nanometers. The experimental results are in accordance with an analytic theory developed. The evaporation process could be monitored with high accuracy even at the last stage of evaporation because (1) cantilever deflections can be measured with nanometer resolution and (2) the time resolution, given by the inverse of the resonance frequency of the cantilever of approximately 0.3 ms, is much faster than the typical evaporation time of 1 s. Experimental results indicate that evaporation of the last thin layer of water is significantly slower than the rest of the drop, which can be due to surface forces. This drop-on-cantilever system can also be used to analyze the drop impact dynamics on a surface and to determine the spring constant of cantilevers.     

Coupled electrostatic, hydrodynamic, and mechanical properties of bacterial interfaces in aqueous media

The interactions of bacteria with their environment are governed by a complex interplay between biological and physicochemical phenomena. The main challenge is the joint determination of the intertwined interfacial characteristics of bacteria such as mechanical and hydrodynamic softness, interfacial heterogeneity, and electrostatic properties. In this study, we have combined electrokinetics and force spectroscopy to unravel this intricate coupling for two types of Shewanella bacterial strains that vary according to the nature of their outer, permeable, charged gel-like layers. The theoretical interpretation of the bacterial electrokinetic response allows for the estimation of the hydrodynamic permeability, degree of interfacial heterogeneity, and volume charge density for the soft layer that constitutes the outer permeable part of the bacteria. Additionally, the electrostatic interaction forces between an AFM probe and the bacteria were calculated on the basis of their interfacial properties obtained from advanced soft particle electrokinetic analysis. For both bacterial strains, excellent agreement between experimental and theoretical force curves is obtained, which highlights the necessity to account for the interfacial heterogeneity of the bioparticle to interpret AFM and electrokinetic data consistently. From the force profiles, we also derived the relevant mechanical parameters in relation to the turgor pressure within the cell and the nature of the bacterial outer surface layer. These results corroborate the heterogeneous representation of the bacterial interface and show that the decrease in the turgor pressure of the cell with increasing ionic strength is more pronounced for bacteria with a thin surface gel-like layer.     

Simultaneous measurement of structural and hydrodynamic forces between colloidal surfaces in complex fluids

An AFM study was performed to measure the effect of approach/retraction speed on the interaction force between a colloidal particle and a flat substrate in aqueous solutions containing silica nanospheres at concentrations of 4.5 and 6.5 vol.%. The total force consisted of contributions of electrostatic, depletion, structural and hydrodynamic forces. The hydrodynamic component of the force could be isolated by comparing the force profiles measured upon approach and retraction. It was found that when the hydrodynamic component was subtracted from the total force, the resulting force profiles measured at scan speeds of 80, 800, 2400, 4800 and 11,200 nm/s all overlaid, indicating that the surface forces (electrostatic, depletion and structural) were not affected by the scan speed. This result was further supported by an approximation of the rates of viscous and diffusive motion in the gap region. In addition, the variation of the hydrodynamic force with particle/plate separation distance agreed relatively well with a prediction made using the mobility correction factor developed for simple fluids, suggesting that the nanoparaticles do not alter the flow in the lubrication layer at these concentrations.     

Forces between a rigid probe particle and a liquid interface. II. The general case

The semianalytic theory developed previously (Chan, D. Y. C., Dagastine, R. R., and White, L. R., J. Colloid Interface Sci. 236, 141 (2001)) to predict the force curve of an AFM measurement at a liquid interface using a colloidal probe has been expanded to incorporate a general force law with both attractive and repulsive forces. Expressions for the gradient of the force curve are developed to calculate the point at which the probe particle on the cantilever will spontaneously jump in toward the liquid interface. The calculation of the jump instability is reduced to a straightforward embroidery of the simple algorithms presented in Chan et al. In a variety of sample calculations using force laws including van der Waals, electrostatic, and hydrophobic forces for both oil/water and bubble/water interfaces, we have duplicated the general behaviors observed in several AFM investigations at liquid interfaces. The behavior of the drop as a Hookean spring and the numerical difficulties of a full numerical calculation of F(deltaX) are also discussed.     

Spatially resolved force spectroscopy of bacterial surfaces using force-volume imaging

Force spectroscopy using the atomic force microscope (AFM) is a powerful technique for measuring physical properties and interaction forces at microbial cell surfaces. Typically for such a study, the point at which a force measurement will be made is located by first imaging the cell using AFM in contact mode. In this study, we image the bacterial cell Shewanella putrefaciens for subsequent force measurements using AFM in force-volume mode and compare this to contact-mode images. It is known that contact-mode imaging does not accurately locate the apical surface and periphery of the cell since, in contact mode, a component of the applied load laterally deforms the cell during the raster scan. Here, we illustrate that contact-mode imaging does not accurately locate the apical surface and periphery of the cell since, in contact mode, a component of the applied load laterally deforms the cell during the raster scan. This is an artifact due to the deformability and high degree of curvature of bacterial cells. We further show that force-volume mode imaging avoids the artifacts associated with contact-mode imaging due to surface deformation since it involves the measurement of a grid of individual force profiles. The topographic image is subsequently reconstructed from the zero-force height (the contact distance between the AFM tip and the surface) at each point on the cell surface. We also show how force-volume measurements yield applied load versus indentation data from which mechanical properties of the cell such as Young's modulus, cell turgor pressure and elastic and plastic energies can be extracted.     

Hydrophobic attraction as revealed by AFM force measurements and molecular dynamics simulation

Spherical calcium dioleate particles ( approximately 10 mum in diameter) were used as AFM (atomic force microscope) probes to measure interaction forces of the collector colloid with calcite and fluorite surfaces. The attractive AFM force between the calcium dioleate sphere and the fluorite surface is strong and has a longer range than the DLVO (Derjaguin-Landau-Verwey-Overbeek) prediction. The AFM force between the calcium dioleate sphere and the mineral surfaces does not agree with the DLVO prediction. Consideration of non-DLVO forces, including the attractive hydrophobic force and the repulsive hydration force, was necessary to explain the experimental results. The non-DLVO interactions considered were justified by the different interfacial water structures at calcite- and fluorite-water interfaces as revealed by the numerical computation experiments with molecular dynamics simulation.     

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.     

Modification of Surface Forces by Metal Ion Adsorption

Abstract

Sorption of ions may lead to variations in interparticle forces and, thus, changes in the stability of colloidal particles. Chemical interactions between metal ions and colloidal particles modify the molecular structure of the surface, the surface charge, and the electrical potential between colloidal particles. These modifications to the surface and to the electrical double layer due to metal ion sorption are reflected in the interaction force between a particle and another surface, which is measured in this study by atomic force microscopy (AFM). Specifically, AFM is used to investigate the sorption of copper ions from aqueous solutions by silica particles. The influence of metal ion concentration and solution ionic strength on surface forces is studied under transient conditions. Results show that as the metal ion concentration is decreased, charge reversal occurs and a longer period of time is required for the system to reach equilibrium. The ionic strength has no significant effect on sorption kinetics. Furthermore, neither metal concentration nor ionic strength exhibits any effect on sorption equilibria, indicating that for the experimental conditions used in this study, the surface sites of the silica particle are fully occupied by copper ions.     

Atomic force microscopy study of the interaction between adsorbed poly(ethylene oxide) layers: effects of surface modification and approach velocity

The interaction forces between layers of the triblock copolymer Pluronic F108 adsorbed onto hydrophobic radio frequency glow discharge (RFGD) thin film surfaces and hydrophilic silica, in polymer-free 0.15 M NaCl solution, have been measured using the atomic force microscope (AFM) colloid probe technique. Compression of Pluronic F108 layers adsorbed on the hydrophobic RFGD surfaces results in a purely repulsive force due to the steric overlap of the layers, the form of which suggests that the PEO chains adopt a brush conformation. Subsequent fitting of these data to the polymer brush models of Alexander-de Gennes and Milner, Witten, and Cates confirms that the adsorbed Pluronic F108 adsorbs onto hydrophobic surfaces as a polymer brush with a parabolic segment density profile. In comparison, the interaction between Pluronic F108 layers adsorbed on silica exhibits a long ranged shallow attractive force and a weaker steric repulsion. The attractive component is reasonably well described by van der Waals forces, but polymer bridging cannot be ruled out. The weaker steric component of the force suggests that the polymer is less densely packed on the surface and is less extended into solution, existing as polymeric isolated mushrooms. When the surfaces are driven together at high piezo ramp velocities, an additional repulsive force is measured, attributable to hydrodynamic drainage forces between the surfaces. In comparing theoretical predictions of the hydrodynamic force to the experimentally obtained data, agreement could only be obtained if the flow profile of the aqueous solution penetrated significantly into the polymer brush. This finding is in line with the theoretical predictions of Milner and provides further evidence that the segment density profile of the adsorbed polymer brush is parabolic. A velocity dependent additional stepped repulsive force, reminiscent of a solvation oscillatory force, is also observed when the adsorbed layers are compressed under high loads. This additional force is presumably a result of hindered drainage of water due to the presence of a high volume fraction of polymer chains between the surfaces.     

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.