Hamaker Constant Research Articles

Measurements of dispersion forces between colloidal latex particles with the atomic force microscope and comparison with Lifshitz theory

Interaction forces between carboxylate colloidal latex particles of about 2 μm in diameter immersed in aqueous solutions of monovalent salts were measured with the colloidal probe technique, which is based on the atomic force microscope. We have systematically varied the ionic strength, the type of salt, and also the surface charge densities of the particles through changes in the solution pH. Based on these measurements, we have accurately measured the dispersion forces acting between the particles and estimated the apparent Hamaker constant to be (2.0 ± 0.5) × 10(-21) J at a separation distance of about 10 nm. This value is basically independent of the salt concentration and the type of salt. Good agreement with Lifshitz theory is found when roughness effects are taken into account. The combination of retardation and roughness effects reduces the value of the apparent Hamaker constant and its ionic strength dependence with respect to the case of ideally smooth surfaces.

Aggregation of anthracite and graphite dispersions under the action of alkaline-earth metal carbonates

A model for the electrical conductivity of a heterogeneous system based on alkaline-earth metal carbonates and anthracite and graphite dispersions is proposed. The electrical properties of heterogeneous dispersions in the carbonates of alkaline-earth metals depend on several basic parameters. The degree of aggregation of electrically conducting particles and the electrical conductivity of a single aggregate are the most important of these parameters. The threshold concentration of the electrical conductivity of graphite dispersions in alkaline-earth metal carbonates, which is 0.05, is much lower than the threshold concentration of electrical conductivity for the liquid systems of graphite dispersions in electrolytes, which is 0.15. This is likely due to a higher value of the Hamaker constant in the test systems. The aggregation of the dispersions of anthracites is insignificant, and particles are evenly distributed in the volume. The apparent activation energies of electrical conductivity were determined for the dispersions of anthracites and graphites in alkaline-earth metal carbonates. It was found that the activation energy of electrical conductivity increased with the weight fraction of dispersions. Lower values of the apparent activation energy of electrical conductivity were observed in barium and strontium carbonates.

Influence of the surface chemistry on TiO2 – TiO2 nanocontact forces as measured by an UHV–AFM

Particle-wall contact forces between a TiO2 film coated AFM tip and TiO2(110) single crystal surfaces were analyzed by means of UHV–AFM. As a reference system an octadecylphosphonic acid monolayer covered TiO2(110) surface was studied. The defect chemistry of the TiO2 substrate was modified by Ar ion bombardment, water dosing at 3×10−6Pa and an annealing step at 473K which resulted in a varying density of Ti(III) states. The observed contact forces are correlated to the surface defect density and are discussed in terms of the change in the electronic structure and its influence on the Hamaker constant.

On the effect of van der Waals attractions on the critical salt concentration for inhibiting bubble coalescence

The coalescence of gas bubbles in many salt solutions such as NaCl is significantly inhibited if the salt concentration exceeds a critical concentration which is unique for each salt. It has been predicted as a function of the Hamaker constants of van der Waals attractions between two bubbles. In this paper, the Lifshitz theory on the van der Waals interaction energy and the available spectrum for water dielectric permittivity are applied to determine the Hamaker constants for liquid films between bubbles in pure water and salt solutions. Using the new values for Hamaker constants for thin films of saline solutions, we show that the effect of van der Waals attractions on the critical salt concentration is significantly weaker than previously hypothesized. The predictions based on van der Waals attractions significantly under-estimate the experimental critical concentrations. The failure of the van der Waals attraction in predicting the critical salt concentration highlights the urgent need of revising the available theories on bubble coalescence in salt solutions and saline water.

Nanoscale Cell Wall Deformation Impacts Long-Range Bacterial Adhesion Forces on Surfaces

Adhesion of bacteria occurs on virtually all natural and synthetic surfaces and is crucial for their survival. Once they are adhering, bacteria start growing and form a biofilm, in which they are protected against environmental attacks. Bacterial adhesion to surfaces is mediated by a combination of different short- and long-range forces. Here we present a new atomic force microscopy (AFM)-based method to derive long-range bacterial adhesion forces from the dependence of bacterial adhesion forces on the loading force, as applied during the use of AFM. The long-range adhesion forces of wild-type Staphylococcus aureus parent strains (0.5 and 0.8 nN) amounted to only one-third of these forces measured for their more deformable isogenic Δpbp4 mutants that were deficient in peptidoglycan cross-linking. The measured long-range Lifshitz-Van der Waals adhesion forces matched those calculated from published Hamaker constants, provided that a 40% ellipsoidal deformation of the bacterial cell wall was assumed for the Δpbp4 mutants. Direct imaging of adhering staphylococci using the AFM peak force-quantitative nanomechanical property mapping imaging mode confirmed a height reduction due to deformation in the Δpbp4 mutants of 100 to 200 nm. Across naturally occurring bacterial strains, long-range forces do not vary to the extent observed here for the Δpbp4 mutants. Importantly, however, extrapolating from the results of this study, it can be concluded that long-range bacterial adhesion forces are determined not only by the composition and structure of the bacterial cell surface but also by a hitherto neglected, small deformation of the bacterial cell wall, facilitating an increase in contact area and, therewith, in adhesion force.

Thermodynamic Analysis of Wall Effects on Phase Stability and Homogeneous Nucleation in Nanochannels Containing Superheated Liquid

Rapid heating or sudden depressurization can create highly superheated liquid conditions in stationary or flowing liquid in nanochannels. In these situations, the phase stability of the liquid and the conditions for the onset of bubble nucleation are important factors in the fluid behavior and heat transfer in applications. In the investigation summarized here, a statistical thermodynamics analysis is used to derive a modified version of the Redlich-Kwong fluid property model that accounts for attractive forces between the solid wall surface atoms and liquid molecules in the fluid within a high aspect ratio (parallel plate) nanochannel. In this model, the wall–fluid attractive forces are quantified in terms of Hamaker constants, which makes it possible to assess the effect of wall–fluid force interactions on the spinodal conditions for a variety of fluid and surface material combinations. At large channel widths the fluid properties exhibit wall effects very near each wall, with bulk fluid property values being predicted in the center of the channel. As the channel width decreases, the fluid in the center of the channel begins to feel the effects of both walls and the properties deviate from the bulk values throughout the channel; importantly, the spinodal temperature increases significantly above the bulk fluid value. The results of this analysis imply that in nano- and micropassages and near walls with nano- to microscale roughness, fluid may experience a stabilizing effect due to its proximity to nearby walls, which may, in turn, inhibit bubble nucleation.

Computations of Lifshitz–van der Waals interaction energies between irregular particles and surfaces at all separations for resuspension modelling

The phenomenon of particle resuspension plays a vital role in numerous fields. Among many aspects of particle resuspension dynamics, a dominant concern is the accurate description and formulation of the van der Waals (vdW) interactions between the particle and substrate. Current models treat adhesion by incorporating a material-dependent Hamaker's constant which relies on the heuristic Hamaker's two-body interactions. However, this assumption of pairwise summation of interaction energies can lead to significant errors in condensed matter as it does not take into account the many-body interaction and retardation effects. To address these issues, an approach based on Lifshitz continuum theory of vdW interactions has been developed to calculate the principal many-body interactions between arbitrary geometries at all separation distances to a high degree of accuracy through Lifshitz's theory. We have applied this numerical implementation to calculate the many-body vdW interactions between spherical particles and surfaces with sinusoidally varying roughness profile and also to non-spherical particles (cubes, cylinders, tetrahedron etc) orientated differently with respect to the surface. Our calculations revealed that increasing the surface roughness amplitude decreases the adhesion force and non-spherical particles adhere to the surfaces more strongly when their flatter sides are oriented towards the surface. Such practical shapes and structures of particle–surface systems have not been previously considered in resuspension models and this rigorous treatment of vdW interactions provides more realistic adhesion forces between the particle and the surface which can then be coupled with computational fluid dynamics models to improve the predictive capabilities of particle resuspension dynamics.

Adhesion enhancement of biomimetic dry adhesives by nanoparticle in situ synthesis

A novel method to increase the adhesion strength of a gecko-inspired dry adhesive is presented. Gold nanoparticles are synthesized on the tips of the microfibrils of a polymeric dry adhesive to increase its Hamaker constant. Formation of the gold nanoparticles is qualitatively studied through a colour change in the originally transparent substance and quantitatively analysed using ultraviolet–visible spectrophotometry. A pull-off force test is employed to quantify the adhesion enhancement. Specifically, adhesion forces of samples with and without embedded gold nanoparticles are measured and compared. The experimental results indicate that an adhesion improvement of 135% can be achieved.

Aggregation Kinetics of Manganese Dioxide Colloids in Aqueous Solution: Influence of Humic Substances and Biomacromolecules

In this work, the early stage aggregation kinetics of manganese dioxide (MnO2) colloids in aqueous solution and the effects of constituents of natural organic matter (i.e., Suwannee River fulvic acid (SRFA), Suwannee River humic acid (SRHA), alginate, and bovine serum albumin (BSA)) were investigated by time-resolved dynamic light scattering. MnO2 colloids were significantly aggregated in the presence of monovalent and divalent cations. The critical coagulation concentrations were 28, 0.8, and 0.45 mM for NaNO3, Mg(NO3)2, and Ca(NO3)2, respectively. The Hamaker constant of MnO2 colloids in aqueous solution was 7.84 × 10(-20) J. All the macromolecules tested slowed MnO2 colloidal aggregation rates greatly. The steric repulsive forces, originated from organic layers adsorbed on MnO2 colloidal surfaces, may be mainly responsible for their stabilizing effects. However, the complexes formed by alginate and Ca(2+) (>5 mM) might play a bridging role and thus enhanced MnO2 colloidal aggregation instead. These results may be important for assessing the fate and transport of MnO2 colloids and associated contaminants.

Monte Carlo simulation of micron size spherical particle removal and resuspension from substrate under fluid flows

Particle detachment from surfaces and subsequent entrainment into fluid flow occurs in many natural and industrial applications. In this study, a Monte Carlo model for particle resuspension from substrate under turbulent flow conditions was developed. The forces and torque acting on a particle were evaluated and the criteria for the rolling detachment of rough spherical and nearly spherical particles from substrate under turbulent flow conditions were used in the analysis. The statistical variations of physical parameters that were relevant to particle resuspension as well as occurrence of turbulence bursts in the viscous sublayer region were included in the model through a series of Monte Carlo simulations. The fluctuating velocities were assumed to follow a Gaussian distribution and the resuspension fractions were evaluated for a range of conditions. The effects of surface roughness, particle and substrate material properties including Hamaker constant and particle sizes were studied. The model predictions were compared with the available experimental data and good agreement was found.

Dielectric properties of lignin and glucomannan as determined by spectroscopic ellipsometry and Lifshitz estimates of non-retarded Hamaker constants

We present in this study a quantitative estimate of the dispersive interactions between lignin, hemicellulose and cellulose, which are the dominating components in wood and also extensively used to ...

A population balance equation model to predict regimes of controlled nanoparticle aggregation

Forming stable clusters or aggregates of nanoparticles is of interest in a number of emerging applications. While formation of unstable fractal aggregates and flocs has been well-studied with both experiments and theory, the conditions that lead to stable, finite-sized clusters is not as well understood. Here, we present an integrated experimental and modeling study to explore aggregation in concentrated attractive colloidal suspensions. A population balance equation (PBE) model is used to predict the aggregation dynamics of quiescent colloidal suspensions. A DLVO (Derjaguin–Landau–Verwey–Overbeek) type potential is used to describe the interparticle potential, with attractive interactions arising from van der Waals forces and long-range repulsive interactions caused by electrostatics. The PBE model includes a full calculation of stability ratio variations as a function of aggregate size, such that the energy barrier increases with increasing size. As the ionic strength is decreased, the model predicts three regimes of behavior: uncontrolled aggregation into large flocs, controlled aggregation into stable clusters, and no aggregation. The model is tested experimentally using latex particles at different salt concentrations and particle concentrations. When the Hamaker constant and surface potential are fit to aggregate size measurements collected at one salt concentration, the model accurately predicts the final mean aggregate size and regimes of aggregation at other salt concentrations and the same particle concentration. This result suggests that van der Waals and electrostatic forces are the dominant particle interactions in determining the final aggregate state. The mean aggregate size and aggregation regimes at different particle concentrations could be accurately predicted by adjusting the surface potential. This parameter adjustment is consistent with the expectation that increasing colloid weight fractions cause aggregates to have a more fractal nature and hence have a lower effective repulsion. However, the model predicts much faster aggregation rates than what are observed experimentally. This discrepancy may be due to hydrodynamic effects or another slow dynamical process which is not accounted for in the model. Nevertheless, this study presents the first PBE model that can successfully predict stable aggregate size and aggregation regimes of charged colloidal particles over a range of salt concentrations and particle concentrations.

Fluctuational-Electrodynamics Calculations of the van der Waals Potential in Nanoparticle Superlattices

Based on fluctuational electrodynamics and a Green’s tensor formalism, we present a theoretical method which provides the correct van der Waals potential of nanocolloidal assemblies. We calculate the total van der Waals potential in superlattices of metallic nanoparticles where we find, in particular, that the pairwise summation approximation fails notably even for dilute superlattices. Furthermore, by comparing our method with the traditional Hamaker theory for the van der Waals interactions in colloidal systems, we find that the retrieved corresponding Hamaker constant depends dramatically on the lattice constant of the superlattices of the same nanoparticle size, signifying the total breakdown of the Hamaker theory for such systems. Since the only input of the presented theory for the van der Waals potential is the size and the dielectric function of the nanoparticles, we show that we can predict the lattice constant of stable nanoparticle superlattices without the use of empirical parameters as in Hamaker theory.

Direct measurements of forces between different charged colloidal particles and their prediction by the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO)

Force measurements between three types of latex particles of diameters down to 1 μm with sulfate and carboxyl surface functionalities were carried out with the multi-particle colloidal probe technique. The experiments were performed in monovalent electrolyte up to concentrations of about 5 mM. The force profiles could be quantified with the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) by invoking non-retarded van der Waals forces and the Poisson-Boltzmann description of double layer forces within the constant regulation approximation. The forces measured in the symmetric systems were used to extract particle and surface properties, namely, the Hamaker constant, surface potentials, and regulation parameters. The regulation parameter is found to be independent of solution composition. With these values at hand, the DLVO theory is capable to accurately predict the measured forces in the asymmetric systems down to distances of 2-3 nm without adjustable parameters. This success indicates that DLVO theory is highly reliable to quantify interaction forces in such systems. However, charge regulation effects are found to be important, and they must be considered to obtain correct description of the forces. The use of the classical constant charge or constant potential boundary conditions may lead to erroneous results. To make reliable predictions of the force profiles, the surface potentials must be extracted from direct force measurements too. For highly charged surfaces, the commonly used electrophoresis techniques are found to yield incorrect estimates of this quantity.

AFM Tip Effect on a Thin Liquid Film

We study the interaction between an AFM probe and a liquid film deposited over a flat substrate. We investigate the effects of the physical and geometrical parameters, with a special focus on the film thickness E, the probe radius R, and the distance D between the probe and the free surface. Deformation profiles have been calculated from the numerical simulations of the Young-Laplace equation by taking into account the probe/liquid and the liquid/substrate interactions, characterized by the Hamaker constants, Hpl and Hls. We demonstrate that the deformation of a shallow film is determined by a particular characteristic length λF = (2πγE(4)/Hls)(1/2), resulting from the balance between the capillary force (γ is the surface tension) and the van der Waals liquid/substrate attraction. For the case of a bulk liquid, the extent of the interface deformation is simply controlled by the capillary length λC = (γ/Δρg)(1/2). These trends point out two asymptotic regimes, which in turn are bounded by two characteristic film thicknesses Eg = (Hls/2πΔρg)(1/4) and Eγ = (R(2)Hls/2πγ)(1/4). For E > Eg, the bulk behavior is recovered, and for E < Eγ, we show the existence of a particular shallow film regime in which a localized tip effect is observed. This tip effect is characterized by the small magnitude of the deformation and an important restriction of its radial extent λF localized below the probe. In addition, we have found that the film thickness has a significant effect on the threshold separation distance Dmin below which the irreversible jump-to-contact process occurs: Dmin is probe radius-dependent for the bulk whereas it is film-thickness-dependent for shallow films. These results have an important impact on the optimal AFM scanning conditions.

Influence of surface conductivity on the apparent zeta potential of TiO2 nanoparticles: Application to the modeling of their aggregation kinetics

Titanium dioxide nanoparticles (TiO2 NPs) are extensively used in consumer products. The release of these NPs into aquatic environments raises the question of their possible risks to the environment and human health. The magnitude of the threat may depend on whether TiO2 NPs are aggregated or dispersed. Currently, limited information is available on this subject. A new approach based on DLVO theory is proposed to describe aggregation kinetics of TiO2 NPs in aqueous dispersions. It has the advantage of using zeta potentials directly calculated by an electrostatic surface complexation model whose parameters are calibrated by ab initio calculations, crystallographic studies, potentiometric titration and electrophoretic mobility experiments. Indeed, the conversion of electrophoretic mobility measurements into zeta potentials is very complex for metal oxide nanoparticles. This is due to their very high surface electrical conductivity associated with the electromigration of counter and co-ions in their electrical double layer. Our model has only three adjustable parameters (the minimum separation distance between NPs, the Hamaker constant, and the effective interaction radius of the particle), and predicts very well the stability ratios of TiO2 NPs measured at different pH values and over a broad range of ionic strengths (KCl aqueous solution). We found an effective interaction radius that is significantly smaller than the radius of the aggregate and corresponds to the radius of surface crystallites or small clusters of surface crystallites formed during synthesis of primary particles. Our results confirm that DLVO theory is relevant to predict aggregation kinetics of TiO2 NPs if the double layer interaction energy is estimated accurately.

Adhesion of Explosives

It is of increasing importance to understand how explosive particles adhere to surfaces in order to understand how to remove them for detection in airport or other security settings. In this study, adhesion forces between royal demolition explosive (cyclotrimethylenetrinitramine) (RDX), pentaerythritol tetranitrate (PETN), and trinitrotoluene (TNT) in their crystalline forms and aluminum coupons with three finishes, acrylic melamine (clear coating), polyester acrylic melamine (white coating) automotive finishes, and a green military-grade finish, were measured and modeled. The force measurements were performed using the atomic force microscopy (AFM)-based colloidal probe microscopy (CPM) method. Explosive particles were mounted on AFM cantilevers and repeatedly brought in and out of contact with the surfaces of interest while the required force needed to pull out of contact was recorded. An existing Matlab-based simulator was used to describe the observed adhesion force distributions, with excellent agreement. In these simulations, the measured topographies of the interacting surfaces were considered, although the geometries were approximated. The simulations were performed using a van der Waals force-based adhesion model and a composite effective Hamaker constant. It was determined that certain combinations of roughness on the interacting surfaces led to preferred particle-substrate orientations that produced extreme adhesion forces.

Fundamental Roles of Nonevaporating Film and Ultrahigh Heat Flux Associated With Nanoscale Meniscus Evaporation in Nucleate Boiling

The three-phase moving contact line present at the base of a bubble in nucleate boiling has been a widely researched topic over the past few decades. It has been traditionally divided into three regions: nonevaporating film (order of nanometers), evaporating film (order of microns), and bulk meniscus (order of millimeters). This multiscale nature of the contact line has made it a challenging and complex problem, and led to an incomplete understanding of its dynamic behavior. The evaporating film and bulk meniscus regions have been investigated rigorously through analytical, numerical and experimental means; however, studies focused on the nonevaporating film region have been very sparse. The nanometer length scale and the fluidic nature of the nonevaporating film has limited the applicability of experimental techniques, while its numerical analysis has been questionable due to the presumed continuum behavior and lack of known input parameters, such as the Hamaker constant. Thus in order to gain fundamental insights and understanding, we have used molecular dynamics simulations to study the formation and characteristics of the nonevaporating film for the first time in published literature, and outlined a technique to obtain Hamaker constants from such simulations. Further, in this review, we have shown that the nonevaporating film can exist in a metastable state of reduced/negative liquid pressures. We have also performed molecular simulations of nanoscale meniscus evaporation, and shown that the associated ultrahigh heat flux is comparable to the maximum-achievable kinetic limit of evaporation. Thus, the nonevaporating film and its adjacent nanoscale regions have a significant impact on the overall macroscale dynamics and heat flux behavior of nucleate boiling, and hence should be included in greater details in nucleate boiling simulations and analysis.

Effects of Outer Membrane Protein TolC on the Transport of Escherichia coli within Saturated Quartz Sands

The outer membrane protein (OMP) TolC is the cell surface component of several drug efflux pumps that are responsible for bacterial resistance against a variety of antibiotics. In this research, we investigated the effects of OMP TolC on E. coli transport within saturated sands through column experiments using a wild-type E. coli K12 strain (with OMP TolC), as well as the corresponding transposon mutant (tolC::kan) and the markerless deletion mutant (ΔtolC). Our results showed OMP TolC could significantly enhance the transport of E. coli when the ionic strength was 20 mM NaCl or higher. The deposition rate coefficients for the wild-type E. coli strain (with OMP TolC) was usually >50% lower than those of the tolC-negative mutants. The measurements of contact angles using three probe liquids suggested that TolC altered the surface tension components of E. coli cells and lead to lower Hamaker constants for the cell-water-sand system. The interaction energy calculations using the extended Derjaguin-Landau-Verwey-Overbeek (XDLVO) theory suggested that the deposition of the E. coli cell primarily occurred at the secondary energy minimum. The depth of the secondary energy minimum increased with ionic strength, and was greater for the TolC-deletion strains under high ionic strength conditions. Overall, the transport behavior of three E. coli strains within saturated sands could be explained by the XDLVO calculations. Results from this research suggested that antibiotic resistant bacteria expressing OMP TolC could spread more widely within sandy aquifers.

Dispersion Stability and Electrokinetic Properties of Intrinsic Plutonium Colloids: Implications for Subsurface Transport

Subsurface transport of plutonium (Pu) may be facilitated by the formation of intrinsic Pu colloids. While this colloid-facilitated transport is largely governed by the electrokinetic properties and dispersion stability (resistance to aggregation) of the colloids, reported experimental data is scarce. Here, we quantify the dependence of ζ-potential of intrinsic Pu(IV) colloids on pH and their aggregation rate on ionic strength. Results indicate an isoelectric point of pH 8.6 and a critical coagulation concentration of 0.1 M of 1:1 electrolyte at pH 11.4. The ζ-potential/pH dependence of the Pu(IV) colloids is similar to that of goethite and hematite colloids. Colloid interaction energy calculations using these values reveal an effective Hamaker constant of the intrinsic Pu(IV) colloids in water of 1.85 × 10(-19) J, corresponding to a relative permittivity of 6.21 and refractive index of 2.33, in agreement with first principles calculations. This relatively high Hamaker constant combined with the positive charge of Pu(IV) colloids under typical groundwater aquifer conditions led to two contradicting hypotheses: (a) the Pu(IV) colloids will exhibit significant aggregation and deposition, leading to a negligible subsurface transport or (b) the Pu(IV) colloids will associate with the relatively stable native groundwater colloids, leading to a considerable subsurface transport. Packed column transport experiments supported the second hypothesis.