Long-range attraction between charge-mosaic surfaces across water

The surface force balance: direct measurement of interactions in fluids and soft matter

Over the last half-century, direct measurements of surface forces have been instrumental in the exploration of a multitude of phenomena in liquid, soft, and biological matter. Measurements of van der Waals interactions, electrostatic interactions, hydrophobic interactions, structural forces, depletion forces, and many other effects have checked and challenged theoretical predictions and motivated new models and understanding. The gold-standard instrument for these measurements is thesurface force balance(SFB), orsurface forces apparatus, where interferometry is used to detect the interaction force and distance between two atomically smooth planes, with 0.1 nm resolution, over separations from about 1 µm down to contact. The measured interaction forcevs.distance gives access to the free energy of interaction across the fluid film; a fundamental quantity whose general form and subtle features reveal the underlying molecular and surface interactions and their variation. Motivated by new challenges in emerging fields of research, such as energy storage, biomaterials, non-equilibrium and driven systems, innovations to the apparatus are now clearing the way for new discoveries. It is now possible to measure interaction forces (and free energies) with control of electric field, surface potential, surface chemistry; to measure time-dependent effects; and to determine structurein situ. Here, we provide an overview the operating principles and capabilities of the SFB with particular focus on the recent developments and future possibilities of this remarkable technique.

Protein adsorption on a nanoparticle with a nanostructured surface

In the present study, the adsorption of a protein on a nanoparticle with a nanostructured surface, which is created using successively patterned Gaussian pillars (GPs), is simulated by considering the charge regulation within the electrical double layer of a silica nanoparticle (NP). Namely, the mathematical models for the adsorption mechanism, such as classical Langmuir model, extended Langmuir model, and two-state model, are coupled with charge regulation model. By this means, size and pH variables are able to included to the calculations. Moreover, free space, surface curvature, and conformational changes are also taken into account. For systematic investigation, the solution's pH, surface charge density, initial protein concentration, electrostatic charge of the protein, and the diameter of the spherical NP are varied. As a result, the vital properties of a nanoparticle, such as protonation/deprotonation, polarization, topography, and morphology, are considered in the current simulations. The surface charge density and surface chemistry change with NP and GP sizes. The present results reveal that the protein adsorption on an NP with a smooth surface reaches a faster complete surface coverage than an NP with a nanostructured surface. Both states of conformational changes are also affected by the presence of the GP.

Probing Hydrophobic Interactions between Polymer Surfaces and Air Bubbles or Oil Droplets: Effects of Molecular Weight and Surfactants

Hydrophobic interaction plays an important role in numerous interfacial phenomena and biophysical and industrial processes. In this work, polystyrene (PS) was used as a model hydrophobic polymer for investigating its hydrophobic interaction with highly deformable objects (i.e., air bubbles and oil droplets) in aqueous solutions. The effects of polymer molecular weight, solvent (i.e., addition of ethanol to water), the presence of surface-active species, and hydrodynamic conditions were investigated, via direct surface force measurements using the bubble/drop probe atomic force microscopy (AFM) technique and theoretical calculations based on the Reynolds lubrication theory and augmented Young-Laplace equation by including the effect of disjoining pressure. It was found that the PS of low molecular weight (i.e., PS590 and PS810) showed slightly weaker hydrophobic interactions with air bubbles or oil droplets, as compared to glassy PS of higher molecular weight (i.e., PS1110, PS2330, PS46300, and PS1M). The hydrophobic interaction between PS and air bubbles in a 1 M NaCl aqueous solution with 10 vol % ethanol was weaker than that in the bare aqueous solution. Such effects on the hydrophobic interactions are possibly achieved by influencing the structuring/ordering of water molecules close to the hydrophobic polymer surfaces by tuning the surface chain mobility and surface roughness of polymers. It was found that the addition of three surface-active species, i.e., cetyltrimethylammonium chloride (CTAC), Pluronic F-127, and sodium dodecyl sulfate (SDS), to the aqueous media could suppress the attachment of the hydrophobic polymer and air bubbles or oil droplets, most likely caused by the additional steric repulsion due to the adsorbed surface-active species at the bubble/polymer/oil interfaces. Our results have improved the fundamental understanding of the interaction mechanisms between hydrophobic polymers and gas bubbles or oil droplets, with useful implications on developing effective methods for modulating the related interfacial interactions in many engineering applications.

Modulation of soft glassy dynamics in aqueous suspensions of an anisotropic charged swelling clay through pH adjustment

HYPOTHESIS

Sodium-montmorillonite (Na-Mt) particles are geometrically anisometric that carry a pH dependent anisotropic surface charge. Therefore, it should be possible to manipulate the particle-particle interaction of colloidal range Na-Mt suspensions through pH changes which in turn should alter the soft glassy dynamics of Na-Mt suspensions.

EXPERIMENTS

Rheological experiments were used to probe the impact of pH mediated colloidal particle-particle interaction on the physical aging, linear viscoelastic response, and yield stress behavior of Na-Mt suspension.

FINDINGS

The temporal evolution of the storage modulus (G') was stronger in the acid regime (pH < 9.5) than the base (pH ≥ 9.5) pH regime. Horizontal shifting of the aging curves in the acid and base regimes led to aging time-H⁺ concentration and aging time-OH^- concentration superposition. An aging time-Na-Mt concentration superposition was also observed in both pH regimes. The critical stress associated with the viscosity bifurcation behavior increased linearly with G' but with different slopes for acid and base regime. We propose that positively charged patches on the Na-Mt particle edge merge with the characteristic surface as a function of H⁺ ions in the system. This leads to a strongly associated microstructure at low pH and a relatively weak but associated microstructure at natural pH, hence confirming the hypothesis.

Surface alignment disorder and thermal Casimir forces in smectic-A liquid crystalline films

Disorder components in surface anchoring orientation of a smectic-A liquid crystalline film (occurring, e.g., due to surface contamination sources) modify the thermal pseudo-Casimir interaction mediated between the bounding surfaces of the film. By considering a plane-parallel slab with bounding surfaces positioned normal to the layering field of the film, we study the anchoring disorder effects by assuming that the disorder source is present on one of the two substrates, producing a Gaussian-weighted distribution for the preferred molecular anchoring orientation (easy axis) on that substrate, with a finite mean and variance or, more generally, with a homogeneous in-plane, two-point correlation function. We show that the presence of disorder, either of quenched or annealed type, leads to a significant reduction in the magnitude of the net pseudo-Casimir force between the confining substrates of the film. This force can be attractive or repulsive depending on the boundary conditions. In the quenched case, the interaction force reduction is a direct consequence of an additive free energy term dependent on the variance of the disorder, while in the annealed case, the suppression of the interaction force can be understood based on a disorder-renormalized, effective anchoring strength. We predict a regime of behavior, exhibiting non-monotonic dependence for the interaction pressure as a function of separation. We also show that, by increasing the disorder variance, the interaction pressure changes sign and becomes a monotonically decreasing function of the separation between the substrates.

Direct Measurement of the Contents, Thickness, and Internal Pressure of Molybdenum Disulfide Nanoblisters

Nanoblisters have attracted attention due to their ability to controllably modulate the properties of two-dimensional materials. The accurate measurement or estimation of their properties is nontrivial and largely based on Hencky's theory. However, these estimates require a priori knowledge of material properties and propagate large errors. Here we show, through a systematic atomic force microscopy study, several strategies that lead to vastly enhanced characterization of nanoblisters. First, we find that nanoblisters may contain both liquid and gas, resolving an ongoing debate in the literature. Second, we demonstrate how to definitively determine the membrane thickness of a nanoblister and show that Hencky's theory can only reliably predict membrane thicknesses for small aspect ratios and small membrane thicknesses. Third, we develop a novel technique to measure the internal pressures of nanoblisters, which quantitatively agrees with Hencky's theory but carries a 1 order smaller propagated error.

The long-range attraction between hydrophobic macroscopic surfaces

Direct measurements of the long-range strongly attractive force observed between macroscopic hydrophobic surfaces across aqueous solutions are reexamined in light of recent experiments and theoretical developments. The focus is on systems in the absence of submicroscopic bubbles (preexistent or induced) to avoid capillary bridging forces. Other possible interferences to the measurements are also eliminated. The force-distance profiles are obtained directly (no contributions from electrical double layer or hydrodynamics) between symmetric identical hydrophobic surfaces, overall charge-neutral, at the thermodynamic equilibrium and in a quenched state. Therefore in the well-defined geometry of crossed-cylinders, sphere-flat, or sphere-sphere, there is no additional interaction to be considered except the ever-present dispersion forces, negligible at large separations. For the three main categories of substrates rendered hydrophobic, namely surfaces obtained with surfactant monolayers physically adsorbed from solution to deposited ones, and substrates coated with a hydrophobizing agent bonded chemically onto the surface, the interaction energy scales as A exp (-2κD)/2κD at large separations, with measured decay lengths in accord with theoretical predictions, simply being half the Debye screening length, κ^-1/2, at least in non vanishing electrolyte. Taken together with the prefactor A scaling as the ionic strength, the interaction energy is demonstrated to have an electrostatic origin in all the systems. Thanks to our recent SFAX coupling force measurements with x-ray solution scattering under controlled nano-confinement, the microstructuration of the adsorbed film emerges as an essential feature in the molecular mechanism for explaining the observed attraction of larger magnitude than dispersion forces. The adsorption of pairs of positive and negative ions on small islands along the interface, the fluctuation of the surface charge density around a zero mean-value with desorption into or adsorption from the electrolyte solution, the correlations in the local surface ion concentrations along the surfaces, the redistribution of counterions upon intersurface variation, all contribute and are tuned finely by the inhomogeneities and defects present in the hydrophobic layers. It appears that the magnitude of the interacting energy can be described by a single master curve encompassing all the systems.

Salt-induced swelling transitions of a lamellar amphiphile-Polyelectrolyte complex

We report salt-induced swelling transitions of a lamellar complex of the anionic polyelectrolyte, poly(acrylic acid sodium salt) (PAANa), and the cationic amphiphile, didodecyldimethylammonium chloride (DDAC). Increasing the concentration of NaCl in the solution is found to lead to a collapsed → swollen → collapsed transition of the complex. The swelling transition is driven by an abrupt increase in PAANa adsorption on DDAC bilayers above a threshold salt concentration. The lamellar periodicity of the swollen phase is not determined by the thickness of the adsorption layer, and additional mechanisms have to be invoked to understand the extent of its swelling. The swelling transition is not observed for the highest molecular weight of PAANa used, but a gradual transformation between the two collapsed structures is seen on increasing the salt concentration. The polyelectrolyte chains desorb from the bilayers at a very high salt concentration, in a process similar to the well-known destabilization of complexes of oppositely charged polyelectrolytes. However, unlike the PAANa chains, the polymer-free bilayers do not disperse uniformly in the solution. Instead, they form a collapsed lamellar stack containing very little water due to the van der Waals attraction between them. The occurrence of an abrupt swelling transition at intermediate salt concentrations in this system contrasts sharply with the gradual swelling reported in other complexes with increasing salt concentration. Furthermore, this behavior does not seem to have been anticipated by theories of complexation of oppositely charged macroions. More experiments are required for a clear understanding of the interactions stabilizing the different phases observed in this system.

Measuring Inner Layer Capacitance with the Colloidal Probe Technique

The colloidal probe technique was used to measure the inner layer capacitance of an electrical double layer. In particular, the forces were measured between silica surfaces and sulfate latex surfaces in solutions of monovalent salts of different alkali metals. The force profiles were interpreted with Poisson-Boltzmann theory with charge regulation, whereby the diffuse layer potential and the regulation properties of the interface were obtained. While the diffuse layer potential was measured in this fashion in the past, we are able to extract the regulation properties of the inner layer, in particular, its capacitance. We find systematic trends with the type of alkali metal ion and the salt concentration. The observed trends could be caused by difference in ion hydration, variation of the binding capacitance, and changes of the effective dielectric constant within the Stern layer. Our results are in agreement with recent experiments involving the water-silica interface based on a completely independent method using X-ray photoelectron spectroscopy in a liquid microjet. This agreement confirms the validity of our approach, which further provides a means to probe other types of interfaces than silica.

Charged nanorods at heterogeneously charged surfaces

We study the spatial and orientational distribution of charged nanorods (rodlike counterions) as well as the effective interaction mediated by them between two plane-parallel surfaces that carry fixed (quenched) heterogeneous charge distributions. The nanorods are assumed to have an internal charge distribution, specified by a multivalent monopolar moment and a finite quadrupolar moment, and the quenched surface charge is assumed to be randomly distributed with equal mean and variance on the two surfaces. While equally charged surfaces are known to repel within the traditional mean-field theories, the presence of multivalent counterions has been shown to cause attractive interactions between uniformly charged surfaces due to the prevalence of strong electrostatic couplings that grow rapidly with the counterion valency. We show that the combined effects due to electrostatic correlations (caused by the coupling between the mean surface field and the multivalent, monopolar, charge valency of counterions) as well as the disorder-induced interactions (caused by the coupling between the surface disorder field and the quadrupolar moment of counterions) lead to much stronger attractive interactions between two randomly charged surfaces. The interaction profile turns out to be a nonmonotonic function of the intersurface separation, displaying an attractive minimum at relatively small separations, where the ensuing attraction can exceed the maximum strong-coupling attraction (produced by multivalent monopolar counterions between uniformly charged surfaces) by more than an order of magnitude.

Direct Measurement of Lateral Correlations under Controlled Nanoconfinement

Lateral correlations along hydrophobic surfaces whose separation can be varied continuously are measured by x-ray scattering using a modified surface force apparatus coupled with synchrotron radiation, named SFAX. A weak isotropic diffuse scattering along the equatorial plane is revealed for mica surfaces rendered hydrophobic and charge neutral by immersion in cationic surfactant solutions at low concentrations. The peak corresponds to a lateral surface correlation length ξ≈12  nm, without long-range order. These findings are compatible with the atomic force microscopy imaging of a single surface, where adsorbed surfactant stripes appear surrounded by bare mica zones. Remarkably, the scattering patterns remain stable for gap widths D larger than the lateral period but change in intensity and shape (to a lesser extent) as soon as D<ξ. This evolution codes for a redistribution of counterions (counterion release from antagonistic patches) and the associated new x-ray labeling of the patterns. The redistribution of counterions is also the key mechanism to the long-range electrostatic attraction between similar, overall charge-neutral walls, reported earlier.

From discrete to continuous description of spherical surface charge distributions

The importance of electrostatic interactions in soft matter and biological systems can often be traced to non-uniform charge effects, which are commonly described using a multipole expansion of the corresponding charge distribution. The standard approach when extracting the charge distribution of a given system is to treat the constituent charges as points. This can, however, lead to an overestimation of multipole moments of high order, such as dipole, quadrupole, and higher moments. Focusing on distributions of charges located on a spherical surface - characteristic of numerous biological macromolecules, such as globular proteins and viral capsids, as well as of inverse patchy colloids - we develop a novel way of representing spherical surface charge distributions based on the von Mises-Fisher distribution. This approach takes into account the finite spatial extension of individual charges, and leads to a simple yet powerful way of describing surface charge distributions and their multipole expansions. In this manner, we analyze charge distributions and the derived multipole moments of a number of different spherical configurations of identical charges with various degrees of symmetry. We show how the number of charges, their size, and the geometry of their configuration influence the behavior and relative importance of multipole magnitudes of different order. Importantly, we clearly demonstrate how neglecting the effect of charge size leads to an overestimation of high-order multipoles. The results of our work can be applied to construct analytical models of electrostatic interactions and multipole expansion of charged particles in diverse soft matter and biological systems.

Electrostatics of patchy surfaces

In the study of colloidal, biological and electrochemical systems, it is customary to treat surfaces, macromolecules and electrodes as homogeneously charged. This simplified approach is proven successful in most cases, but fails to describe a wide range of heterogeneously charged surfaces commonly used in experiments. For example, recent experiments have revealed a long-range attraction between overall neutral surfaces, locally charged in a mosaic-like structure of positively and negatively charged domains ("patches"). Here, we review experimental and theoretical studies addressing the stability of heterogeneously charged surfaces, their effect on ionic profiles in solution, and the interaction between two such surfaces. We focus on electrostatics, and highlight the important new physical parameters appearing in the heterogeneous case, such as the largest patch size and inter-surface charge correlations.

Screened Coulomb interactions with non-uniform surface charge

The screened Coulomb interaction between a pair of infinite parallel planes with spatially varying surface charge is considered in the limit of small electrical potentials for arbitrary Debye lengths. A simple expression for the disjoining pressure is derived in terms of a two-dimensional integral in Fourier space. The integral is evaluated for periodic and random charge distributions and the disjoining pressure is expressed as a sum over Fourier–Bloch reciprocal lattice vectors or in terms of an integral involving the autocorrelation function, respectively. The force between planes with a finite area of uniform charge, a model for the DLVO interaction between finite surfaces, is also calculated. It is shown that the overspill of the charge cloud beyond the region immediately between the charged areas results in a reduction of the disjoining pressure, as reported by us recently in the long Debye length limit for planes of finite width.

Electrostatic attraction between overall neutral surfaces

Two overall neutral surfaces with positively and negatively charged domains ("patches") have been shown in recent experiments to exhibit long-range attraction when immersed in an ionic solution. Motivated by the experiments, we calculate analytically the osmotic pressure between such surfaces within the Poisson-Boltzmann framework, using a variational principle for the surface-averaged free energy. The electrostatic potential, calculated beyond the linear Debye-Hückel theory, yields an overall attraction at large intersurface separations, over a wide range of the system's controlled length scales. In particular, the attraction is stronger and occurs at smaller separations for surface patches of larger size and charge density. In this large patch limit, we find that the attraction-repulsion crossover separation is inversely proportional to the square of the patch-charge density and to the Debye screening length.

Probing the Surface Properties of Gold at Low Electrolyte Concentration

Using the surface force balance (SFB), we studied the surface properties of gold in aqueous solution with low electrolyte concentration (∼10(-5) M and pH = 5.8), i.e., water with no added salt, by directly measuring the interaction between an ultrasmooth gold surface (ca. 0.2 nm rms roughness) and a mica surface. Under these conditions, specific adsorption of ions is minimized and its influence on the surface charge and surface potential of gold is markedly reduced. At open circuit potential, the electrostatic interaction between gold and mica was purely attractive and gold was found to be positively charged. This was further confirmed by force measurements against a positively charged surface, poly-l-lysine coated mica. Successive force measurements unambiguously showed that once gold and mica reach contact all counterions are expelled from the gap, confirming that at contact the surface charge of gold is equal and opposite in charge to that of mica. Further analysis of adhesion energy between the surfaces indicated that adhesion is mostly governed by vdW dispersion force and to a lesser extent by electrostatic interaction. Force measurements under external applied potentials showed that the gold-mica interaction can be regulated as a function of applied potential even at low electrolyte concentration. The gold-mica interaction was described very precisely by the nonlinearized Poisson-Boltzmann (PB) equation, where one of the surfaces is at constant charge, i.e., mica, and the other, i.e., gold, is at constant potential. Consequently, the gold surface potential could be determined accurately both at open circuit potential (OCP) and under different applied potentials. Using the obtained surface potentials, we were able to derive fundamental characteristics of the gold surface, e.g., its surface charge density and potential of zero charge (PZC), at very low electrolyte concentration.

Ion-mediated interactions between net-neutral slabs: Weak and strong disorder effects

We investigate the effective interaction between two randomly charged but otherwise net-neutral, planar dielectric slabs immersed in an asymmetric Coulomb fluid containing a mixture of mobile monovalent and multivalent ions. The presence of charge disorder on the apposed bounding surfaces of the slabs leads to substantial qualitative changes in the way they interact, as compared with the standard picture provided by the van der Waals and image-induced, ion-depletion interactions. While, the latter predict purely attractive interactions between strictly neutral slabs, we show that the combined effects from surface charge disorder, image depletion, Debye (or salt) screening, and also, in particular, their coupling with multivalent ions, give rise to a more diverse behavior for the effective interaction between net-neutral slabs at nano-scale separations. Disorder effects show large variation depending on the properly quantified strength of disorder, leading either to non-monotonic effective interaction with both repulsive and attractive branches when the surface charges are weakly disordered (small disorder variance) or to a dominating attractive interaction that is larger both in its range and magnitude than what is predicted from the van der Waals and image-induced, ion-depletion interactions, when the surfaces are strongly disordered (large disorder variance).

Strong coupling electrostatics for randomly charged surfaces: antifragility and effective interactions

We study the effective interaction mediated by strongly coupled Coulomb fluids between dielectric surfaces carrying quenched, random monopolar charges with equal mean and variance, both when the Coulomb fluid consists only of mobile multivalent counterions and when it consists of an asymmetric ionic mixture containing multivalent and monovalent (salt) ions in equilibrium with an aqueous bulk reservoir. We analyze the consequences that follow from the interplay between surface charge disorder, dielectric and salt image effects, and the strong electrostatic coupling that results from multivalent counterions on the distribution of these ions and the effective interaction pressure they mediate between the surfaces. In a dielectrically homogeneous system, we show that the multivalent counterions are attracted towards the surfaces with a singular, disorder-induced potential that diverges logarithmically on approach to the surfaces, creating a singular but integrable counterion density profile that exhibits an algebraic divergence at the surfaces with an exponent that depends on the surface charge (disorder) variance. This effect drives the system towards a state of lower thermal 'disorder', one that can be described by a renormalized temperature, exhibiting thus a remarkable antifragility. In the presence of an interfacial dielectric discontinuity, the singular behavior of counterion density at the surfaces is removed but multivalent counterions are still accumulated much more strongly close to randomly charged surfaces as compared with uniformly charged ones. The interaction pressure acting on the surfaces displays in general a highly non-monotonic behavior as a function of the inter-surface separation with a prominent regime of attraction at small to intermediate separations. This attraction is caused directly by the combined effects from charge disorder and strong coupling electrostatics of multivalent counterions, which dominate the surface-surface repulsion due to the (equal) mean charges on the two surfaces and the osmotic pressure of monovalent ions residing between them. These effects can be quite significant even with a small degree of surface charge disorder relative to the mean surface charge. The strong coupling, disorder-induced attraction is typically much stronger than the van der Waals interaction between the surfaces, especially within a range of several nanometers for the inter-surface separation, where such effects are predicted to be most pronounced.

Developing a general interaction potential for hydrophobic and hydrophilic interactions

We review direct force measurements on a broad class of hydrophobic and hydrophilic surfaces. These measurements have enabled the development of a general interaction potential per unit area, W(D) = -2γ(i)Hy exp(-D/D(H)) in terms of a nondimensional Hydra parameter, Hy, that applies to both hydrophobic and hydrophilic interactions between extended surfaces. This potential allows one to quantitatively account for additional attractions and repulsions not included in the well-known combination of electrostatic double layer and van der Waals theories, the so-called Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The interaction energy is exponentially decaying with decay length D(H) ≈ 0.3-2 nm for both hydrophobic and hydrophilic interactions, with the exact value of D(H) depending on the precise system and conditions. The pre-exponential factor depends on the interfacial tension, γ(i), of the interacting surfaces and Hy. For Hy > 0, the interaction potential describes interactions between partially hydrophobic surfaces, with the maximum hydrophobic interaction (i.e., two fully hydrophobic surfaces) corresponding to Hy = 1. Hydrophobic interactions between hydrophobic monolayer surfaces measured with the surface forces apparatus (SFA) are shown to be well described by the proposed interaction potential. The potential becomes repulsive for Hy < 0, corresponding to partially hydrophilic (hydrated) interfaces. Hydrated surfaces such as mica, silica, and lipid bilayers are discussed and reviewed in the context of the values of Hy appropriate for each system.

Electrostatic interaction between nonuniformly charged colloids: experimental and numerical study

The influence of the surface charge distribution on the interaction between nanosized particles in water is reported. The distribution of charges at the surface of initially neutral microemulsion droplets has been modulated by additions of various oligomeric cationic surfactants. The osmotic compressibility of the doped microemulsions was measured by light and small-angle neutrons scattering and reveals that the overall effective interaction induced by the ionic groups is repulsive. However, particular charge distributions decrease the osmotic compressibility much less than others. Independent measurements of the activity of the bromide counterions with specific electrodes evidence a significant decrease in the effective charge, which, however, cannot account for the osmotic compressibility in the framework of the primitive model. The q dependence of the structure factor reveals an attractive contribution over a short distance. Numerical studies assign this attractive contribution to the overlap of hydration shells that are extended as a result of the charge localization.

Measuring forces and spatiotemporal evolution of thin water films between an air bubble and solid surfaces of different hydrophobicity

A combination of atomic force microscopy (AFM) and reflection interference contrast microscopy (RICM) was used to measure simultaneously the interaction force and the spatiotemporal evolution of the thin water film between a bubble in water and mica surfaces with varying degrees of hydrophobicity. Stable films, supported by the repulsive van der Waals-Casimir-Lifshitz force were always observed between air bubble and hydrophilic mica surfaces (water contact angle, θ(w) < 5°) whereas bubble attachment occurred on hydrophobized mica surfaces. A theoretical model, based on the Reynolds lubrication theory and the augmented Young-Laplace equation including the effects of disjoining pressure, provided excellent agreement with experiment results, indicating the essential physics involved in the interaction between air bubble and solid surfaces can be elucidated. A hydrophobic interaction free energy per unit area of the form: WH(h) = -γ(1 - cos θ(w))exp(-h/D(H)) can be used to quantify the attraction between bubble and hydrophobized solid substrate at separation, h, with γ being the surface tension of water. For surfaces with water contact angle in the range 45° < θ(w) < 90°, the decay length DH varied between 0.8 and 1.0 nm. This study quantified the hydrophobic interaction in asymmetric system between air bubble and hydrophobic surfaces, and provided a feasible method for synchronous measurements of the interaction forces with sub-nN resolution and the drainage dynamics of thin films down to nm thickness.

Contact time- and pH-dependent adhesion and cohesion of low molecular weight chitosan coated surfaces

Low molecular weight chitosan (LMW chitosan, ∼5 kDa) potentially has many desirable biomedical applications such as anti-microbial, anti-tumor, and anti-diabetes. Unlike high molecular weight chitosan, LMW chitosan is easily dissolvable in aqueous solutions even at neutral and basic pH, but its dissolution mechanism is not well understood. Here, we measured adhesion and cohesion of molecularly thin LMW chitosan films in aqueous solutions in different buffer pHs (from 3.0 to 8.5) using a surface forces apparatus (SFA). Interestingly, significantly lower adhesion force was measured for LMW chitosan films compared to the high molecular weight chitosan (∼150 kDa) films. Not only the strength of adhesion is lower, but also the critical contact time where adhesion starts to increase with contact time is longer. The results from both the SFA and atomic force microscopy (AFM) indicate that, in physiological and basic conditions, the low cohesion of LMW chitosan due to the stiffness of the chain which cause strong electrostatic correlation energy penalty when they are aggregated. Here, we propose the reduction in cohesion for shorter chitosan (LMW chitosan) as an explanation of its high solubility of LMW chitosan in physiological pHs.

Influence of molecular dipole orientations on long-range exponential interaction forces at hydrophobic contacts in aqueous solutions

Strong and particularly long ranged (>100 nm) interaction forces between apposing hydrophobic lipid monolayers are now well understood in terms of a partial turnover of mobile lipid patches, giving rise to a correlated long-range electrostatic attraction. Here we describe similarly strong long-ranged attractive forces between self-assembled monolayers of carboranethiols, with dipole moments aligned either parallel or perpendicular to the surface, and hydrophobic lipid monolayers deposited on mica. We compare the interaction forces measured at very different length scales using atomic force microscope and surface forces apparatus measurements. Both systems gave a long-ranged exponential attraction with a decay length of 2.0 ± 0.2 nm for dipole alignments perpendicular to the surface. The effect of dipole alignment parallel to the surface is larger than for perpendicular dipoles, likely due to greater lateral correlation of in-plane surface dipoles. The magnitudes and range of the measured interaction forces also depend on the surface area of the probe used: At extended surfaces, dipole alignment parallel to the surface leads to a stronger attraction due to electrostatic correlations of freely rotating surface dipoles and charge patches on the apposing surfaces. In contrast, perpendicular dipoles at extended surfaces, where molecular rotation cannot lead to large dipole correlations, do not depend on the scale of the probe used. Our results may be important to a range of scale-dependent interaction phenomena related to solvent/water structuring on dipolar and hydrophobic surfaces at interfaces.

Restructuring of a model hydrophobic surface: Monte Carlo simulations using a simple coarse-grained model

A lattice model is proposed to explain the restructuring of an ionic surfactant absorbed on a charged surface. When immersed in water, an ionic mica plate initially covered by a monolayer of surfactants rearranges to a surface inhomogeneously covered by patches of surfactant bilayer and bare mica. The model considers four species that can cover lattice sites of a surface. These species include (i) a surfactant molecule with its headgroup down, (ii) surfactant molecule with the headgroup up, (iii) a surfactant dimer arranged in a tail-to-tail configuration, which is a part of a bilayer, and (iv) a mica lattice site covered by water. We consider that only nearest neighbors on the lattice interact and describe the interactions by an interaction matrix. Using this model, we perform Monte Carlo simulations and study how the structure of the inhomogeneous surface depends on the interaction between water covered lattice site and its neighboring surfactant species covered sites. We observe that when this interaction is absent, the system undergoes phase separation into a bilayer phase and mica surface covered with water. When this interaction is taken into account, patches of surfactant bilayer and water are present in our system. The interaction between mica surfaces covered by patches of ionic surfactants is studied in experiments to understand the nature of long-ranged "hydrophobic" forces.

pH-Dependent aggregation and disaggregation of native β-lactoglobulin in low salt

The aggregation of β-lactoglobulin (BLG) near its isoelectric point was studied as a function of ionic strength and pH. We compared the behavior of native BLG with those of its two isoforms, BLG-A and BLG-B, and with that of a protein with a very similar pI, bovine serum albumin (BSA). Rates of aggregation were obtained through a highly precise and convenient pH/turbidimetric titration that measures transmittance to ±0.05 %T. A comparison of BLG and BSA suggests that the difference between pHmax (the pH of the maximum aggregation rate) and pI is systematically related to the nature of protein charge asymmetry, as further supported by the effect of localized charge density on the dramatically different aggregation rates of the two BLG isoforms. Kinetic measurements including very short time periods show well-differentiated first and second steps. BLG was analyzed by light scattering under conditions corresponding to maxima in the first and second steps. Dynamic light scattering (DLS) was used to monitor the kinetics, and static light scattering (SLS) was used to evaluate the aggregate structure fractal dimensions at different quench points. The rate of the first step is relatively symmetrical around pHmax and is attributed to the local charges within the negative domain of the free protein. In contrast, the remarkably linear pH dependence of the second step is related to the uniform reduction in global protein charge with increasing pH below pI, accompanied by an attractive force due to surface charge fluctuations.

Tunable soft structure in charged fluids confined by dielectric interfaces

Fluids of charged particles act as the supporting medium for chemical reactions and physical, dynamical, and biological processes. The local structure in an electrolytic background is deformed by micro- and nanoscopic polarizable objects. Vice versa, the forces between the objects are regulated by the cohesive properties of the background. We study here the range and strength of these forces and the microscopic origin from which they emerge. We find the forces to be sensitively dependent on the material properties of the charged fluid and the immersed solutes. The induced interactions can be varied over decades, offering high tunability and aided by accurate theory, control in experiments and applications. To distinguish correlational effects from simple ionic screening, we describe electrolyte-induced forces between neutral objects. The interplay of thermal motion, short-range repulsions, and electrostatic forces is responsible for a soft structure in the fluid. This structure changes near polarizable interfaces and causes diverse attractions between confining walls that seem well-exploited by microbiological systems. For parameters that correspond to monovalent electrolytes in biologically and technologically relevant aqueous environments, we find induced forces between nanoscopic areas of the order of piconewtons over a few nanometers.

Attractive Forces between Charged Colloidal Particles Induced by Multivalent Ions Revealed by Confronting Aggregation and Direct Force Measurements

Interactions involving charged particles in the presence of multivalent ions are relevant in wide-range of phenomena, including condensation of nucleic acids, cement hardening, or water treatment. Here, we study such interactions by combining direct force measurements with atomic force microscopy (AFM) and aggregation studies with time-resolved light scattering for particles originating from the same colloidal suspension for the first time. Classical DLVO theory is found to be only applicable for monovalent and divalent ions. For ions of higher valence, charge inversion and additional non-DLVO attractive forces are observed. These attractive forces can be attributed to surface charge heterogeneities, which leads to stability ratios that are calculated from direct force measurements to be higher than the experimental ones. Ion-ion correlations are equally important as they induce the charge inversion in the presence of trivalent or tetravalent ions, and they enhance the surface charge heterogeneities. Such heterogeneities therefore play an essential role in controlling interactions in particle suspensions containing multivalent ions.

Interaction between heterogeneously charged surfaces: surface patches and charge modulation

When solid surfaces are immersed in aqueous solutions, some of their charges can dissociate and leave behind charged patches on the surface. Although the charges are distributed heterogeneously on the surface, most of the theoretical models treat them as homogeneous. For overall non-neutral surfaces, the assumption of surface charge homogeneity is rather reasonable since the leading terms of two such interacting surfaces depend on the nonzero average charge. However, for overall neutral surfaces the nature of the surface charge distribution is crucial in determining the intersurface interaction. In the present work we study the interaction between two charged surfaces across an aqueous solution for several charge distributions. The analysis is preformed within the framework of the linearized Poisson-Boltzmann theory. For periodic charge distributions the interaction is found to be repulsive at small separations, unless the two surface distributions are completely out-of-phase with respect to each other. For quenched random charge distributions we find that due to the presence of the ionic solution in between the surfaces, the intersurface repulsion dominates over the attraction in the linear regime of the Poisson-Boltzmann theory. The effect of quenched charge heterogeneity is found to be particularly substantial in the case of large charged domains.

Electrostatic interaction of heterogeneously charged surfaces with semipermeable membranes

In this paper we study the electrostatic interaction of a heterogeneously charged wall with a neutral semipermeable membrane. The wall consists of periodic stripes, where the charge density varies in one direction. The membrane is in contact with a bulk reservoir of an electrolyte solution and separated from the wall by a thin film of salt-free liquid. One type of ions (small counterions) permeates into the gap. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure due to an overlap of counterion clouds in the gap. To quantify it we use two complementary approaches. First, we propose a mean-field theory based on a linearized Poisson-Boltzmann equation and Fourier analysis. These calculations allow us to estimate the effect of a heterogeneous charge pattern at the wall on the induced heterogeneous membrane potential, and the value of the disjoining pressure as a function of the gap. Second, we perform Langevin dynamics simulations of the same system with explicit ions. The results of the two approaches are in good agreement with each other at low surface charges and small gaps, but differ due to nonlinearity at higher charges. These results demonstrate that a heterogeneity of the wall charge can lead to a huge reduction in the electrostatic repulsion, which could dramatically facilitate self-assembly in complex synthetic and biological systems.

Time dependence of interactions between a surfactant-coated substrate and a uniformly charged surface

Using the surface force balance (SFB), we recorded the changes with time of the adhesion, normal, and shear interactions between a monolayer of cetyltrimethylammonium bromide (CTAB) on mica and a bare mica surface across surfactant-free water. In this asymmetric case, the bare mica acts a stable probe of the interactions between the two surfaces as the CTAB-coated one undergoes changes with time. As previously demonstrated, when a CTAB monolayer on mica is immersed in water, it reorganized to form bilayer patches, exposing the bare mica surface, followed by a gradual release of free surfactants to the bulk. We probe how this degradation with time affects both the normal force vs distance interaction profiles, and adhesion between the CTAB-coated surface and a bare mica surface. We demonstrate that the CTAB layer leads to a reduction in the sliding friction relative to that between bare mica surfaces, which is reversed only at advanced degradation levels, whereupon an abrupt increase in the friction occurs. This change is ascribed to adhesion between exposed bare mica surfaces, which sets on when the density of CTAB patches is low. The reproducibility of the normal force profiles and of adhesion forces on sequential approaches at the same contact spot indicates that there is no substantial transfer of materials between the surfaces while they are in adhesive contact.

Nanofluids mediating surface forces

Fluids containing nanostructures, known as nanofluids, are increasingly found in a wide array of applications due to their unique physical properties as compared with their base fluids and larger colloidal suspensions. With several tuneable parameters such as the size, shape and surface chemistry of nanostructures, as well as numerous base fluids available, nanofluids also offer a new paradigm for mediating surface forces. Other properties such as local surface plasmon resonance and size dependent magnetism of nanostructures also present novel mechanisms for imparting tuneable surface interactions. However, our fundamental understanding, experimentally and theoretically, of how these parameters might affect surface forces remains incomplete. Here we review recent results on equilibrium and dynamic surface forces between macroscopic surfaces in nanofluids, highlighting the overriding trends in the correlation between the physical parameters that characterise nanofluids and the surface forces they mediate. We also discuss the challenges that confront existing surface force knowledge as a result of this new paradigm.

Long-ranged attraction between disordered heterogeneous surfaces

Interactions in aqueous media between uniformly charged surfaces are well understood, but most real surfaces are heterogeneous and disordered. Here we show that two such heterogeneous surfaces covered with random charge domains experience a long-range attraction across water that is orders of magnitude stronger than van der Waals forces, even in the complete absence of any charge correlations between the opposing surfaces. We demonstrate that such strong attraction may arise generally, even for overall neutral surfaces, from the inherent interaction asymmetry between equally and between oppositely charged domains.

Effect of charge inhomogeneity and mobility on colloid aggregation

The aggregation of inhomogeneously charged colloids with the same average charge is analyzed using Monte Carlo simulations. We find aggregation of colloids for sizes in the range 10-200 nm, which is similar to the range in which aggregation is observed in several experiments. The attraction arises from the strongly correlated electrostatic interactions associated with the increase in the counterion density in the region between the particles; this effect is enhanced by the discreteness and mobility of the surface charges. Larger colloids attract more strongly when their surface charges are discrete. We study the aggregation as functions of the surface charge density, counterion valence, and volume fraction.

Forces between hydrophobic solids in concentrated aqueous salt solution

Much research has focused on the discovery and description of long-ranged forces between hydrophobic solids immersed in water. Here we show that the force between high contact-angle solids in concentrated salt solution (1 M KCl) agrees very well with van der Waals forces calculated from Lifshitz theory for separations greater than 5 nm. The hydrophobic solids are octadecyltrichlorosilane-coated glass, with an advancing contact angle of 108°. Thus, in 1 M salt solution, it is unnecessary to invoke the presence of a hydrophobic force at separations greater than 5 nm. Through measurement in salt solution, we avoid the necessity of accounting for large electrostatic forces that frequently occur in pure water and may obscure resolution of other forces.

Sample-to-sample torque fluctuations in a system of coaxial randomly charged surfaces

Polarizable randomly charged dielectric objects have been recently shown to exhibit long-range lateral and normal interaction forces even when they are effectively net-neutral. These forces stem from an interplay between the quenched statistics of random charges and the induced dielectric image charges. This type of interaction has recently been evoked to interpret measurements of Casimir forces in vacuo, where a precise analysis of such disorder-induced effects appears to be necessary. Here we consider the torque acting on a randomly charged dielectric surface (or a sphere) mounted on a central axle next to another randomly charged surface and show that although the resultant mean torque is zero, its sample-to-sample fluctuation exhibits a long-range behavior with the separation distance between the juxtaposed surfaces and that, in particular, its root-mean-square value scales with the total area of the surfaces. Therefore, the disorder-induced torque between two randomly charged surfaces is expected to be much more pronounced than the disorder-induced lateral force and may provide an effective way to determine possible disorder effects in experiments, in a manner that is independent of the usual normal force measurement.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: theory versus experiment

Aqueous dispersions of phosphatidylglycerol (PG) lipids may present an anomalous chain-melting transition at low ionic strengths, as seen by different experimental techniques such as calorimetry or light scattering. The anomaly disappears at high ionic strengths or for longer acyl-chain lengths. In this article, we use a statistical model for the bilayer that distinguishes both lipid chain and headgroup states in order to compare model and experimental thermotropic and electrical properties. The effective van der Waals interactions among hydrophobic chains compete with the electrostatic repulsions between polar headgroups, which may be ionized (counterion dissociated) or electrically neutral (associated with counterions). Electric degrees of freedom introduce new thermotropic charge-ordered phases in which headgroup charges may be spatially ordered, depending on the electrolyte ionic strength, introducing a new rationale for experimental data on PGs. The thermal phases presented by the model for different chain lengths, at fixed ionic strength, compare well with an experimental phase diagram constructed on the basis of differential scanning calorimetry profiles. In the case of dispersions of DMPG (dimyristoyl phosphatidylglycerol) with added monovalent salt, the model properties reproduce the main features displayed by data from differential scanning calorimetry as well as the characteristic profile for the degree of ionization of the bilayer surface across the anomalous transition region, obtained from the theoretical interpretation of electrokinetic (conductivity and electrophoretic mobility) measurements.

Restructuring of hydrophobic surfaces created by surfactant adsorption to mica surfaces

Hydrophobic surfaces created by the adsorption of a monolayer of surfactants, such as CTAB or DODAB, to mica display long-range mutual attraction when placed in water. Initially, this attraction was considered to be due to hydrophobic interaction, but more careful measurements using AFM showed that the surfactant monolayer undergoes rearrangements to produce charged patches on the surface; therefore, the nature of the long-range interaction is due to the electrostatic interaction between patches. The monolayer rearrangement depends on the nature of the surfactant and its counterion. To study possible monolayer rearrangements in molecular detail, we performed detailed molecular dynamics computer simulations on systems containing a monolayer of surfactants RN(CH(3))(3)(+)Cl(-) (R indicates a saturated hydrocarbon chain) adsorbed on a mica surface and immersed in water. We observe that when chain R is 18 carbons long the monolayer rearranges into a micelle but it remains a monolayer when the chain contains 24 carbons.

Long-range interaction between heterogeneously charged membranes

Despite their neutrality, surfaces or membranes with equal amounts of positive and negative charge can exhibit long-range electrostatic interactions if the surface charge is heterogeneous; this can happen when the surface charges form finite-size domain structures. These domains can be formed in lipid membranes where the balance of the different ranges of strong but short-ranged hydrophobic interactions and longer-ranged electrostatic repulsion result in a finite, stable domain size. If the domain size is large enough, oppositely charged domains in two opposing surfaces or membranes can be strongly correlated by the electrostatic interactions; these correlations give rise to an attractive interaction of the two membranes or surfaces over separations on the order of the domain size. We use numerical simulations to demonstrate the existence of strong attractions at separations of tens of nanometers. Large line tensions result in larger domains but also increase the charge density within the domain. This promotes correlations and, as a result, increases the intermembrane attraction. On the other hand, increasing the salt concentration increases both the domain size and degree of domain anticorrelation, but the interactions are ultimately reduced due to increased screening. The result is a decrease in the net attraction as salt concentration is increased.

Sample-to-sample fluctuations of electrostatic forces generated by quenched charge disorder

It has been recently shown that randomly charged surfaces can exhibit-long range electrostatic interactions even when they are net neutral. These forces depend on the specific realization of charge disorder and thus exhibit sample-to-sample fluctuations about their mean value. We analyze the fluctuations of these forces in the parallel slab configuration and in the sphere-plane geometry via the proximity force approximation. The fluctuations of the normal forces, which have a finite mean value, are computed exactly. Surprisingly, we also show that fluctuations in lateral forces are present, despite the fact that they have a zero mean, and that they have the same scaling behavior as the normal force fluctuations. The measurement of these lateral force fluctuations could help us to characterize the effects of charge disorder in experimental systems, leading to estimates of their magnitudes that are complementary to those given by normal force measurements.