Structure of electrolyte solutions at nonuniformly charged surfaces on a variety of length scales

The structures of dilute electrolyte solutions close to nonuniformly charged planar substrates are systematically studied within the entire spectrum of microscopic to macroscopic length scales by means of a unified classical density functional theory approach. This is in contrast to previous investigations, which are applicable either to short or to long length scales. It turns out that interactions with microscopic ranges, e.g., due to the hard cores of the fluid molecules and ions, have a negligible influence on the formation of nonuniform lateral structures of the electrolyte solutions. This partly justifies the Debye-Hückel approximation schemes applied in previous studies of that system. In general, a coupling between the lateral and the normal fluid structures leads to the phenomenology that, upon increasing the distance from the substrate, fewer details of the lateral nonuniformities contribute to the fluid structure, such that ultimately only large-scale surface features remain relevant. It can be expected that this picture also applies to other fluids characterized by several length scales.

Structural and electrostatic properties between pH-responsive polyelectrolyte brushes studied by augmented strong stretching theory

In this paper, we study electrostatic and structural properties between pH-responsive polyelectrolyte brushes by using a strong stretching theory accounting for excluded volume interactions, the density of polyelectrolyte chargeable sites and the Born energy difference between the inside and outside of the brush layer.In a free energy framework, we obtain self-consistent field equations to determine electrostatic properties between two pH-responsive polyelectrolyte brushes. We elucidate that in the region between two pH-responsive polyelectrolyte brushes, electrostatic potential at the centerline and osmotic pressure increase not only with excluded volume interaction, but also with density of chargeable sites on a polyelectrolyte molecule. Importantly, we clarify that when two pH-responsive polyelectrolyte brushes approach each other, the brush thickness becomes short and that a large excluded volume interaction and a large density of chargeable sites yield the enhanced contract of polyelectrolyte brushes. In addition, we also demonstrate how the influence of such quantities as pH, the number of Kuhn monomers, the density of charged sites, the lateral separation between adjacent polyelectrolyte brushes, Kuhn length on the electrostatic and structural properties between the two polyelectrolyte brushes is affected by the exclusion volume interaction. Finally, we investigate the influence of Born energy difference on the thickness of polyelectrolyte brushes and the osmotic pressure between two pH-responsive polyelectrolyte brushes.

Unifying disparate rate-dependent rheological regimes in non-Brownian suspensions

A typical dense non-Brownian particulate suspension exhibits shear thinning (decreasing viscosity) at low shear rate or stress followed by a Newtonian plateau (constant viscosity) at intermediate shear rate or stress values which transitions to shear thickening (increasing viscosity) beyond a critical shear rate or stress value and finally undergoes a second shear thinning transition at extremely high shear rate or stress values. In this study, we unify and quantitatively reproduce all the disparate rate-dependent regimes and the corresponding transitions for a dense non-Brownian suspension with increasing shear rate or stress. We employ discrete particle dynamics simulations based on the proposed mechanism to elucidate its accuracy. We find that a competition between interparticle interactions of hydrodynamic and nonhydrodynamic origins and the switching in the dominant stress scale with increasing the shear rate or stress lead to each of the above transitions. Inclusion of traditional hydrodynamic interactions, attractive or repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions the interparticle contact interactions, and a constant friction (or other constraint mechanism) reproduces the initial thinning as well as the shear thickening transition. However, to quantitatively capture the intermediate Newtonian plateau and the second shear thinning, an additional nonhydrodynamic interaction of non-DLVO origin and a decreasing coefficient of friction, respectively, are essential, thus providing an explanation for the presence of the intermediate Newtonian plateau along with reproducing the second shear thinning in a single framework. Expressions utilized for various interactions and friction are determined from experimental measurements and hence result in excellent quantitative agreement between the simulations and previous experiments.

Effect of Nonzero Solid Permittivity on the Electrical Repulsion between Charged Surfaces

The electrical repulsion between two charged solid surfaces separated by an electrolyte is studied as a function of the permittivity ϵ_s of the solid in the limit in which potentials are small, and the gap between the plane solid surfaces is small compared to the Debye length κ^-1 within the electrolyte. The solid surfaces are uniformly charged in a central region |x|< L outside which they are uncharged. When ϵ_s = 0, ions from the charge cloud between the charged surfaces spill out into regions of length O(κ^-1) beyond x = ± L, thereby reducing the pressure between the surfaces from that predicted by Derjaguin-Landau-Verwey-Overbeek theory for infinite, uniformly charged surfaces. When ϵ_s>0, ions spill out over much larger O(L) regions, thereby reducing still further both the electrical potential between the solid surfaces and the repulsive force between them. However, this reduction becomes smaller as κL becomes large.

Adhesion Properties of Freestanding Hydrophobin Bilayers

Hydrophobins are a family of small-sized proteins featuring a distinct hydrophobic patch on the protein's surface, rendering them amphiphilic. This particularity allows hydrophobins to self-assemble into monolayers at any hydrophilic/hydrophobic interface. Moreover, stable pure protein bilayers can be created from two interfacial hydrophobin monolayers by contacting either their hydrophobic or their hydrophilic sides. In this study, this is achieved via a microfluidic approach, in which also the bilayers' adhesion energy can be determined. This enables us to study the origin of the adhesion of hydrophobic and hydrophilic core bilayers made from the class II hydrophobins HFBI and HFBII. Using different fluid media in this setup and introducing genetically modified variants of the HFBI molecule, the different force contributions to the adhesion of the bilayer sheets are studied. It was found that in the hydrophilic contact situation, the adhesive interaction was higher than that in the hydrophobic contact situation and could be even enhanced by reducing the contributions of electrostatic interactions. This effect indicates that the van der Waals interaction is the dominant contribution that explains the stability of the observed bilayers.

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.

Electrostatic interaction of soft particles

Theories of the electrostatic interaction between two soft particles (i.e., particles covered with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution are reviewed. Interactions of soft particles after contact of their surface layers are particularly discussed. Interaction in a salt-free medium and the discrete-charge effect are also treated.

Polyelectrolyte adsorption, interparticle forces, and colloidal aggregation

This review summarizes the current understanding of adsorption of polyelectrolytes to oppositely charged solid substrates, the resulting interaction forces between such substrates, and consequences for colloidal particle aggregation. The following conclusions can be reached based on experimental findings. Polyelectrolytes adsorb to oppositely charged solid substrates irreversibly up to saturation, whereby loose and thin monolayers are formed. The adsorbed polyelectrolytes normally carry a substantial amount of charge, which leads to a charge reversal. Frequently, the adsorbed films are laterally heterogeneous. With increasing salt levels, the adsorbed mass increases leading to thicker and more homogeneous films. Interaction forces between surfaces coated with saturated polyelectrolyte layers are governed at low salt levels by repulsive electric double layer interactions, and particle suspensions are stable under these conditions. At appropriately high salt levels, the forces become attractive, principally due to van der Waals interactions, but eventually also through other forces, and suspensions become unstable. This situation can be rationalized with the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). Due to the irreversible nature of the adsorption process, stable unsaturated layers form in colloidal particle suspensions at lower polyelectrolyte doses. An unsaturated polyelectrolyte layer can neutralize the overall particle surface charge. Away from the charge reversal point, electric double layer forces are dominant and particle suspensions are stable. As the charge reversal point is approached, attractive van der Waals forces become important, and particle suspensions become unstable. This behaviour is again in line with the DLVO theory, which may even apply quantitatively, provided the polyelectrolyte films are sufficiently laterally homogeneous. For heterogeneous films, additional attractive patch-charge interactions may become important. Depletion interactions may also lead to attractive forces and suspension destabilization, but such interactions become important only at high polyelectrolyte concentrations.

Dendrimer induced interaction forces between colloidal particles revealed by direct force and aggregation measurements

Interaction forces and aggregation rates were determined in order to characterize colloid stability of negative carboxyl latex particles in the presence of oppositely charged poly(amido amine) (PAMAM) dendrimers of three different generations G4, G7 and G10. The force profiles were measured by the atomic force microscopy (AFM) based on multi-particle colloidal probe technique. Close to the isoelectric point, the measured force profiles were more attractive than the pure van der Waals interactions. This behavior was rationalized in term of an additional electrostatic patch-charge contribution whose magnitude increases by increasing the dendrimer generation. The aggregation rates were calculated from these results using the classical theory developed by Derjaguin, Landau, Verwey and Overbeek (DLVO) as well as including the additional attractive term and a radially symmetric force field. The calculated aggregation rates were compared to the ones obtained directly from time-resolved dynamic light scattering (DLS) measurements using exactly the same latex particles as in the AFM study. The results from these two methods were in good agreement in the case of dendrimers of lower generation, while at higher generation, significant differences were found. In the latter case, the stability ratio in the slow aggregation regime extracted from direct force measurements was much higher than the one measured experimentally by DLS. Despite the fact that the additional attractive term was included in the calculation, the discrepancy between the two different stability ratios suggests that the assumption of radial symmetric interaction is weak.

Poisson-Boltzmann description of interaction forces and aggregation rates involving charged colloidal particles in asymmetric electrolytes

Forces and aggregation rates involving spherical particles are studied numerically within the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) for asymmetric and mixed electrolytes. Thereby, the double layer interactions are treated at the Debye-Hückel (DH) and Poisson-Boltzmann (PB) levels. The DH model is applicable for weakly charged systems, and effects of ion valence enter only implicitly through the ionic strength. The PB model is necessary for more highly charged systems, and depends on the actual ionic composition. One finds that forces in asymmetric electrolytes at fixed ionic strength weaken when the valence of the counterions is increased or when the valence of the coions is decreased. In symmetric electrolytes, the effect of counterions is more important than the one of the coions. For weakly charged systems, the critical coagulation concentration (CCC) decreases with the square of the valence in symmetric electrolytes, while this decrease is weaker in asymmetric ones. With increasing charge density, the dependence of the CCC on the valence becomes stronger, but the classical Schulze-Hardy decrease with the sixths power of the valence is only recovered for unrealistically high charge densities. Mixtures of electrolytes are treated within the same framework, and one observes that already small amounts of multivalent ions affect the system considerably. An empirical mixing rule is proposed to describe the calculated CCCs.

Investigating forces between charged particles in the presence of oppositely charged polyelectrolytes with the multi-particle colloidal probe technique

Direct force measurements are used to obtain a comprehensive picture of interaction forces acting between charged colloidal particles in the presence of oppositely charged polyelectrolytes. These measurements are achieved by the multi-particle colloidal probe technique based on the atomic force microscope (AFM). This novel extension of the classical colloidal probe technique offers three main advantages. First, the technique works in a colloidal suspension with a huge internal surface area of several square meters, which simplifies the precise dosing of the small amounts of the polyelectrolytes needed and makes this approach less sensitive to impurities. Second, the particles are attached in-situ within the fluid cell, which avoids the formation of nanobubbles on the latex particles used. Third, forces between two similar particles from the same batch are being measured, which allows an unambiguous determination of the surface potential due to the symmetry of the system. Based on such direct force measurements involving positively and negatively charged latex particles and different polyelectrolytes, we find the following forces to be relevant. Repulsive electrostatic double-layer forces and attractive van der Waals forces as described by the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) are both important in these systems, whereby the electrostatic forces dominate away from the isoelectric point (IEP), while at this point they vanish. Additional non-DLVO attractive forces are operational, and they have been identified to originate from the electrostatic interactions between the patch-charge heterogeneities of the adsorbed polyelectrolyte films. Highly charged polyelectrolytes induce strong patch-charge attractions, which become especially important at low ionic strengths and high molecular mass. More weakly charged polyelectrolytes seem to form more homogeneous films, whereby patch-charge attractions may become negligible. Individual bridging events could be only rarely identified from the retraction part of the force profiles, and therefore we conclude that bridging forces are unimportant in these systems.

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.

Influence of the degree of ionization and molecular mass of weak polyelectrolytes on charging and stability behavior of oppositely charged colloidal particles

Positively charged amidine latex particles are studied in the presence of poly(acrylic acid) (PAA) with different molecular masses under neutral and acidic conditions by electrophoresis and time-resolved dynamic light scattering. Under neutral conditions, where PAA is highly charged, the system is governed by the charge reversal induced by the quantitatively adsorbing polyelectrolyte and attractive patch-charge interactions. Under acidic conditions, where PAA is more weakly charged, the following two effects come into play. First, the lateral structure of the adsorbed layers becomes more homogeneous, which weakens the attractive patch-charge interactions. Second, polyelectrolyte adsorption is no longer quantitative and partitioning into the solution phase is observed, especially for PAA of low molecular mass.

Self-assembled bilayers from the protein HFBII hydrophobin: nature of the adhesion energy

The hydrophobins are a class of amphiphilic proteins which spontaneously adsorb at the air/water interface and form elastic membranes of high mechanical strength as compared to other proteins. The mechanism of hydrophobin adhesion is of interest for fungal biology and for various applications in electronics, medicine, and food industry. We established that the drainage of free foam films formed from HFBII hydrophobin solutions ends with the appearance of a 6 nm thick film, which consists of two layers of protein molecules, that is, it is a self-assembled bilayer (S-bilayer), with hydrophilic domains pointing inward and hydrophobic domains pointing outward. Its formation is accompanied by a considerable energy gain, which is much greater than that typically observed with free liquid films. The experiments at different pH show that this attraction between the "hydrophilic" parts of the HFBII molecules is dominated by the short-range hydrophobic interaction rather than by the patch-charge electrostatic attraction.

Electrostatic potential and double layer force in a semiconductor-electrolyte-semiconductor heterojunction

This paper reports a theoretical study of the electrostatic potential within a so-called pen-heterojunction made up of two semi-infinite, doped semiconductor media separated by an electrolyte region. An external potential is then applied across the entire system. Both the electrostatic potentials and double layer surface forces are studied as functions of the usual double layer system properties, semiconductor properties such as doping concentrations of acceptor and donator atoms, as well as applied potential. We find that both attractive and repulsive forces are possible depending on the surface charges on the electrolyte-semiconductor interfaces, and that these forces can be significantly modified by the applied potential and by the doping levels in the semiconductors.

Electrokinetics of heterogeneous interfaces

The influence of surface heterogeneity of various types on electrokinetic parameters is reviewed. The scope of the paper covers classical electrokinetic phenomena characterized by linear dependence of electrokinetic parameters vs. related driving forces. Neither non-linear effects nor the effects of non-equilibrium electric double layer are considered. A historical description of hydrodynamic aspect of electrokinetic phenomena exploiting the slip plane idea is briefly outlined. Attempts to estimate the slip plane location by comparing the diffuse layer and zeta potential values for some model systems are presented. The surface heterogeneity was divided into three categories. Heterogeneity of the first type was related to geometrical morphology of an interfacial region characterized by a considerable surface development producing a three-dimensional interfacial region. The effects of solid roughness, hairy surface, dense polymer layers and gel-like layers are discussed here. The very high surface conductivity detected for such interfaces seems to be a good indicator of the presence of structured layers of this type. Heterogeneous interfaces of the second class cover systems exhibiting non-uniform distribution of surface charge. The non-uniform surface charge distribution can be either of a molecular (discrete charges) or of a microscale (two-dimensional micropatches or three-dimensional structures formed by polyelectrolyte multilayers). The last class of systems examined includes interfaces composed of charged substrate covered by charged bulky objects (particles). In comparison to the homogeneous surfaces, adsorbed charged particles modify both hydrodynamic flow and the electrostatic field significantly altering the electrokinetic parameters. The new description of electrokinetics of composed interfaces presented here takes into account both hydrodynamic and electric field modification and is free of the previously assumed slip plane shift caused by adsorbed objects. This theoretical approach verified by experiments performed on well defined model systems can be successfully applied to the interpretation of experimental data obtained for surfaces covered by objects difficult to detect.

Lateral inhomogeneous lipid membranes: theoretical aspects

The physical concepts underlying the lateral distribution of the components forming a lamellar assembly of amphiphiles are discussed in this review. The role of amphiphiles' molecular structure and/or aqueous environment (ionic strength, water soluble substances) on formation and stability of lateral patterns is investigated. A considerable effort is devoted to the analysis of the properties of patterned structure which can be different from those of randomly mixed multi-component lamellae. Examples include adhesion and fusion among laterally inhomogeneous bilayers, enhanced interfacial adsorption of ions and polymers, enhanced transport across the bilayer, modified mechanical properties, local stabilization of non-planar geometries (pores, edges) and related phenomena (electroporation, budding transition and so on). Furthermore, an analysis of chemical reactivity within or at the water interface of a laterally inhomogeneous bilayer is briefly discussed. A link between these concepts and experimental findings taken from the biological literature is attempted throughout the review.