Attractive Electrostatic Forces between Identical Colloidal Particles Induced by Adsorbed Polyelectrolytes

Critical adsorption and charge reversal in polyelectrolyte solutions: Analytical mean-field theory

An analytical linearized mean-field theory is presented to describe the adsorption behavior of polyelectrolytes near charged colloidal surfaces with additional short-ranged non-electrostatic interactions. The coupling between the polyelectrolyte segment density and electrostatic potential is explicitly accounted for in a self-consistent manner. This coupling gives rise to highly non-linear behavior, such as oscillations of the electrostatic potential. We derive analytical expressions for the critical surface charge density σc, after which adsorption takes place, and recover the well-known σc∼ns3/2 scaling regime, where ns is the salt concentration. In addition, the theory yields a new ns1 scaling regime if the surface is hard and a unified ns1 scaling regime if the surface also possesses some short-ranged attraction with the polyelectrolyte. Furthermore, we derive an analytical expression to describe the critical polyelectrolyte concentration φc to achieve complete charge reversal, which is found to scale as φc ∼ σ2/(f2c2), where c is related to the magnitude of short-ranged interactions and f is the average charge per monomer of the polyelectrolyte. It is observed that within our theory, complete charge reversal can only take place if the short-ranged interactions are sufficiently strong to completely compensate for the entropy loss of adsorption.

An efficient method to establish electrostatic screening lengths of restricted primitive model electrolytes

We present a novel, and computationally cheap, way to estimate electrostatic screening lengths from simulations of restricted primitive model (RPM) electrolytes. We demonstrate that the method is accurate by comparisons with simulated long-ranged parts of the charge density, at various Bjerrum lengths, salt concentrations and ion diameters. We find substantial underscreening in low dielectric solvent, but with an "aqueous" solvent, there is instead overscreening, the degree of which increases with ion size. Our method also offers a possible path to (future) more accurate classical density functional treatments of ionic fluids.

Probing and Manipulating Noncovalent Interactions in Functional Polymeric Systems

Noncovalent interactions, which usually feature tunable strength, reversibility, and environmental adaptability, have been recognized as driving forces in a variety of biological and chemical processes, contributing to the recognition between molecules, the formation of molecule clusters, and the establishment of complex structures of macromolecules. The marriage of noncovalent interactions and conventional covalent polymers offers the systems novel mechanical, physicochemical, and biological properties, which are highly dependent on the binding mechanisms of the noncovalent interactions that can be illuminated via quantification. This review systematically discusses the nanomechanical characterization of typical noncovalent interactions in polymeric systems, mainly through direct force measurements at microscopic, nanoscopic, and molecular levels, which provide quantitative information (e.g., ranges, strengths, and dynamics) on the binding behaviors. The fundamental understandings of intermolecular and interfacial interactions are then correlated to the macroscopic performances of a series of noncovalently bonded polymers, whose functions (e.g., stimuli-responsiveness, self-healing capacity, universal adhesiveness) can be customized through the manipulation of the noncovalent interactions, providing insights into the rational design of advanced materials with applications in biomedical, energy, environmental, and other engineering fields.

Repulsive Interactions of Eco-corona-Covered Microplastic Particles Quantitatively Follow Modeling of Polymer Brushes

The environmental fate and toxicity of microplastic particles are dominated by their surface properties. In the environment, an adsorbed layer of biomolecules and natural organic matter forms the so-called eco-corona. A quantitative description of how this eco-corona changes the particles' colloidal interactions is still missing. Here, we demonstrate with colloidal probe-atomic force microscopy that eco-corona formation on microplastic particles introduces a compressible film on the surface, which changes the mechanical behavior. We measure single particle-particle interactions and find a pronounced increase of long-range repulsive interactions upon eco-corona formation. These force-separation characteristics follow the Alexander-de Gennes (AdG) polymer brush model under certain conditions. We further compare the obtained fitting parameters to known systems like polyelectrolyte multilayers and propose these as model systems for the eco-corona. Our results show that concepts of fundamental polymer physics, like the AdG model, also help in understanding more complex systems like biomolecules adsorbed to surfaces, i.e., the eco-corona.

Nanoparticle and bioparticle deposition kinetics

Mechanisms and kinetic of particle deposition at solid surfaces leading to the formation of self-assembled layers of controlled structure and density were reviewed. In the first part theoretical aspects were briefly discussed, comprising limiting analytical solutions for the linear transport under flow and diffusion. Methods of the deposition kinetics analysis for non-linear regimes affected by surface blocking were also considered. Characteristic monolayer formation times under diffusion and flow for the nanoparticle size range were calculated. In the second part illustrative experimental results obtained for micro- and nanoparticles were discussed. Deposition at planar substrates was analyzed with emphasis focused on the stability of layers and the release kinetics of silver particles. Applicability of the quartz microbalance measurements (QCM) for quantitative studies of nanoparticle deposition kinetic was also discussed. Except for noble metal and polymer particles, representative results for virus deposition at abiotic surfaces were analyzed. Final part of the review was devoted to nanoparticle corona formation at polymer carrier particles investigated by combination of the concentration depletion, AFM, SEM and the in situ electrokinetic method. It is argued that the results obtained for colloid particles can be used as reliable reference systems for interpretation of protein and other bioparticle deposition, confirming the thesis that simple is universal.

Interactions between conducting surfaces in salt solutions

In this work, we simulate interactions between two perfectly conducting surfaces, immersed in a salt solution. We demonstrate that these forces are quantitatively different from those between (equally charged) non-conducting surfaces. There is, for instance, a significant repulsion between net neutral surfaces. On the other hand, there are also qualitative similarities, with behaviours found with non-conducting surfaces. For instance, there is a non-monotonic dependence of the free energy barrier height, on the salt concentration, and the minimum essentially coincides with a flat profile of the apparent surface charge density (i.e. the effective net surface charge density, some distance away from the surface, when accounting for ion neutralization), outside the so-called Stern layer. These conditions can be described as "perfect surface charge neutralization". Despite observed quantitative differences, we demonstrate that it might be possible to mimic a dispersion containing charged colloidal metal particles by a simpler model system with charged non-conducting particles, using modified particle-ion interactions.

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.

Overcharging and Free Energy Barriers for Equally Charged Surfaces Immersed in Salt Solutions

The stability of dispersions containing charged particles may obviously be regulated by salt. In some systems, the effective charge, as measured by the potential some small distance away from the particles, can have a sign opposite to the bare surface charge. If charge reversal takes place, there is typically a salt concentration regime within which colloidal stability increases with added salt. These experimental findings on dispersions have been corroborated by atomic force microscopy investigations, where an attraction is found at short separations. This attraction is stronger than expected from standard DLVO theory, and there has been considerable debate concerning its origin. In this work, we use simple coarse-grained models of these systems, where the bare surfaces carry a uniform charge density, and ion-specific adsorption is absent. Our hypothesis is that these experimental observations can be explained by such a simplistic pure Coulomb based model. Our approach entails grand canonical Metropolis Monte Carlo (MC) simulations as well as correlation-corrected Poisson-Boltzmann (cPB) calculations. In the former case, all ions have a common size, while the cPB utilizes a point-like model. We devote significant attention on apparent surface charge densities and interactions between large flat model surfaces immersed in either a 2:1 salt or a 3:1 salt. In contrast to most of the previous theoretical efforts in this area, we mainly focus on the weak long-ranged repulsion and its connection to an effective surface charge. We find a charge reversal and a concomitant development of a free energy barrier for both salts. The experimentally observed nonmonotonic dependence of colloidal stability on the salt concentration is reproduced using MC simulations as well as cPB calculations. A strong attraction is observed at short range for all investigated cases. We argue that in our model, all non-DLVO aspects can be traced to ion-ion correlations.

Nonelectrostatic Adsorption of Polyelectrolytes and Mediated Interactions between Solid Surfaces

Polymer-mediated interaction between two solid surfaces is directly connected to the properties of the adsorbed polymer layers. Nonelectrostatic interactions with a surface can significantly impact the adsorption of polyelectrolytes to charged surfaces. We use a classical density functional theory to study the effect of various polyelectrolyte solution properties on the adsorption and interaction between two like-charged surfaces. Our results show that nonelectrostatic interactions not only enhance polyelectrolyte adsorption but can also result in qualitatively different salt effects with respect to the adsorbed amount. In particular, we observe decreasing, increasing, and a previously unreported nonmonotonic behavior in the adsorbed amount of polymer with added salt under the conditions studied, although the nonmonotonic regime only occurs for a narrow range in the parameter space. With sufficient nonelectrostatic adsorption, the adsorbed polymer layers produce a long-range repulsive barrier that is strong enough to overcome dispersive interactions that cause surfaces to attract. Concurrently, a short-range bridging attraction is observed when the two polyelectrolyte layers span both the surfaces. Both the repulsive barrier and bridging attraction depend on the charge density of the polymer backbone and the bulk salt concentration but not on the chain length in the semidilute regime studied.

Oscillatory structural forces between charged interfaces in solutions of oppositely charged polyelectrolytes

Forces between negatively charged micron-sized silica particles were measured in aqueous solutions of cationic polyelectrolytes with an atomic force microscope (AFM). In these oppositely charged systems, damped oscillatory force profiles were systematically observed in systems at higher polyelectrolyte concentrations, typically around few g L-1. The wavelength of these oscillations is decreasing with increasing concentration. When the wavelength and concentration are normalized with the cross-over concentration, universal power-law dependence is found. Thereby, the corresponding scaling exponent changes from 1/3 in the dilute regime to 1/2 in the semi-dilute regime. This dependence is the same as in the like-charged systems, which were described in the literature earlier. This common behavior suggests that these oscillatory forces are related to the structuring of the polyelectrolyte solutions. The reason that the oppositely charged systems behave similarly to like-charged ones is that the former systems undergo a charge reversal due to the adsorption of the polyelectrolytes to the oppositely charged surface, whereby sufficiently homogeneous adsorbed layers are being formed. The main finding of the present study is that at higher polyelectrolyte concentrations such oscillatory forces are the rule, including the oppositely charged ones.

Layer-by-layer adsorption: Factors affecting the choice of substrates and polymers

The electrostatic layer-by-layer technique for fabrication of multi-layered structures of various sizes and shapes using flat and colloidal templates coupled with polyelectrolyte layer-forming materials has attracted significant interest among both academic and industrial researchers due to its versatility and relative simplicity of the procedures involved in its execution. Fabrication of the multi-layered structures using the electrostatic layer-by-layer method involves several distinct stages each of which holds great importance when considering the production of a high-quality product. These stages include selection of materials (both template and a pair of construction polyelectrolytes), adsorption of the first polyelectrolyte layer onto the selected templates, formation of the second layer comprised of the oppositely charged polyelectrolyte and guided by the interactions between the two chosen polyelectrolytes, and multi-layering, where a selected number of layers are produced, and which is conditioned by both intrinsic properties of the involved construction materials and external fabrication conditions such as temperature, pH and ionic strength. The current review summarises the most important aspects of each stage mentioned above and gives examples of the materials suitable for utilization of the technique and describes the underlying physics involved.

Ag-doping on ZnO support mediated by bio-analytes rich in ascorbic acid for photocatalytic degradation of dipyrone drug

The analytes such as ascorbic acid (AA) present in Sechium edule were extracted (294 mg AA kg^-1 fruit) in an aqueous media for its potential application for Ag-doping onto wurtzite ZnO. The bandgap of ZnO was decreased to 2.85 eV at the optimal Ag-loading of 1.18% (w/w) against 3.13 eV for the control catalyst without using the analytes and, the commercial AA only could reduce the bandgap to 2.91 eV. The saturation photo-electrochemical current density (46.68 mA cm^-2) at E_anode ≥ 0.31 V vs. Ag/AgCl was almost double than pristine ZnO under visible light illumination (λ_mean = 525 nm, 18 K lux) and, the current density was insignificant in the dark. The doped catalyst exhibited the maximum 79.5% degradation (71% COD removal) of an anti-analgesic drug, dipyrone (100 μg L^-1 dipyrone, catalyst 100 mg L^-1) resulted from the formation of O₂^•- radical (g-factor of 2.002-2.008) and paramagnetic oxygen vacancies (g-factor of 2.020) and, no effect of dye-sensitization was noted. The highest quantum yield was found to be 34.7%. The catalyst loss was 6% after the fourth cycle and the dipyrone degradation was reduced to 70.8%.

Formation of hematite nanoparticle monolayers of controlled coverage and structure at polymeric microparticles

The deposition of hematite nanoparticles (22nm and 29nm in diameter) on negatively charged polystyrene microspheres (820nm in diameter) was studied by micro-electrophoretic measurements and AFM. The influence of ionic strength, varied between 10^-4 and 10^-2M, was determined. Initially, the electrophoretic mobility change of microspheres upon the addition of controlled amount of hematite nanoparticles were measured. These dependencies were quantitatively interpreted in terms of the general electrokinetic model. This allowed to determine the coverage of nanoparticles on microspheres under in situ conditions, which increased with ionic strength attaining 0.35 for the ionic strength of 10^-2M and 29 in diameter hematite particles. This effect, attributed to the decreasing range of lateral electrostatic repulsion among deposited particles, was accounted for by the random sequential adsorption model. However, the coverages attained for lower ionic strength exceeded the theoretical predictions. This effect was interpreted in terms of an additional electrostatic screening due to polymeric chains present at the microparticle surface. The acid base properties of the hematite monolayers were also acquired by applying thorough micro-electrophoretic measurements. The obtained results confirmed a feasibility of preparing hematite nanoparticle monolayers on polymeric carrier microspheres having well-defined coverage and structure.

Reconciling DLVO and non-DLVO Forces and Their Implications for Ion Rejection by a Polyamide Membrane

Recognizing the significance of surface interactions for ion rejection and membrane fouling in nanofiltration, we revise the theories of DLVO (named after Derjaguin, Landau, Verwey, and Overbeek) and non-DLVO forces in the context of polyamide active layers. Using an atomic force microscope, surface forces between polyamide active layers and a micrometer-large and smooth silica colloid were measured in electrolyte solutions of representative monovalent and divalent ions. While the analysis of DLVO forces, accounting for surface roughness, provides how surface charge of the active layer changes with electrolyte concentration, scrutiny of non-DLVO hydration forces gives molecular insight into the composition of the membrane-solution interface. Importantly, we report an expansion of the diffuse layer at high ionic strength, consistent with the recent development of the electrical double layer theory, but in contrast to the widely accepted phenomenon of aggregation in the secondary minimum. Further, the enhanced repulsion acting on modified membranes via polyelectrolyte adsorption can be quantitatively predicted by DLVO and non-DLVO forces. This work serves to solve past misunderstandings about the interaction forces acting on nanofiltration membranes, and it provides guidance for future work on the relation between surface properties and rejection mechanisms and fouling.

Extending the limits of direct force measurements: colloidal probes from sub-micron particles

Direct force measurements by atomic force microscopy (AFM) in combination with the colloidal probe technique are widely used to determine interaction forces in colloidal systems. However, a number of limitations are still preventing a more universal applicability of this technique. Currently, one of the most significant limitations is that only particles with diameters of several micrometers can be used as probe particles. Here, we present a novel approach, based on the combination of nanofluidics and AFM (also referred to as FluidFM-technique), that allows to overcome this size limit and extend the size of suitable probe particles below diameters of 500 nanometers. Moreover, by aspiration of colloidal particles with a hollow AFM-cantilever, the immobilization process is independent of the particle's surface chemistry. Furthermore, the probe particles can be exchanged in situ. The applicability of the FluidFM-technique is demonstrated with silica particles, which are also the types of particles most often used for the preparation of colloidal probes. By comparing 'classical' colloidal probes, i.e. probes from particles irreversibly attached with glue, and various particle sizes aspirated by the FluidFM-technique, we can quantitatively evaluate the instrumental limits. Evaluation of the force profiles demonstrate that even for 500 nm silica particles the diffuse layer properties can be evaluated quantitatively. Therefore, direct force measurements on the level of particle sizes used in industrial formulations will become available in the future.

Understanding the fate and biological effects of Ag- and TiO₂-nanoparticles in the environment: The quest for advanced analytics and interdisciplinary concepts

Engineered inorganic nanoparticles (EINP) from consumers' products and industrial applications, especially silver and titanium dioxide nanoparticles (NP), are emitted into the aquatic and terrestrial environments in increasing amounts. However, the current knowledge on their environmental fate and biological effects is diverse and renders reliable predictions complicated. This review critically evaluates existing knowledge on colloidal aging mechanisms, biological functioning and transport of Ag NP and TiO2 NP in water and soil and it discusses challenges for concepts, experimental approaches and analytical methods in order to obtain a comprehensive understanding of the processes linking NP fate and effects. Ag NP undergo dissolution and oxidation with Ag2S as a thermodynamically determined endpoint. Nonetheless, Ag NP also undergo colloidal transformations in the nanoparticulate state and may act as carriers for other substances. Ag NP and TiO2 NP can have adverse biological effects on organisms. Whereas Ag NP reveal higher colloidal stability and mobility, the efficiency of NOM as a stabilizing agent is greater towards TiO2 NP than towards Ag NP, and multivalent cations can dominate the colloidal behavior over NOM. Many of the past analytical obstacles have been overcome just recently. Single particle ICP-MS based methods in combination with field flow fractionation techniques and hydrodynamic chromatography have the potential to fill the gaps currently hampering a comprehensive understanding of fate and effects also at a low field relevant concentrations. These analytical developments will allow for mechanistically orientated research and transfer to a larger set of EINP. This includes separating processes driven by NP specific properties and bulk chemical properties, categorization of effect-triggering pathways directing the EINP effects towards specific recipients, and identification of dominant environmental parameters triggering fate and effect of EINP in specific ecosystems (e.g. soil, lake, or riverine systems).

Shear rheology of mixed protein adsorption layers vs their structure studied by surface force measurements

The hydrophobins are proteins that form the most rigid adsorption layers at liquid interfaces in comparison with all other investigated proteins. The mixing of hydrophobin HFBII with other conventional proteins is expected to reduce the surface shear elasticity and viscosity, E(sh) and η(sh), proportional to the fraction of the conventional protein. However, the experiments show that the effect of mixing can be rather different depending on the nature of the additive. If the additive is a globular protein, like β-lactoglobulin and ovalbumin, the surface rigidity is preserved, and even enhanced. The experiments with separate foam films indicate that this is due to the formation of a bilayer structure at the air/water interface. The more hydrophobic HFBII forms the upper layer adjacent to the air phase, whereas the conventional globular protein forms the lower layer that faces the water phase. Thus, the elastic network formed by the adsorbed hydrophobin remains intact, and even reinforced by the adjacent layer of globular protein. In contrast, the addition of the disordered protein β-casein leads to softening of the HFBII adsorption layer. Similar (an even stronger) effect is produced by the nonionic surfactant Tween 20. This can be explained with the penetration of the hydrophobic tails of β-casein and Tween 20 between the HFBII molecules at the interface, which breaks the integrity of the hydrophobin interfacial elastic network. The analyzed experimental data for the surface shear rheology of various protein adsorption layers comply with a viscoelastic thixotropic model, which allows one to determine E(sh) and η(sh) from the measured storage and loss moduli, G' and G″. The results could contribute for quantitative characterization and deeper understanding of the factors that control the surface rigidity of protein adsorption layers with potential application for the creation of stable foams and emulsions with fine bubbles or droplets.

Adsorbed Mass of Polymers on Self-Assembled Monolayers: Effect of Surface Chemistry and Polymer Charge

The adsorbed mass of polymers on surfaces with different chemistry is presented, and the related adsorption mechanism is discussed. Strong and weak polyelectrolytes of negative and positive charge are studied, as well as an uncharged polymer. Self-assembled monolayers of alkanethiols on gold are used in reflectometry and quartz crystal microbalance (QCM-D) experiments as adsorbing substrates bearing different terminal moieties, namely, methyl, hydroxyl, carboxyl, and amine groups. The various polymer-surface combinations allow the systematic investigation of the role of surface chemistry and polymer charge on adsorbed amount. Interactions of different nature and range drive polymer adsorption: the measured adsorbed amounts reveal information about their relative contribution. When electrostatic chain-surface attraction is present, the largest adsorbed masses are observed. However, significant mass is measured even when an electrostatic barrier to adsorption is present, suggesting the importance of forces of nonelectrostatic origin, which include both hydrophobic interactions and specific forces acting at short distances. This mechanism results in large adsorbed amounts for the adsorption of weak polyelectrolytes, and it is apparent especially in the adsorption behavior of a neutral polymer.

Long-ranged and soft interactions between charged colloidal particles induced by multivalent coions

Forces between charged particles in aqueous solutions containing multivalent coions and monovalent counterions are studied by the colloidal probe technique. Here, the multivalent ions have the same charge as the particles, which must be contrasted to the frequently studied case where multivalent ions have the opposite sign as the substrate. In the present case, the forces remain repulsive and are dominated by the interactions of the double layers. The valence of the multivalent coion is found to have a profound influence on the shape of the force curve. While for monovalent coions the force profile is exponential down to separations of a few nanometers, the interaction is much softer and longer-ranged in the presence of multivalent coions. The force profiles in the presence of multivalent coions and in the mixtures of monovalent and multivalent coions can be accurately described by Poisson-Boltzmann theory. These results are accurate for different surfaces and even in the case of highly charged particles. This behavior can be explained by the fact that the force profile follows the near-field limit to much larger distances for multivalent coions than for monovalent ones. This limit corresponds to the conditions with no salt, where the coions are expelled between the two surfaces.

Interactions between colloidal particles in the presence of an ultrahighly charged amphiphilic polyelectrolyte

A novel amphiphilic polyelectrolyte denoted as PAGC8 and a traditional amphiphilic polyelectrolyte denoted as PASC8 were prepared. PAGC8 consisted of gemini-type surfactant segment based on 1,3-bis (N,N-dimethyl-N-octylammonium)-2-propyl acrylate dibromide, while PASC8 incorporated acryloyloxyethyl-N,N-dimethyl-N-dodecylammonium bromide as single chain surfactant units within its repeat unit structure. Turbidity, stability, and zeta potential measurements were performed in the presence of PAGC8 and PASC8, respectively, to evaluate their effectiveness in inducing solid/liquid separations. It was found that the maximum transmittance was observed before the zeta potential values reached the isoelectric point, implying that not only charge neutralization but also charge-patch mechanism contributed to the separation process. Colloid probe atomic force microscopy technique was introduced to directly determine the interactions between surfaces in the presence of ultrahighly charged amphiphilic polyelectrolyte. On the basis of the AFM results, we have successfully interpreted the influence of the charge density of the polyelectrolytes on the phase stability. Electrostatic interaction played the dominant role in the flocculation processes, although both electrostatic interaction and hydrophobic effect provided contributions to the colloidal dispersions. The attractions upon surfaces approach in the case of PAGC8 were significantly larger than that of PASC8 due to the higher charge density. The strong peeling events upon retraction in the presence of PAGC8 implied that the hydrophobic effect was stronger than that of PASC8, which displayed the loose pulling events. A strong attraction was identified at shorter separation distances for both systems. However, these interactions cannot be successfully described by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloid stability due to the participation of charge-patch and strong hydrophobic effect. To account for the additional interactions, we proposed an extended DLVO empirical model to explain the non-DLVO forces in the systems. A reasonable physical model was also proposed to further describe the interactions between surfaces in the two amphiphilic polyelectrolyte systems.

Electric double-layer potentials and surface regulation properties measured by colloidal-probe atomic force microscopy

We show how the colloidal-probe technique, which is based on force measurements made with the atomic force microscope, can be used to accurately determine the charging parameters of water-solid interfaces. Besides yielding accurate values of the double-layer or diffuse-layer potential, the method also allows reliable determination of the charge regulation properties of the surfaces. The latter can be quantified with a regulation parameter, which is essential to properly describe forces between interfaces, especially in asymmetric situations when one of the interfaces is charged and the other one is close to neutral. The technique relies on a highly charged probe particle, for which the charging properties are accurately determined by interpreting the double-layer contribution of the measured force profiles in the symmetric sphere-sphere geometry with Poisson-Boltzmann (PB) theory. Once the probe particle is calibrated, this particle is used to measure the force profile between an unknown substrate in the asymmetric sphere-sphere or sphere-plane geometry. From this profile, the diffuse-layer potential and regulation parameter of the substrate can be again determined with PB theory. The technique is highly versatile, as it can be used for a wide variety of substrates, including colloidal particles and planar substrates. The technique is also applicable in salt solutions containing multivalent ions. The current drawbacks of the technique are that it can only be applied up to moderately high salt levels, typically to 10 mM, and only for relatively large particles, typically down to about 1 μm in diameter. How the technique could be extended to higher salt levels and smaller particle size is also briefly discussed.

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.

Mechanism of nanoparticle deposition on polystyrene latex particles

The deposition of positive amidine latex particles (98 nm in diameter) on negative polystyrene latex particles (820 nm in diameter) was studied by SEM imaging, microelectrophoretic and concentration depletion methods involving AFM. The role of ionic strength varied between 10(-4) and 10(-2) M and was systematically studied. The number of deposited positive latex particles (surface coverage) was evaluated by a direct counting procedure exploiting the SEM images. This allowed one to calibrate the results obtained from measurements of the electrophoretic mobility of larger latex particles covered by a controlled amount of the positive latex. These dependencies were quantitatively interpreted in terms of the 3D electrokinetic model previously used for planar interfaces. This allowed us to determine the coverage of nanoparticles on latex carriers under in situ conditions. Additionally, the maximum coverage of the positive latex was determined via AFM where the kinetics of the residual amidine latex deposition on mica was measured. The maximum coverage monotonically increased with ionic strength, attaining 0.52 for 10(-2) M NaCl. This effect was interpreted in terms of reduced electrostatic repulsion among positive latex particles and theoretically accounted for by the random sequential adsorption model. The obtained results have significance for basic science, indicating that the results obtained for curved interfaces (polymeric carrier particles) by the microelectrophoretic method can be exploited to interpret the deposition of nanoparticles and proteins on planar interfaces and vice versa.

Polyelectrolyte adsorption on solid surfaces: theoretical predictions and experimental measurements

This work utilizes a combination of theory and experiments to explore the adsorption of two different cationic polyelectrolytes onto oppositely charged silica surfaces at pH 9. Both polymers, poly(diallyldimethylammonium chloride), PDADMAC, and poly(4-vinyl N-methylpyridinium iodide), PVNP, are highly charged and highly soluble in water. Another important aspect is that a silica surface carries a relatively high surface charge density at this pH level. This means that we have specifically chosen to investigate adsorption under conditions where electrostatics can be expected to dominate the interactions. Of specific focus in this work is the response of the adsorption to the addition of simple salt (i.e., a process where electrostatics is gradually screened out). Theoretical predictions from a recently developed correlation-corrected classical density functional theory for polyelectrolytes are evaluated by direct quantitative comparisons with corresponding experimental data, as obtained by ellipsometry measurements. We find that, at low concentrations of simple salt, the adsorption increases with ionic strength, reaching a maximum at intermediate levels (about 200 mM). The adsorption then drops but retains a finite level even at very high salt concentrations, indicating the presence of nonelectrostatic contributions to the adsorption. In the theoretical treatment, the strength of this relatively modest but otherwise largely unknown nonelectrostatic surface affinity was estimated by matching predicted and experimental slopes of adsorption curves at high ionic strength. Given these estimates for the nonelectrostatic part, experimental adsorption data are essentially captured with quantitative accuracy by the classical density functional theory.

Cation bridging studied by specular neutron reflection

The binding of an anionic surfactant onto an anionic surface by addition of divalent ions is reported based on experimental data from specular neutron reflection (NR) and attenuated total internal reflection IR spectroscopy (ATR-IR). Similar measurements using monovalent ions (sodium) do not show any evidence of such adsorption, even though the amount of surfactant can be much higher. This data is interpreted in terms of the so-called bridging mechanism of ion binding.

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.

Destabilization of colloidal suspensions by multivalent ions and polyelectrolytes: from screening to overcharging

The destabilization of charged colloidal suspensions is studied in the presence of polyelectrolytes and the corresponding oligomers. Two different systems are investigated, namely, negatively charged particles in the presence of polyamines and positively charged ones in the presence of polycarboxylates. Multivalent oligomers of low valence destabilize the particles by screening according to the Schulze-Hardy rule. Polyelectrolytes induce destabilization by overcharging. Both regimes can be observed for oligomers of intermediate valence. The stability data of any valence can be rather well described by the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO), indicating that the interactions are mainly governed by van der Waals and electrostatic double-layer forces.

Structure of adsorbed polyelectrolyte monolayers investigated by combining optical reflectometry and piezoelectric techniques

Polyelectrolyte monolayers on solid substrates are studied with optical reflectivity and the quartz crystal microbalance (QCM). In particular, we investigate the adsorption of anionic poly(styrene sulfonate) (PSS) on amino-functionalized silica as well as cationic poly(allylamine hydrochloride) (PAH) and poly-L-lysine (PLL) on bare silica. By comparing the dry and wet masses measured on identical substrates with these two techniques, we obtain information on the layer thickness and water content of these layers. Monolayers typically feature an adsorbed dry mass of about 0.1-2 mg/m(2), a layer thickness of 0.5-2 nm, and a water content of 20-50%. One finds that the layer thickness increases with increasing concentrations of monovalent salts and polyelectrolytes.

Polyelectrolyte adsorption: electrostatic mechanisms and nonmonotonic responses to salt addition

The main question addressed in this work is as follows: Under pure electrosorption conditions, that is, disregarding nonelectrostatic effects, how does the net adsorption of a polyelectrolyte at an oppositely charged surface respond to the addition of simple salt? Previous simulations and mean-field calculations have suggested that the polymers will desorb. However, we will demonstrate that an increased adsorption also is possible, even for pure electrosorption, at low and intermediate levels of salt. As this is a correlation-driven effect, mean field approaches will fail to capture it. Using simulations, one will in general need to simulate large systems and relatively long polymers. Also important is the presence of a proper bulk solution, with a finite and well-defined polyelectrolyte concentration. We have performed a theoretical study of polyelectrolyte adsorption, assuming screened Coulomb interactions between monomers; that is, the salt is implicit. This work focuses on the effects from ionic screening and polymer length. Specifically, the adsorption at a weakly charged colloidal particle, with a diameter of 200 nm, is monitored for various salt concentrations, in the presence of highly charged chains. Using simulations, we investigate polymers with two different degrees of polymerization: 40 and 160, respectively. These simulations are complemented by predictions from classical polymer density functional theory, utilizing a recently developed correlation-correction (Forsman, J.; Nordholm, S. Langmuir, in press). The agreement with corresponding simulations is semiquantitative, and because the calculations run many orders of magnitude faster than the simulations, longer and more realistic polymers could be studied with this approach. However, switching off the correlation-correction leads to a mean-field theory, which fails to even qualitatively reproduce the simulated response to screening.

Polyelectrolyte mediated interactions in colloidal dispersions: hierarchical screening, simulations, and a new classical density functional theory

The pair interaction between two charged colloidal particles, in the presence of a polyelectrolyte as well as simple salt, is analyzed theoretically. Of particular interest is the way in which such a combination of salts can be used to induce a strong, long-range attraction, with at most a minor free energy barrier. We show that the nature of the simple salt is highly relevant, i.e., 2:1, 1:1, and 1:2 salts generate quite different particle interaction free energies at the same overall ionic strength. We adopt several different theoretical levels of description. Defining simulations at the primitive model level with explicit simple salt as our reference, we invoke stepwise coarse-graining with careful evaluations of each approximation. Representing monovalent simple ions by the ionic screening they generate is one such simplification. In order to proceed further, with additional computational savings, we also develop a correlation-corrected classical density functional theory. We analyze the performance of this theory with explicit spherical particles as well as in a flat surface geometry, utilizing Derjaguin's approximation. The calculations are particularly fast in the latter case, facilitating computational savings of many (typically 5-7) orders of magnitude, compared to corresponding simulations with explicit salt. Yet, the predictions are remarkably accurate, and considering the crudeness of the model itself, the density functional theory is a very attractive alternative to simulations.

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.