Oscillatory Packing and Depletion of Polyelectrolyte Molecules at an Oxide−Water Interface

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.

Parametric Study of Colloidal Particle Confinement near a Surface in the Presence of DLVO and Structural Interactions Using Brownian Dynamic Simulations

Total internal reflection microscopy (TIRM) has become a crucial technique for understanding the surface interactions and dynamics of Brownian colloidal particles near a surface. However, for select colloidal systems, experimental limitations associated with TIRM can occlude exploration of nano- and submicrometer colloids dispersed in complex or structured fluids. It should be possible to use Brownian dynamic simulations to quantify, explore, or circumvent these limitations to extend the TIRM technique further. A Brownian dynamics algorithm based on the Langevin equation was utilized to identify favorable colloidal systems for conducting TIRM experiments in electrolyte and nonadsorbing polyelectrolyte solutions. In electrolyte solution, the motion of polystyrene and silica particles of nanometer- and micrometer-sized radii was simulated near a glass slide in the presence of retarded van der Waals and electric double-layer forces to develop potential energy profiles. In the case of nonadsorbing polyelectrolyte solutions, a structural force was also implemented into the simulation, and the influence of structural interactions on particle confinement was explored as a function of particle size, particle density, and polyelectrolyte concentration. In electrolyte solutions, our results were able to identify the minimum particle size required for TIRM experiments as well as insight into particle selection based on material density. For structural or oscillatory forces, our results show that prior to conducting TIRM experiments, Brownian dynamics simulation can be used to select the appropriate particle size, material, and polyelectrolyte concentration range where the colloidal particle can sample multiple structural energy wells without confinement. These results provide insight into the colloidal system suitable to experimentally study near-surface particle diffusion dynamics for a range of separations in the presence of structural interactions.

Thickness of the particle-free layer near charged interfaces in suspensions of like-charged nanoparticles

When a suspension of charged nanoparticles is in contact with a like-charged water-solid interface, next to this interface a particle-free layer is formed. The present study provides reliable measurements of the thickness of this particle-free layer with three different techniques, namely optical reflectivity, quartz crystal microbalance (QCM), and direct force measurements with atomic force microscopy (AFM). Suspensions of negatively charged nanoparticles of different size and type are investigated. When the measured layer thickness is normalized to the particle size, one finds that this normalized thickness shows universal inverse square root dependence on the particle volume fraction. This universal dependence can be also derived from Poisson-Boltzmann theory for highly asymmetric electrolytes, whereby one has to assume that the nanoparticles represent the multivalent coions.

Structural and Double Layer Forces between Silica Surfaces in Suspensions of Negatively Charged Nanoparticles

Direct force measurements between negatively charged silica microparticles are carried out in suspensions of like-charged nanoparticles with atomic force microscopy (AFM). In agreement with previous studies, oscillatory force profiles are observed at larger separation distances. At smaller distances, however, soft and strongly repulsive forces are present. These forces are caused by double layer repulsion between the like-charged surfaces and can be quantitatively interpreted with the Poisson-Boltzmann (PB) model. However, the PB model must be adapted to a strongly asymmetric electrolyte to capture the nonexponential nature of these forces. Thereby, the nanoparticles are modeled as highly charged co-ions, while the counter ions are monovalent. This model permits extraction of the effective charge of the nanoparticles, which is well comparable to the one obtained from electrophoresis. The PB model also explains the presence of a particle-free layer close to the interface.

Depletion Forces Induced by Mixed Micelles of Nonionic Block Copolymers and Anionic Surfactants

Depletion forces were measured between a silica sphere and a silica plate in solutions containing nonionic Pluronic P123 poly(ethylene oxide-b-propylene oxide-b-ethylene oxide) triblock copolymers and anionic sodium dodecyl sulfate (SDS) surfactants using colloidal probe atomic force microscopy. Prior research established synergistic depletion force enhancement in solutions containing SDS and unimeric Pluronic F108 block copolymers via formation of large pseudo-polyelectrolyte complexes. The current work addresses a more complex system where the polymer is above its critical micelle concentration, and surfactant binding alters not only the size and charge of the micelles but also the number of polymers per micelle. Force profiles were measured in 10 000 ppm P123 (1 wt %, corresponding to 1.72 mM based on average molar mass) solutions containing SDS at concentrations up to 64 mM and compared to micellar P123 solutions and to P123-free SDS solutions. Whereas force profiles in the SDS-free micellar P123 solutions were purely repulsive, P123/SDS complexation produced synergistic depletion force enhancement for SDS concentrations between 2 and 32 mM. The synergism that occurred within a finite SDS concentration range was explained by comparing the hydrodynamic size, molar mass, charge, and concentration of depletants in P123/SDS mixtures and their respective single-component solutions obtained with the aid of dynamic light scattering, static light scattering, and dodecyl sulfate ion-selective electrode measurements. These measurements showed that complexation produced effects that would be mutually counteracting with respect to depletion forces: decreasing the mixed micelle hydrodynamic diameter relative to SDS-free P123 micelles would tend to weaken depletion forces, while adding charge and decreasing the aggregation number of polymers per micelle (thereby increasing the number concentration of micellar depletants) would tend to strengthen depletion forces.

Colloidal Depletion and Structural Force Synergism or Antagonism in Solutions of Mutually Repelling Polyelectrolytes and Ionic Surfactants

Depletion and structural forces were measured between a silica sphere and plate in solutions containing sodium polyacrylate (Na-PAA) anionic polyelectrolyte and sodium dodecyl sulfate (SDS) anionic surfactant using colloidal probe atomic force microscopy, at high pH where the two species are electrostatically repelling from each other and from the silica surfaces. Measurements were performed for a range of SDS and Na-PAA concentrations to span conditions where only one of the species or both of the species would exert a detectable depletion or structural force when present in a single-component solution. In mixed solutions, conditions were identified (i) where depletion attraction was synergistically enhanced or antagonistically weakened relative to single component solutions; (ii) where the range of the depletion attraction was significantly extended and the repulsive structural force barrier was eliminated, due to simultaneous depletion of both species over different length scales; and (iii) where one species was the dominant depletant and forces in mixtures were indistinguishable from those in a single component solution of the dominant depletant. Force measurements were interpreted with the aid of pyrene solubilization assays of SDS micellization and dynamic light scattering investigation of the state of assembly of the polyelectrolyte or surfactant. The variety of colloidal force effects were attributed to ionic strength and excluded volume effects of Na-PAA on SDS micellization, ionic strength effects of SDS on Na-PAA chain clustering in solution, and ionic strength effects on the counterion contribution to polyelectrolyte osmotic pressure. While prior studies have shown that depletion force synergism occurs when polymers and surfactants form mixed complexes, this work shows that it can occur in noncomplexing mixtures as well, and it indicates the variety of effects that should be taken into account when attempting to predict forces in such mixtures.

Depletion and double layer forces acting between charged particles in solutions of like-charged polyelectrolytes and monovalent salts

Interaction forces between silica particles were measured in aqueous solutions of the sodium salt of poly(styrene sulphonate) (PSS) and NaCl using the colloidal probe technique based on an atomic force microscope (AFM). The observed forces can be rationalized through a superposition of damped oscillatory forces and double layer forces quantitatively. The double layer forces are modeled using Poisson-Boltzmann (PB) theory for a mixture of a monovalent symmetric electrolyte and a highly asymmetric electrolyte, whereby the multivalent coions represent the polyelectrolyte chains. The effective charge of the polyelectrolyte is found to be smaller than the bare number of charged groups residing on one polyelectrolyte molecule. This effect can be explained by counterion condensation. The interplay between depletion and double layer forces can be further used to predict the phase of the depletion force oscillations. However, this picture holds only at not too elevated concentrations of the polyelectrolyte and salt. At higher salt concentrations, attractive van der Waals forces become important, while at higher polyelectrolyte concentrations, the macromolecules adsorb onto the like-charged silica interface.

Measuring the Surface-Surface Interactions Induced by Serum Proteins in a Physiological Environment

In this work, we applied total internal reflection microscopy (TIRM) to directly measure the interactions between three different kinds of macroscopic surfaces: namely bare polystyrene (PS) particle and bare silica surface (bare-PS/bare-silica), PS particle and silica surfaces both coated with bovine serum albumin (BSA) (BSA-PS/BSA-silica), and PS particle and silica surfaces both modified with polyethylene glycol (PEG) (PEG-PS/PEG-silica) polymers, in phosphate buffer solution (PBS) and fetal bovine serum (FBS). Our results showed that in PBS, all the bare-PS, BSA-PS, and PEG-PS particles were irreversibly deposited onto the bare silica surface or surfaces coated either with BSA or PEG. However, in FBS, the interaction potentials between the particle and surface exhibited both free-diffusing particle and stuck particle profiles. Dynamic light scattering (DLS) and elliposmeter measurements indicated that there was a layer of serum proteins adsorbed on the PS particle and silica surface. TIRM measurement revealed that such adsorbed serum proteins can mediate the surface-surface interactions by providing additional stabilization under certain conditions, but also promoting bridging effect between the two surfaces. The measured potential profile of the stuck particle in FBS thus was much wider than in PBS. These quantitative measurements provide insights that serum proteins adsorbed onto surfaces can regulate surface-surface interactions, thus leading to unique moving behavior and stability of colloidal particles in the serum environment.

Direct AFM force measurements between air bubbles in aqueous monodisperse sodium poly(styrene sulfonate) solutions

Structural forces play an important role in the rheology, processing and stability of colloidal systems and complex fluids, with polyelectrolytes representing a key class of structuring colloids. Here, we explore the interactions between soft colloids, in the form of air bubbles, in solutions of monodisperse sodium poly(styrene sulfonate) as a model polyelectrolyte. It is found that by self-consistently modelling the force oscillations due to structuring of the polymer chains along with deformation of the bubbles, it is possible to precisely predict the interaction potential between approaching bubbles. In line with polyelectrolyte scaling theory, two distinct regimes of behaviour are seen, corresponding to dilute and semi-dilute polymer solutions. It is also seen that by blending monodisperse systems to give a bidisperse sample, the interaction forces between soft colloids can be controlled with a high degree of precision. At increasing bubble collision velocity, it is revealed that hydrodynamic flow overwhelms oscillatory structural interactions, showing the important disparity between equilibrium behaviour and dynamic interactions.

Two spheres translating in tandem through a colloidal suspension

Using laser tweezers, two colloidal particles are held parallel to a uniformly flowing suspension of similarly sized bath particles at an effective volume fraction ϕ(eff)=0.41. The local deformation in the bath suspension is imaged by confocal microscopy, and, concurrently, the drag forces exerted on both the leading and the trailing probe particles are measured as a function of probe separation and velocity. The bath structure changes in response to the velocity and separation of the probes. A depleted region between probes is observed at sufficiently high velocities. Both probes experience the same drag force and the drag force increases with probe separation. The results indicate that bath-probe and probe-probe hydrodynamic interactions contribute microstructure and drag force and that drag exerted by direct bath-probe collisions is reduced compared to an isolated probe.

Measurements of long-range interactions between protein-functionalized surfaces by total internal reflection microscopy

Understanding the interaction between protein-functionalized surfaces is an important subject in a variety of protein-related processes, ranging from coatings for biomedical implants to targeted drug carriers and biosensors. In this work, utilizing a total internal reflection microscope (TIRM), we have directly measured the interactions between micron-sized particles decorated with three types of common proteins concanavalin A (ConA), bovine serum albumin (BSA), lysozyme (LYZ), and glass surface coated with soy proteins (SP). Our results show that the protein adsorption greatly affects the charge property of the surfaces, and the interactions between those protein-functionalized surfaces depend on solution pH values. At pH 7.5-10.0, all these three protein-functionalized particles are highly negatively charged, and they move freely above the negatively charged SP-functionalized surface. The net interaction between protein-functionalized surfaces captured by TIRM was found as a long-range, nonspecific double-layer repulsion. When pH was decreased to 5.0, both protein-functionalized surfaces became neutral and double-layer repulsion was greatly reduced, resulting in adhesion of all three protein-functionalized particles to the SP-functionalized surface due to the hydrophobic attraction. The situation is very different at pH = 4.0: BSA-decorated particles, which are highly charged, can move freely above the SP-functionalized surfaces, while ConA- and LYZ-decorated particles can only move restrictively in a limited range. Our results quantify these nonspecific kT-scale interactions between protein-functionalized surfaces, which will enable the design of surfaces for use in biomedical applications and study of biomolecular interactions.

Tuning the particle-surface interactions in aqueous solutions by soft microgel particles

Due to the softness and deformability, interaction between colloidal surfaces induced by soft particles varies in a more complex way than for solid particles and thus has attracted much attention in recent years. In the present study, we use total internal reflection microscopy (TIRM) to directly measure the interaction between polystyrene (PS) microparticles and a flat glass surface in a poly(N-isopropylacrylamide) (PNIPAM) microgel dispersion with concentration varying from dilute (0.1 wt %) to highly concentrated regime (7.5 wt %). Our result shows that the PS particle-surface interactions mediated by the soft microgels are greatly affected by the particle concentration, the configuration of those microgels adsorbed on the surfaces, and the structure and packing of microgels in bulk solution. With increasing the microgel concentration (Cmicrogel), the interaction between the PS particle and surface turned from bridging attraction to steric repulsion, and then depletion attraction, which were mainly governed by the adsorption amount and configuration of microgels on the two surfaces. By further increasing Cmicrogel to condensed situation, structural force with oscillated energy wells was detected. The variation of interactions induced by the soft microgels was further confirmed by optical imaging. Crystallization of the PS microparticles appeared at moderate Cmicrogel; however, crystallization was hindered at higher Cmicrogel where the microgels are highly packed in the bulk solution. Furthermore, using TIRM, microgel packing with local energy well (0.1-1.0 kBT) at the highly condensed state (7.5 wt %) was resolved from the interaction profiles. Therefore, the shear force and modulus generated by such microgel packing can be determined as ∼0.2 pN and tens of mPa, respectively, which are much weaker than data given by conventional active methods.

Interactions between solid surfaces mediated by polyethylene oxide polymers: effect of polymer concentration

Using total internal reflection microscopy (TIRM), we have systematically measured the interactions between a microsphere and a flat hydrophilic surface in the presence of polyethylene oxide (PEO) polymer solution. Our results reveal that PEO significantly mediates the interaction forces between the two surfaces. At low polymer concentration, the interactions between two surfaces in the presence of PEO are mainly dominated by repulsive forces, originating from diffuse layer overlap. At intermediate polymer concentration, a long-range and weak attraction sets in. This force is likely attributed to the depletion attraction due to the presence of free PEO chains in bulk solution; however, a simple hard-sphere AO model fails to precisely describe the attraction. At high polymer concentration where PEO chains overlap, the attraction disappears, and levitation of the microsphere probe is detected. We argue that at this overlapping region, the correlation length of PEO chains is much smaller than the size of single PEO molecule, leading to weakening and disappearing of the depletion attraction. Finally, at very high concentration, oscillatory structural force is obviously found, indicating the significant structural ordering of the PEO chains under confinement.

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.

Depletion attraction between a polystyrene particle and a hydrophilic surface in a pluronic aqueous solution

In practice, many colloidal suspensions also contain polymers where their presence has a major effect on the stability of colloidal particles. In this work, we use total internal reflection microscopy to directly measure the interactions between a approximately 6.0 microm polystyrene spherical particle and a hydrophilic flat surface with the presence of an triblock copolymer, poly(ethylene oxide-block-propylene oxide-block-ethylene oxide) (Pluronic PE10500), in an aqueous solution with low ionic strength. A discernible attractive force between the particle and surface is observed with the measurable range of up to approximately 100 nm. Dynamic laser light scattering study reveals that monomers, micelles, and larger nanobubbles (approximately 166 nm) coexist when PE10500 triblock copolymer is spontaneously dissolved in the low ionic strength aqueous solution. We attribute this measured long-range attractive force to the creation of a significant depletion force between the particle and surface as caused by the existence of relatively large nanobubbles free in solution. Replacement of the PE10500 copolymer solution with salt solution removes the nanobubbles, which is reflected in disappearing of the attractive force. Moreover, we find that the adsorbed PE10500 chains at both charged particle and flat surface may cause a redistribution of counterions and colons that make up the electric double layer of the surfaces, thus displacing the repulsive potential between the particle and surface.

Steric interactions between physically adsorbed polymer-coated colloidal particles: soft or hard?

The steric interaction potential between colloidal particles imparted by adsorbed polymer layers is directly related to their structure. Due to the complexity of these interfacial structures, the steric potential may behave differently at different interparticle separations. In this study, we proposed a combined model of the equivalent hard-sphere model (EHS) and the Hayter-Penfold/Yukawa model (HPY) to describe the steric potential due to adsorbed homopolymers on colloidal particles. The EHS potential describes the dense train/small-loop region and the HPY potential the more diffuse tail/long-loop region. The steric potential was extracted from the structure factors measured by small-angle neutron scattering (SANS). It was found that this combined model gave better agreement with experimental data than either of its component models alone. This study also shows that the adsorbed polymer layer in a good solvent partially collapses when the layers approach one another, which is also supported by an NMR solvent relaxation study.

Investigation of short-time particle dynamics near an interface in the presence of nonadsorbed macro-ions

The optical technique of total internal reflection microscopy was used to study the normal Brownian motion of a single colloidal particle near an interface. The measurements were made using a recently developed technique in which the diffusion coefficient was determined by the variance of the short-time (Deltat --> 0) motion of the particle. Experiments were performed in solutions containing either silica nanospheres or clay platelets (Laponite RD) to investigate the effect of nonadsorbed material on the dynamics of near-contact particle motion. The change in the diffusion coefficient with separation distance between the particle and plate in solutions containing nonadsorbed macro-ions was well-described by the theory developed for simple fluids. These results suggest that, in dilute solutions of nonadsorbed material in which the bulk rheological properties remain similar to those of the pure fluid, the mobility and diffusion coefficient correction factors developed for simple fluids remain valid.

Small-angle neutron scattering study of concentrated colloidal dispersions: the electrostatic/steric composite interactions between colloidal particles

Small-angle neutron scattering was used to investigate the interactions in concentrated colloidal dispersions containing silica or polystyrene latex with adsorbed polyethyleneoxide (PEO). In these dispersions of charged particles, both electrostatic and steric repulsions are present. The PEO layer was made invisible to neutrons through contrast matching. The effect of the interparticle repulsion was clearly shown in the scattering spectra by the appearance of a peak at low Q. The effective potentials can be well described by the Hayter-Penfold/Yukawa (HPY) potential. In the silica dispersions studied, the layer thickness is small, hence the electrostatic potential dominates and the potential has a lower concentration dependence. In the dispersions of polystyrene latex, the adsorbed layer is thicker; consequently, the electrostatic potential dominates at low volume fraction (the potential has a lower concentration dependence), and the steric potential dominates at higher volume fraction (the potential has a higher concentration dependence). This study also suggests that when more than one potential is present the stronger one has a dominant influence in determining the structure factor. This finding makes it possible to describe the multicomponential interactions by a single function.

Direct comparison of atomic force microscopic and total internal reflection microscopic measurements in the presence of nonadsorbing polyelectrolytes

We have investigated the structural and depletion forces between silica glass surfaces in aqueous, salt-free solutions of sodium poly(styrene sulfonate). The interaction forces were investigated by two techniques: total internal reflectance microscopy (TIRM) and colloid probe atomic force microscopy (AFM). The TIRM technique measures the potential energy of interaction directly, while the AFM is a force balance. Comparison between the data sets was used to independently calibrate the AFM data since the separation distances cannot be unequivocally determined by this technique. Oscillatory structural forces are excellent for this work since they give multiple reference points against which to analyze. Comparison of the data from the two techniques highlighted significant uncertainties in the AFM data. At low polymer concentrations, a significant uncertainty in the apparent zero separation distance was seen as a result of the AFM cantilever reaching an apparent constant compliance region prior to any real contact between the surfaces. Further complications arising from the number and position of the measured minima were also seen in the dilute polymer concentration regime as a result of hydrodynamic drainage between the approaching surfaces in the AFM perturbing the delicate structural components in the fluid.

Generalized Fragment-Substructure Based Property Prediction Method

The need for fast and accurate predictors of pharmaceutically important properties has been increasing due to pressure from high-throughput screening, in-silico screening, and the need to more rapidly identify potential pharmacokinetic issues before drugs advance to the more expensive clinical development stages. A novel method for making predictive models based on decomposing 2D structure into component structural fragments is used to model logP, water solubility, and melting point. The fragment orientation of the method facilitates understanding of how molecules might be altered to improve the desired properties. The 2D structure-based descriptor is computed by analysis of the target molecules with a substructure searching algorithm and a set of fragments selected for chemical and pharmaceutical relevance. These are combined with partial least squares to create predictive models. The correlation coefficients achieved are 0.86 for logP (SE = 0.68), 0.73 for logS (SE = 0.89), and 0.64 (SE = 48.9 degrees) for melting point over diverse data sets of 11,447, 2427, and 5598 molecules, respectively. The models were verified via test sets of compounds not included in the training set.

Altering surface charge nonuniformity on individual colloidal particles

Charge nonuniformity (sigmazeta) was altered on individual polystyrene latex particles and measured using the novel experimental technique of rotational electrophoresis. It has recently been shown that unaltered sulfated latices often have significant charge nonuniformity (sigmazeta = 100 mV) on individual particles. Here it is shown that anionic polyelectrolytes and surfactants reduce the native charge nonuniformity on negatively charged particles by 80% (sigmazeta = 20 mV), even while leaving the average surface charge density almost unchanged. Reduction of charge uniformity occurs as large domains of nonuniformity are minimized, giving a more random distribution of charge on individual particle surfaces. Targeted reduction of charge nonuniformity opens new opportunities for the dispersion of nanoparticles and the oriented assembly of particles.