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.

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.

Heteroaggregation between Charged and Neutral Particles.

Experimentally determined heteroaggregation rates between charged and neutral colloidal particles are reported for the first time. Different positively and negatively charged polystyrene latex particles are investigated. The neutral particles are obtained through adsorption of an appropriate amount of oppositely charged additives, such as aliphatic oligoamines, iron cyanide complexes, or alkyl sulfates. Heteroaggregation rates were measured with time-resolved multiangle light scattering. One observes that heteroaggregation between charged and neutral particles is always fast and diffusion controlled. These experimental values are compared with calculations of the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, whereby one finds that this heteroaggregation process is highly sensitive to charge regulation conditions. The comparison with experiments shows unambiguously that the surface of the neutral particles regulates strongly and probably behaves close to a constant potential surface. This observation is in line with direct force measurements on similar systems and further agrees with the fact that for neutral surfaces the capacitance of the diffuse layer is expected to be much smaller than the one of the inner layer.

Structuring of colloidal silica nanoparticle suspensions near water-silica interfaces probed by specular neutron reflectivity.

Structuring of aqueous suspensions of colloidal silica nanoparticles near an isolated planar silica-water interface is studied by specular neutron reflectivity. The reflectivity data clearly show that the suspensions develop a damped, oscillatory concentration profile in the normal direction to the interface. The wavelengths of these oscillations agree well with those independently determined by direct force measurements in the slit-geometry. The reflectivity data further demonstrate that the oscillatory structure persists over several layers and that the first particle layer is separated from the interface by a particle-free region.

Measuring slow heteroaggregation rates in the presence of fast homoaggregation.

Homoaggregation and heteroaggregation involving amidine and sulfate latex particles in the presence of the anionic surfactant octyl sulfate (OS) is studied by light scattering. This surfactant causes a charge reversal of the amidine particles. This reversal induces a rapid homoaggregation near the charge reversal point. In the presence of the same surfactant, the sulfate particles remain negatively charged and stable. The heteroaggregation process is probed in mixed suspensions of amidine and sulfate latex particles with multi-angle time-resolved dynamic light scattering. This technique allows differentiating between the contributions of homoaggregation and heteroaggregation, and permits to measure the heteroaggregation rate. By optimally choosing the sizes of the particles, one can optimize the contrast and extract heteroaggregation stability ratio over a wide range. The heteroaggregation rate is fast at low OS concentrations, where the two particles are oppositely charged. This rate slows down at higher OS concentrations due to double layer repulsion between the negatively charged particles. However, the onset of this slow heteroaggregation occurs at lower OS concentrations than for homoaggregation. The reason for this shift is that the double layer repulsion between two OS-decorated amidine particles is weaker than between one sulfate particle and one OS-decorated amidine particle. These measurements compare favorably with calculations with the theory by Derjaguin, Landau, Verwey, and Overbeek (DLVO). These calculations suggest that constant potential boundary conditions are more appropriate than the ones of constant charge. In the system studied, the present light scattering technique permits to extract heteroaggregation stability ratios over almost three orders of magnitude. This study is the first of its kind, where such a large range is being probed.

Forces between solid surfaces in aqueous electrolyte solutions.

This review addresses experimental findings obtained with direct force measurements between two similar or dissimilar solid surfaces in aqueous electrolyte solutions. Interpretation of these measurements is mainly put forward in terms of the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). This theory invokes a superposition of attractive van der Waals forces and repulsive double layer forces. DLVO theory is shown to be extremely reliable, even in the case of multivalent ions. However, such a description is only successful, when appropriate surface charge densities, charge regulation characteristics, and ion pairing or complexation equilibria in solution are considered. Deviations from DLVO theory only manifest themselves at distances of typically below few nm. More long-ranged non-DLVO forces can be observed in some situations, particularly, in concentrated electrolyte solutions, in the presence of strongly adsorbed layers, or for hydrophobic surfaces. The latter forces probably originate from patch-charge surface heterogeneities, which can be induced by ion-ion correlation effects, charge fluctuations, or other types of surface heterogeneities.

In situ Imaging of Single Polyelectrolyte Chains with the Atomic Force Microscope.

This article discusses the possibilities offered by modern atomic force microscopes (AFMs) with ultra-small cantilevers to perform in situ imaging of single adsorbed polyelectrolytes in aqueous solutions. We demonstrate that such AFM techniques permit high quality images of single polyelectrolyte molecules to be obtained. These images can then be used to qualitatively address differences in the adsorbed conformations for different polyelectrolyte architectures. Moreover, such images can be also analyzed quantitatively. As an example, we discuss the determination of the persistence length of adsorbed polyelectrolytes.

Unexpectedly Large Decay Lengths of Double-Layer Forces in Solutions of Symmetric, Multivalent Electrolytes.

Double-layer forces acting between micron-sized silica particles are measured with the atomic force microscope in solutions of symmetric, multivalent electrolytes. In particular, the 2:2 electrolytes, CuSO4 and MgSO4, and the 3:3 electrolyte LaFe(CN)6 were investigated. For the multivalent electrolytes, the measured decay lengths are substantially larger than the ones expected on the basis of simple Debye-Hückel (DH) theory. These deviations can be explained quantitatively by the formation of neutral ion pairs. The measured surface charge density decreases in magnitude with increasing valence. Both effects are caused by ion-ion correlations, which are not included in the classical DH theory. However, this theory remains applicable, provided one considers the formation of ion pairs in solution and an effective surface charge density. This effective charge is substantially smaller in magnitude than the one of the bare surface. This reduction results from adsorption of counterions, which becomes stronger with increasing valence. These observations reveal that DH theory is applicable even in the presence of multivalent ions, provided the effective parameters are chosen appropriately.

Aggregation of Colloidal Particles in the Presence of Hydrophobic Anions: Importance of Attractive Non-DLVO Forces.

Aqueous suspensions of amidine latex (AL) and sulfate latex (SL) particles containing sodium tetraphenylborate and NaCl are studied with electrokinetic and time-resolved light-scattering techniques. In monovalent salt solutions, AL is positively charged, whereas SL is negatively charged. Electrophoretic mobility measurements demonstrate that adsorption of tetraphenylborate anions leads to a charge reversal of AL particles. At higher concentrations, both types of particles accumulate negative charge. For AL particles, the charge reversal leads to a narrow fast aggregation region and an intermediate regime of slow aggregation. For SL particles, the intermediate slow regime is also observed. These aspects can be explained with classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). Another regime of fast aggregation is observed at intermediate concentrations, and the existence of this regime can be rationalized by an additional attractive non-DLVO force. We suspect that this additional force is caused by surface charge heterogeneities.

Aggregation and charging of sulfate and amidine latex particles in the presence of oxyanions.

Electrophoretic mobility and time resolved light scattering are used to measure the effect on charging and aggregation of amidine and sulfate latex particles of different oxyanions namely, phosphate, arsenate, sulfate, and selenate. In the case of negatively charged sulfate latex particles oxyanions represent the coions, while they represent counterions in the case of the positively charged amidine latex. Repulsive interaction between the sulfate latex surface and the coions results in weak ion specific effects on the charging and aggregation. On the other hand the interaction of oxyanions with the amidine latex surface is highly specific. The monovalent dihydrogen phosphate ion strongly adsorbs to the positively charged surface and reverses the charge of the particle. This charge reversal leads also to the restabilization of the amidine latex suspension at the intermediate phosphate concentrations. In the case of dihydrogen arsenate the adsorption to amidine latex surface is weaker and no charge reversal and restabilization occurs. Similar differences are seen between the sulfate and selenate analogues, where selenate adsorbs more strongly to the surface as compared to the sulfate ion and invokes charge reversal. The present results indicate that ion specificity is much more pronounced in the case of counterions.

Interactions between similar and dissimilar charged interfaces in the presence of multivalent anions.

Direct force measurements involving amidine latex (AL) and sulfate latex (SL) particles in aqueous solutions containing multivalent ferrocyanide anions are presented. These measurements feature three different pairs of particles, namely SL-SL, AL-SL, and AL-AL. The force profiles are quantitatively interpreted in terms of the theory by Derjaguin, Landau, Verwey, and Overbeek (DLVO) that is combined with a short-ranged exponential attraction. In monovalent salt solutions, the AL particles are positively charged, while the SL particles are negatively charged. In solutions containing ferrocyanide, the charge of the AL particles is reversed as the concentration is increased. The longer-ranged component of all force profiles is fully compatible with DLVO theory, provided effects of charge regulation are included. At shorter distances, an additional exponential attraction must be introduced, whereby the respective decay length is about 2 nm for the AL-AL pair, and below 1 nm for the SL-SL pair. This non-DLVO force is intermediate for the asymmetric AL-SL pair. These additional forces are probably related to charge fluctuations, patch-charged interactions, or hydrophobic forces.

Attractive non-DLVO forces induced by adsorption of monovalent organic ions.

Direct force measurements between negatively charged colloidal particles were carried out using an atomic force microscope (AFM) in aqueous solutions containing monovalent organic cations, namely tetraphenylarsonium (Ph4As+), 1-hexyl-3-methylimidazolium (HMIM+), and 1-octyl-3-methylimidazolium (OMIM+). These ions adsorb to the particle surface, and induce a charge reversal. The forces become attractive at the charge neutralization point, but they are stronger than van der Waals forces. This additional and unexpected attraction decays exponentially with a decay length of a few nanometers, and is strikingly similar to the one previously observed in the presence of multivalent ions. This attractive force probably originates from coupled spontaneous charge fluctuations on the respective surfaces as initially suggested by Kirkwood and Shumaker.

Heteroaggregation of oppositely charged particles in the presence of multivalent ions.

Time-resolved dynamic light scattering is used to measure absolute heteroaggregation rate coefficients and the corresponding stability ratios for heteroaggregation between amidine and sulfate latex particles. These measurements are complemented by the respective quantities for the homoaggregation of the two systems and electrophoresis. Based on the latter measurements, the stability ratios are calculated using Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. In monovalent salt solutions, the two types of particles investigated are oppositely charged. In the presence of multivalent ions, however, one particle type reverses its charge, while the charge of the other particle type is hardly affected. In this region, the heteroaggregation stability ratio goes through a pronounced maximum when plotted versus concentration. This region of slow aggregation is wider than the one observed in the corresponding homoaggregation process. One also finds that the onset of this region sensitively depends on the boundary conditions used to calculate the double layer force. The present results are more in line with constant potential boundary conditions.

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.

Quantitative Nano-characterization of Polymers Using Atomic Force Microscopy.

The present article offers an overview on the use of atomic force microscopy (AFM) to characterize the nanomechanical properties of polymers. AFM imaging reveals the conformations of polymer molecules at solid- liquid interfaces. In particular, for polyelectrolytes, the effect of ionic strength on the conformations of molecules can be studied. Examination of force versus extension profiles obtained using AFM-based single molecule force spectroscopy gives information on the entropic and enthalpic elasticities in pN to nN force range. In addition, single molecule force spectroscopy can be used to trigger chemical reactions and transitions at the molecular level when force-sensitive chemical units are embedded in a polymer backbone.

Colloidal Stability in Asymmetric Electrolytes: Modifications of the Schulze-Hardy Rule.

The Schulze-Hardy rule suggests a strong dependence of the critical coagulation concentration (CCC) on the ionic valence. This rule is addressed theoretically and confronted with recent experimental results. The commonly presented derivation of this rule assumes symmetric electrolytes and highly charged particles. Both assumptions are incorrect. Symmetric electrolytes containing multivalent ions are hardly soluble, and experiments are normally carried out with the well-soluble salts of asymmetric electrolytes containing monovalent and multivalent ions. In this situation, however, the behavior is completely different whether the multivalent ions represent the counterions or co-ions. When these ions represent the counterions, meaning that the multivalent ions have the opposite sign than the charge of the particle, they adsorb strongly to the particles. Thereby, they progressively reduce the magnitude of the surface charge with increasing valence. In fact, this dependence of the charge density on the counterion valence is mainly responsible for the decrease of the CCC with the valence. In the co-ion case, where the multivalent ions have the same sign as the charge of the particle, the multivalent ions are repelled from the particles, and the surfaces remain highly charged. In this case, the inverse Schulze-Hardy rule normally applies, whereby the CCC varies inversely proportional to the co-ion valence.

Influence of Solvent Quality on the Force Response of Individual Poly(styrene) Polymer Chains.

Single molecule mechanics of poly(styrene) polymer chains is investigated in different organic solvents with atomic force microscopy (AFM). The acquired force-extension profiles can be well fitted with a modified freely jointed chain (FJC) model. The model describes the force-extension profiles in terms of an apparent Kuhn length and an elasticity constant. The elasticity constant is found to be the same for all different solvents investigated. Best fit of the force-extension profiles with the FJC model reveals that the Kuhn length varies systematically with solvent quality. In fact, one can establish a good correlation between the Kuhn length and the Flory-Huggins interaction parameter. The increase in the Kuhn length with increasing solvent quality reflects the larger extent of swelling of the polymer in good solvents.

Influence of ligand-receptor interactions on force-extension behavior within the freely jointed chain model.

We study the influence of receptor-ligand interactions on the force response of single polymer chains theoretically. The extension of the chain is modeled in terms of freely jointed chain or elastic freely jointed chain (EFJC) models. The situation involving noninteracting bonds is solved exactly, while effects of interactions are treated within a mean-field approximation. The form with shorter bonds governs the low force situation, while the form with longer bonds is relevant in the high force regime. We further discuss the accuracy of approximate relations, which were used to describe the response of the EFJC model.

Mechanically induced cis-to-trans isomerization of carbon-carbon double bonds using atomic force microscopy.

Cis-to-trans isomerization of carbon-carbon double bonds can be induced by the application of mechanical force. Using single molecule force spectroscopy by means of atomic force microscopy (AFM) we pulled polymer molecules which contained cis double bonds in the backbone. In the force versus extension profiles of these polymers, a sudden extension increase is observed which is due to the conversion of shorter cis isomers into longer trans isomers. The added length to the polymer results in relaxation in probed force. We find that the isomerization occurs at forces of 800 ± 60 pN, independent of AFM tip and solid substrate chemistries. Investigation of similar polymers which exclusively contained single bonds in the backbone showed no evidence of a similar transition.