Gregor Trefalt

Charge Regulation in the Electrical Double Layer: Ion Adsorption and Surface Interactions.

Charge regulation in the electrical double layer has important implications for ion adsorption, interparticle forces, colloidal stability, and deposition phenomena. Although charge regulation generally receives little attention, its consequences can be major, especially when considering interactions between unequally charged surfaces. The present article discusses common approaches to quantify such phenomena, especially within classical Poisson-Boltzmann theory, and pinpoints numerous situations where a consideration of charge regulation is essential. For the interpretation of interaction energy profiles, we advocate the use of the constant regulation approximation, which summarizes the surface properties in terms of two quantities, namely, the diffuse layer potential and the regulation parameter. This description also captures some pronounced regulation effects observed in the presence of multivalent ions.

Specific Ion Effects on Particle Aggregation Induced by Monovalent Salts within the Hofmeister Series

Ion specific effects of monovalent salts on charging and aggregation for two types of polystyrene latex particles were investigated by electrophoresis and time-resolved light scattering. The chemical composition of the electrolytes was systematically varied in the experiments. Accordingly, NaH2PO4, NaF, NaCl, NaBr, NaNO3, and NaSCN were used to vary the anions and N(CH3)4Cl, NH4Cl, CsCl, KCl, NaCl, and LiCl for the cations. The salt concentration dependence of the electrophoretic mobilities indicates that the surface charge was screened by the counterions when their concentrations increased. For the SCN(-) ions, adsorption on positively charged particles leads to charge reversal. The aggregation rates are small at low electrolyte concentrations indicating stable dispersions under these conditions, and they increase with the salt concentration. When viscosity corrections are taken into account, no ion specific effects in the fast aggregation regime can be established. The slow and fast aggregation regimes are separated by the critical coagulation concentration (CCC). Within the experimental error, the CCCs are the same in systems containing different co-ions but the same counterions, with the exception of ammonium salts. However, the variation of counterions leads to different CCC values due to specific interaction of the counterions with the surface. These values follow the Hofmeister series for negatively charged sulfate latex particles, while the reversed order was observed for positively charged amidine latex. Comparison between experimental CCCs and those calculated by the theory of Derjaguin, Landau, Verwey, and Owerbeek reveals that variations in the surface charge due to ionic adsorption are mainly responsible for the ion specific effects in the aggregation process.

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

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

Aggregation of negatively charged colloidal particles in the presence of multivalent cations.

The aggregation and charging behavior of sulfate and carboxyl latex particles in the presence of different multivalent salts was studied. Time-resolved light scattering and electrophoresis are the main experimental techniques used. In particular, the influence of the type of counterion is investigated. The main conclusion is that the valence of the counterion is highly relevant in determining the aggregation behavior, whereas its chemical nature is rather unimportant. Multivalent ions of higher valence destabilize the suspensions more effectively, in particular, by shifting the critical coagulation concentration (CCC) to lower values. This behavior reflects the classical Schulze-Hardy rule. Comparison with literature data reveals that the presently investigated systems behave similarly to the ones described earlier, but the observed dependence on valence is weaker than in some other systems. Moreover, we observe a slowdown of the aggregation at high electrolyte concentrations. This slowdown can be explained by the greater viscosity of the electrolyte solutions under these conditions.

Measurements of dispersion forces between colloidal latex particles with the atomic force microscope and comparison with Lifshitz theory

Interaction forces between carboxylate colloidal latex particles of about 2 μm in diameter immersed in aqueous solutions of monovalent salts were measured with the colloidal probe technique, which is based on the atomic force microscope. We have systematically varied the ionic strength, the type of salt, and also the surface charge densities of the particles through changes in the solution pH. Based on these measurements, we have accurately measured the dispersion forces acting between the particles and estimated the apparent Hamaker constant to be (2.0 ± 0.5) × 10(-21) J at a separation distance of about 10 nm. This value is basically independent of the salt concentration and the type of salt. Good agreement with Lifshitz theory is found when roughness effects are taken into account. The combination of retardation and roughness effects reduces the value of the apparent Hamaker constant and its ionic strength dependence with respect to the case of ideally smooth surfaces.

Predicting Aggregation Rates of Colloidal Particles from Direct Force Measurements

Direct force measurements between negatively charged colloidal latex particles of a diameter of 1 μm were carried out in aqueous solutions of various inorganic monovalent and multivalent cations with the multiparticle colloidal probe technique based on the atomic force microscope (AFM). The observed force profiles were rationalized within the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). In the presence of monovalent and divalent cations, this theory was capable to describe the force profiles correctly down to distances of a few nm. At shorter distances, however, a strong non-DLVO attraction was identified. For more highly charged cations, an additional and more long-ranged non-DLVO attractive force is observed, and it was interpreted by surface charge heterogeneities. On the basis of these force profiles, the aggregation rates, which were independently measured by light scattering, can be predicted relatively well. The main conclusion of this study is that, in the present system, direct force measurements do capture the principal interactions driving aggregation in colloidal suspensions.

Accurate predictions of forces in the presence of multivalent ions by Poisson-Boltzmann theory.

Forces between positively and negatively charged colloidal particles across aqueous salt solutions containing multivalent ions are measured directly with the atomic force microscope (AFM). The measurements are interpreted quantitatively with Poisson-Boltzmann (PB) theory. Thereby, the surface potentials and regulation properties of the particle surfaces are extracted from symmetric measurements between the same types of particles. This information is used to predict force profiles in the asymmetric situations involving different types of particles without any adjustable parameters. These predictions turn out to be very accurate, which demonstrates that the mean-field PB theory is reliable down to distances of about 5 nm. While various reports in the literature indicate that this theory should fail due to neglect of ion correlations, such effects seem important only at higher concentrations and smaller distances.

Particle aggregation mechanisms in ionic liquids

Aggregation of sub-micron and nano-sized polystyrene latex particles was studied in room temperature ionic liquids (ILs) and in their water mixtures by time-resolved light scattering. The aggregation rates were found to vary with the IL-to-water molar ratio in a systematic way. At the water side, the aggregation rate is initially small, but increases rapidly with increasing IL content, and reaches a plateau value. This behaviour resembles simple salts, and can be rationalized by the competition of double-layer and van der Waals forces as surmised by the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). At the IL side, aggregation slows down again. Two generic mechanisms could be identified to be responsible for the stabilization in ILs, namely viscous stabilization and solvation stabilization. Viscous stabilization is important in highly viscous ILs, as it originates from the slowdown of the diffusion controlled aggregation due to the hindrance of the diffusion in a viscous liquid. The solvation stabilization mechanism is system specific, but can lead to a dramatic slowdown of the aggregation rate in ILs. This mechanism is related to repulsive solvation forces that are operational in ILs due to the layering of the ILs close to the surfaces. These two stabilization mechanisms are suspected to be generic, as they both occur in different ILs, and for particles differing in surface functionalities and size.

Interaction Forces and Aggregation Rates of Colloidal Latex Particles in the Presence of Monovalent Counterions

Force profiles and aggregation rates involving positively and negatively charged polystyrene latex particles are investigated in monovalent electrolyte solutions, whereby the counterions are varied within the Hofmeister series. The force measurements are carried out with the colloidal probe technique, which is based on the atomic force microscope (AFM), while the aggregation rates are measured with time-resolved multiangle light scattering. The interaction force profiles cannot be described by classical DLVO theory, but an additional attractive short-ranged force must be included. An exponential force profile with a decay length of about 0.5 nm is consistent with the measured forces. Furthermore, the Hamaker constants extracted from the measured force profiles are substantially smaller than the theoretical values calculated from dielectric spectra. The small surface roughness of the latex particles (below 1 nm) is probably responsible for this deviation. Based on the measured force profiles, the aggregation rates can be predicted without adjustable parameters. The measured absolute aggregation rates in the fast regime are somewhat lower than the calculated ones. The critical coagulation concentration (CCC) agrees well with the experiment, including the respective shifts of the CCC within the Hofmeister series. These shifts are particularly pronounced for the positively charged particles. However, the consideration of the additional attractive short-ranged force is essential to quantify these shifts correctly. In the slow regime, the calculated rates are substantially smaller than the experimental ones. This disagreement is probably related to surface charge heterogeneities.

Interaction Forces, Heteroaggregation, and Deposition Involving Charged Colloidal Particles

Force profiles as well as aggregation and deposition rates are studied for asymmetrically charged particles and surfaces in aqueous electrolytes theoretically. Interactions are calculated within the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, whereby the electrostatic part is modeled at Poisson-Boltzmann (PB) level. Unequally charged surfaces are examined, from the symmetric system, where both surfaces are equally charged, to fully asymmetric systems, where the surfaces are oppositely charged. Charged-neutral systems, where one surface is charged and the other is neutral, emerge as an essential scenario. In this case, the choice of boundary conditions used for solving the PB equation is crucial, whereby constant charge and constant potential boundary conditions lead to either fully repulsive or fully attractive forces. Consequently, charge regulation has a major influence on particle aggregation and deposition rates too. In the charge-neutral case, substantial shifts in the critical coagulation concentration (CCC) are observed when the regulation properties are changed. In the presence of multivalent ions, these systems behave similarly to the symmetrically charged ones. The CCC decreases with the square of the valence in weakly charged systems, while unrealistically high charge densities are needed to recover the classical Schulze-Hardy limit, which predicts a sixth power dependence on valence.