Derivation of the inverse Schulze-Hardy rule

Colloidal Interactions of Microplastic Particles with Anionic Clays in Electrolyte Solutions

Homoaggregation of polystyrene microplastics (MPs) and heteroaggregation of MPs with anionic clay minerals, namely, layered double hydroxide (LDH), in different salt (NaCl, CaCl2, and Na2SO4) solutions were systematically investigated using light scattering techniques. The salt type and ionic strength had significant effects on the stability of both MPs and LDH particles individually and the results could be explained by DLVO theory and the Schulze-Hardy rule. However, once stable colloidal dispersions of the individual particles were mixed, heteroaggregation occurred between the oppositely charged MPs and LDH, which was also confirmed by transmission electron microscopy and X-ray scattering. Adsorption of the LDH particles resulted in neutralization and reversal of MPs surface charge at appropriate LDH doses. Once LDH adsorption neutralized the negative charges of the MP spheres, rapid aggregation was observed in the dispersions, whereas stable samples formed at high and low LDH concentrations. The governing interparticle interactions included repulsive electrical double-layer forces, as well as van der Waals and patch-charge attractions, the strength of which depended on the mass ratio of the interacting particles and the composition of the aqueous solvent. Our results shed light on the colloidal behavior of MPs in a complex aquatic environment and, in the long term, are also useful for developing LDH-based approaches for water remediation to remove contamination with MP particles.

Effects of ionic valence on aggregation kinetics of colloidal particles with and without a mixing flow

HYPOTHESIS

The classical Schulze-Hardy rule states that the critical coagulation concentration (CCC) of colloidal particles is inversely proportional to the counter-ionic valence at powers ranging from 2 to 6. However, the inverse Schulze-Hardy rule has recently been proposed, suggesting that the CCC can also be inversely proportional to the co-ionic valence. Previous studies on these rules did not consider the effect of flow on aggregation kinetics and the CCC. This study aims to investigate the effect of multivalent counter-ions and co-ions on aggregation kinetics and the CCCs in systems with and without a mixing flow.

EXPERIMENTS

We measured the aggregation rate coefficients of polystyrene sulfate latex particles as a function of the salt concentration with different ionic species. Furthermore, we analyzed these measurements using theoretical models based on hydrodynamic pair-diffusion in a random flow and trajectory analysis in two steady flows. The analysis was conducted using zeta potentials determined through electrophoretic measurements.

FINDINGS

Although the trajectory analysis underestimates the CCCs, the hydrodynamic pair-diffusion model can capture the shift of critical coagulation concentrations in the mixing flow to higher values than those in Brownian aggregation and also shows a better agreement with the experimental results. This result suggests that combining random flow and Brownian diffusion is crucial for developing a consistent framework for predicting both Brownian aggregation and aggregation in a mixing flow.

Structure-Stability Relationship in Aqueous Colloids of Latex Particles and Gemini Surfactants

The influence of gemini surfactants (GSs) on the charging and aggregation features of anionic sulfate modified latex (SL) particles was investigated by light scattering techniques in aqueous dispersions. The GSs of short alkyl chains (2-4-2 and 4-4-4) resembled simple inert salts and aggregated the particles by charge screening. The adsorption of GSs of longer alkyl chains (8-4-8, 12-4-12, and 12-6-12) on SL led to charge neutralization and overcharging of the particles, giving rise to destabilization and restabilization of the dispersions, respectively. The comparison of the interfacial behavior of dimeric and the corresponding monomeric surfactants revealed that the former shows a more profound influence on the colloidal stability due to the presence of double positively charged head groups and hydrophobic tails, which is favorable to enhancing both electrostatic and hydrophobic particle-GS and GS-GS interactions at the interface. The different extent of the particle-GS interactions was responsible for the variation of the GS destabilization power, following the 2-4-2 < 4-4-4 < 8-4-8 < 12-4-12 order, while the length of the GS spacer did not affect the adsorption and aggregation processes. The valence of the background salts strongly influenced the stability of the SL-GS dispersions through altering the electrostatic interactions, which was more pronounced for multivalent counterions. These findings indicate that both electrostatic and hydrophobic effects play crucial roles in the adsorption of GSs on oppositely charged particles and in the corresponding aggregation mechanism. The major interparticle forces can be adjusted by changing the structure and concentration of the GSs and inorganic electrolytes present in the systems.

Synthesis of CuO nanoparticles stabilized with gelatin for potential use in food packaging applications

In the present study, a method for the synthesis of gelatin-stabilized copper oxide nanoparticles was developed. Synthesis was carried out by direct chemical precipitation. Copper sulfate, chloride, and acetate were used as precursors for the copper oxide synthesis. Gelatin was used as a stabilizer. It was found that the formation of monophase copper oxide II only occurred when copper acetate was used as a precursor. Our results showed that particles of the smallest diameter are formed in an aqueous medium (18 ± 6 nm), and those of th largest diameter—in an isobutanol medium (370 ± 131 nm). According to the photon correlation spectroscopy data, copper oxide nanoparticles synthesized in an aqueous medium were highly stable and had a monomodal size distribution with an average hydrodynamic radius of 61 nm. The study of the pH effect on the colloidal stability of copper oxide nanoparticles showed that the sample was stable in the pH range of 6.8 to 11.98. A possible mechanism for the pH influence on the stability of copper oxide nanoparticles is described. The effect of the ionic strength of the solution on the stability of the CuO nanoparticles sol was also studied, and the results showed that Ca²⁺ ions had the greatest effect on the sample stability. IR spectroscopy showed that the interaction of CuO nanoparticles with gelatin occurred through the hydroxyl group. It was found that CuO nanoparticles stabilized with gelatin have a fungicidal activity at concentration equivalent 2.5 · 10⁻³ mol/L and as a material for food nanopackaging can provide an increase in the shelf life of products on the example of strawberries and tomatoes. We investigated the possibility of using methylcellulose films modified with CuO nanoparticles for packaging and storage of hard cheese “Holland”. The distribution of CuO nanoparticles in the methylcellulose film was uniform. We found that methylcellulose films modified with CuO nanoparticles inhibited the growth and development of QMAFAM, coliforms, yeast and mold in experimental cheese sa mples. Our research has shown that during the cheese storage in thermostat at 35 ± 1 °C for 7 days, CuO nanoparticles migrated to the product from the film. Nevertheless, it is worth noting that the maximum change in the concentration of copper in the experimental samples was only 0.12 µg/mg, which is not a toxic concentration. In general, the small value of migration of CuO nanoparticles confirms the high stability of the developed preparation. Our results indicated that the CuO nanoparticles stabilized with gelatin have a high potential for use in food packaging – both as an independent nanofilm and as part of other packaging materials.

Aggregation of Halloysite Nanotubes in the Presence of Multivalent Ions and Ionic Liquids

Colloidal stability was investigated in two types of particle systems, namely, with bare (h-HNT) and polyimidazolium-functionalized (h-HNT-IP-2) alkali-treated halloysite nanotubes in solutions of metal salts and ionic liquids (ILs). The valence of the metal ions and the number of carbon atoms in the hydrocarbon chain of the IL cations (1-methylimidazolium (MIM+), 1-ethyl-3-methylimidazolium (EMIM+), 1-butyl-3-methylimidazolium (BMIM+), and 1-hexyl-3-methylimidazolium (HMIM+)) were altered in the measurements. For the bare h-HNT with a negative surface charge, multivalent counterions destabilized the dispersions at low values of critical coagulation concentration (CCC) in line with the Schulze-Hardy rule. In the presence of ILs, significant adsorption of HMIM+ took place on the h-HNT surface, leading to charge neutralization and overcharging at appropriate concentrations. A weaker affinity was observed for MIM+, EMIM+, and BMIM+, while they adsorbed on the particles to different extents. The order HMIM+ < BMIM+ < EMIM+ < MIM+ was obtained for the CCCs of h-HNT, indicating that HMIM+ was the most effective in the destabilization of the colloids. For h-HNT-IP-2 with a positive surface charge, no specific interaction was observed between the salt and the IL constituent cations and the particles, i.e., the determined charge and aggregation parameters were the same within experimental error, irrespective of the type of co-ions. These results clearly indicate the relevance of ion adsorption in the colloidal stability of the nanotubes and thus provide useful information for further design of processable h-HNT dispersions.

Specific Ion Effects on Aggregation and Charging Properties of Boron Nitride Nanospheres

The charging and aggregation properties of boron nitride nanospheres (BNNSs) were investigated in the presence of electrolytes of different compositions and valences in aqueous suspensions. The influence of mono- and multivalent cations (counterions) and anions (coions) on the colloidal stability of the negatively charged particles was studied over a wide range of salt concentrations. For monovalent ions, similar trends were determined in the stability and charging of the particles irrespective of the salt composition, i.e., no ion-specific effects were observed. Once multivalent counterions were involved, the critical coagulation concentrations (CCCs) decreased with the valence in line with the direct Schulze-Hardy rule. The dependence indicated an intermediate charge density for BNNSs. The influence of the coions on the CCCs was weaker and the destabilization ability followed the inverse Schulze-Hardy rule. The predominant interparticle forces were identified as electrical double-layer repulsion and van der Waals attraction. These findings offer useful information to design stable BNNS dispersions in various applications, where mono- and multivalent electrolytes or their mixtures are present in the samples.

Organic Functionalized Graphene Oxide Behavior in Water

Surface modified graphene oxide (GO) has received broad interest as a potential platform material for sensors, membranes, and sorbents, among other environmental applications. However, compared to parent (unmodified) GO, there is a dearth of information regarding the behavior of subsequently (secondary) modified GO, other than bulk natural organic matter (NOM) coating(s). Here, we systematically explore the critical role of organic functionalization with respect to GO stability in water. Specifically, we synthesized a matrix of GO-based materials considering a carefully chosen range of bound organic molecules (hydrophobic coatings: propylamine, tert-octylamine, and 1-adamantylamine; hydrophilic coatings: 3-amino-1-propanol and 3-amino-1-adamantanol), so that chemical structures and functional groups could be directly compared. GO (without organic functionalization) with varying oxidation extent(s) was also included for comparison. The material matrix was evaluated for aqueous stability by comparing critical coagulation concentration (CCC) as a function of varied ionic strength and type (NaCl, CaCl₂, MgCl₂, and MgSO₄) at pH 7.0. Without surface derivatization (i.e., pristine GO), increased stability was observed with an increase in the GO oxidation state, which is supported by plate–plate Derjaguin, Landau, Verwey and Overbeek (DLVO) energy interaction analyses. For derivatized GO, we observed that hydrophilic additions (phi-GO) are relatively more stable than hydrophobic organic coated GO (pho-GO). We further explored this by altering a single OH group in the adamantane-x structure (3-amino-1-adamantanol vs. 1-adamantylamine). As expected, Ca²⁺ and monovalent co-ions play an important role in the aggregation of highly oxidized GO (HGO) and phi-GO, while the effects of divalent cations and co-ions were less significant for pho-GO. Taken together, this work provides new insight into the intricate dynamics of GO-based material stability in water as it relates to surface functionalization (surface energies) and ionic conditions including type of co- and counter-ion, valence, and concentration.

Effect of Ionic Compounds of Different Valences on the Stability of Titanium Oxide Colloids

Titanium oxide particles of various morphologies have been prepared for applications of scientific or industrial interest in recent decades. Besides development of novel synthetic routes and solid-state characterization of the obtained particles, colloidal stability of titanium oxide dispersions was the focus of numerous research groups due to the high importance of this topic in applications in heterogeneous systems. The influence of dissolved ionic compounds, including monovalent salts, multivalent ions and polyelectrolytes, on the charging and aggregation behaviour of titanium oxide materials of spherical and elongated structures will be discussed in the present review.

Electrostatic double-layer interaction between stacked charged bilayers

The inapplicability of the DLVO theory to multilayered anionic bilayers is found in terms of the co-ion-valence dependence of the lamellar repeat distance. Most of the added salt is expelled from the interlamellar space to the bulk due to the Gibbs-Donnan effect on multiple bilayers with the bulk. The electrostatic double-layer interaction is well expressed by the formula recently proposed by Trefalt. The osmotic pressure due to the expelled ions, rather than the van der Waals interaction, is the main origin of the attractive force between the bilayers.

Interactions between silica particles in the presence of multivalent coions

Forces between charged silica particles in solutions of multivalent coions are measured with colloidal probe technique based on atomic force microscopy. The concentration of 1 : z electrolytes is systematically varied to understand the behavior of electrostatic interactions and double-layer properties in these systems. Although the coions are multivalent the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory perfectly describes the measured force profiles. The diffuse-layer potentials and regulation properties are extracted from the forces profiles by using the DLVO theory. The dependencies of the diffuse-layer potential and regulation parameter shift to lower concentration with increasing coion valence when plotted as a function of concentration of 1 : z salt. Interestingly, these profiles collapse to a master curve if plotted as a function of monovalent counterion concentration.

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.

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.

Interplay between Depletion and Double-Layer Forces Acting between Charged Particles in Solutions of Like-Charged Polyelectrolytes

Direct force measurements between negatively charged silica particles in the presence of a like-charged strong polyelectrolyte were carried out with an atomic force microscope. The force profiles can be quantitatively interpreted as a superposition of depletion and double-layer forces. The depletion forces are modeled with a damped oscillatory profile, while the double-layer forces with the mean-field Poisson-Boltzmann theory for a strongly asymmetric electrolyte, whereby an effective valence must be assigned to the polyelectrolyte. This effective valence is substantially smaller than the bare valence due to ion condensation effects. The unusual aspect of the electrical double layer in these systems is the exclusion of the like-charged polyelectrolyte from the vicinity of the surface, leading to a strongly nonexponential diffuse ionic layer that is dominated by counterions and has a well-defined thickness. As the oscillatory depletion force sets in right after this layer, this condition can be used to predict the phase of the oscillatory depletion force.