Surface Charge Density Of Particles Research Articles

Experimental study on decarburization of fine fly ash by electric separation

ABSTRACT The effect of rotary triboelectric separation parameters on decarburization of fly ash was systematically studied to prove that the technology was an effective means to purify fly ash. The results showed that obvious mismatch of carbon particles occurs when separation voltage was greater than 25 kV, while mismatch of other mineral particles was generated when separation voltage was greater than 30kV; The decarburization effect of fly ash could be significantly reduced due to the decrease of particle surface charge density when the feed frequency was greater than 20 hz. The feed was also affected by the speed and direction of the particle feed, the closer to the middle of the feed port, the higher the probability of the particle being effectively separated; when rotation speed of the friction wheel exceeded 4000 r/min, the particle mismatch in the separation chamber becomes more and more obvious. In addition, the speed of the friction wheel also affected flow field in separation chamber, which may have an adverse effect on separation effect; Co-flow velocity affected retention time of particles in the separation chamber. 6 m/s is the best co-flow velocity for fly ash decarburization. In this case, the flow field generated by the co-flow is uniform to ensure stable transport of particles.

Composites with Immobilized Bioactive Spirulina on an Inorganic Substrate (Yellow Clay, Hydroxyapatite, SiO2, TiO2, ZnO).

In order to improve the structural properties of clays and composites of powdered spirulina, clay, nanosilica, hydroxyapatite, TiO2 and ZnO were used as an additive for mechanical processing. As a result, composites with natural nanostructured materials (NNM) are prepared with improved structural properties and bioactivity. The mixtures based on NNM with crystalline kaolinite, clays and admixtures were processed in a knife mill. The materials were characterized using FTIR spectroscopy, nitrogen adsorption and desorption, SEM release of bioactive components (anthocyanin 0,004-0,07 mg/g; chlorophyll 20-29 mg/g), composite toxicity level (below 25%), particle size measurement and surface charge density, zeta potential. Adsorption enthalpies during the formation of an intermolecular complex during the interactions of an anthocyanin molecule with the appropriate component of the composite were also calculated. There are regularities in the characteristics depending on the type of NNM, particle morphology and textural features of solids. The morphological and structural properties of the components changed slighty in the blends because the processing was conducted under relatively low mechanical stress. The morphological, textural and structural characteristics of the composites as well as the transformation to a nanostructured state, assume great bioactive activity of the composites, interesting for practical applications in medicine and cosmetics.

Assessing Activation Quality through Evaporative Drying Patterns of Zr-MOF (UiO-66) Colloidal Droplets.

We demonstrate a simple droplet diagnostic approach to monitor the UiO-66 MOF (metal-organic framework) synthesis and its quality using the sessile droplet drying phenomenon. Drying a sessile droplet involves evaporation-driven hydrodynamic flow and particle-nature-dependent self-assembled deposition. In general, the MOF synthesis process involves different sizes and physicochemical nature of particles in every synthesis stage. Equivalent quantities of each of purified pore-activated UiO-66 MOF, yet-to-be-purified pore-inactivated UiO-66 MOF, and reaction precursors of UiO-66 MOF give different deposition patterns when a well-dispersed aqueous droplet of these materials undergoes drying over substrates of varying stiffness and wettability. Yet-to-be-purified, pore-inactivated UiO-66 MOF nanoparticles undergo transport toward the droplet periphery, leading to a thick ring-like deposition at the dried droplet edge. Under appropriate drying conditions, such a deposit leads to desiccation-type mud-like reticular cracking. We study the origin of such ring-like deposits and cracks to understand how the surface charge density of UiO-66 particles controls their stability. We demonstrate that ZrOCl2 salt trapped in a nonpurified pore-inactivated UiO-66 MOF moiety is the principal reason for ring-like deposit formation and subsequent cracking in its dried aqueous droplet edge. Qualitatively, we identified Lewis acid salts that are capable of acting as Bro̷nsted acid upon hydrolysis (like FeCl3, SnCl2, and ZrOCl2), influence surface charge density and colloidal stability of dispersed UiO-66 MOF particles. As a result, immediate particle coagulation is avoided, so those travel to the droplet edge, forming ring-like deposition and subsequent cracking upon drying. Further, we show that crack patterns on such deposits are highly dependent on the stiffness and temperature of depositing substrates via a competition between axial and lateral strains at the deposit-substrate interface.

Free iron oxides modulate the surface properties of Benggang soil on Southern China: insights into erosive mechanisms

Benggang, an erosional phenomenon located in southern China, exhibits distinctive characteristics that can have profound ecological and agricultural consequences as well as pose risks to human life. Previous investigations have primarily focused on elucidating the relationships between the physical and chemical attributes of soils collected from Benggang. However, the precise role of free iron oxides in the surface properties of Benggang soil and its contribution to the formation of Benggang remains largely unexplored. In this study, we aim to investigate the role of free iron oxides in Benggang soil by removing them and subsequently introducing goethite to evaluate their impact on the soil’s surface properties. Our results reveal a decrease in the surface charge density of soil colloidal particles with increasing soil depth. Specifically, the uppermost red soil layer exhibits the highest value, followed by the sandy soil and the lowermost clastic layer. Upon removing free iron oxide, we documented reductions of 44.28% (red soil), 20.62% (sandy soil), and 8.70% (clastic layer) in the surface charge density of colloidal particles. The red soil layer presented an over 18-fold increase compared to the initial linear shrinkage, followed by the sandy soil and clastic layer. Notably, the addition of goethite to the iron oxide-free soil layers resulted in the recovery of approximately 81.93%, 121.13%, and 104.35% of the initial surface charge density, respectively. Moreover, significant changes in volume shrinkage were observed, with approximately 97.54% (red soil), 94.75% (sandy soil), and 89.72% (clastic layer) of the initial values being influenced. These findings underscore the substantial influence of free iron oxide on the physicochemical properties of Benggang soil and contribute to a comprehensive understanding of the erosive mechanisms underlying Benggang formation.

Selected Textural and Electrochemical Properties of Nanocomposite Fillers Based on the Mixture of Rose Clay/Hydroxyapatite/Nanosilica for Cosmetic Applications.

In order to improve the properties and characteristics of rose clay composites with acai, hydroxyapatite (HA), and nanosilica, the systems were mechanically treated. This treatment provides the preparation of better nanostructured composites with natural and synthetic nanomaterials with improved properties. The materials were characterized using XRD, nitrogen adsorption and desorption, particle sizing, zeta potential, and surface charge density measurements. For the systems tested in the aqueous media, the pH value of the point of zero charge (pHPZC) ranges from 8 to 9.9. However, the isoelectric point (pHIEP) values for all composites are below pH 2. This large difference between pHPZC and pHIEP is due to the complexity of the electrical double layer (EDL) and the relation of these points to different layers of the EDL. The tested samples as composite/electrolyte solutions are colloidally unstable. The toxicity level of the ingredients and release of anthocyanins as bioactive substances from acai in the composites were determined. The composites demonstrate an enhanced release of anthocyanins. There are some regularities in the characteristics depending on the type of components, morphology, and textural features of solids. The morphological, electrochemical, and structural characteristics of the components have changed in composites. The release of anthocyanins is greater for the composites characterized by minimal confined space effects in comparison with rose clay alone. The morphological, electrochemical, and structural characteristics allow us to expect high efficiency of composites as bioactive systems that are interesting for practical applications in cosmetics.

Phase Inversion of Pickering Emulsions Induced by Interfacial Electrostatic Attraction

Phase inversion of Pickering emulsions from water-in-oil (W/O) to oil-in-water (O/W) is achieved by the formation of an interfacial particle bilayer using negatively charged and positively charged particles dispersed in water and oil, respectively, before emulsification. A mechanism based on electrostatic attraction across the toluene-water interface is proposed and verified by systematic investigation of the parameters that affect the surface charge of negatively charged particles such as pH and salt concentration. Cationic silica-FITC particles (600 nm) can be dispersed in toluene and stabilize W/O emulsions alone; phase inversion of this emulsion can be induced by the addition of anionic silica-RB particles in the aqueous phase at a concentration of 1.0 wt % or above. It is revealed that silica-RB particles of a smaller size (100 nm) can induce emulsion phase inversion at a much lower concentration (0.4 wt %) and an interfacial particle bilayer is clearly revealed by CLSM and SEM images. By tuning the surface charge density of silica-RB particles, the electrostatic attraction mechanism leading to the formation of the interfacial particle bilayer is confirmed and emulsion stability can be tuned as demonstrated by osmotic pressure enhancement results obtained from centrifugation.

Solution composition dependent Soret coefficient using commercial MicroScale Thermophoresis instrument.

Thermal diffusion of particles in dilute aqueous suspensions is driven by the interactions between the dispersing medium and the particle, which are largely influenced by the properties of the medium. Using a commercial instrument to generate thermophoresis, we developed a method to quantify the migration of colloids in a temperature gradient and further studied how it varies based on the composition and pH of the dispersing medium and with an anionic surfactant, at different salt concentrations. Thermophoretic migration of aqueous suspensions of carboxylate-modified polystyrene particles with different compositions is measured as MicroScale Thermophoresis (MST) traces and a mathematical model is developed to extract the Soret coefficient (ST). Soret coefficient measurements obtained using the developed method are in-line with previous theories and scientific findings from other literature, indicating a dependence of the ST on the Debye length and surface charge density of the suspended particles, both of which are controlled by the composition of the dispersing medium. The thermophobic/thermophilic behavior of particles is also found to be strongly influenced by the thermoelectric effect of the buffer ions. In this paper, a new analytical model is introduced and applied to complex systems to understand their thermophoretic behavior as a function of solvent properties.

Colloidal Crystals of Charged-Polymer-Brush-Decorated Hybrid Particles in Low-Polarity Solvents

Colloidal crystals are self-assembled systems that are suitable as models for studying crystallization; they are also attractive as nanostructures with a periodic arrangement of materials that have different refractive indices. Here, we present a method of constructing colloidal crystals in an organic solvent using charged-polymer-brush-decorated core-shell-type hybrid particles synthesized by surface-initiated living radical polymerization. The core-shell-type hybrid particles consisted of a silica particle core surrounded by a shell of polymer brushes obtained by the polymerization of methyl methacrylate and a small amount of a cationic monomer, [2-(methacryloyloxy)ethyl]trimethylammonium chloride. When the core-shell-type hybrid particles were dispersed in a low-polarity solvent with a dielectric constant of ∼11, colloidal crystals formed when the particle volume fraction exceeded a certain threshold, and remarkably, the interparticle distance in the colloidal crystal reached more than several micrometers under certain colloidal crystallization conditions. The colloidal crystallization behavior depended upon the surface charge density of the hybrid particles, ionic strength of the suspension, and dielectric constant of the solvent. The proposed method to construct colloidal crystals using electrostatic interactions between charged polymer brushes will promote the development of systems exhibiting particle self-assembly.

Regulating Surface Wettability and Charge Density of Porous Carbon Particles by In Situ Growth of Polyaniline for Constructing an Efficient Electrical Percolation Network in Flow-Electrode Capacitive Deionization.

Both electrical conductivity and surface wettability are required for the selection of active carbon materials in flow-electrode capacitive deionization, while a trade-off exists between these two properties. In this work, a hybrid material with a thin layer of polyaniline (PANI) coating on activated carbon (AC/PANI) was successfully developed to retain excellent electrical conductivity and acquire good surface wettability. By adjusting the dosage of initiator, AC/PANI composites with different loading fractions of PANI were obtained. The electrochemical testing demonstrated that the AC/PANI composites have higher specific capacitance and lower ion diffusion resistance compared to pure AC, resulting in better desalinization performance. Specifically, with a feed concentration of 1600 mg/L, excellent adsorption capacity and high charge efficiency can be simultaneously achieved at 13.51 mg/g and 92.21%, respectively. Benefiting from the formation of a continuous electrical percolation network and reduced solid/liquid interfacial transport resistance, a 39% enhancement of average salt adsorption rate (from 0.54 to 0.75 μmol/min/cm2) was obtained.

Relevance of Colloid Inherent Salt Estimated by Surface Complexation Modeling of Surface Charge Densities for Different Silica Colloids

Potentiometric titrations have been routinely used to measure the proton-related surface charge density (SCD) of particles in solution. Here, we quantify the SCD of silica nanoparticles (NPs) that are commercially available as charge-stabilized colloids (by the addition of NaOH) in the presence of known amounts of added NaCl. The experimental results are simulated by surface complexation models (SCMs) of the electrical double layer (EDL). The modeling results suggest that involving only the added NaCl electrolyte yields poor agreement between the experiment and the best achievable fit. An increase in the Na concentration accounting for the colloid inherent salt (CIS) associated with these charge-stabilized colloids results in much better simulations. In the available literature, this CIS has often been disregarded. However, in the modeling, the total concentration of Na must be known for a consistent mole balance and derivation of reliable ion-pair binding constants. If the CIS is not accounted for or the original suspensions are not dialyzed, the presence of CIS renders the study of those colloids difficult, particularly when investigating specific ion effects, since the CIS always interferes. In the present work, we show that the SCM-estimated amount of CIS from varying the total salt and solid concentration agrees surprisingly well with the manufacturer specification.

Characteristic curves and relationships for surface charging parameters of nonelectrolyte-immersed aqueous cavities

Most properties of charged particles’ dispersions are closely related to the amount of charge residing on the surface of particles. Very few works have been done so far to investigate curvature-dependence of surface potential and charge density of dispersed charged particles. Although there are some experimental studies in the literature on this subject, only a few of them have examined the mathematical relationship between particle size and surface charging parameters, resulting in contradictory findings. Indeed, a universal behavior is yet to be inferred from analysis of the outcomes of these studies since they reported either a roughly constant or decreasing trend of surface charge density with increasing particle radius. Unfortunately, the majority of the limited research efforts on surface charging have focused on dispersion of charged particles in aqueous solutions, but there are systems in biological and engineering worlds where an electrolyte solution is encapsulated in the core of charged particles and immersed in a background non-electrolyte medium. In an attempt to fill this scientific gap and gain a better understanding of surface charging, analytical models are developed in the present work for prediction of surface potential, surface charge, and surface charge density for cylindrical and spherical particles in such systems.First, the problem under investigation is non-dimensionalized to facilitate the modeling process, consider the simultaneous effects of key variables, and generalize the results and behaviors. Then, the mutual relationship between every pair of variables is extracted by employing Gauss's law and combining it with the electro-neutrality condition in an aqueous cavity. Afterwards, the resulting generalized seemingly simple, but inherently complex, integral equations are solved to build the characteristic curves and regressed to derive explicit characteristic equations. Finally, the derived characteristic equations are transformed into a dimensional form to obtain simple formulas for explicit calculations of charging parameters on the surface of electrolyte-encapsulating charged particles in terms of easily measurable properties of the electrolyte solution, the size of the cavity, and thermodynamic conditions. This predictive capability of the new models will significantly reduce the time, costs, and efforts required to simultaneously characterize the size and charging parameters of particles because it removes the need for such a challenging measurement as charging parameters are explicitly related to particle size through thermodynamic conditions, as well as available or easy-to-measure properties of the solution.

Machine Learning Approach to Predict the Surface Charge Density of Monodispersed Particles in Gas-Solid Fluidized Beds.

Gas–solid fluidized beds are complex particle systems, and the electrostatic behavior of particles in fluidized beds is even more complex, which is influenced by numerous factors such as particle properties and operating conditions. Current studies focus on the effect of a certain factor on particle charging without a global picture. Furthermore, there is no mathematical model that can describe the interaction of multiple factors on particle charging because it is difficult to build a model for such a complex system. Therefore, a new approach is needed. In this study, a model capable of accurately predicting the surface charge density of particles in monodispersed gas–solid fluidized beds within a certain range was developed based on the literature and experimental data through several machine learning methods including kernel ridge regression (KRR), support vector machine regression (SVR), and multilayer perceptron (MLP). SVR and MLP models gave the best results with R2 equal to 0.980 and 0.979, respectively. However, the sensitivity analysis showed that the MLP model was more reliable than the SVR model. In conclusion, the feasibility of using machine learning to analyze the charging behavior of particles in fluidized beds is demonstrated, and the proposed MLP model can serve as an accurate correlative tool for fast and effective estimation of particle surface charge density in gas–solid fluidized beds.

Geochemical, Geotechnical, and Microbiological Changes in Mg/Ca Bentonite after Thermal Loading at 150 °C

Bentonite buffers at temperatures beyond 100 °C could reduce the amount of high-level radioactive waste in a deep geological repository. However, it is necessary to demonstrate that the buffer surrounding the canisters withstands such elevated temperatures, while maintaining its safety functions (regarding long-term performance). For this reason, an experiment with thermal loading of bentonite powder at 150 °C was arranged. The paper presents changes that the Czech Mg/Ca bentonite underwent during heating for one year. These changes were examined by X-ray diffraction (XRD), thermal analysis with evolved gas analysis (TA-EGA), aqueous leachates, Cs sorption, cation exchange capacity (CEC), specific surface area (SSA), free swelling, saturated hydraulic conductivity, water retention curves (WRC), quantitative polymerase chain reaction (qPCR), and next-generation sequencing (NGS). It was concluded that montmorillonite was partially altered, in terms of the magnitude of the surface charge density of montmorillonite particles, based on the measurement interpretations of CEC, SSA, and Cs sorption. Montmorillonite alteration towards low- or non-swelling clay structures corresponded well to significantly lower swelling ability and water uptake ability, and higher saturated hydraulic conductivity of thermally loaded samples. Microbial survivability decreased with the thermal loading time, but it was not completely diminished, even in samples heated for one year.

Silica Nanoparticle Reinforced Composites as Transparent Elastomeric Damping Materials

Inspired by the structure of the cornea, which is the transparent front part of the eye, we developed a transparent and tough silica composite elastomer consisting of poly[di(ethylene glycol)methyl ether methacrylate] (PMEO2MA) and 110 nm spherical silica particles without using an organic cross-linking agent. While filler composite elastomers, such as reinforced rubbers, have complex compositions containing multiple additives (dispersants, plasticizers, vulcanizing agents, etc.), the composition of our composite elastomer is very simple. With an increased amount of silica particles, the fracture energy of the composite elastomer (20.2 MJ m–3) was improved by 25 times compared to that of unfilled PMEO2MA (0.8 MJ m–3). Nanoscale mapping using atomic force microscopy elucidated the presence of an interface layer (IL) of approximately 15 nm thickness with a high elastic modulus near the silica particles in the composite elastomer. The fracture energy of the composite elastomer was found to be a maximum when the particle surface distance was approximately 30 nm. This particle surface distance meant that the ILs were just in contact with each other. The surface charge density and Hansen solubility parameter of the silica particles indicated the ionization of silanol groups and interactions caused by hydrogen bonding between polymer chains and the silica surface. The array of silica particles embedded with intervals of a few nanometers was expected to be able to effectively dissipate deformation energy as heat due to shear strain and friction between the particle surface and polymer matrices. Measurements of the vibration-damping properties revealed that the loss factor of the composite elastomer was significantly higher than that of the unfilled elastomer, indicating that the composite elastomer in this study could be applied as an interlayer film for laminated glass in automotive and architectural applications.

Control of Particle Size in the Self-Assembly of Amphiphilic Statistical Copolymers.

A range of amphiphilic statistical copolymers is synthesized where the hydrophilic component is either methacrylic acid (MAA) or 2-(dimethylamino)ethyl methacrylate (DMAEMA) and the hydrophobic component comprises methyl, ethyl, butyl, hexyl, or 2-ethylhexyl methacrylate, which provide a broad range of partition coefficients (log P). Small-angle X-ray scattering studies confirm that these amphiphilic copolymers self-assemble to form well-defined spherical nanoparticles in an aqueous solution, with more hydrophobic copolymers forming larger nanoparticles. Varying the nature of the alkyl substituent also influenced self-assembly with more hydrophobic comonomers producing larger nanoparticles at a given copolymer composition. A model based on particle surface charge density (PSC model) is used to describe the relationship between copolymer composition and nanoparticle size. This model assumes that the hydrophilic monomer is preferentially located at the particle surface and provides a good fit to all of the experimental data. More specifically, a linear relationship is observed between the surface area fraction covered by the hydrophilic comonomer required to achieve stabilization and the log P value for the hydrophobic comonomer. Contrast variation small-angle neutron scattering is used to study the internal structure of these nanoparticles. This technique indicates partial phase separation within the nanoparticles, with about half of the available hydrophilic comonomer repeat units being located at the surface and hydrophobic comonomer-rich cores. This information enables a refined PSC model to be developed, which indicates the same relationship between the surface area fraction of the hydrophilic comonomer and the log P of the hydrophobic comonomer repeat units for the anionic (MAA) and cationic (DMAEMA) comonomer systems. This study demonstrates how nanoparticle size can be readily controlled and predicted using relatively ill-defined statistical copolymers, making such systems a viable attractive alternative to diblock copolymer nanoparticles for a range of industrial applications.

Fluorescence on-off-on with small and charge-tunable nanoparticles enables highly sensitive intracellular microRNA imaging in living cells

Nanomaterial-based on-off-on fluorescence sensing strategies are significant particularly in intracellular nucleic acids imaging assay. There still remains challenge to rationally balance fluorescence quenching efficiency and recovery dynamics. We assume that the performance of on-off-on fluorescence sensing strategy can be fundamentally improved on small zero-dimensional (0D) nanomaterial with precisely modulated surface charge. For a proof-of-concept demonstration, silicon nanoparticle (SiNP) with ~4 nm was synthesized and used as the quencher model, of which the surface charge density was modulated by modification of triphenylphosphonium (TPP). The influence of particle size, surface charge and charge density of the nanomaterials on sensing performance was systematically investigated. The strategy showed a low limit of detection (LOD) as 26 pM for target model miR-494, which is one of the lowest in nanomaterial-based on-off-on sensing platforms. And the LOD is even comparable to amplification-based methods in a greatly shortened assay time (2.5 h). The miR-494 expresses in cancerous and normal living cells of human cervical carcinoma (HeLa), human lung carcinoma (A549), human breast cancer (MCF-7), and normal human mammary epithelial (MCF-10A) cells were imaged and localized with significantly improved sensitivity and specificity. These excellent performances insure it a promising candidate as convenient and non-enzymatic sensing platform for miRNA-associated disease detection and early diagnosis.

Controllable synthesis of terminal carboxyl hyperbranched polyester and their retarding effect on concrete

Concrete retarders could efficiently extend the hydration time of cement and maintain the plasticity of concrete slurry. However, some inherent shortcomings, such as a short setting time and poor compatibility, severely limits their application. To solve these problems, in this work, a series of carboxyl-terminated hyperbranched polymers (CTHP) were controllably synthesized and their retarding effects on the concrete setting were investigated. The results showed that the final setting time of concrete was increased by nearly 4 times as the addition amount of third generation CTHP was 1.5%, demonstrating an excellent retarding effect. Furthermore, the compressive strength was increased by 43% after 7 d of curing. The results of resistivity and Zeta potential demonstrated that CTHP could change the surface charge density of cement particles and affect the flocculation of cement particles and thus extend the retarding time. The results of Tg、XRD and SEM demonstrated that the CTHP could induce a decrease in the content of Ca(OH)2 and an increase in the content of ettringaite (AFt) during the hydration procedure, drastically enhancing the strength of the concrete. These CTHP would demonstrate the enormous potential to commercial concrete for the rapid demand in the engineering field.

Mechanistic Investigation of Surfactant-Free Emulsion Polymerization Using Magnetite Nanoparticles Modified by Citric Acid as Stabilizers.

Fe3O4-armored latexes were successfully synthesized by using modified Fe3O4 (IO) nanoparticles as stabilizers without a surfactant. The particle size, conversion, and particle number density of latex particles during the formation process were studied in detail. The surface charge density and the particle size evolutions of latexes were studied by dynamic light scattering. The use of scanning electron microscopy confirmed that IO nanoparticles were adsorbed on the polymer particle surface. Furthermore, the efficiency of iron oxide incorporation (IE) was evaluated by thermogravimetric analysis. The effect of pH, solid content, and zeta potential of IO nanoparticles on the results of polymerization was also discussed in detail. Attempts were made to explain the change of latex particle surface charge density by using Guy-Chapman-Stern's electric double layer theory. In addition, the effect of ionic strength of ammonium sulfate on particle number density of latex particles was described using P. John Feeney's equation. Finally, the mechanistic insights were discussed by studying polymerization kinetics.

Surface charging parameters of charged particles in symmetrical electrolyte solutions.

Surface electric charge of dispersed particles is an essential determinant of physicochemical properties, coagulation and flocculation processes, and stability of colloidal solutions. Size-dependence of surface potential, charge density, and total surface charge of suspended charged particles has recently received attention in the literature. Despite the clear significance of understanding such dependence, very few studies have been devoted to this problem, with contradictory results of the relationship type. Currently, there is no analytical formula to represent explicit relationships between surface charging parameters and particle size. This research work is directed at development of accurate physics-based formulas for quantification of curvature-dependence of surface potential, surface charge density, and total surface charge for cylindrical and spherical charged particles immersed in a symmetrical electrolyte solution. First, a non-dimensional approach is adopted to simplify the problems, overcoming the difficulty of dealing with multiple influential variables. Then, to reduce the degrees of freedom of the problems under consideration, Gauss's law is combined with the condition of electro-neutrality in an electrical double layer (EDL). Next, the resulting complex integral equations are solved to construct characteristic curves and to express the dimensionless surface charging parameters explicitly as a function of the dimensionless particle radius. The new theoretical expressions are founded on approximate analytical and numerical solutions of the nonlinear Poisson-Boltzmann (PB) equation in cylindrical and spherical geometries. Afterwards, the solutions of the non-dimensionalized problems are dimensionalized to derive accurate explicit closed-form expressions, describing how surface charging parameters are related to the radius of a charged particle, properties of the solution, and thermodynamic conditions. These analytical formulas enable researchers to properly determine surface potential, surface charge density, total surface charge, and radius of dispersed particles by characterizing only one of them. Finally, the validity of the commonly-held hypothesis that surface charge density is independent of particle size is examined at the end of this study.

Single-Dimer Formation Rate Reveals Heterogeneous Particle Surface Reactivity.

Biofunctionalized micro- and nanoparticles are important for a wide range of applications, but methodologies to measure, modulate, and model interactions between individual particles are scarce. Here, we describe a technique to measure the aggregation rate of two particles to a single dimer, by recording the trajectory that a particle follows on the surface of another particle as a function of time. The trajectory and the interparticle potential are controlled by a magnetic field. Particles were studied with and without conjugated antibodies in a wide range of pH conditions. The data shows that the aggregation process strongly depends on the particle surface charge density and hardly on the antibody surface coverage. Furthermore, microscopy videos of single particle dimers reveal the presence of reactive patches and thus heterogeneity in the particle surface reactivity. The aggregation rates measured with the single-dimer experiment are compared to data from an ensemble aggregation experiment. Quantitative agreement is obtained using a model that includes the influence of surface heterogeneity on particle aggregation. This single-dimer experiment clarifies how heterogeneities in particle reactivity play a role in colloidal stability.